Research ArticleInstantaneous Power Theory with Fourier and OptimalPredictive Controller Design for Shunt Active Power Filter
Suksan Tiyarachakun Kongpol Areerak and Kongpan Areerak
School of Electrical Engineering Institute of Engineering Suranaree University of Technology Nakhon Ratchasima 30000 Thailand
Correspondence should be addressed to Kongpol Areerak kongpolsutacth
Received 24 March 2014 Revised 22 May 2014 Accepted 22 May 2014 Published 24 June 2014
Academic Editor Aiguo Song
Copyright copy 2014 Suksan Tiyarachakun et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper presents a novel harmonic identification algorithm of shunt active power filter for balanced and unbalanced three-phasesystems based on the instantaneous power theory called instantaneous power theory with Fourier Moreover the optimal designof predictive current controller using an artificial intelligence technique called adaptive Tabu search is also proposed in the paperThese enhancements of the identification and current control parts are the aim of the good performance for shunt active powerfilter The good results for harmonic mitigation using the proposed ideas in the paper are confirmed by the intensive simulationusing SPS in SIMULINKThe simulation results show that the enhanced shunt active power filter can provide theminimumTHD(Total Harmonic Distortion) of source currents and unity power factor after compensation In addition the THD also followsthe IEEE Std519-1992
1 Introduction
Power systems connected nonlinear loads can generate theharmonics into the systems These harmonics cause a lot ofdisadvantages such as loss in transmission lines and electricdevices protective device failures and short-life electronicequipment in the system [1ndash3]Therefore it is very importantto reduce or eliminate the harmonics in the system It iswell known that the harmonic elimination via a shunt activepower filter (SAPF) [4] provides higher efficiency and moreflexibility comparedwith a passive power filterThere are fourmain parts (part AndashD) for using the SAPF to mitigate theharmonics in the system as shown in Figure 1
The Part A is the harmonic identification method tocalculate the reference currents for SAPF There are manymethods for harmonic identification such as an instantaneouspower theory (PQ) [5 6] a synchronous reference frame(SRF) [7] a synchronous detection (SD) [8] a slidingwindowFourier analysis (SWFA) [9] an a-b-c reference frame [10]and a DQ-axis with Fourier (DQF) [11]
The Part B is the SAPF structure There are two typesof SAPF topology such as the voltage source inverter (VSI)[12 13] and the current source inverter (CSI) [13 14] with six
IGBTs The VSI topology is used in the paper because thistopology is simple and provides the good performance forharmonic elimination
The Part C is the control technique to control thecompensating current of SAPF There are several techniquesto control the compensating current injection such as a hys-teresis control [15 16] a PWM technique with PI controller[15 16] a sliding mode control [17 18] a predictive control[19ndash21] a fuzzy logic control [22 23] and a neural networkcontrol [16]
The Part D is the last part for harmonic elimination usingSAPF This part is the DC bus voltage control of SAPF Thereare various types of the voltage control to regulate the DC busvoltage such as PI controller [24 25] fuzzy logic controller[26] and RST controller [24] In the paper the PI controlleris used to control the DC bus voltage
The aim of this paper is the minimum THD of sourcecurrents after compensation via SAPF The Part A and PartC are the significant parts to achieve the minimum THDTherefore the performances of Part A and Part C mustbe improved In Part A the PQ method is selected forimprovement because this algorithm is simple and becauseof unity power factor confirmation after compensation The
Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2014 Article ID 381760 20 pageshttpdxdoiorg1011552014381760
2 Modelling and Simulation in Engineering
ic
ic
6-pulse
Three-phase source
Shunt active
DC bus voltagecontroller
Compensatingcurrent
controller
iS
Harmonicidentification
algorithm
Nonlinearload
Part A
Part BPart C
Part D
PCCLS
uS
Udc
power filteriL
iL
icref
UdcrefuPCC
uPCC
Figure 1 The harmonic elimination system via shunt active power filter
conventional PQ method uses the analog filter to drawthe harmonic component of the instantaneous active powerfrom fundamental component This approach has an errorto calculate the harmonic component Therefore the SWFAtechnique is applied to draw the harmonic component forharmonic identification improvement The PQ with SWFAmethod called an instantaneous power theory with Fourier(PQF) algorithm is presented in the paper The details of thePQF algorithm and the performance comparison betweenthe PQ and PQF for balanced and unbalanced systems areexplained in Section 2
There are many advantages for minimum THD ofsource currents such as minimum loss in transmission linesand electric devices more accuracy of protective devicesand long-life electronic equipmentsTherefore theminimumTHD of source currents is necessary Normally manyresearch works [13 14 19 21 24 27 28] focus on how toreduce THD of the system to follow the IEEE Std519-1992 but do not care about the minimum THD Theimprovement of harmonic identification part (Part A) is notsufficient to achieve the minimumTHD nearly global solu-tionTherefore the development of the compensating currentcontroller (Part C) is the additional approach to presentin the paper The predictive current control is selected toimprovement in Part C because this controller compensatesthe delay incurred through digital control implementationand provides good static and dynamic performances Theconventional predictive current control uses the first-orderLagrange equation to approximate the predicted referencecurrents Presently it is well known that there are manyartificial intelligence (AI) techniques to apply for the opti-mization problems in the engineering researches such as themultiobjective harmony search (MOHS) [29] artificial beecolony (ABC) [30 31] competition particle swarm optimiza-tion (CPSO) [32] genetic algorithm (GA) [33] and adaptiveTabu search (ATS) [34ndash47] The ATS method is developedby Puangdownreong et al in 2002 [34] In order to performits effectiveness the ATS has tested against several well-known benchmark functions that is Bohachevsky RastriginShekelrsquos foxholds Shubert and Schwefel functions [42ndash46]Moreover the convergence property of the ATS has been
proved to assure that it can reach the optimal solution withinfinite search time [42ndash47] Thus the ATS is selected todesign the predictive current controller in the paperTheATSapproach can provide the good performance to control thecompensating currents injection and guarantees the optimalsolution for searchingThe review of the conventional predic-tive current control on dq-axis is described in Section 3 TheATSmethod is briefly explained in Section 4 In Section 5 theoptimal design of the predictive current controller using theATS method is fully shown Finally Section 6 concludes anddiscusses the advantages of the proposed ideas to enhancethe performance of SAPF In the paper the improvementof the harmonic identification and current controller designparts of SAPF is called the enhanced shunt active power filter(ESAPF)
2 Instantaneous Power Theory with Fourier
The harmonic identification algorithm for reference currentcalculations is very important for the harmonic mitigationwith SAPF The perfect reference currents are necessary foran enhanced shunt active power filter or ESAPF Therefore anovel algorithm to calculate the reference currents of ESAPFis presented in this section This algorithm is called theinstantaneous power theory with Fourier algorithm or PQFThe PQF algorithm is developed from the instantaneouspower theory (PQ)The PQ algorithm is firstly public in 1983by Akagi et al [5] The performance comparison betweenthe PQ and PQF algorithm is discussed in this section Theperformance indices for comparison are THD of sourcecurrents and power factor after compensationThe harmonicmitigation systems with the ideal shunt active power filter forbalanced and unbalanced systems as shown in Figures 2 and7 respectively In Figure 2 the three-phase bridge rectifierfeeding resistive and inductive loads (R = 130Ω and L = 4H)behaves as a nonlinear load into the balanced three-phasesystem In Figure 7 the three single-phase bridge rectifierswith different RL loads are the nonlinear load for an unbal-anced three-phase systemThe ideal current source is used torepresent the ideal shunt active power filter to perfectly injectthe compensating currents (119894
119888119886 119894119888119887 119894119888119888) into the power system
Modelling and Simulation in Engineering 3
SAPF
Three-phasebridge rectifier
iLc
iLb
iLa
n
Harmonicidentification
algorithm(PQ or PQF)
iLa
+
minus
LL
LL
LL
Nonlinear loadisa
isb
isc
iLb iLc
ica
icb
usa
usc usb
PCC
PCC
PCC
icc
380Vrms
50Hz
icareficbreficcref uPCCc
uPCCb
uPCCa
130Ω
4H
Figure 2 The balanced power system with ideal shunt active power filter
at the point of common coupling (PCC) The compensatingcurrents are equal to the reference currents (119894
119888119886ref 119894119888119887ref 119894119888119888ref)because of using the ideal current sourcemodel for SAPFTheblock diagram to calculate the reference currents using PQand PQF algorithm for balanced and unbalanced three-phasesystems is depicted in Figure 3 Figure 3 shows that there aresix steps to calculate the reference currents
Step 1 Three-phase voltages at PCC point (119906PCC119886 119906PCC119887119906PCC119888) are transformed to 1205721205730 frame (119906PCC120572 119906PCC120573 119906PCC0)using equation in block number 1
Step 2 Transform the three-phase load currents (119894119871119886 119894119871119887 119894119871119888)
to the 1205721205730 frame (119894119871120572 119894119871120573 1198941198710) by the block number 2
Step 3 Calculate the instantaneous active power (119901119871) and
reactive power (119902119871) on the 1205721205730 frame in the block number 3
The 119901119871from the block number 3 consists of two components
the fundamental component (119901119871) and the harmonic compo-
nent (119901119871)
Step 4 Draw the 119901119871from the 119901
119871 For PQ algorithm the
separation of the fundamental and harmonic componentsuses the analog filter (high-pass filter HPF) In this paperthe cutoff frequencies of HPF for balanced and unbalancedsystems are equal to 280Hz and 50Hz respectively On theother hand the sliding window Fourier analysis (SWFA) isused to separate these components for PQF algorithm In thisstep the method to separate the fundamental and harmoniccomponents is the different point between the PQ and PQFalgorithm After to draw the 119901
119871from 119901
119871 the reference active
power (119901119888) can be obtained from subtracting between 119901
119871and
119901119889119888(output of the PI controller in the DC bus voltage control
part) In the paper the reference reactive power is set equalto 119902119871because of the unity power factor after compensation
Step 5 Calculate the reference currents on the 1205721205730 frame(119894119888120572ref 119894119888120573ref 1198941198880ref) by the equation of block number 5
Step 6 Calculate the three-phase reference currents (119894119888119886ref
119894119888119887ref 119894119888119888ref) for SAPF using the equation of block number 6
FromFigure 3 it can be seen that the zero sequence calcu-lations are necessary for unbalanced three-phase system Forthe balanced system the zero sequence quantities are equalto zero
The SWFA technique for PQF algorithm uses the Fourierseries of active power as shown in (1) From this equation1198600119901 119860ℎ119901 and 119861
ℎ119901are the Fourier series coefficients 119879
119904is
the sampling interval 119896 is time index ℎ is the harmonicorder and 120596 is the angular fundamental frequency of thesystem The fundamental component (or DC component) ofactive power is represented by119860
0119901coefficient as shown in (2)
The 119860ℎ119901
coefficient in (1) can be calculated by (3) The 1198600119901
coefficient or DC component can be calculated by substituteℎ = 0 in (3) as shown in (4) The 119873
0and 119873 in (3) and (4)
are the starting point for computing and the total numberof sampled point in one cycle respectively The calculationof 1198600119901
in the first period can be calculated using (4) so asto achieve the initial value for the PQF algorithm For thenext period the 119860
0119901can be calculated by (5) in which this
approach is called SWFA [9] The SWFA approach can besummarized in Figure 4
119901119871(119896119879119904)=
1198600119901
2+
infin
sum
ℎ=1
[119860ℎ119901cos (ℎ120596119896119879
119904) + 119861ℎ119901sin (ℎ120596119896119879
119904)]
(1)
119901119871(119896119879119904) =
1198600119901
2 (2)
4 Modelling and Simulation in Engineering
5
pc
pc
pdc
pL
pL
pL
HPF
HPF
SWFA
SWFA
PI controller
orSWFA for PQF
HPF for PQ
pL
UdcUdcref
minus
+
minus
+
minus
+
uPCC(1205721205730)
uPCC(1205721205730)
qL(1205721205730)
iL(1205721205730)
iL(abc)u
DC bus voltage control
pL
pL
pL
PCC(abc)
cp0ref
i
cp120572ref
= =
=
=
=
=
=
u 120572u 120573
u 0
radic 2
3radic 2
2
3
1
1
0
1
radic2
1
2radic3
3
21
radic2
1
radic2
1
0
1
radic2
1
2radic3
21
radic2
1
radic2
u b
u c
iL120572iL120573iL0
iLaa
iLbiLc
pL = u 120572iL120572 + u 120573iL120573 + u 0iL0
u 120573iL0 minus u 0iL120573u 0iL120572 minus u 120572iL0u 120572iL120573 minus u 120573iL120572
i
i
icq120572icq120573icq0
1
u 1205722 + u 120573
2 + u 02
u 1205722 + u 120573
2 + u 02
u 120572
u 120573
u 0
u 0qL120573 minus u 120573qL0u 120572qL0 minus u 0qL120572u 120573qL120572 minus u 120572qL120573
ic120572ic120573ic0
i +
i + icq120573i +
icaicbicc
1 01
radic2
minus1
2
radic3
2
1
radic2
minus1
2minusradic3
2
1
radic2
ic120572ic120573ic0
radic 2
3
[ ] [ ] [ ] [ ]
[ ]
[
[ ]
]
[ ] [ ]
[ ] [ ]
[
[
]
[ ]
]
[[ [[[[
minus
radic3
2minus
1
2minusminus
6
4
PCCPCCPCC
u3
2minusradic2
1minus
PCC
PCCPCC
PCC
PCC
PCCPCC
PCCPCC PCC
PCC
PCC
PCC PCC PCC PCCPCCPCC
PCCPCCPCCPCCPCC
PCCPCCPCC
PCC
cq120572refref
cq0ref
refrefref
refrefref
refref
ref
refref
ref
qL120572qL120573qL0
ic(1205721205730)ref
icp120572ref
i
cp120573refcp0ref
cp120573ref
Figure 3 The block diagram of PQ and PQF algorithms
Modelling and Simulation in Engineering 5
N
N0 + 1
n = N0
sum 2
NA0p
N0 + N
N0 + N minus 1
Entering pL(kTs)
N0 minus 1 Leaving pL(kTs)
Figure 4 The flow chart of the SWFA approach
Table 1 The performance comparison between the PQ and PQF algorithms for balanced system
Harmonic identification algorithm Before compensation After compensationTHD
119901119871(119899119879119904) cos (119899ℎ120596119879
119904) (3)
1198600119901=2
119873
1198730+119873minus1
sum
119899=1198730
119901119871(119899119879119904) (4)
1198600119901
(new)= 1198600119901
(old)minus2
119873119901119871[(1198730minus 1) 119879
119904]
+2
119873119901119871[(1198730+ 119873)119879
119904]
(5)
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the balanced systemin Figure 2 with 119871
119871= 10mH are addressed in Table 1 The
cutoff frequency of HPF for PQ method is set to 280Hz Theaverage THD of source currents (THD
119894av) and the powerfactor after compensation (pf) are the performance indices forthe comparisonThe THDav and pf can be calculated by (6)and (8) respectively The THD of source currents in eachphase (THD
119894119896) can be calculated by (7) The fundamental
and harmonic (order n) values in (7) are denoted by subscript1 and n respectively The pfdisp and pfdist in (8) are the
displacement and distortion power factors in which thesevalues can be calculated by (9) and (10) respectively
THD119894av =
radicsum119896=119886119887119888
THD2119894119896
3
(6)
THD119894119896=
radicsuminfin
119899=21198682
119899119896
I1119896
times 100 (7)
pf = 119875
119878= pfdisp times pfdist (8)
pfdisp =119875
S1
(9)
pfdisp =1
radic1 + THD2119906times radic1 + THD2i
(10)
The results from Table 1 show that the PQF algorithmcan provide the best performance in term of THD
119894avFrom Table 1 the THD
119894av of the source currents beforecompensation is equal to 2448 in which this value isextremely greater than the IEEE std519-1992The source cur-rent waveforms before compensation (119894
119904119886 119894119904119887 119894119904119888) are highly
6 Modelling and Simulation in Engineering
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000
500
minus5000
500
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
30
minus3
30
minus3
30
minus3
i La
i Lb
i Lc
i cc
i sa
i sb
Time (s)
uPC
Cb
uPC
Ca
Before
compensation
Initialization
Reactive power and harmonic
compensations
i sc
uPC
Cc
i cb
i ca
Figure 5 The simulation results using PQF algorithm for ideal shunt active power filter with balanced system
Table 2 The error of instantaneous active power for harmonic component calculation
Figure 6 The spectrum of instantaneous active power for harmonic components
iLc
iLbn
LL
LLisb
isc
ica
icb
usa
usb
PCC
PCC
icc
Harmonicidentification
algorithm(PQ or PQF)
380Vrms
50Hz
iLaLLPCCisa
SAPF
iLa iLb iLc
+
minus
+
minus
+
minus
usc
icareficbreficcref uPCCc
uPCCb
uPCCa
130Ω
4H
120Ω
110Ω
05H
01H
Nonlinear load
Single-phase bridge rectifier
Figure 7 The unbalanced power system with ideal shunt active power filter
distorted as shown in Figure 5 These waveforms are equal tothe load currents (119894
119871119886 119894119871119887 119894119871119888) before compensation because
the SAPF is not connected to the system From Figure 5 thecompensating currents (119894
119888119886 119894119888119887 119894119888119888) from SAPF are injected
into the system at t = 004 s For t = 004ndash006 s thecompensation is nonperfect because this interval is usedfor initial of SWFA algorithm The SWFA algorithm is
the main approach for PQF method After t = 006 s theSAPF generates the perfectly compensating currents intothe system (reactive power and harmonic compensations)From Figure 5 (119905 ge 006 s) it can be seen that the sourcecurrents after compensation are nearly sinusoidal waveformsThe THD
119894av of these currents is equal to 095 and 004 forPQ and PQF respectively as shown in Table 1 These values
8 Modelling and Simulation in Engineering
Table 3 The performance comparison between the PQ and PQF algorithms for unbalanced system
Harmonicidentificationalgorithm
THD119894119886
THD119894119887
THD119894119888
THD119894119886V
119894119904119886
(rms)119894119904119887
(rms)119894119904119888
(rms) unbalance
Before compensation4284 3275 851 3152 146 161 192 1543
are satisfied under IEEE std519-1992 Moreover the powerfactor after compensation is unity while before compensationthe power factor is equal to 095
From Figure 3 the different point between the PQ andPQF algorithm is the method to separate the fundamentaland harmonic components Therefore the accurate instanta-neous active power for harmonic component (119901
119871) is themain
objective to identify the harmonic currents of the systemThespectrum comparison of the 119901
119871values calculated by PQF and
PQ algorithms is shown in Figure 6The119901119871act is the spectrum
of the instantaneous harmonic active power calculated byFFT approach fromMATLAB programmingThe 119901
119871PQF and119901119871PQ are calculated by PQF and PQ algorithms respectively
From Figure 6 it can be seen that the 119901119871PQF value calculated
by PQF algorithm is nearly the same as the 119901119871act value
The errors between the 119901119871values calculated by PQF and
PQ algorithms compared with the 119901119871act value are shown in
Table 2 In the paper the authors focus on the total error(119864tot) for the performance comparison between the PQ andPQF algorithms From Table 2 the 119864tot from PQF algorithm(056) is less than the PQ algorithm (156) Thereforethe PQF algorithm is the perfect method to calculate thereference currents for ESAPF
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the unbalancedsystem in Figure 7 are addressed in Table 3 The results fromTable 3 show that the PQF algorithm can provide the bestperformance in term of THD
119894av and unbalance aftercompensationTheunbalance in this table can be calculatedby (11) From Table 3 the THD
119894av and unbalance ofsource currents before compensation are equal to 3152and 1543 respectively The waveforms of source current(119894119904119886 119894119904119887 119894119904119888) before compensation (119905 = 0ndash004 s) are extremely
distorted and unbalanced as depicted in Figure 8 For 119905 =
004ndash006 s this interval is the initial calculation for PQFalgorithm using a SWFA technique For 119905 ge 006 s the PQFalgorithm can completely eliminate the harmonic currentsand balance the amplitude and phase of source currents aftercompensation The THD
119894av of these currents are equal to060 and 001 for PQ andPQF respectively as given inTable 3The unbalance after compensation using PQ and PQFalgorithms is equal to 043 and 0 respectively It means thatthe source currents after compensation are perfectly balancedusing the PQF algorithm compared with the unbalancebefore compensation (1543) From the simulation resultsof the balanced and unbalanced system the PQF algorithm
is the perfect method to calculate the reference currents forESAPF In the future works the positive sequence detectionis added to the PQF algorithm for the harmonic currentelimination in the distorted and unbalanced voltage systems
unbalance
=
1003816100381610038161003816maximumcurrent deviation from average rms current1003816100381610038161003816average rms current
times 100(11)
3 Predictive Current Control on dq-Axis
In this section the predictive current control for SAPF withbalanced three-phase system is proposed The predictivecurrent control technique is applied to control the injectionof compensating currents with SAPF as shown in Figure 9The voltage source inverter with six IGBTs is the SAPFtopology in the paper The PQF algorithm described in theprevious section is used to identify the harmonic currents inthe system The three-phase bridge rectifier feeding resistiveand inductive loads behaves as a nonlinear load into thepower system The predictive current control is the suitabletechnique for a digital control [21] The equivalent circuit inFigure 10 is used to derive the relationship equation betweenthe SAPF output voltages (u
(119886119887119888)) and the voltages at PCC
point (uPCC(119886119887119888)) as given in (12) The compensating currentsor active filter currents are represented by i
119888(119886119887119888) The discrete
form of (12) can be represented by (13) and119879sc is the samplingtime of the controller
u(119886119887119888)
= 119871119891(119889i119888(119886119887119888)
119889119905) + uPCC(119886119887119888) (12)
u(119886119887119888)
(119896) =
119871119891
119879sc[i119888(119886119887119888)
(119896 + 1) minus i119888(119886119887119888)
(119896)] + uPCC(119886119887119888) (119896)
(13)
The concept of the reference currents prediction is shownin Figure 11 From this figure the three-phase referencecurrent at time instants 119905(119896) and 119905(119896 + 1) is denoted byi119888(119886119887119888)ref(119896) and i
119888(119886119887119888)ref(119896 + 1) respectively The predictedthree-phase reference currents (i
119888119901(119886119887119888)ref(119896 + 1)) for thenext sampling period are calculated by (14) The predictedcurrents (i
119888119901(119886119887119888)ref(119896 + 1)) are equal to the reference currents(i119888(119886119887119888)ref(119896 + 1)) at time instant 119905(119896 + 1) The 119886
0and 1198861are the
Modelling and Simulation in Engineering 9
i La
i Lb
i Lc
i cc
i sa
i sb
uPC
Cb
uPC
Ca
i sc
uPC
Cc
i cb
i ca
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000500
minus5000
500
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
30
minus3
30
minus3
30
minus3
Beforecompensation
Initialization
Reactive power and harmoniccompensations
Time (s)
Figure 8 The simulation results using PQF algorithm for ideal shunt active power filter with unbalanced system
10 Modelling and Simulation in Engineering
380Vrms
50Hz
n
isa
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
130Ω
4H
on dq-axis
u120572
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 1 The harmonic elimination system via shunt active power filter
conventional PQ method uses the analog filter to drawthe harmonic component of the instantaneous active powerfrom fundamental component This approach has an errorto calculate the harmonic component Therefore the SWFAtechnique is applied to draw the harmonic component forharmonic identification improvement The PQ with SWFAmethod called an instantaneous power theory with Fourier(PQF) algorithm is presented in the paper The details of thePQF algorithm and the performance comparison betweenthe PQ and PQF for balanced and unbalanced systems areexplained in Section 2
There are many advantages for minimum THD ofsource currents such as minimum loss in transmission linesand electric devices more accuracy of protective devicesand long-life electronic equipmentsTherefore theminimumTHD of source currents is necessary Normally manyresearch works [13 14 19 21 24 27 28] focus on how toreduce THD of the system to follow the IEEE Std519-1992 but do not care about the minimum THD Theimprovement of harmonic identification part (Part A) is notsufficient to achieve the minimumTHD nearly global solu-tionTherefore the development of the compensating currentcontroller (Part C) is the additional approach to presentin the paper The predictive current control is selected toimprovement in Part C because this controller compensatesthe delay incurred through digital control implementationand provides good static and dynamic performances Theconventional predictive current control uses the first-orderLagrange equation to approximate the predicted referencecurrents Presently it is well known that there are manyartificial intelligence (AI) techniques to apply for the opti-mization problems in the engineering researches such as themultiobjective harmony search (MOHS) [29] artificial beecolony (ABC) [30 31] competition particle swarm optimiza-tion (CPSO) [32] genetic algorithm (GA) [33] and adaptiveTabu search (ATS) [34ndash47] The ATS method is developedby Puangdownreong et al in 2002 [34] In order to performits effectiveness the ATS has tested against several well-known benchmark functions that is Bohachevsky RastriginShekelrsquos foxholds Shubert and Schwefel functions [42ndash46]Moreover the convergence property of the ATS has been
proved to assure that it can reach the optimal solution withinfinite search time [42ndash47] Thus the ATS is selected todesign the predictive current controller in the paperTheATSapproach can provide the good performance to control thecompensating currents injection and guarantees the optimalsolution for searchingThe review of the conventional predic-tive current control on dq-axis is described in Section 3 TheATSmethod is briefly explained in Section 4 In Section 5 theoptimal design of the predictive current controller using theATS method is fully shown Finally Section 6 concludes anddiscusses the advantages of the proposed ideas to enhancethe performance of SAPF In the paper the improvementof the harmonic identification and current controller designparts of SAPF is called the enhanced shunt active power filter(ESAPF)
2 Instantaneous Power Theory with Fourier
The harmonic identification algorithm for reference currentcalculations is very important for the harmonic mitigationwith SAPF The perfect reference currents are necessary foran enhanced shunt active power filter or ESAPF Therefore anovel algorithm to calculate the reference currents of ESAPFis presented in this section This algorithm is called theinstantaneous power theory with Fourier algorithm or PQFThe PQF algorithm is developed from the instantaneouspower theory (PQ)The PQ algorithm is firstly public in 1983by Akagi et al [5] The performance comparison betweenthe PQ and PQF algorithm is discussed in this section Theperformance indices for comparison are THD of sourcecurrents and power factor after compensationThe harmonicmitigation systems with the ideal shunt active power filter forbalanced and unbalanced systems as shown in Figures 2 and7 respectively In Figure 2 the three-phase bridge rectifierfeeding resistive and inductive loads (R = 130Ω and L = 4H)behaves as a nonlinear load into the balanced three-phasesystem In Figure 7 the three single-phase bridge rectifierswith different RL loads are the nonlinear load for an unbal-anced three-phase systemThe ideal current source is used torepresent the ideal shunt active power filter to perfectly injectthe compensating currents (119894
119888119886 119894119888119887 119894119888119888) into the power system
Modelling and Simulation in Engineering 3
SAPF
Three-phasebridge rectifier
iLc
iLb
iLa
n
Harmonicidentification
algorithm(PQ or PQF)
iLa
+
minus
LL
LL
LL
Nonlinear loadisa
isb
isc
iLb iLc
ica
icb
usa
usc usb
PCC
PCC
PCC
icc
380Vrms
50Hz
icareficbreficcref uPCCc
uPCCb
uPCCa
130Ω
4H
Figure 2 The balanced power system with ideal shunt active power filter
at the point of common coupling (PCC) The compensatingcurrents are equal to the reference currents (119894
119888119886ref 119894119888119887ref 119894119888119888ref)because of using the ideal current sourcemodel for SAPFTheblock diagram to calculate the reference currents using PQand PQF algorithm for balanced and unbalanced three-phasesystems is depicted in Figure 3 Figure 3 shows that there aresix steps to calculate the reference currents
Step 1 Three-phase voltages at PCC point (119906PCC119886 119906PCC119887119906PCC119888) are transformed to 1205721205730 frame (119906PCC120572 119906PCC120573 119906PCC0)using equation in block number 1
Step 2 Transform the three-phase load currents (119894119871119886 119894119871119887 119894119871119888)
to the 1205721205730 frame (119894119871120572 119894119871120573 1198941198710) by the block number 2
Step 3 Calculate the instantaneous active power (119901119871) and
reactive power (119902119871) on the 1205721205730 frame in the block number 3
The 119901119871from the block number 3 consists of two components
the fundamental component (119901119871) and the harmonic compo-
nent (119901119871)
Step 4 Draw the 119901119871from the 119901
119871 For PQ algorithm the
separation of the fundamental and harmonic componentsuses the analog filter (high-pass filter HPF) In this paperthe cutoff frequencies of HPF for balanced and unbalancedsystems are equal to 280Hz and 50Hz respectively On theother hand the sliding window Fourier analysis (SWFA) isused to separate these components for PQF algorithm In thisstep the method to separate the fundamental and harmoniccomponents is the different point between the PQ and PQFalgorithm After to draw the 119901
119871from 119901
119871 the reference active
power (119901119888) can be obtained from subtracting between 119901
119871and
119901119889119888(output of the PI controller in the DC bus voltage control
part) In the paper the reference reactive power is set equalto 119902119871because of the unity power factor after compensation
Step 5 Calculate the reference currents on the 1205721205730 frame(119894119888120572ref 119894119888120573ref 1198941198880ref) by the equation of block number 5
Step 6 Calculate the three-phase reference currents (119894119888119886ref
119894119888119887ref 119894119888119888ref) for SAPF using the equation of block number 6
FromFigure 3 it can be seen that the zero sequence calcu-lations are necessary for unbalanced three-phase system Forthe balanced system the zero sequence quantities are equalto zero
The SWFA technique for PQF algorithm uses the Fourierseries of active power as shown in (1) From this equation1198600119901 119860ℎ119901 and 119861
ℎ119901are the Fourier series coefficients 119879
119904is
the sampling interval 119896 is time index ℎ is the harmonicorder and 120596 is the angular fundamental frequency of thesystem The fundamental component (or DC component) ofactive power is represented by119860
0119901coefficient as shown in (2)
The 119860ℎ119901
coefficient in (1) can be calculated by (3) The 1198600119901
coefficient or DC component can be calculated by substituteℎ = 0 in (3) as shown in (4) The 119873
0and 119873 in (3) and (4)
are the starting point for computing and the total numberof sampled point in one cycle respectively The calculationof 1198600119901
in the first period can be calculated using (4) so asto achieve the initial value for the PQF algorithm For thenext period the 119860
0119901can be calculated by (5) in which this
approach is called SWFA [9] The SWFA approach can besummarized in Figure 4
119901119871(119896119879119904)=
1198600119901
2+
infin
sum
ℎ=1
[119860ℎ119901cos (ℎ120596119896119879
119904) + 119861ℎ119901sin (ℎ120596119896119879
119904)]
(1)
119901119871(119896119879119904) =
1198600119901
2 (2)
4 Modelling and Simulation in Engineering
5
pc
pc
pdc
pL
pL
pL
HPF
HPF
SWFA
SWFA
PI controller
orSWFA for PQF
HPF for PQ
pL
UdcUdcref
minus
+
minus
+
minus
+
uPCC(1205721205730)
uPCC(1205721205730)
qL(1205721205730)
iL(1205721205730)
iL(abc)u
DC bus voltage control
pL
pL
pL
PCC(abc)
cp0ref
i
cp120572ref
= =
=
=
=
=
=
u 120572u 120573
u 0
radic 2
3radic 2
2
3
1
1
0
1
radic2
1
2radic3
3
21
radic2
1
radic2
1
0
1
radic2
1
2radic3
21
radic2
1
radic2
u b
u c
iL120572iL120573iL0
iLaa
iLbiLc
pL = u 120572iL120572 + u 120573iL120573 + u 0iL0
u 120573iL0 minus u 0iL120573u 0iL120572 minus u 120572iL0u 120572iL120573 minus u 120573iL120572
i
i
icq120572icq120573icq0
1
u 1205722 + u 120573
2 + u 02
u 1205722 + u 120573
2 + u 02
u 120572
u 120573
u 0
u 0qL120573 minus u 120573qL0u 120572qL0 minus u 0qL120572u 120573qL120572 minus u 120572qL120573
ic120572ic120573ic0
i +
i + icq120573i +
icaicbicc
1 01
radic2
minus1
2
radic3
2
1
radic2
minus1
2minusradic3
2
1
radic2
ic120572ic120573ic0
radic 2
3
[ ] [ ] [ ] [ ]
[ ]
[
[ ]
]
[ ] [ ]
[ ] [ ]
[
[
]
[ ]
]
[[ [[[[
minus
radic3
2minus
1
2minusminus
6
4
PCCPCCPCC
u3
2minusradic2
1minus
PCC
PCCPCC
PCC
PCC
PCCPCC
PCCPCC PCC
PCC
PCC
PCC PCC PCC PCCPCCPCC
PCCPCCPCCPCCPCC
PCCPCCPCC
PCC
cq120572refref
cq0ref
refrefref
refrefref
refref
ref
refref
ref
qL120572qL120573qL0
ic(1205721205730)ref
icp120572ref
i
cp120573refcp0ref
cp120573ref
Figure 3 The block diagram of PQ and PQF algorithms
Modelling and Simulation in Engineering 5
N
N0 + 1
n = N0
sum 2
NA0p
N0 + N
N0 + N minus 1
Entering pL(kTs)
N0 minus 1 Leaving pL(kTs)
Figure 4 The flow chart of the SWFA approach
Table 1 The performance comparison between the PQ and PQF algorithms for balanced system
Harmonic identification algorithm Before compensation After compensationTHD
119901119871(119899119879119904) cos (119899ℎ120596119879
119904) (3)
1198600119901=2
119873
1198730+119873minus1
sum
119899=1198730
119901119871(119899119879119904) (4)
1198600119901
(new)= 1198600119901
(old)minus2
119873119901119871[(1198730minus 1) 119879
119904]
+2
119873119901119871[(1198730+ 119873)119879
119904]
(5)
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the balanced systemin Figure 2 with 119871
119871= 10mH are addressed in Table 1 The
cutoff frequency of HPF for PQ method is set to 280Hz Theaverage THD of source currents (THD
119894av) and the powerfactor after compensation (pf) are the performance indices forthe comparisonThe THDav and pf can be calculated by (6)and (8) respectively The THD of source currents in eachphase (THD
119894119896) can be calculated by (7) The fundamental
and harmonic (order n) values in (7) are denoted by subscript1 and n respectively The pfdisp and pfdist in (8) are the
displacement and distortion power factors in which thesevalues can be calculated by (9) and (10) respectively
THD119894av =
radicsum119896=119886119887119888
THD2119894119896
3
(6)
THD119894119896=
radicsuminfin
119899=21198682
119899119896
I1119896
times 100 (7)
pf = 119875
119878= pfdisp times pfdist (8)
pfdisp =119875
S1
(9)
pfdisp =1
radic1 + THD2119906times radic1 + THD2i
(10)
The results from Table 1 show that the PQF algorithmcan provide the best performance in term of THD
119894avFrom Table 1 the THD
119894av of the source currents beforecompensation is equal to 2448 in which this value isextremely greater than the IEEE std519-1992The source cur-rent waveforms before compensation (119894
119904119886 119894119904119887 119894119904119888) are highly
6 Modelling and Simulation in Engineering
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000
500
minus5000
500
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
30
minus3
30
minus3
30
minus3
i La
i Lb
i Lc
i cc
i sa
i sb
Time (s)
uPC
Cb
uPC
Ca
Before
compensation
Initialization
Reactive power and harmonic
compensations
i sc
uPC
Cc
i cb
i ca
Figure 5 The simulation results using PQF algorithm for ideal shunt active power filter with balanced system
Table 2 The error of instantaneous active power for harmonic component calculation
Figure 6 The spectrum of instantaneous active power for harmonic components
iLc
iLbn
LL
LLisb
isc
ica
icb
usa
usb
PCC
PCC
icc
Harmonicidentification
algorithm(PQ or PQF)
380Vrms
50Hz
iLaLLPCCisa
SAPF
iLa iLb iLc
+
minus
+
minus
+
minus
usc
icareficbreficcref uPCCc
uPCCb
uPCCa
130Ω
4H
120Ω
110Ω
05H
01H
Nonlinear load
Single-phase bridge rectifier
Figure 7 The unbalanced power system with ideal shunt active power filter
distorted as shown in Figure 5 These waveforms are equal tothe load currents (119894
119871119886 119894119871119887 119894119871119888) before compensation because
the SAPF is not connected to the system From Figure 5 thecompensating currents (119894
119888119886 119894119888119887 119894119888119888) from SAPF are injected
into the system at t = 004 s For t = 004ndash006 s thecompensation is nonperfect because this interval is usedfor initial of SWFA algorithm The SWFA algorithm is
the main approach for PQF method After t = 006 s theSAPF generates the perfectly compensating currents intothe system (reactive power and harmonic compensations)From Figure 5 (119905 ge 006 s) it can be seen that the sourcecurrents after compensation are nearly sinusoidal waveformsThe THD
119894av of these currents is equal to 095 and 004 forPQ and PQF respectively as shown in Table 1 These values
8 Modelling and Simulation in Engineering
Table 3 The performance comparison between the PQ and PQF algorithms for unbalanced system
Harmonicidentificationalgorithm
THD119894119886
THD119894119887
THD119894119888
THD119894119886V
119894119904119886
(rms)119894119904119887
(rms)119894119904119888
(rms) unbalance
Before compensation4284 3275 851 3152 146 161 192 1543
are satisfied under IEEE std519-1992 Moreover the powerfactor after compensation is unity while before compensationthe power factor is equal to 095
From Figure 3 the different point between the PQ andPQF algorithm is the method to separate the fundamentaland harmonic components Therefore the accurate instanta-neous active power for harmonic component (119901
119871) is themain
objective to identify the harmonic currents of the systemThespectrum comparison of the 119901
119871values calculated by PQF and
PQ algorithms is shown in Figure 6The119901119871act is the spectrum
of the instantaneous harmonic active power calculated byFFT approach fromMATLAB programmingThe 119901
119871PQF and119901119871PQ are calculated by PQF and PQ algorithms respectively
From Figure 6 it can be seen that the 119901119871PQF value calculated
by PQF algorithm is nearly the same as the 119901119871act value
The errors between the 119901119871values calculated by PQF and
PQ algorithms compared with the 119901119871act value are shown in
Table 2 In the paper the authors focus on the total error(119864tot) for the performance comparison between the PQ andPQF algorithms From Table 2 the 119864tot from PQF algorithm(056) is less than the PQ algorithm (156) Thereforethe PQF algorithm is the perfect method to calculate thereference currents for ESAPF
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the unbalancedsystem in Figure 7 are addressed in Table 3 The results fromTable 3 show that the PQF algorithm can provide the bestperformance in term of THD
119894av and unbalance aftercompensationTheunbalance in this table can be calculatedby (11) From Table 3 the THD
119894av and unbalance ofsource currents before compensation are equal to 3152and 1543 respectively The waveforms of source current(119894119904119886 119894119904119887 119894119904119888) before compensation (119905 = 0ndash004 s) are extremely
distorted and unbalanced as depicted in Figure 8 For 119905 =
004ndash006 s this interval is the initial calculation for PQFalgorithm using a SWFA technique For 119905 ge 006 s the PQFalgorithm can completely eliminate the harmonic currentsand balance the amplitude and phase of source currents aftercompensation The THD
119894av of these currents are equal to060 and 001 for PQ andPQF respectively as given inTable 3The unbalance after compensation using PQ and PQFalgorithms is equal to 043 and 0 respectively It means thatthe source currents after compensation are perfectly balancedusing the PQF algorithm compared with the unbalancebefore compensation (1543) From the simulation resultsof the balanced and unbalanced system the PQF algorithm
is the perfect method to calculate the reference currents forESAPF In the future works the positive sequence detectionis added to the PQF algorithm for the harmonic currentelimination in the distorted and unbalanced voltage systems
unbalance
=
1003816100381610038161003816maximumcurrent deviation from average rms current1003816100381610038161003816average rms current
times 100(11)
3 Predictive Current Control on dq-Axis
In this section the predictive current control for SAPF withbalanced three-phase system is proposed The predictivecurrent control technique is applied to control the injectionof compensating currents with SAPF as shown in Figure 9The voltage source inverter with six IGBTs is the SAPFtopology in the paper The PQF algorithm described in theprevious section is used to identify the harmonic currents inthe system The three-phase bridge rectifier feeding resistiveand inductive loads behaves as a nonlinear load into thepower system The predictive current control is the suitabletechnique for a digital control [21] The equivalent circuit inFigure 10 is used to derive the relationship equation betweenthe SAPF output voltages (u
(119886119887119888)) and the voltages at PCC
point (uPCC(119886119887119888)) as given in (12) The compensating currentsor active filter currents are represented by i
119888(119886119887119888) The discrete
form of (12) can be represented by (13) and119879sc is the samplingtime of the controller
u(119886119887119888)
= 119871119891(119889i119888(119886119887119888)
119889119905) + uPCC(119886119887119888) (12)
u(119886119887119888)
(119896) =
119871119891
119879sc[i119888(119886119887119888)
(119896 + 1) minus i119888(119886119887119888)
(119896)] + uPCC(119886119887119888) (119896)
(13)
The concept of the reference currents prediction is shownin Figure 11 From this figure the three-phase referencecurrent at time instants 119905(119896) and 119905(119896 + 1) is denoted byi119888(119886119887119888)ref(119896) and i
119888(119886119887119888)ref(119896 + 1) respectively The predictedthree-phase reference currents (i
119888119901(119886119887119888)ref(119896 + 1)) for thenext sampling period are calculated by (14) The predictedcurrents (i
119888119901(119886119887119888)ref(119896 + 1)) are equal to the reference currents(i119888(119886119887119888)ref(119896 + 1)) at time instant 119905(119896 + 1) The 119886
0and 1198861are the
Modelling and Simulation in Engineering 9
i La
i Lb
i Lc
i cc
i sa
i sb
uPC
Cb
uPC
Ca
i sc
uPC
Cc
i cb
i ca
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000500
minus5000
500
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
30
minus3
30
minus3
30
minus3
Beforecompensation
Initialization
Reactive power and harmoniccompensations
Time (s)
Figure 8 The simulation results using PQF algorithm for ideal shunt active power filter with unbalanced system
10 Modelling and Simulation in Engineering
380Vrms
50Hz
n
isa
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
130Ω
4H
on dq-axis
u120572
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 2 The balanced power system with ideal shunt active power filter
at the point of common coupling (PCC) The compensatingcurrents are equal to the reference currents (119894
119888119886ref 119894119888119887ref 119894119888119888ref)because of using the ideal current sourcemodel for SAPFTheblock diagram to calculate the reference currents using PQand PQF algorithm for balanced and unbalanced three-phasesystems is depicted in Figure 3 Figure 3 shows that there aresix steps to calculate the reference currents
Step 1 Three-phase voltages at PCC point (119906PCC119886 119906PCC119887119906PCC119888) are transformed to 1205721205730 frame (119906PCC120572 119906PCC120573 119906PCC0)using equation in block number 1
Step 2 Transform the three-phase load currents (119894119871119886 119894119871119887 119894119871119888)
to the 1205721205730 frame (119894119871120572 119894119871120573 1198941198710) by the block number 2
Step 3 Calculate the instantaneous active power (119901119871) and
reactive power (119902119871) on the 1205721205730 frame in the block number 3
The 119901119871from the block number 3 consists of two components
the fundamental component (119901119871) and the harmonic compo-
nent (119901119871)
Step 4 Draw the 119901119871from the 119901
119871 For PQ algorithm the
separation of the fundamental and harmonic componentsuses the analog filter (high-pass filter HPF) In this paperthe cutoff frequencies of HPF for balanced and unbalancedsystems are equal to 280Hz and 50Hz respectively On theother hand the sliding window Fourier analysis (SWFA) isused to separate these components for PQF algorithm In thisstep the method to separate the fundamental and harmoniccomponents is the different point between the PQ and PQFalgorithm After to draw the 119901
119871from 119901
119871 the reference active
power (119901119888) can be obtained from subtracting between 119901
119871and
119901119889119888(output of the PI controller in the DC bus voltage control
part) In the paper the reference reactive power is set equalto 119902119871because of the unity power factor after compensation
Step 5 Calculate the reference currents on the 1205721205730 frame(119894119888120572ref 119894119888120573ref 1198941198880ref) by the equation of block number 5
Step 6 Calculate the three-phase reference currents (119894119888119886ref
119894119888119887ref 119894119888119888ref) for SAPF using the equation of block number 6
FromFigure 3 it can be seen that the zero sequence calcu-lations are necessary for unbalanced three-phase system Forthe balanced system the zero sequence quantities are equalto zero
The SWFA technique for PQF algorithm uses the Fourierseries of active power as shown in (1) From this equation1198600119901 119860ℎ119901 and 119861
ℎ119901are the Fourier series coefficients 119879
119904is
the sampling interval 119896 is time index ℎ is the harmonicorder and 120596 is the angular fundamental frequency of thesystem The fundamental component (or DC component) ofactive power is represented by119860
0119901coefficient as shown in (2)
The 119860ℎ119901
coefficient in (1) can be calculated by (3) The 1198600119901
coefficient or DC component can be calculated by substituteℎ = 0 in (3) as shown in (4) The 119873
0and 119873 in (3) and (4)
are the starting point for computing and the total numberof sampled point in one cycle respectively The calculationof 1198600119901
in the first period can be calculated using (4) so asto achieve the initial value for the PQF algorithm For thenext period the 119860
0119901can be calculated by (5) in which this
approach is called SWFA [9] The SWFA approach can besummarized in Figure 4
119901119871(119896119879119904)=
1198600119901
2+
infin
sum
ℎ=1
[119860ℎ119901cos (ℎ120596119896119879
119904) + 119861ℎ119901sin (ℎ120596119896119879
119904)]
(1)
119901119871(119896119879119904) =
1198600119901
2 (2)
4 Modelling and Simulation in Engineering
5
pc
pc
pdc
pL
pL
pL
HPF
HPF
SWFA
SWFA
PI controller
orSWFA for PQF
HPF for PQ
pL
UdcUdcref
minus
+
minus
+
minus
+
uPCC(1205721205730)
uPCC(1205721205730)
qL(1205721205730)
iL(1205721205730)
iL(abc)u
DC bus voltage control
pL
pL
pL
PCC(abc)
cp0ref
i
cp120572ref
= =
=
=
=
=
=
u 120572u 120573
u 0
radic 2
3radic 2
2
3
1
1
0
1
radic2
1
2radic3
3
21
radic2
1
radic2
1
0
1
radic2
1
2radic3
21
radic2
1
radic2
u b
u c
iL120572iL120573iL0
iLaa
iLbiLc
pL = u 120572iL120572 + u 120573iL120573 + u 0iL0
u 120573iL0 minus u 0iL120573u 0iL120572 minus u 120572iL0u 120572iL120573 minus u 120573iL120572
i
i
icq120572icq120573icq0
1
u 1205722 + u 120573
2 + u 02
u 1205722 + u 120573
2 + u 02
u 120572
u 120573
u 0
u 0qL120573 minus u 120573qL0u 120572qL0 minus u 0qL120572u 120573qL120572 minus u 120572qL120573
ic120572ic120573ic0
i +
i + icq120573i +
icaicbicc
1 01
radic2
minus1
2
radic3
2
1
radic2
minus1
2minusradic3
2
1
radic2
ic120572ic120573ic0
radic 2
3
[ ] [ ] [ ] [ ]
[ ]
[
[ ]
]
[ ] [ ]
[ ] [ ]
[
[
]
[ ]
]
[[ [[[[
minus
radic3
2minus
1
2minusminus
6
4
PCCPCCPCC
u3
2minusradic2
1minus
PCC
PCCPCC
PCC
PCC
PCCPCC
PCCPCC PCC
PCC
PCC
PCC PCC PCC PCCPCCPCC
PCCPCCPCCPCCPCC
PCCPCCPCC
PCC
cq120572refref
cq0ref
refrefref
refrefref
refref
ref
refref
ref
qL120572qL120573qL0
ic(1205721205730)ref
icp120572ref
i
cp120573refcp0ref
cp120573ref
Figure 3 The block diagram of PQ and PQF algorithms
Modelling and Simulation in Engineering 5
N
N0 + 1
n = N0
sum 2
NA0p
N0 + N
N0 + N minus 1
Entering pL(kTs)
N0 minus 1 Leaving pL(kTs)
Figure 4 The flow chart of the SWFA approach
Table 1 The performance comparison between the PQ and PQF algorithms for balanced system
Harmonic identification algorithm Before compensation After compensationTHD
119901119871(119899119879119904) cos (119899ℎ120596119879
119904) (3)
1198600119901=2
119873
1198730+119873minus1
sum
119899=1198730
119901119871(119899119879119904) (4)
1198600119901
(new)= 1198600119901
(old)minus2
119873119901119871[(1198730minus 1) 119879
119904]
+2
119873119901119871[(1198730+ 119873)119879
119904]
(5)
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the balanced systemin Figure 2 with 119871
119871= 10mH are addressed in Table 1 The
cutoff frequency of HPF for PQ method is set to 280Hz Theaverage THD of source currents (THD
119894av) and the powerfactor after compensation (pf) are the performance indices forthe comparisonThe THDav and pf can be calculated by (6)and (8) respectively The THD of source currents in eachphase (THD
119894119896) can be calculated by (7) The fundamental
and harmonic (order n) values in (7) are denoted by subscript1 and n respectively The pfdisp and pfdist in (8) are the
displacement and distortion power factors in which thesevalues can be calculated by (9) and (10) respectively
THD119894av =
radicsum119896=119886119887119888
THD2119894119896
3
(6)
THD119894119896=
radicsuminfin
119899=21198682
119899119896
I1119896
times 100 (7)
pf = 119875
119878= pfdisp times pfdist (8)
pfdisp =119875
S1
(9)
pfdisp =1
radic1 + THD2119906times radic1 + THD2i
(10)
The results from Table 1 show that the PQF algorithmcan provide the best performance in term of THD
119894avFrom Table 1 the THD
119894av of the source currents beforecompensation is equal to 2448 in which this value isextremely greater than the IEEE std519-1992The source cur-rent waveforms before compensation (119894
119904119886 119894119904119887 119894119904119888) are highly
6 Modelling and Simulation in Engineering
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000
500
minus5000
500
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
30
minus3
30
minus3
30
minus3
i La
i Lb
i Lc
i cc
i sa
i sb
Time (s)
uPC
Cb
uPC
Ca
Before
compensation
Initialization
Reactive power and harmonic
compensations
i sc
uPC
Cc
i cb
i ca
Figure 5 The simulation results using PQF algorithm for ideal shunt active power filter with balanced system
Table 2 The error of instantaneous active power for harmonic component calculation
Figure 6 The spectrum of instantaneous active power for harmonic components
iLc
iLbn
LL
LLisb
isc
ica
icb
usa
usb
PCC
PCC
icc
Harmonicidentification
algorithm(PQ or PQF)
380Vrms
50Hz
iLaLLPCCisa
SAPF
iLa iLb iLc
+
minus
+
minus
+
minus
usc
icareficbreficcref uPCCc
uPCCb
uPCCa
130Ω
4H
120Ω
110Ω
05H
01H
Nonlinear load
Single-phase bridge rectifier
Figure 7 The unbalanced power system with ideal shunt active power filter
distorted as shown in Figure 5 These waveforms are equal tothe load currents (119894
119871119886 119894119871119887 119894119871119888) before compensation because
the SAPF is not connected to the system From Figure 5 thecompensating currents (119894
119888119886 119894119888119887 119894119888119888) from SAPF are injected
into the system at t = 004 s For t = 004ndash006 s thecompensation is nonperfect because this interval is usedfor initial of SWFA algorithm The SWFA algorithm is
the main approach for PQF method After t = 006 s theSAPF generates the perfectly compensating currents intothe system (reactive power and harmonic compensations)From Figure 5 (119905 ge 006 s) it can be seen that the sourcecurrents after compensation are nearly sinusoidal waveformsThe THD
119894av of these currents is equal to 095 and 004 forPQ and PQF respectively as shown in Table 1 These values
8 Modelling and Simulation in Engineering
Table 3 The performance comparison between the PQ and PQF algorithms for unbalanced system
Harmonicidentificationalgorithm
THD119894119886
THD119894119887
THD119894119888
THD119894119886V
119894119904119886
(rms)119894119904119887
(rms)119894119904119888
(rms) unbalance
Before compensation4284 3275 851 3152 146 161 192 1543
are satisfied under IEEE std519-1992 Moreover the powerfactor after compensation is unity while before compensationthe power factor is equal to 095
From Figure 3 the different point between the PQ andPQF algorithm is the method to separate the fundamentaland harmonic components Therefore the accurate instanta-neous active power for harmonic component (119901
119871) is themain
objective to identify the harmonic currents of the systemThespectrum comparison of the 119901
119871values calculated by PQF and
PQ algorithms is shown in Figure 6The119901119871act is the spectrum
of the instantaneous harmonic active power calculated byFFT approach fromMATLAB programmingThe 119901
119871PQF and119901119871PQ are calculated by PQF and PQ algorithms respectively
From Figure 6 it can be seen that the 119901119871PQF value calculated
by PQF algorithm is nearly the same as the 119901119871act value
The errors between the 119901119871values calculated by PQF and
PQ algorithms compared with the 119901119871act value are shown in
Table 2 In the paper the authors focus on the total error(119864tot) for the performance comparison between the PQ andPQF algorithms From Table 2 the 119864tot from PQF algorithm(056) is less than the PQ algorithm (156) Thereforethe PQF algorithm is the perfect method to calculate thereference currents for ESAPF
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the unbalancedsystem in Figure 7 are addressed in Table 3 The results fromTable 3 show that the PQF algorithm can provide the bestperformance in term of THD
119894av and unbalance aftercompensationTheunbalance in this table can be calculatedby (11) From Table 3 the THD
119894av and unbalance ofsource currents before compensation are equal to 3152and 1543 respectively The waveforms of source current(119894119904119886 119894119904119887 119894119904119888) before compensation (119905 = 0ndash004 s) are extremely
distorted and unbalanced as depicted in Figure 8 For 119905 =
004ndash006 s this interval is the initial calculation for PQFalgorithm using a SWFA technique For 119905 ge 006 s the PQFalgorithm can completely eliminate the harmonic currentsand balance the amplitude and phase of source currents aftercompensation The THD
119894av of these currents are equal to060 and 001 for PQ andPQF respectively as given inTable 3The unbalance after compensation using PQ and PQFalgorithms is equal to 043 and 0 respectively It means thatthe source currents after compensation are perfectly balancedusing the PQF algorithm compared with the unbalancebefore compensation (1543) From the simulation resultsof the balanced and unbalanced system the PQF algorithm
is the perfect method to calculate the reference currents forESAPF In the future works the positive sequence detectionis added to the PQF algorithm for the harmonic currentelimination in the distorted and unbalanced voltage systems
unbalance
=
1003816100381610038161003816maximumcurrent deviation from average rms current1003816100381610038161003816average rms current
times 100(11)
3 Predictive Current Control on dq-Axis
In this section the predictive current control for SAPF withbalanced three-phase system is proposed The predictivecurrent control technique is applied to control the injectionof compensating currents with SAPF as shown in Figure 9The voltage source inverter with six IGBTs is the SAPFtopology in the paper The PQF algorithm described in theprevious section is used to identify the harmonic currents inthe system The three-phase bridge rectifier feeding resistiveand inductive loads behaves as a nonlinear load into thepower system The predictive current control is the suitabletechnique for a digital control [21] The equivalent circuit inFigure 10 is used to derive the relationship equation betweenthe SAPF output voltages (u
(119886119887119888)) and the voltages at PCC
point (uPCC(119886119887119888)) as given in (12) The compensating currentsor active filter currents are represented by i
119888(119886119887119888) The discrete
form of (12) can be represented by (13) and119879sc is the samplingtime of the controller
u(119886119887119888)
= 119871119891(119889i119888(119886119887119888)
119889119905) + uPCC(119886119887119888) (12)
u(119886119887119888)
(119896) =
119871119891
119879sc[i119888(119886119887119888)
(119896 + 1) minus i119888(119886119887119888)
(119896)] + uPCC(119886119887119888) (119896)
(13)
The concept of the reference currents prediction is shownin Figure 11 From this figure the three-phase referencecurrent at time instants 119905(119896) and 119905(119896 + 1) is denoted byi119888(119886119887119888)ref(119896) and i
119888(119886119887119888)ref(119896 + 1) respectively The predictedthree-phase reference currents (i
119888119901(119886119887119888)ref(119896 + 1)) for thenext sampling period are calculated by (14) The predictedcurrents (i
119888119901(119886119887119888)ref(119896 + 1)) are equal to the reference currents(i119888(119886119887119888)ref(119896 + 1)) at time instant 119905(119896 + 1) The 119886
0and 1198861are the
Modelling and Simulation in Engineering 9
i La
i Lb
i Lc
i cc
i sa
i sb
uPC
Cb
uPC
Ca
i sc
uPC
Cc
i cb
i ca
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000500
minus5000
500
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
30
minus3
30
minus3
30
minus3
Beforecompensation
Initialization
Reactive power and harmoniccompensations
Time (s)
Figure 8 The simulation results using PQF algorithm for ideal shunt active power filter with unbalanced system
10 Modelling and Simulation in Engineering
380Vrms
50Hz
n
isa
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
130Ω
4H
on dq-axis
u120572
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
119901119871(119899119879119904) cos (119899ℎ120596119879
119904) (3)
1198600119901=2
119873
1198730+119873minus1
sum
119899=1198730
119901119871(119899119879119904) (4)
1198600119901
(new)= 1198600119901
(old)minus2
119873119901119871[(1198730minus 1) 119879
119904]
+2
119873119901119871[(1198730+ 119873)119879
119904]
(5)
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the balanced systemin Figure 2 with 119871
119871= 10mH are addressed in Table 1 The
cutoff frequency of HPF for PQ method is set to 280Hz Theaverage THD of source currents (THD
119894av) and the powerfactor after compensation (pf) are the performance indices forthe comparisonThe THDav and pf can be calculated by (6)and (8) respectively The THD of source currents in eachphase (THD
119894119896) can be calculated by (7) The fundamental
and harmonic (order n) values in (7) are denoted by subscript1 and n respectively The pfdisp and pfdist in (8) are the
displacement and distortion power factors in which thesevalues can be calculated by (9) and (10) respectively
THD119894av =
radicsum119896=119886119887119888
THD2119894119896
3
(6)
THD119894119896=
radicsuminfin
119899=21198682
119899119896
I1119896
times 100 (7)
pf = 119875
119878= pfdisp times pfdist (8)
pfdisp =119875
S1
(9)
pfdisp =1
radic1 + THD2119906times radic1 + THD2i
(10)
The results from Table 1 show that the PQF algorithmcan provide the best performance in term of THD
119894avFrom Table 1 the THD
119894av of the source currents beforecompensation is equal to 2448 in which this value isextremely greater than the IEEE std519-1992The source cur-rent waveforms before compensation (119894
119904119886 119894119904119887 119894119904119888) are highly
6 Modelling and Simulation in Engineering
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000
500
minus5000
500
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
30
minus3
30
minus3
30
minus3
i La
i Lb
i Lc
i cc
i sa
i sb
Time (s)
uPC
Cb
uPC
Ca
Before
compensation
Initialization
Reactive power and harmonic
compensations
i sc
uPC
Cc
i cb
i ca
Figure 5 The simulation results using PQF algorithm for ideal shunt active power filter with balanced system
Table 2 The error of instantaneous active power for harmonic component calculation
Figure 6 The spectrum of instantaneous active power for harmonic components
iLc
iLbn
LL
LLisb
isc
ica
icb
usa
usb
PCC
PCC
icc
Harmonicidentification
algorithm(PQ or PQF)
380Vrms
50Hz
iLaLLPCCisa
SAPF
iLa iLb iLc
+
minus
+
minus
+
minus
usc
icareficbreficcref uPCCc
uPCCb
uPCCa
130Ω
4H
120Ω
110Ω
05H
01H
Nonlinear load
Single-phase bridge rectifier
Figure 7 The unbalanced power system with ideal shunt active power filter
distorted as shown in Figure 5 These waveforms are equal tothe load currents (119894
119871119886 119894119871119887 119894119871119888) before compensation because
the SAPF is not connected to the system From Figure 5 thecompensating currents (119894
119888119886 119894119888119887 119894119888119888) from SAPF are injected
into the system at t = 004 s For t = 004ndash006 s thecompensation is nonperfect because this interval is usedfor initial of SWFA algorithm The SWFA algorithm is
the main approach for PQF method After t = 006 s theSAPF generates the perfectly compensating currents intothe system (reactive power and harmonic compensations)From Figure 5 (119905 ge 006 s) it can be seen that the sourcecurrents after compensation are nearly sinusoidal waveformsThe THD
119894av of these currents is equal to 095 and 004 forPQ and PQF respectively as shown in Table 1 These values
8 Modelling and Simulation in Engineering
Table 3 The performance comparison between the PQ and PQF algorithms for unbalanced system
Harmonicidentificationalgorithm
THD119894119886
THD119894119887
THD119894119888
THD119894119886V
119894119904119886
(rms)119894119904119887
(rms)119894119904119888
(rms) unbalance
Before compensation4284 3275 851 3152 146 161 192 1543
are satisfied under IEEE std519-1992 Moreover the powerfactor after compensation is unity while before compensationthe power factor is equal to 095
From Figure 3 the different point between the PQ andPQF algorithm is the method to separate the fundamentaland harmonic components Therefore the accurate instanta-neous active power for harmonic component (119901
119871) is themain
objective to identify the harmonic currents of the systemThespectrum comparison of the 119901
119871values calculated by PQF and
PQ algorithms is shown in Figure 6The119901119871act is the spectrum
of the instantaneous harmonic active power calculated byFFT approach fromMATLAB programmingThe 119901
119871PQF and119901119871PQ are calculated by PQF and PQ algorithms respectively
From Figure 6 it can be seen that the 119901119871PQF value calculated
by PQF algorithm is nearly the same as the 119901119871act value
The errors between the 119901119871values calculated by PQF and
PQ algorithms compared with the 119901119871act value are shown in
Table 2 In the paper the authors focus on the total error(119864tot) for the performance comparison between the PQ andPQF algorithms From Table 2 the 119864tot from PQF algorithm(056) is less than the PQ algorithm (156) Thereforethe PQF algorithm is the perfect method to calculate thereference currents for ESAPF
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the unbalancedsystem in Figure 7 are addressed in Table 3 The results fromTable 3 show that the PQF algorithm can provide the bestperformance in term of THD
119894av and unbalance aftercompensationTheunbalance in this table can be calculatedby (11) From Table 3 the THD
119894av and unbalance ofsource currents before compensation are equal to 3152and 1543 respectively The waveforms of source current(119894119904119886 119894119904119887 119894119904119888) before compensation (119905 = 0ndash004 s) are extremely
distorted and unbalanced as depicted in Figure 8 For 119905 =
004ndash006 s this interval is the initial calculation for PQFalgorithm using a SWFA technique For 119905 ge 006 s the PQFalgorithm can completely eliminate the harmonic currentsand balance the amplitude and phase of source currents aftercompensation The THD
119894av of these currents are equal to060 and 001 for PQ andPQF respectively as given inTable 3The unbalance after compensation using PQ and PQFalgorithms is equal to 043 and 0 respectively It means thatthe source currents after compensation are perfectly balancedusing the PQF algorithm compared with the unbalancebefore compensation (1543) From the simulation resultsof the balanced and unbalanced system the PQF algorithm
is the perfect method to calculate the reference currents forESAPF In the future works the positive sequence detectionis added to the PQF algorithm for the harmonic currentelimination in the distorted and unbalanced voltage systems
unbalance
=
1003816100381610038161003816maximumcurrent deviation from average rms current1003816100381610038161003816average rms current
times 100(11)
3 Predictive Current Control on dq-Axis
In this section the predictive current control for SAPF withbalanced three-phase system is proposed The predictivecurrent control technique is applied to control the injectionof compensating currents with SAPF as shown in Figure 9The voltage source inverter with six IGBTs is the SAPFtopology in the paper The PQF algorithm described in theprevious section is used to identify the harmonic currents inthe system The three-phase bridge rectifier feeding resistiveand inductive loads behaves as a nonlinear load into thepower system The predictive current control is the suitabletechnique for a digital control [21] The equivalent circuit inFigure 10 is used to derive the relationship equation betweenthe SAPF output voltages (u
(119886119887119888)) and the voltages at PCC
point (uPCC(119886119887119888)) as given in (12) The compensating currentsor active filter currents are represented by i
119888(119886119887119888) The discrete
form of (12) can be represented by (13) and119879sc is the samplingtime of the controller
u(119886119887119888)
= 119871119891(119889i119888(119886119887119888)
119889119905) + uPCC(119886119887119888) (12)
u(119886119887119888)
(119896) =
119871119891
119879sc[i119888(119886119887119888)
(119896 + 1) minus i119888(119886119887119888)
(119896)] + uPCC(119886119887119888) (119896)
(13)
The concept of the reference currents prediction is shownin Figure 11 From this figure the three-phase referencecurrent at time instants 119905(119896) and 119905(119896 + 1) is denoted byi119888(119886119887119888)ref(119896) and i
119888(119886119887119888)ref(119896 + 1) respectively The predictedthree-phase reference currents (i
119888119901(119886119887119888)ref(119896 + 1)) for thenext sampling period are calculated by (14) The predictedcurrents (i
119888119901(119886119887119888)ref(119896 + 1)) are equal to the reference currents(i119888(119886119887119888)ref(119896 + 1)) at time instant 119905(119896 + 1) The 119886
0and 1198861are the
Modelling and Simulation in Engineering 9
i La
i Lb
i Lc
i cc
i sa
i sb
uPC
Cb
uPC
Ca
i sc
uPC
Cc
i cb
i ca
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000500
minus5000
500
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
30
minus3
30
minus3
30
minus3
Beforecompensation
Initialization
Reactive power and harmoniccompensations
Time (s)
Figure 8 The simulation results using PQF algorithm for ideal shunt active power filter with unbalanced system
10 Modelling and Simulation in Engineering
380Vrms
50Hz
n
isa
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
130Ω
4H
on dq-axis
u120572
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
119901119871(119899119879119904) cos (119899ℎ120596119879
119904) (3)
1198600119901=2
119873
1198730+119873minus1
sum
119899=1198730
119901119871(119899119879119904) (4)
1198600119901
(new)= 1198600119901
(old)minus2
119873119901119871[(1198730minus 1) 119879
119904]
+2
119873119901119871[(1198730+ 119873)119879
119904]
(5)
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the balanced systemin Figure 2 with 119871
119871= 10mH are addressed in Table 1 The
cutoff frequency of HPF for PQ method is set to 280Hz Theaverage THD of source currents (THD
119894av) and the powerfactor after compensation (pf) are the performance indices forthe comparisonThe THDav and pf can be calculated by (6)and (8) respectively The THD of source currents in eachphase (THD
119894119896) can be calculated by (7) The fundamental
and harmonic (order n) values in (7) are denoted by subscript1 and n respectively The pfdisp and pfdist in (8) are the
displacement and distortion power factors in which thesevalues can be calculated by (9) and (10) respectively
THD119894av =
radicsum119896=119886119887119888
THD2119894119896
3
(6)
THD119894119896=
radicsuminfin
119899=21198682
119899119896
I1119896
times 100 (7)
pf = 119875
119878= pfdisp times pfdist (8)
pfdisp =119875
S1
(9)
pfdisp =1
radic1 + THD2119906times radic1 + THD2i
(10)
The results from Table 1 show that the PQF algorithmcan provide the best performance in term of THD
119894avFrom Table 1 the THD
119894av of the source currents beforecompensation is equal to 2448 in which this value isextremely greater than the IEEE std519-1992The source cur-rent waveforms before compensation (119894
119904119886 119894119904119887 119894119904119888) are highly
6 Modelling and Simulation in Engineering
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000
500
minus5000
500
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
50
minus5
30
minus3
30
minus3
30
minus3
i La
i Lb
i Lc
i cc
i sa
i sb
Time (s)
uPC
Cb
uPC
Ca
Before
compensation
Initialization
Reactive power and harmonic
compensations
i sc
uPC
Cc
i cb
i ca
Figure 5 The simulation results using PQF algorithm for ideal shunt active power filter with balanced system
Table 2 The error of instantaneous active power for harmonic component calculation
Figure 6 The spectrum of instantaneous active power for harmonic components
iLc
iLbn
LL
LLisb
isc
ica
icb
usa
usb
PCC
PCC
icc
Harmonicidentification
algorithm(PQ or PQF)
380Vrms
50Hz
iLaLLPCCisa
SAPF
iLa iLb iLc
+
minus
+
minus
+
minus
usc
icareficbreficcref uPCCc
uPCCb
uPCCa
130Ω
4H
120Ω
110Ω
05H
01H
Nonlinear load
Single-phase bridge rectifier
Figure 7 The unbalanced power system with ideal shunt active power filter
distorted as shown in Figure 5 These waveforms are equal tothe load currents (119894
119871119886 119894119871119887 119894119871119888) before compensation because
the SAPF is not connected to the system From Figure 5 thecompensating currents (119894
119888119886 119894119888119887 119894119888119888) from SAPF are injected
into the system at t = 004 s For t = 004ndash006 s thecompensation is nonperfect because this interval is usedfor initial of SWFA algorithm The SWFA algorithm is
the main approach for PQF method After t = 006 s theSAPF generates the perfectly compensating currents intothe system (reactive power and harmonic compensations)From Figure 5 (119905 ge 006 s) it can be seen that the sourcecurrents after compensation are nearly sinusoidal waveformsThe THD
119894av of these currents is equal to 095 and 004 forPQ and PQF respectively as shown in Table 1 These values
8 Modelling and Simulation in Engineering
Table 3 The performance comparison between the PQ and PQF algorithms for unbalanced system
Harmonicidentificationalgorithm
THD119894119886
THD119894119887
THD119894119888
THD119894119886V
119894119904119886
(rms)119894119904119887
(rms)119894119904119888
(rms) unbalance
Before compensation4284 3275 851 3152 146 161 192 1543
are satisfied under IEEE std519-1992 Moreover the powerfactor after compensation is unity while before compensationthe power factor is equal to 095
From Figure 3 the different point between the PQ andPQF algorithm is the method to separate the fundamentaland harmonic components Therefore the accurate instanta-neous active power for harmonic component (119901
119871) is themain
objective to identify the harmonic currents of the systemThespectrum comparison of the 119901
119871values calculated by PQF and
PQ algorithms is shown in Figure 6The119901119871act is the spectrum
of the instantaneous harmonic active power calculated byFFT approach fromMATLAB programmingThe 119901
119871PQF and119901119871PQ are calculated by PQF and PQ algorithms respectively
From Figure 6 it can be seen that the 119901119871PQF value calculated
by PQF algorithm is nearly the same as the 119901119871act value
The errors between the 119901119871values calculated by PQF and
PQ algorithms compared with the 119901119871act value are shown in
Table 2 In the paper the authors focus on the total error(119864tot) for the performance comparison between the PQ andPQF algorithms From Table 2 the 119864tot from PQF algorithm(056) is less than the PQ algorithm (156) Thereforethe PQF algorithm is the perfect method to calculate thereference currents for ESAPF
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the unbalancedsystem in Figure 7 are addressed in Table 3 The results fromTable 3 show that the PQF algorithm can provide the bestperformance in term of THD
119894av and unbalance aftercompensationTheunbalance in this table can be calculatedby (11) From Table 3 the THD
119894av and unbalance ofsource currents before compensation are equal to 3152and 1543 respectively The waveforms of source current(119894119904119886 119894119904119887 119894119904119888) before compensation (119905 = 0ndash004 s) are extremely
distorted and unbalanced as depicted in Figure 8 For 119905 =
004ndash006 s this interval is the initial calculation for PQFalgorithm using a SWFA technique For 119905 ge 006 s the PQFalgorithm can completely eliminate the harmonic currentsand balance the amplitude and phase of source currents aftercompensation The THD
119894av of these currents are equal to060 and 001 for PQ andPQF respectively as given inTable 3The unbalance after compensation using PQ and PQFalgorithms is equal to 043 and 0 respectively It means thatthe source currents after compensation are perfectly balancedusing the PQF algorithm compared with the unbalancebefore compensation (1543) From the simulation resultsof the balanced and unbalanced system the PQF algorithm
is the perfect method to calculate the reference currents forESAPF In the future works the positive sequence detectionis added to the PQF algorithm for the harmonic currentelimination in the distorted and unbalanced voltage systems
unbalance
=
1003816100381610038161003816maximumcurrent deviation from average rms current1003816100381610038161003816average rms current
times 100(11)
3 Predictive Current Control on dq-Axis
In this section the predictive current control for SAPF withbalanced three-phase system is proposed The predictivecurrent control technique is applied to control the injectionof compensating currents with SAPF as shown in Figure 9The voltage source inverter with six IGBTs is the SAPFtopology in the paper The PQF algorithm described in theprevious section is used to identify the harmonic currents inthe system The three-phase bridge rectifier feeding resistiveand inductive loads behaves as a nonlinear load into thepower system The predictive current control is the suitabletechnique for a digital control [21] The equivalent circuit inFigure 10 is used to derive the relationship equation betweenthe SAPF output voltages (u
(119886119887119888)) and the voltages at PCC
point (uPCC(119886119887119888)) as given in (12) The compensating currentsor active filter currents are represented by i
119888(119886119887119888) The discrete
form of (12) can be represented by (13) and119879sc is the samplingtime of the controller
u(119886119887119888)
= 119871119891(119889i119888(119886119887119888)
119889119905) + uPCC(119886119887119888) (12)
u(119886119887119888)
(119896) =
119871119891
119879sc[i119888(119886119887119888)
(119896 + 1) minus i119888(119886119887119888)
(119896)] + uPCC(119886119887119888) (119896)
(13)
The concept of the reference currents prediction is shownin Figure 11 From this figure the three-phase referencecurrent at time instants 119905(119896) and 119905(119896 + 1) is denoted byi119888(119886119887119888)ref(119896) and i
119888(119886119887119888)ref(119896 + 1) respectively The predictedthree-phase reference currents (i
119888119901(119886119887119888)ref(119896 + 1)) for thenext sampling period are calculated by (14) The predictedcurrents (i
119888119901(119886119887119888)ref(119896 + 1)) are equal to the reference currents(i119888(119886119887119888)ref(119896 + 1)) at time instant 119905(119896 + 1) The 119886
0and 1198861are the
Modelling and Simulation in Engineering 9
i La
i Lb
i Lc
i cc
i sa
i sb
uPC
Cb
uPC
Ca
i sc
uPC
Cc
i cb
i ca
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000500
minus5000
500
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
30
minus3
30
minus3
30
minus3
Beforecompensation
Initialization
Reactive power and harmoniccompensations
Time (s)
Figure 8 The simulation results using PQF algorithm for ideal shunt active power filter with unbalanced system
10 Modelling and Simulation in Engineering
380Vrms
50Hz
n
isa
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
130Ω
4H
on dq-axis
u120572
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 6 The spectrum of instantaneous active power for harmonic components
iLc
iLbn
LL
LLisb
isc
ica
icb
usa
usb
PCC
PCC
icc
Harmonicidentification
algorithm(PQ or PQF)
380Vrms
50Hz
iLaLLPCCisa
SAPF
iLa iLb iLc
+
minus
+
minus
+
minus
usc
icareficbreficcref uPCCc
uPCCb
uPCCa
130Ω
4H
120Ω
110Ω
05H
01H
Nonlinear load
Single-phase bridge rectifier
Figure 7 The unbalanced power system with ideal shunt active power filter
distorted as shown in Figure 5 These waveforms are equal tothe load currents (119894
119871119886 119894119871119887 119894119871119888) before compensation because
the SAPF is not connected to the system From Figure 5 thecompensating currents (119894
119888119886 119894119888119887 119894119888119888) from SAPF are injected
into the system at t = 004 s For t = 004ndash006 s thecompensation is nonperfect because this interval is usedfor initial of SWFA algorithm The SWFA algorithm is
the main approach for PQF method After t = 006 s theSAPF generates the perfectly compensating currents intothe system (reactive power and harmonic compensations)From Figure 5 (119905 ge 006 s) it can be seen that the sourcecurrents after compensation are nearly sinusoidal waveformsThe THD
119894av of these currents is equal to 095 and 004 forPQ and PQF respectively as shown in Table 1 These values
8 Modelling and Simulation in Engineering
Table 3 The performance comparison between the PQ and PQF algorithms for unbalanced system
Harmonicidentificationalgorithm
THD119894119886
THD119894119887
THD119894119888
THD119894119886V
119894119904119886
(rms)119894119904119887
(rms)119894119904119888
(rms) unbalance
Before compensation4284 3275 851 3152 146 161 192 1543
are satisfied under IEEE std519-1992 Moreover the powerfactor after compensation is unity while before compensationthe power factor is equal to 095
From Figure 3 the different point between the PQ andPQF algorithm is the method to separate the fundamentaland harmonic components Therefore the accurate instanta-neous active power for harmonic component (119901
119871) is themain
objective to identify the harmonic currents of the systemThespectrum comparison of the 119901
119871values calculated by PQF and
PQ algorithms is shown in Figure 6The119901119871act is the spectrum
of the instantaneous harmonic active power calculated byFFT approach fromMATLAB programmingThe 119901
119871PQF and119901119871PQ are calculated by PQF and PQ algorithms respectively
From Figure 6 it can be seen that the 119901119871PQF value calculated
by PQF algorithm is nearly the same as the 119901119871act value
The errors between the 119901119871values calculated by PQF and
PQ algorithms compared with the 119901119871act value are shown in
Table 2 In the paper the authors focus on the total error(119864tot) for the performance comparison between the PQ andPQF algorithms From Table 2 the 119864tot from PQF algorithm(056) is less than the PQ algorithm (156) Thereforethe PQF algorithm is the perfect method to calculate thereference currents for ESAPF
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the unbalancedsystem in Figure 7 are addressed in Table 3 The results fromTable 3 show that the PQF algorithm can provide the bestperformance in term of THD
119894av and unbalance aftercompensationTheunbalance in this table can be calculatedby (11) From Table 3 the THD
119894av and unbalance ofsource currents before compensation are equal to 3152and 1543 respectively The waveforms of source current(119894119904119886 119894119904119887 119894119904119888) before compensation (119905 = 0ndash004 s) are extremely
distorted and unbalanced as depicted in Figure 8 For 119905 =
004ndash006 s this interval is the initial calculation for PQFalgorithm using a SWFA technique For 119905 ge 006 s the PQFalgorithm can completely eliminate the harmonic currentsand balance the amplitude and phase of source currents aftercompensation The THD
119894av of these currents are equal to060 and 001 for PQ andPQF respectively as given inTable 3The unbalance after compensation using PQ and PQFalgorithms is equal to 043 and 0 respectively It means thatthe source currents after compensation are perfectly balancedusing the PQF algorithm compared with the unbalancebefore compensation (1543) From the simulation resultsof the balanced and unbalanced system the PQF algorithm
is the perfect method to calculate the reference currents forESAPF In the future works the positive sequence detectionis added to the PQF algorithm for the harmonic currentelimination in the distorted and unbalanced voltage systems
unbalance
=
1003816100381610038161003816maximumcurrent deviation from average rms current1003816100381610038161003816average rms current
times 100(11)
3 Predictive Current Control on dq-Axis
In this section the predictive current control for SAPF withbalanced three-phase system is proposed The predictivecurrent control technique is applied to control the injectionof compensating currents with SAPF as shown in Figure 9The voltage source inverter with six IGBTs is the SAPFtopology in the paper The PQF algorithm described in theprevious section is used to identify the harmonic currents inthe system The three-phase bridge rectifier feeding resistiveand inductive loads behaves as a nonlinear load into thepower system The predictive current control is the suitabletechnique for a digital control [21] The equivalent circuit inFigure 10 is used to derive the relationship equation betweenthe SAPF output voltages (u
(119886119887119888)) and the voltages at PCC
point (uPCC(119886119887119888)) as given in (12) The compensating currentsor active filter currents are represented by i
119888(119886119887119888) The discrete
form of (12) can be represented by (13) and119879sc is the samplingtime of the controller
u(119886119887119888)
= 119871119891(119889i119888(119886119887119888)
119889119905) + uPCC(119886119887119888) (12)
u(119886119887119888)
(119896) =
119871119891
119879sc[i119888(119886119887119888)
(119896 + 1) minus i119888(119886119887119888)
(119896)] + uPCC(119886119887119888) (119896)
(13)
The concept of the reference currents prediction is shownin Figure 11 From this figure the three-phase referencecurrent at time instants 119905(119896) and 119905(119896 + 1) is denoted byi119888(119886119887119888)ref(119896) and i
119888(119886119887119888)ref(119896 + 1) respectively The predictedthree-phase reference currents (i
119888119901(119886119887119888)ref(119896 + 1)) for thenext sampling period are calculated by (14) The predictedcurrents (i
119888119901(119886119887119888)ref(119896 + 1)) are equal to the reference currents(i119888(119886119887119888)ref(119896 + 1)) at time instant 119905(119896 + 1) The 119886
0and 1198861are the
Modelling and Simulation in Engineering 9
i La
i Lb
i Lc
i cc
i sa
i sb
uPC
Cb
uPC
Ca
i sc
uPC
Cc
i cb
i ca
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000500
minus5000
500
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
30
minus3
30
minus3
30
minus3
Beforecompensation
Initialization
Reactive power and harmoniccompensations
Time (s)
Figure 8 The simulation results using PQF algorithm for ideal shunt active power filter with unbalanced system
10 Modelling and Simulation in Engineering
380Vrms
50Hz
n
isa
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
130Ω
4H
on dq-axis
u120572
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 6 The spectrum of instantaneous active power for harmonic components
iLc
iLbn
LL
LLisb
isc
ica
icb
usa
usb
PCC
PCC
icc
Harmonicidentification
algorithm(PQ or PQF)
380Vrms
50Hz
iLaLLPCCisa
SAPF
iLa iLb iLc
+
minus
+
minus
+
minus
usc
icareficbreficcref uPCCc
uPCCb
uPCCa
130Ω
4H
120Ω
110Ω
05H
01H
Nonlinear load
Single-phase bridge rectifier
Figure 7 The unbalanced power system with ideal shunt active power filter
distorted as shown in Figure 5 These waveforms are equal tothe load currents (119894
119871119886 119894119871119887 119894119871119888) before compensation because
the SAPF is not connected to the system From Figure 5 thecompensating currents (119894
119888119886 119894119888119887 119894119888119888) from SAPF are injected
into the system at t = 004 s For t = 004ndash006 s thecompensation is nonperfect because this interval is usedfor initial of SWFA algorithm The SWFA algorithm is
the main approach for PQF method After t = 006 s theSAPF generates the perfectly compensating currents intothe system (reactive power and harmonic compensations)From Figure 5 (119905 ge 006 s) it can be seen that the sourcecurrents after compensation are nearly sinusoidal waveformsThe THD
119894av of these currents is equal to 095 and 004 forPQ and PQF respectively as shown in Table 1 These values
8 Modelling and Simulation in Engineering
Table 3 The performance comparison between the PQ and PQF algorithms for unbalanced system
Harmonicidentificationalgorithm
THD119894119886
THD119894119887
THD119894119888
THD119894119886V
119894119904119886
(rms)119894119904119887
(rms)119894119904119888
(rms) unbalance
Before compensation4284 3275 851 3152 146 161 192 1543
are satisfied under IEEE std519-1992 Moreover the powerfactor after compensation is unity while before compensationthe power factor is equal to 095
From Figure 3 the different point between the PQ andPQF algorithm is the method to separate the fundamentaland harmonic components Therefore the accurate instanta-neous active power for harmonic component (119901
119871) is themain
objective to identify the harmonic currents of the systemThespectrum comparison of the 119901
119871values calculated by PQF and
PQ algorithms is shown in Figure 6The119901119871act is the spectrum
of the instantaneous harmonic active power calculated byFFT approach fromMATLAB programmingThe 119901
119871PQF and119901119871PQ are calculated by PQF and PQ algorithms respectively
From Figure 6 it can be seen that the 119901119871PQF value calculated
by PQF algorithm is nearly the same as the 119901119871act value
The errors between the 119901119871values calculated by PQF and
PQ algorithms compared with the 119901119871act value are shown in
Table 2 In the paper the authors focus on the total error(119864tot) for the performance comparison between the PQ andPQF algorithms From Table 2 the 119864tot from PQF algorithm(056) is less than the PQ algorithm (156) Thereforethe PQF algorithm is the perfect method to calculate thereference currents for ESAPF
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the unbalancedsystem in Figure 7 are addressed in Table 3 The results fromTable 3 show that the PQF algorithm can provide the bestperformance in term of THD
119894av and unbalance aftercompensationTheunbalance in this table can be calculatedby (11) From Table 3 the THD
119894av and unbalance ofsource currents before compensation are equal to 3152and 1543 respectively The waveforms of source current(119894119904119886 119894119904119887 119894119904119888) before compensation (119905 = 0ndash004 s) are extremely
distorted and unbalanced as depicted in Figure 8 For 119905 =
004ndash006 s this interval is the initial calculation for PQFalgorithm using a SWFA technique For 119905 ge 006 s the PQFalgorithm can completely eliminate the harmonic currentsand balance the amplitude and phase of source currents aftercompensation The THD
119894av of these currents are equal to060 and 001 for PQ andPQF respectively as given inTable 3The unbalance after compensation using PQ and PQFalgorithms is equal to 043 and 0 respectively It means thatthe source currents after compensation are perfectly balancedusing the PQF algorithm compared with the unbalancebefore compensation (1543) From the simulation resultsof the balanced and unbalanced system the PQF algorithm
is the perfect method to calculate the reference currents forESAPF In the future works the positive sequence detectionis added to the PQF algorithm for the harmonic currentelimination in the distorted and unbalanced voltage systems
unbalance
=
1003816100381610038161003816maximumcurrent deviation from average rms current1003816100381610038161003816average rms current
times 100(11)
3 Predictive Current Control on dq-Axis
In this section the predictive current control for SAPF withbalanced three-phase system is proposed The predictivecurrent control technique is applied to control the injectionof compensating currents with SAPF as shown in Figure 9The voltage source inverter with six IGBTs is the SAPFtopology in the paper The PQF algorithm described in theprevious section is used to identify the harmonic currents inthe system The three-phase bridge rectifier feeding resistiveand inductive loads behaves as a nonlinear load into thepower system The predictive current control is the suitabletechnique for a digital control [21] The equivalent circuit inFigure 10 is used to derive the relationship equation betweenthe SAPF output voltages (u
(119886119887119888)) and the voltages at PCC
point (uPCC(119886119887119888)) as given in (12) The compensating currentsor active filter currents are represented by i
119888(119886119887119888) The discrete
form of (12) can be represented by (13) and119879sc is the samplingtime of the controller
u(119886119887119888)
= 119871119891(119889i119888(119886119887119888)
119889119905) + uPCC(119886119887119888) (12)
u(119886119887119888)
(119896) =
119871119891
119879sc[i119888(119886119887119888)
(119896 + 1) minus i119888(119886119887119888)
(119896)] + uPCC(119886119887119888) (119896)
(13)
The concept of the reference currents prediction is shownin Figure 11 From this figure the three-phase referencecurrent at time instants 119905(119896) and 119905(119896 + 1) is denoted byi119888(119886119887119888)ref(119896) and i
119888(119886119887119888)ref(119896 + 1) respectively The predictedthree-phase reference currents (i
119888119901(119886119887119888)ref(119896 + 1)) for thenext sampling period are calculated by (14) The predictedcurrents (i
119888119901(119886119887119888)ref(119896 + 1)) are equal to the reference currents(i119888(119886119887119888)ref(119896 + 1)) at time instant 119905(119896 + 1) The 119886
0and 1198861are the
Modelling and Simulation in Engineering 9
i La
i Lb
i Lc
i cc
i sa
i sb
uPC
Cb
uPC
Ca
i sc
uPC
Cc
i cb
i ca
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000500
minus5000
500
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
30
minus3
30
minus3
30
minus3
Beforecompensation
Initialization
Reactive power and harmoniccompensations
Time (s)
Figure 8 The simulation results using PQF algorithm for ideal shunt active power filter with unbalanced system
10 Modelling and Simulation in Engineering
380Vrms
50Hz
n
isa
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
130Ω
4H
on dq-axis
u120572
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
are satisfied under IEEE std519-1992 Moreover the powerfactor after compensation is unity while before compensationthe power factor is equal to 095
From Figure 3 the different point between the PQ andPQF algorithm is the method to separate the fundamentaland harmonic components Therefore the accurate instanta-neous active power for harmonic component (119901
119871) is themain
objective to identify the harmonic currents of the systemThespectrum comparison of the 119901
119871values calculated by PQF and
PQ algorithms is shown in Figure 6The119901119871act is the spectrum
of the instantaneous harmonic active power calculated byFFT approach fromMATLAB programmingThe 119901
119871PQF and119901119871PQ are calculated by PQF and PQ algorithms respectively
From Figure 6 it can be seen that the 119901119871PQF value calculated
by PQF algorithm is nearly the same as the 119901119871act value
The errors between the 119901119871values calculated by PQF and
PQ algorithms compared with the 119901119871act value are shown in
Table 2 In the paper the authors focus on the total error(119864tot) for the performance comparison between the PQ andPQF algorithms From Table 2 the 119864tot from PQF algorithm(056) is less than the PQ algorithm (156) Thereforethe PQF algorithm is the perfect method to calculate thereference currents for ESAPF
The simulation results of the performance comparisonbetween the PQ and PQF algorithms for the unbalancedsystem in Figure 7 are addressed in Table 3 The results fromTable 3 show that the PQF algorithm can provide the bestperformance in term of THD
119894av and unbalance aftercompensationTheunbalance in this table can be calculatedby (11) From Table 3 the THD
119894av and unbalance ofsource currents before compensation are equal to 3152and 1543 respectively The waveforms of source current(119894119904119886 119894119904119887 119894119904119888) before compensation (119905 = 0ndash004 s) are extremely
distorted and unbalanced as depicted in Figure 8 For 119905 =
004ndash006 s this interval is the initial calculation for PQFalgorithm using a SWFA technique For 119905 ge 006 s the PQFalgorithm can completely eliminate the harmonic currentsand balance the amplitude and phase of source currents aftercompensation The THD
119894av of these currents are equal to060 and 001 for PQ andPQF respectively as given inTable 3The unbalance after compensation using PQ and PQFalgorithms is equal to 043 and 0 respectively It means thatthe source currents after compensation are perfectly balancedusing the PQF algorithm compared with the unbalancebefore compensation (1543) From the simulation resultsof the balanced and unbalanced system the PQF algorithm
is the perfect method to calculate the reference currents forESAPF In the future works the positive sequence detectionis added to the PQF algorithm for the harmonic currentelimination in the distorted and unbalanced voltage systems
unbalance
=
1003816100381610038161003816maximumcurrent deviation from average rms current1003816100381610038161003816average rms current
times 100(11)
3 Predictive Current Control on dq-Axis
In this section the predictive current control for SAPF withbalanced three-phase system is proposed The predictivecurrent control technique is applied to control the injectionof compensating currents with SAPF as shown in Figure 9The voltage source inverter with six IGBTs is the SAPFtopology in the paper The PQF algorithm described in theprevious section is used to identify the harmonic currents inthe system The three-phase bridge rectifier feeding resistiveand inductive loads behaves as a nonlinear load into thepower system The predictive current control is the suitabletechnique for a digital control [21] The equivalent circuit inFigure 10 is used to derive the relationship equation betweenthe SAPF output voltages (u
(119886119887119888)) and the voltages at PCC
point (uPCC(119886119887119888)) as given in (12) The compensating currentsor active filter currents are represented by i
119888(119886119887119888) The discrete
form of (12) can be represented by (13) and119879sc is the samplingtime of the controller
u(119886119887119888)
= 119871119891(119889i119888(119886119887119888)
119889119905) + uPCC(119886119887119888) (12)
u(119886119887119888)
(119896) =
119871119891
119879sc[i119888(119886119887119888)
(119896 + 1) minus i119888(119886119887119888)
(119896)] + uPCC(119886119887119888) (119896)
(13)
The concept of the reference currents prediction is shownin Figure 11 From this figure the three-phase referencecurrent at time instants 119905(119896) and 119905(119896 + 1) is denoted byi119888(119886119887119888)ref(119896) and i
119888(119886119887119888)ref(119896 + 1) respectively The predictedthree-phase reference currents (i
119888119901(119886119887119888)ref(119896 + 1)) for thenext sampling period are calculated by (14) The predictedcurrents (i
119888119901(119886119887119888)ref(119896 + 1)) are equal to the reference currents(i119888(119886119887119888)ref(119896 + 1)) at time instant 119905(119896 + 1) The 119886
0and 1198861are the
Modelling and Simulation in Engineering 9
i La
i Lb
i Lc
i cc
i sa
i sb
uPC
Cb
uPC
Ca
i sc
uPC
Cc
i cb
i ca
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
0 002 004 006 008 01 012 014 016 018 02
minus5000
500
minus5000500
minus5000
500
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
40
minus4
30
minus3
30
minus3
30
minus3
Beforecompensation
Initialization
Reactive power and harmoniccompensations
Time (s)
Figure 8 The simulation results using PQF algorithm for ideal shunt active power filter with unbalanced system
10 Modelling and Simulation in Engineering
380Vrms
50Hz
n
isa
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
130Ω
4H
on dq-axis
u120572
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 8 The simulation results using PQF algorithm for ideal shunt active power filter with unbalanced system
10 Modelling and Simulation in Engineering
380Vrms
50Hz
n
isa
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
130Ω
4H
on dq-axis
u120572
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 9 The balanced power system with the predictive current control of SAPF
Ls
KVL
PCC
Lf(abc) (abc)++ + minusminusminus
PCC(abc)
(abc)Lf
uuu
ic
Figure 10 The equivalent circuit of the SAPF connected with the voltages at the PCC point
coefficients of the first-order in Lagrange equation (1198860= 2
1198861= minus1) The Lagrange equation is used to approximate
the reference currents one sampling instant ahead by usingknown values from a few previous sampling instant Theoutput voltages of SAPF are assumed to be constant duringthe one sampling time
Equations (12)ndash(14) are used for three-phase values Inthe paper the predictive current control is applied on dq-axis Therefore the equations to calculate the output voltagesof SAPF and the predicted reference currents on dq-axis areshown in (15) and (16) respectivelyTheParkrsquos transformationis used to transform the three-phase quantities to dq-axisquantities The overall procedure to calculate the outputvoltages of SAPF using predictive current control is depicted
in Figure 12The output voltages of SAPF are used to generatethe six-pulse of IGBTs (119878
1minus 1198786) via the PWM technique
u(dq) (119896) =
119871119891
119879sc[i119888119901(dq)ref (119896 + 1) minus i
The simulation results of the system with 119871119904= 001mH
and 119871119871= 10mH in Figure 9 are shown in Table 4 The
inductor (119871119891) capacitor (119862dc) and the DC bus reference
voltage (119880dcref) of SAPF are equal to 39mH 250 120583F and750V respectivelyThe PI controller is applied to regulate theDC bus voltage (119870
119901= 3 119870
119868= 24) The THD
119894av of sourcecurrents (119894
119904119886 119894sb 119894119904119888) before compensation is equal to 2491
Modelling and Simulation in Engineering 11
t(k) t(k + 1)
c(abc)ref (k + 1)
c(abc)ref (k)
(abc)(k)
Tsc
u
i i
i
cp(abc)ref (k + 1)
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 11 The concept of predictive current control
ic( )(k)
[ud(k)uq(k)
] =Lf
Tsc[ icpdref (k + 1) minus icd(k)
icpqref (k + 1) minus icq(k)] + Lf120596[minusicq(k)icd(k)
] + [ d(k)
q(k)]
120596 =d120579
dt
u
u
(dq)(k)
(PWM)
S1 S2 S3 S4 S5 S6
[fdfq] = [ [ cos(120579) cos(120579 minus 2120587
3)
(120579 minus 2120587
3)
cos(120579 + 2120587
3)
(120579 + 2120587
3)minussin(120579) minussin minussin
fafbfc
][radic 2
3
[ ][uaubuc
] =
cos(120579) minussin(120579)cos(120579 minus 2120587
3)
2120587
3
minus sin(120579 minus 2120587
3)
cos(120579 + ) minus sin(120579 + 2120587
3)
uduq
[radic 2
3[
[icpqref (k + 1)
] = a0[ icqref (k)] + a1[ icdref (k minus 1)
icqref (k minus 1)]icpdref (k + 1) icdref (k)
120579
120579
120579
120596
)(k)
u )(k)
u (dq)(k)
119946
ic(abc)(k)ic(abc)ref (k) PCC(abc
c( ) (k)
dq
(abc
PCC
dq ref
icp(dq)ref (k + 1)
uPCCuPCC
Pulse-width modulation
Figure 12 The overall procedure of the predictive current control for SAPF
12 Modelling and Simulation in Engineering
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
06 062 064 066 068 07 072 074 076 078 08
760750740
Time (s)
Udc
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 13 The simulation results using first-order Lagrange equation
Modelling and Simulation in Engineering 13
Search space
Neighborhood
S0
R
best neighbor
Figure 14 Random 1198780in search space
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
while THD119894av after compensation with predictive current
control technique using first-order Lagrange equation is140 The current and voltage waveforms of the system inFigure 9 are depicted in Figure 13
In Figure 13 the compensating currents (119894119888119886 119894119888119887 119894119888119888) from
SAPF are injected into the systemThe source currents beforecompensation are highly distorted waveform (THD
119894av =2491) After compensation the source currents are nearlysinusoidal waveform (THD
119894av = 140) Moreover the PIcontroller can regulate the DC bus voltage to 750V Thedesign of the predictive current control using the adaptiveTabu search (ATS) method without the first-order Lagrangeequation is explained in Section 5
4 Review of ATS Algorithm
The adaptive Tabu search or ATS method [34ndash47] is usedto design the predictive current controller to minimizeTHD
119894av of source currents after compensation The reviewof the ATS algorithm is described in this section The ATSalgorithm is improved from the Tabu Search (TS) method byadding twomechanisms namely back-tracking and adaptivesearch radius The modified version of the TS method hasbeen named the adaptive tabu search of ATS The ATSalgorithm can be outlined as follows
Step 1 Initialize the tabu list TL and Count (a number ofsearch round) = 0
Step 2 Randomly select the initial solution 1198780from the search
space 1198780is set as a local minimum and 119878
0= best neighbor as
shown in Figure 14
Step 3 Update Count then randomly select 119873 new solutionsfrom the search space of a radius 119877 Let 119878
1(119903) be a set
containing119873 solutions as shown in Figure 15
Step 4 Compute the cost value of each member of 1198781(119903)
Then choose the best solution and assign it as best neighbor1(see Figure 15)
Step 5 If best neighbor1 lt best neighbor then keepbest neighbor in the TL set best neighbor = best neighbor1
Search space
S0
N
S1(r)
Neighborhood
best neighbor1
best neighbor
Neighbor1
Figure 15 Neighborhood around 1198780
best neighbor =best neighbor1
Search space
NeighborhoodN
Neighbor1
Figure 16 Assign a new best neighbor
(see Figure 16) and set 1198780= best neighbor (see Figure 17)
Otherwise put best neighbor1 in the TL instead
Step 6 Evaluate the termination criteria (TC) and the aspi-ration criteria (AC) If Count MAX Count (the maximumnumber allowance of search round) stop the searchingprocess The current best solution is the overall best solutionOtherwise go back to Step 2 and start the searching processagain until all criteria is satisfied (see Figure 18)
The back-tracking process allows the system to go backand look up the previous solutions in TLThe better solutionis then chosen among the current and the previous solutionsFigure 19 illustrates details of the back-tracking process
Given this new search space to explore the search processis likely to have more chances of escaping from the localoptimum The back-tracking mechanism can be added intoStep 5 to improve the searching performance
The adaptive radius process as depicted in Figure 20decreases the search area during the searching process Theadaptive radius mechanism has been developed to adjust theradius (R) by using the cost of the solution The criterion foradapting the search radius is given as follows
radiusnew =radiusold
DF (17)
where DF is a decreasing factor The adaptive search radiusmechanism can be added into the end of Step 6 to improve thesearching performance The more details of ATS algorithmcan be found in [34ndash47]
14 Modelling and Simulation in Engineering
Table 4 The simulation results
Case Parameters THD119894119886V
1198860
1198861
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Before compensation After compensationFirst-order Lagrange equation 2 minus1 2491 140Designed by ATS method 285 minus186 096
Search space
NeighborhoodN
S0 =
Neighbor1
best neighbor
Figure 17 Assign a new 1198780
Search direction
of Neighbor1
Neighbor2Neighbor2best neighbor
of Neighbor1best neighbor
Figure 18 Searching process in the next iteration
5 Optimal Design of PredictiveCurrent Controller
In Section 3 the predicted currents are calculated by the first-order Lagrange equation in (14) with 119886
0= 2 119886
1= minus1
In this section the ATS algorithm is applied to determinethe appropriate coefficients (119886
0and 1198861) of (14) for THD
119894avminimization The block diagram to explain how to searchthe 1198860and 1198861coefficients using the ATS algorithm is depicted
in Figure 21 As can be seen in Figure 21 the ATS will try tosearch the best coefficients of (14) to achieve the minimumTHD
119894avThe cost value of the ATS searching is THD119894av of
source currents In each searching round the THD119894av value
can be calculated by M-file programming while the actualthree-phase source currents are obtained from Simulink asshown in Figure 21
In the ATS process the 1198860and 1198861coefficients are adjusted
to achieve the best solution here it is theminimumTHD119894av
The convergence of theTHD119894av value is shown in Figure 22
It can be seen that THD119894av can converge to the minimum
pointTheTHD119894av in Figure 22 can escape the local point to
get the better solution because of the back tracking approachin the ATS algorithm Moreover the convergences of 119886
0
and 1198861coefficient values are shown in Figures 23 and 24
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Figure 19 Back-tracking in ATS algorithm
+
Search space
S0
Back-tracking
Local found
(near) global found
Negative peak
Positive peak
New direction
New search space
Nn
Nm
N1
R1
Rn
Rm
Adaptive radius
Adaptive radius
Figure 20 ATS algorithm with adaptive search radius mechanism
respectively In the paper themaximumof searching iterationfor ATS is set to 300 rounds number of initial solution= 400 number of N neighborhood = 40 initial radius ofsearch space = 04 and decreasing factor value (DF) = 12From the ATS searching results 119886
0and 119886
1coefficients are
equal to 285 and minus186 respectivelyThe simulation results ofthe system in Figure 9 with the predictive current controllerdesigned by ATS algorithm are shown in Figure 25 Thesource currents after compensation are nearly sinusoidalwaveform and THD
119894av of these currents are equal to 096as shown in Table 4 From the results the predictive currentcontroller designed byATS algorithm can provide the smallerTHD
119894av compared with the current controller using first-order Lagrange equation The results show that the ATSapproach is very useful and more convenient for the optimaldesign of predictive current control in SAPF system The
Modelling and Simulation in Engineering 15
380Vrms
50Hz
n
isa
isb
isb
isc
usa
usc usb
iLc
iLb
iLaLL
LL
LL
ica
icb
icb
PCC
PCC
PCC
icc
icc
Three-phasebridge rectifier
+
minus
Nonlinear load
iLa iLb iLc
Harmonicidentification
algorithm (PQF)
Ls
Ls
Ls
120579
u120573
Predictivecurrent control
6-pulse
PI controller+
+
minus
minus
LfLf Lf
a b c
S1
S2
S3
S4
S5
S6
Shunt active power filter (SAPF)
icareficbreficcref
ica
Udcref
Udc
uPCCc
uPCCc
uPCCb
uPCCb
uPCCa
uPCCa
pdc
3120601
120572120573120579 = tanminus1( u120573
u120572)
Cdc
THDia = f(a0 a1)
130Ω
4H
on dq-axis
u120572
isa
isc
Simulink
Datatransmission
M-file
ATS method Objective functionSearching parameters
isa isb isca0 a1
a0 a1
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 21 The design of predictive current controller using ATS algorithm
simulation results for harmonic currents elimination withdynamic load changing are shown in Figure 26 From thisfigure the load of three-phase bridge rectifier is suddenlychanged at 119905 = 1 s After load changing the SAPF canalso mitigate the harmonic currents and the DC bus voltagecontroller can also regulate the DC voltage equal to 750V
6 Conclusion
The instantaneous power theory with Fourier or PQF algo-rithm is proposed in the paperThe performance comparisonbetween the PQ and PQF is also presented by the simulationvia the software packageThe simulation results show that thePQF algorithm can provide the accurate reference currentsfor a shunt active power filter Moreover the optimal designof predictive current controller by ATS method is shown in
the paper This controller can provide the best performanceof harmonic elimination compared with the conventionalpredictive current controlThe shunt active power filter usingthe PQF algorithm to identify the harmonic and using thecompensating current controller designed by ATS method iscalled the enhanced shunt active power filter (ESAPF) Theresults from simulation confirm that the ESAPF provides theminimum THD and unity power factor of power supply atPCC point
List of Symbols
119894119888119886 119894119888119887 119894119888119888 the three-phase compensating
currents119906PCC119886 119906PCC119887 119906PCC119888 the three-phase voltages at PCC
point
16 Modelling and Simulation in Engineering
0 50 100 150 200 250 30009
1
11
12
13
14
15
16
Escape local solution
Count
THDiav
TH
Di
av
= 0957
Figure 22 The convergence of the THD119894av
0 50 100 150 200 250 30018
2
22
24
26
28
3
a0 = 285
a 0
Count
Figure 23 The convergence of 1198860coefficient
0 50 100 150 200 250 300minus2
minus18
minus16
minus14
minus12
minus1
minus08
minus06
a 1
Count
a1 = minus186
Figure 24 The convergence of 1198861coefficient
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
119906PCC120572 119906PCC120573 119906PCC0 the voltages at PCC point on 1205721205730frame
119894119871119886 119894119871119887 119894119871119888 the three-phase load currents
119894119871120572 119894119871120573 1198941198710 the load currents on 1205721205730 frame
119901119871and 119902119871 the instantaneous active power and
reactive power119901119871 the fundamental component of
instantaneous active power119901119871 the harmonic component of
instantaneous active power119901119888 the reference active power
119894119888120572ref 119894119888120573ref 1198941198880ref the reference currents on 1205721205730
frame119894119888119886ref 119894119888119887ref 119894119888119888ref the three-phase reference currents1198600119901 119860ℎ119901 119861ℎ119901 the Fourier series coefficients
119879119904 the sampling interval
119896 time indexℎ the harmonic order120596 the angular fundamental
frequency of the system1198730 the starting point for computing
119873 the total number of sampled pointin one cycle
THD119894av the average THD of source
currentspf the power factor after
compensationpfdisp and pfdist the displacement and distortion
power factors119894119904119886 119894119904119887 119894119904119888 the three-phase source currents
119901119871act the instantaneous harmonic active
power calculated by FFT119901119871PQ the instantaneous harmonic active
power calculated by PQ119901119871PQF the instantaneous harmonic active
power calculated by PQFu(119886119887119888)
the SAPF output voltagesu119871119891(119886119887119888)
the inductive filter voltagesuPCC(119886119887119888) the voltages at PCC pointi119888(119886119887119888)
the compensating currents119879sc the sampling time of the controller119894119888119901(119886119887119888)ref(119896 + 1) the predicted three-phase
the three-phase reference currentat time instants 119905(119896) and 119905(119896 + 1)
1198860 1198861 the coefficients of the first-order in
Lagrange119880dcref the DC bus reference voltage of
SAPF119880dc the DC bus voltage of SAPF119862119900119906119899119905 a number of search round119872119860119883 119862119900119906119899119905 the maximum number allowance
of search roundDF a decreasing factor
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Modelling and Simulation in Engineering 17
uPC
Ca
minus5000
500
06 062 064 066 068 07 072 074 076 078 08u
PCCc
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
uPC
Cb
minus5000
500
06 062 064 066 068 07 072 074 076 078 08
i La
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lb
50
minus506 062 064 066 068 07 072 074 076 078 08
i Lc
50
minus506 062 064 066 068 07 072 074 076 078 08
i ca
30
minus306 062 064 066 068 07 072 074 076 078 08
i cb
30
minus306 062 064 066 068 07 072 074 076 078 08
i cc
30
minus306 062 064 066 068 07 072 074 076 078 08
i sa
50
minus506 062 064 066 068 07 072 074 076 078 08
i sb
50
minus506 062 064 066 068 07 072 074 076 078 08
i sc
50
minus506 062 064 066 068 07 072 074 076 078 08
Time (s)06 062 064 066 068 07 072 074 076 078 08
760750740
Udc
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 25 The simulation results using predictive current control designed by ATS
18 Modelling and Simulation in Engineering
minus5000
500
uPC
Ca
08 09 1 11 12 13 14 15
minus5000
500
uPC
Cb
08 09 1 11 12 13 14 15
minus5000
500u
PCCc
08 09 1 11 12 13 14 15
50
minus5
i La
08 09 1 11 12 13 14 15
50
minus5
i Lb
08 09 1 11 12 13 14 15
50
minus5
i Lc
08 09 1 11 12 13 14 15
30
minus3
i ca
08 09 1 11 12 13 14 15
30
minus3
i cb
08 09 1 11 12 13 14 15
30
minus3
i cc
08 09 1 11 12 13 14 15
50
minus5
i sa
08 09 1 11 12 13 14 15
50
minus5
i sb
08 09 1 11 12 13 14 15
50
minus5
i sc
08 09 1 11 12 13 14 15
800750700
08 09 1 11 12 13 14 15
Time (s)
Udc
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Figure 26 The simulation results for dynamic load changing
Acknowledgments
This work was supported by Suranaree University of Tech-nology (SUT) and by the office of the Higher EducationCommission under NRU project of Thailand The authorwould like to thank Associate Professor Dr Deacha Puang-downreong for providing the useful information of ATSalgorithm
References
[1] J M Ho and C C Liu ldquoThe effects of harmonics on differentialrelay for a transformerrdquo in Proceedings of the 16th InternationalConference and Exhibition on Electricity Distribution IEE Con-ference Publication no 482 vol 2 AmsterdamTheNetherlands2001
[2] D E Rice ldquoAdjustable speed drive and power rectifierharmonicsndashtheir effect on power systems componentsrdquo IEEE
Modelling and Simulation in Engineering 19
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
Transactions on Industry Applications vol 22 no 1 pp 161ndash1771986
[3] V EWagner J C Balda D C Griffith et al ldquoEffects of harmon-ics on equipmentrdquo IEEE Transactions on Power Delivery vol 8no 2 pp 672ndash680 1993
[4] T Thomas K Haddad G Joos and A Jaafari ldquoDesign andperformance of active power filtersrdquo IEEE Industry ApplicationsMagazine vol 4 no 5 pp 38ndash46 1998
[5] H Akagi Y Kanazawa and A Nabae ldquoInstantaneous reactivepower compensators comprising switching devices withoutenergy storage componentsrdquo IEEE Transactions on IndustryApplications vol 20 no 3 pp 625ndash630 1984
[6] R S Herrera and P Salmeron ldquoPresent point of view aboutthe instantaneous reactive power theoryrdquo IET Power Electronicsvol 2 no 5 pp 484ndash495 2009
[7] M Takeda K Ikeda A Teramoto and T Aritsuka ldquoHarmoniccurrent and reactive power compensation with an active filterrdquoin Proceedings of the 19th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo88) vol 2 pp 1174ndash1179 KyotoJapan 1988
[8] C L Chen C E Lin and C L Huang ldquoThe reference activesource current for active power filter in an unbalanced three-phase power system via the synchronous detection methodrdquoin Proceedings of the 10th Anniversary IEEE InstrumentationandMeasurement Technology Conference (IMTC 94) vol 2 pp502ndash505 Hamamatsu Japan May 1994
[9] M El-Habrouk and M K Darwish ldquoDesign and imple-mentation of a modified Fourier analysis harmonic currentcomputation technique for power active filter using DSPsrdquo IEEProceedingsmdashElectric Power Applications vol 148 no 1 pp 21ndash28
[10] G W Chang S K Chen and M Chu ldquoAn efficient a-b-creference frame-based compensation strategy for three-phaseactive power filter controlrdquo Electric Power Systems Research vol60 no 3 pp 161ndash166 2002
[11] S Sujitjorn K-L Areerak and T Kulworawanichpong ldquoTheDQ axis with fourier (DQF) method for harmonic identifica-tionrdquo IEEE Transactions on Power Delivery vol 22 no 1 pp737ndash739 2007
[12] J H Xu C Lott S Saadate and B Davat ldquoSimulation andexperimentation of a voltage source active filter compensatingcurrent harmonics and power factorrdquo in Proceedings of the 20thInternational Conference on Industrial Electronics Control andInstrumentation pp 411ndash415 Bologna Italy September 1994
[13] L Benchaita S Saadate and A Salem nia ldquoA comparisonof voltage source and current source shunt active filter bysimulation and experimentationrdquo IEEE Transactions on PowerSystems vol 14 no 2 pp 642ndash647 1999
[14] Y Hayashi N Sato and K Takahashi ldquoA novel control ofa current-source active filter for ac power system harmoniccompensationrdquo IEEE Transactions on Industry Applications vol27 no 2 pp 380ndash385 1991
[15] S Buso L Malesani and P Mattavelli ldquoComparison of currentcontrol techniques for active filter applicationsrdquo IEEE Transac-tions on Industrial Electronics vol 45 no 5 pp 722ndash729 1998
[16] M P Kazmierkowski and L Malesani ldquoCurrent control tech-niques for three-phase voltage-source pwm converters a sur-veyrdquo IEEE Transactions on Industrial Electronics vol 45 no 5pp 691ndash703 1998
[17] W-P Zhou D-M Liu Z-G Wu L Xia and X-F YangldquoThe optimization-sliding mode control for three-phase three-wire DSP-based active power filterrdquo in Proceedings of the 5th
International Power Electronics and Motion Control Conference(IPEMC 06) vol 3 pp 1680ndash1684 Shanghai China August2006
[18] J Fei T Li F Wang andW Juan ldquoA novel sliding mode controltechnique for indirect current controlled active power filterrdquoMathematical Problems in Engineering vol 2012 Article ID549782 18 pages 2012
[19] N Mendalek F Fnaiech K Al-Haddad and L Dessaint ldquoAnon-linear optimal predictive control of a shunt active powerfilterrdquo in Proceedings of the 37th IAS Annual Meeting and WorldConference on Industrial Applications of Electrical Energy pp70ndash77 Pittsburgh Pa USA October 2002
[20] A M Massoud S J Finney and B W Williams ldquoPredictivecurrent control of a shunt active power filterrdquo in Proceedings ofthe IEEE 35th Annual Power Electronics Specialists Conference(PESC 04) pp 3567ndash3572 Aachen Germany June 2004
[21] MOdavic V Biagini P ZanchettaM Sumner andMDeganoldquoOne-sample-period-ahead predictive current control for high-performance active shunt power filtersrdquo IET Power Electronicsvol 4 no 4 pp 414ndash423 2011
[22] P Prasomsak K-L Areerak and A Srikaew ldquoControl of shuntactive power filters using fuzzy logic controllerrdquo in Proceedingsof the 30th IASTED Conference on Modelling Identification andControl (AsiaMIC 10) pp 107ndash113 PhuketThailand November2010
[23] J Fei and S Hou ldquoAdaptive fuzzy control with supervisorycompensator for three-phase active power filterrdquo Journal ofApplied Mathematics vol 2012 Article ID 654937 13 pages2012
[24] N BruyantMMachmoum and P Chevrel ldquoControl of a three-phase active power filter with optimized design of the energystorage capacitorrdquo in Proceedings of the 29th Annual IEEE PowerElectronics Specialists Conference (PESC rsquo98) vol 1 pp 878ndash883Fukuoka Japan May 1998
[25] T Narongrit Harmonic elimination using active power filterfor balanced three-phase power system [MS thesis] SuranareeUniversity of Technology 2009
[26] F Mekri B Mazari and M Machmoum ldquoControl and opti-mization of shunt active power filter parameters by fuzzy logicrdquoCanadian Journal of Electrical and Computer Engineering vol31 no 3 pp 127ndash134 2006
[27] R F de Camargo and H Pinheiro ldquoThree-phase four-wireshunt active filter to reduce voltage and current distortionsin distribution systemsrdquo in Proceedings of the 32nd AnnualConference on IEEE Industrial Electronics (IECON 06) pp1884ndash1889 Paris France November 2006
[28] T Narongrit K-L Areerak and K-N Areerak ldquoCurrentcontrol of shunt active power filter using space vector PWMrdquoin Proceedings of the 9th International Conference on Electri-cal EngineeringElectronics Computer Telecommunications andInformation Technology (ECTI-CON rsquo12) pp 1ndash4 PhetchaburiThailand May 2012
[29] W Sheng K Liu Y Li Y Liu and X Meng ldquoImprovedmultiobjective harmony search algorithm with application toplacement and sizing of distributed generationrdquo MathematicalProblems in Engineering vol 2014 Article ID 871540 8 pages2014
[30] X He and W Wang ldquoFuzzy multiobjective optimal power flowbased on modified artificial BEE colony algorithmrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 961069 12pages 2014
20 Modelling and Simulation in Engineering
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
[31] W Haiquan L Liao W Dongyun W Shengjun and DMingcong ldquoImproved artificial bee colony algorithm and itsapplication in LQR controller optimizationrdquo MathematicalProblems in Engineering vol 2014 Article ID 695637 8 pages2014
[32] Z Yan C Deng B Li and J Zhou ldquoNovel particle swarmoptimization and its application in calibrating the underwatertransponder coordinatesrdquo Mathematical Problems in Engineer-ing vol 2014 Article ID 672412 12 pages 2014
[33] I S Jesus and R S Barbosa ldquoDesign of fuzzy fractional PD+ I controllers tuned by a genetic algorithmrdquo MathematicalProblems in Engineering vol 2014 Article ID 676121 14 pages2014
[34] D PuangdownreongK-NAreerakA Srikaew S Sujijorn andP Totarong ldquoSystem identification via adaptive Tabu searchrdquo inProceedings of the IEEE International Conference on IndustrialTechnology (ICIT 02) pp 915ndash920 Bangkok Thailand 2002
[35] T Kulworawanichpong K-L Areerak K-N Areerak and SSujitjorn ldquoHarmonic identification for active power filters viaadaptive tabu search methodrdquo in Knowledge-Based IntelligentInformation and Engineering Systems vol 3215 of LectureNotes in Computer Science pp 687ndash694 Springer HeidelbergGermany 2004
[36] D Puangdownreong T Kulworawanichpong and S SujitjornldquoInput weighting optimization for PID controllers based onthe adaptive tabu searchrdquo in Proceedings of the IEEE Region10 Conference on Analog and Digital Techniques in ElectricalEngineering (TENCON 04) vol 4 pp 451ndash454 November2004
[37] D Puangdownreong K-N Areerak K-L Areerak T Kul-worawanichpong and S Sujitjorn ldquoApplication of adaptivetabu search to system identificationrdquo in Proceedings of the 24thIASTED International Conference on Modeling Identificationand Control (MIC rsquo05) pp 178ndash183 Innsbruck Austria Febru-ary 2005
[38] R Leepila E Oki andN Kishi ldquoScheme to find k disjoint pathsinmulti-cost networksrdquo in Proceedings of the IEEE InternationalConference on Communications (ICC 11) pp 1ndash5 Kyoto JapanJune 2011
[39] A Oonsivilai and B Marungsri ldquoApplication of artificialintelligent technique for partial discharges localization in oilinsulating transformerrdquoWSEAS Transactions on Systems vol 7pp 920ndash929 2008
[40] T Defeng L Shixing X Wujun and Z Yongming ldquoA firemonitoring system in ZigBee wireless networkrdquo in Proceedingsof the International Conference on Cyber-Enabled DistributedComputing and Knowledge Discovery (CyberC 10) pp 48ndash51Huangshan China October 2010
[41] K Chaijarurnudomrung K-N Areerak K-L Areerak andA Srikaew ldquoThe controller design of three-phase controlledrectifier using an adaptive tabu search algorithmrdquo inProceedingsof the 8th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology (ECTI-CON 11) pp 605ndash608 KhonKaenThailandMay 2011
[42] J Kluabwang D Puangdownreong and S Sujitjorn ldquoMultipathadaptive tabu search for a vehicle control problemrdquo Journal ofApplied Mathematics vol 2012 Article ID 731623 20 pages2012
[43] D Puangdownreong T Kulworawanichpong and S SujitjornldquoFinite convergence and performance evaluation of adaptivetabu searchrdquo in Knowledge-Based Intelligent Information and
Engineering Systems vol 3215 of Lecture Notes in ComputerScience pp 710ndash717 Springer Heidelberg Germany 2004
[44] T Kulworawanichpong D Puangdownreong and S SujitjornldquoFinite convergence of adaptive Tabu searchrdquo ASEAN Journalon Science and Technology for Development vol 21 no 2-3 pp103ndash115 2004
[45] D Puangdownreong S Sujitjorn and T KulworawanichpongldquoConvergence analysis of adaptive Tabu searchrdquo Science AsiaJournal of the Science Society of Thailand vol 30 no 2 pp 183ndash190 2004
[46] S Sujitjorn J Kluabwang D Puangdownreong andN SarasirildquoAdaptive tabu search and management agentrdquo The ECTITransactions on Electrical Engineering Electronics and Commu-nications vol 7 no 2 pp 1ndash10 2009
[47] S Sujitjorn T Kulworawanichpong D Puangdownreong andK-N Areerak ldquoAdaptive tabu search and applications in engi-neering designrdquo in Integrated Intelligent Systems for EngineeringDesign X F Zha and R J Howlett Eds pp 233ndash257 IOS PressAmsterdam The Netherlands 2006
