Jean de Dieu Nguimfack-Ndongmo1 and Hilaire Bertrand Fotsin2
1Unite de Recherche drsquoAutomatique et drsquoInformatique Appliquee (LAIA) Departement de Genie ElectriqueIUT FOTSO Victor Bandjoun Universite de Dschang BP 134 Bandjoun Cameroon2Unite de Recherche de Matiere Condensee drsquoElectronique et de Traitement du Signal (LAMACETS) Departement de PhysiqueFaculte des Sciences Universite de Dschang BP 69 Dschang Cameroon
Correspondence should be addressed to Godpromesse Kenne godpromessegmailcom
Received 16 May 2017 Revised 17 July 2017 Accepted 17 September 2017 Published 22 October 2017
Academic Editor George E Tsekouras
Copyright copy 2017 Godpromesse Kenne 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 new technique to design a Unified Power Flow Controller (UPFC) for power flow control and DC voltageregulation of an electric power transmission system which is based on a hybrid technique which combines a Radial Basis Function(RBF) neural network (online training) with the sliding mode technique to take advantage of their common featuresThe proposedcontroller does not need the knowledge of the perturbation bounds nor the full state of the nonlinear system Hence it is robust andproduces an optimal response in the presence of system parameter uncertainty and disturbancesThe performance of the proposedcontroller is evaluated through numerical simulations on a Kundur power system and compared with a classical PI controllerSimulation results confirm the effectiveness robustness and superiority of the proposed controller
1 Introduction
Presently it is well established in the scientific communitythat the UPFC has the ability to increase the power flowcapacity and improve the stability of an electric power trans-mission system through the proper design of its controller [1]Over the past several decades linear and nonlinear controltechniques have been successfully proposed and applied inthe literature for the control of UPFC based on modernand classical control theories [2ndash10] However the maindrawback of such techniques is that their application requiresthe development of mathematical models which are difficultto obtainThus only partial and quite weak results have beenobtained in terms of online implementation feasibility
Faced with these difficulties intelligent controls such asfuzzy logic and artificial neural networks have emerged asbetter alternatives to the conventional linear and nonlinearcontrol methods However the complexities associated withthe adaption of membership functions and computation
requirements for defuzzification have hindered the applica-tion of fuzzy logic [11ndash15] Hence recent studies have turnedto artificial neural networks (ANN) to achieve the desiredgoals [16ndash18]
Artificial neural networks have an inherent capabilityto learn and store information regarding the nonlineari-ties of the system and to provide this information when-ever required This renders the neural networks suitablefor system identification and control applications [19ndash21]Although intelligent and hybrid algorithms are already beingimplemented in the domains of image processing roboticsfinancialmanagement and so on their application in the fieldof FACTS devices for power flow control is fairly recent Somerecent results can be found in [12 16 17 22 23]
In [16] a radial basis function neural network hasbeen designed to control the operation of the UPFC inorder to improve its dynamic performance Simulation andexperimental results were presented to demonstrate therobustness of the proposed controller against changes in
HindawiAdvances in Electrical EngineeringVolume 2017 Article ID 7873491 11 pageshttpsdoiorg10115520177873491
2 Advances in Electrical Engineering
Shunt converter
Series converter
Shunttransformer
Seriestransformer
DC-linkSsh = Psh + jQsh Sse = Pse + jQse
+
+ +
Vsh
VseVrVs
minus
VdcC
(a)
+
+
VsepVsp VrpR L
Isep
Ishp
Lsh
Rsh
Vshp
(b)
Figure 1 UPFC in power system (a) Schematic diagram of the UPFC system (b) Single-phase representation of the UPFC system
the transmission system operating conditions Howeverlarge memory and long computation time are required forits proper functioning and in addition the controller isdesigned under the assumption that the upper bound ofthe disturbance is known A comparative study of transientstability and reactive power compensation issues in anautonomous wind-diesel-photovoltaic based hybrid systemusing robust fuzzy-sliding mode based Unified Power FlowController has been presented in [12] but it has the limitationthat a linearized small-signal model of the hybrid systemis considered for the transient stability analysis Hence thesystem will suffer from performance degeneracy when theoperating condition changes In [22] the recently proposed119867infin-learning method for updating the parameter of a singleneuron radial basis function neural network has been usedas a control scheme for the UPFC to improve the transientstability performance of amultimachine power system How-ever the updating control parameters are optimized for eachperturbation using a generic algorithm which increases thecomputational burden and makes the control implementa-tion less feasible A neural network predictive controller forthe UPFC has been designed in [23] to improve the transientstability performance of the power system Neverthelessthe neural network controller is implemented only on theseries branch of the UPFC which limits the performanceof the device In [17] a neural network controller basedon a feedback linearization autoregression average modelis used to design an adaptive-supplementary unified powerflow control for two interconnected areas of a power systemHowever in this paper andmany others the bounds of systemuncertainty and disturbances are assumed to be known Butin practice it is always difficult to determine the exact upperlimit of system uncertainty and disturbances Hence theabove controllers cannot provide satisfactory results
From the above drawbacks in this paper a new hybridapproach which combines RBF neural network with thesliding mode technique to design a UPFC controller forpower flow control and DC voltage regulation of an electricpower transmission system with unknown bounds of systemuncertainty and disturbances is proposed The advantagesof this design philosophy are that the controller is suitablefor practical implementation and it makes the design usefulfor the real world complex power system The remainingsections of this paper are organized as follows In Section 2
the mathematical model of a UPFC in 119889119902 reference frameis described The design of the RBF neurosliding modecontroller is developed in Section 3 In Section 4 simulationresults in a Kundur two-area four-machine power system arepresented Finally in Section 5 some concluding remarks endthe paper
2 System Modeling
Figure 1(a) shows a schematic diagram of a UPFC systemwhile Figure 1(b) shows a single-phase representation of thepower circuit of the UPFC which consists of two back-to-back self-commutated voltage source converters connectedthrough a common DC-link [24 25] The series converter iscoupled to the AC system through a series transformer andthe shunt converter is coupled through a shunt transformerIn Figure 1(b) the series and shunt converters are representedby the voltage sources Vse and Vsh respectivelyThe subscriptsldquo119904rdquo ldquo119903rdquo and ldquo119901rdquo are used to represent the sending-end busreceiving end bus and the three-phase quantities (phases119886 119887 119888) respectively Also119877 and 119871 represent the resistance andleakage inductance of series converter respectively 119894se is theline current 119877sh 119871 sh and 119894sh are the resistance inductanceand current of the shunt converter respectively The seriesand shunt branch currents of the circuit in Figure 1(b) can beexpressed by the following three-phase system of differentialequations [24ndash26]
119889119894se119901119889119905 = 1119871 (minus119877119894se119901 + Vse119901 + V119904119901 minus V119903119901) 119889119894sh119901119889119905 = 1119871 (minus119877119894sh119901 + Vsh119901 minus V119904119901)
(1)
Using Parkrsquos transformation and assuming that theinstantaneous power is kept invariant and the sending-endvoltage vector V119904 is in the 119889-axis (ie V119904 = (V119904119889 + 119895V119904119902) =(V119904119889 + 1198950)) the three-phase system of differential equations(1) can be transformed into an equivalent two-phase (119889 119902)system of equations as follows
119889119894sh119902119889119905 = minus119908119894sh119889 minus 119877sh119871 sh
119894se119902 + 1119871 sh
(Vsh119902) (5)
where 119908119887 = 2120587119891119887 is the fundamental angular frequency ofthe supply voltage and 119908 = 2120587119891 is the angular frequency ofsynchronous reference frame (rads)
Since the series and shunt converters of the UPFC arecoupled through a common DC-link if the losses in theconverters are neglected then the dynamic of the DC-linkvoltage can be expressed as [27]
119889Vdc119889119905 = minus 1Vdc119862dc
(119875se + 119875sh) (6)
where 119875se and 119875sh are the active power supplied by the seriesand shunt converters respectively and Vdc is the voltage of theDC capacitor of capacitance 119862dc
It is clear from (6) that Vdc decreases when 119875se + 119875sh gt0 and it increases when 119875se + 119875sh lt 0 Note that (6) is anonlinear differential equation and has to be investigated atan operating point However the derivative of V2dc can bewritten as
Using (6) and (7) the derivative of V2dc can be expressed as
119889V2dc119889119905 = minus 2119862 (119875se + 119875sh) (8)
Maintaining constant DC-link voltage is very important forthe UPFC control system [1 28 29] The DC-link voltagevaries when 119875se + 119875sh = 0 Since (8) does not containa direct control signal like (4) we will consider 119875sh as anauxiliary input that can be used to maintain the DC-linkvoltage constant
3 UPFC RBF Neurosliding ModeController Design
In this section the method proposed in [30 31] for time-varying parameter estimation will be modified and appliedto design a robust adaptive controller for the UPFC using theRBF neural network
Let us consider the SISO first-order nonlinear system inthe following form
where 119909 isin 119877 119906 isin 119877 and 119910 isin 119877 are state variables systeminput and system output respectively 119891(119909 119905) and 119892(119909 119905) areunknown smooth functions 119891(119909 119905) represents the nominalpart of the system which does not depend upon the controlinput while the uncertainties and external disturbance are
concentrated in the term 119889(119905) assumed to be bounded by anunknown constant 1198890 gt 0 Since all physical plants operate inbounded regions we study the control problem of system (9)whose state 119909 belongs to a compact subsetΩ sub 119877
Let the desired smooth signal 119910lowast = 119909lowast the tracking error119890119909 and augmented item 119878119909 be defined as
119890119909 = 119909 minus 119909lowast119878119909 = 119890119909 + 119862119909 int 119890119909119889119905 (10)
where 119862119909 gt 0 is a design parameter The integral term isincluded in the sliding manifold 119878119909 so as to ensure that thesystem trajectories start on the slidingmanifold from the firstinstant of time From (10) we have
with 120583119909 = 119862119909119890119909 minus lowast(11)
From 119878119909 if the desired sliding mode controller is chosen as[31]
119906lowast119909 = minus 1119892 (119909 119905) (119891 (119909 119905) + 120583119909 + 119889 (119905)) minus
119878119909120598119909 (12)
where 0 lt 120598119909 lt 1 is a design parameter then 119878119909 = 119878119909120598119909 and119878119909 will converge exponentially to 0The above desired controller (12) is not implementable
in practice since the functions 119891(119909 119905) and 119892(119909 119905) and theterms 120583119909 and 119889(119905) are assumed to be unknown Hence inthis work a RBF neural network combined with the slidingmode technique will be applied to approximate the unknowncontroller 119906lowast119909
The control signal (12) can be approximated by the neuralcontroller proposed in [31] as
119908lowast119895 120601 (10038171003817100381710038171003817120594119909 minus 11986211989510038171003817100381710038171003817 ]119895) (13)
where 120601(sdot) denotes a nonlinear function 119862119895 and ]119895 119895 =1 119873 are the center and the width of the 119895th hidden unitrespectively119873 is the number of hidden nodes or Radial BasisFunction (RBF) units 119908lowast is the optimal weight vector andsatisfies 119908lowast le 119877120596 120594119879119909 = (119909 119878119909 119878119909120598119909) is the input vector ofthe RBF network 119890119891(120594119909) is the optimal approximation errorwhich is unknown and bounded forall120594119909 isin Ω119909119862119895 and ]119895 119895 = 1 119873 are chosen respectively using theClustering algorithm [32] as follows
119862119895 = 120594119909min+ 2119895 minus 12 ]119895
(14)
4 Advances in Electrical Engineering
Phasors
Clockt
ABC
ABC
Area 1 B1 Area 2B4B5Line 1a Line 1b(110 km)
Line 2a(110 km)
Line 2B(110 km)
(110 km)
A B CFault
UPFC
Pref (pu)
Qref (pu)
[m]
[m]
TripBy passVdqrefPQrefUPFCA1
A2
B1
B2
C1C2
m
Bypass[PQref]
[PQref]
[Vdqref]
[Vdqref]Vdqref
P Pref (pu)Q Qref (pu)
Vdqref
UPFCmeasurements
measurementsV P Q
B2 B3Series 100MVA 10 injection
Shunt 230 kv 100 MVA
Vconv_phase (deg)
Vpos seq B1 B2 B3 B4P B1 B2 B3 B4 (MW)
Q B1 B2 B3 B4 (MVar)
Vconv_mag (pu)
Scope
Scope 1
d_thetad_theta (deg)
Vt (pu)Machines
Machinesignals
Pa (pu)w (pu)w
Pa
VtStop
Stop
Stop simulationif there is loss of synchronism
++
+ +
Figure 2 Kundur power system test
where 120594119909minand 120594119909max
are the lower and upper bounds ofthe 119894th element of the RBF input vector 120594119879119909 = (119909 119878119909 119878119909120598119909)respectively
Note that the term 120575119906119909(119905) is time-varying and cannot beapproximated by a static neural network In the followinganalysis sliding robust termswill be used in the identificationscheme to compensate the effect of this uncertainty time-varying term The controller 119906lowast119909(120594119909 119905) will be approximatedassuming that the terms 119890119891(120594119909) and 120575119906119909(119905) are bounded byunknown positive constants
For this purpose the following neural controller is pro-posed in order to approximate the control signal 119906lowast119909(120594119909 119905)
where the term 119887119909(119905) is introduced in order to improve theconvergence rate of the neural network in the presence of theuncertainties terms
Consider the systems described by (9) the sliding-neuralnetwork controller (15) and Assumptions 1 and 2 given in[31] If the bias term 119887119909(119905) the learning rule of the weight 119908and the adaptation law for the unknown bound 120582119909 are chosenas
1003816100381610038161003816100381610038161003816100381610038161003816119908119895=119908119895 if 1003816100381610038161003816100381611990811989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909 = 120572119909 if 119878119909 = 00 if 119878119909 = 0
(16)
with120572119909 gt 0 119909(0) = 0 and Proj(sdot) the well-known projectionfunction [33] on the compact set Ω120596 = 120596 120596 le 119877120596then the neural network controller error 119878119909 will convergein finite time to the origin The proof of the convergenceof above neural network controller to zero can be found in[31]
In order to apply the neurosliding controller describedabove to power flow control UPFC sending-end bus voltagecontrol and DC-link voltage control the dynamic equationsof the UPFC completely described by (2) to (5) and (8) can berewritten as
Advances in Electrical Engineering 5
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
REFPINSC
0 01 02 03 04 05 06
(i)
18
2
22
PB3
(pu)
002040608
QB3
(pu)
097098099
1101
VB2
(pu)
099
1
101
VDC
(pu)
01 02 03 04 05 060Time (s)
(a)
0 01 02 03 04 05 06
(iii)
0 01 02 03 04 05 06
(iii)
(vi)
SNCPI
0 01 02 03 04 05 06
(i)
01015
02025
Id_S
H (p
u)
minus04minus02
00204
Iq_S
H (p
u)16
18
2
22
Id_S
E (p
u)
minus020
020406
Iq_S
E (p
u)
01 02 03 04 05 060Time (s)
(b)
Figure 3 Control response to step changes in real and reactive power flow references in the transmission line (a) (i) Active power at busB3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2 (iv) UPFC DC-link voltage (b) (i)119863-axis current of shunt converter (ii)119876-axis current of shunt converter (iii)119863-axis current of series converter (iv) 119876-axis current of series converter
1199063 = Vsh119889 minus V1199041198891199094 = 119894sh119902
1198914 (119909 119905) = minus119908119894sh119889 minus 119877sh119871 sh
1198924 (119909 119905) = 1119871 sh
1199064 = Vsh119902
6 Advances in Electrical Engineering
0 01 02 03 04 05 0608
1
Vd_S
H (p
u)(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus008minus006minus004minus002
0
Vq_S
H (p
u)
minus0050
00501
Vd_S
E (p
u)
01502
02503
Vq_S
E (p
u)
01 02 03 04 05 060Time (s)
(a)
0 01 02 03 04 05 06
(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus240minus220minus200minus180
PB2
(Mw
)
minus125minus120minus115minus110minus105
PB5
(Mw
)
0102030
QB2
(Mva
r)
121416182022
QB5
(Mva
r)
01 02 03 04 050 06Time (s)
(b)
Figure 4 Control response to step changes in real and reactive power flow references in the transmission line (a) (i)119863-axis voltage of shuntconverter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of series converter (iv) 119876-axis voltage of series converter (b) (i) Activepower at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power at bus B5
1199095 = V2dc1198915 (119909 119905) = minus 2119862119875se1198925 (119909 119905) = minus 2119862
1199065 = 119875sh(18)
where 1198891(119905) to 1198895(119905) represent system uncertaintiesThe reference values of the state variables are obtained as
where 119875lowast119903 and119876lowast119903 are the active and reactive power referencesat the receiving end bus of the transmission line respectively
We can design the neurosliding controller lowast119896 using theUPFC dynamics given in (17) as (for 119896 = 1 5)
Figure 5 Control response to load variation (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2(iv) UPFC DC-link voltage (b) (i) Active power at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power atbus B5
1003816100381610038161003816100381610038161003816100381610038161003816119908119896119895=119908119896119895 if 1003816100381610038161003816100381611990811989611989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909119896 = 120572119909119896 if 119878119909119896 = 00 if 119878119909119896 = 0
(20)
4 Simulation Results
The performance of the proposed nonlinear controlleris evaluated through digital simulations using MATLABSIMULINK software The power system used is a Kundurtwo-area four-machine power system shown in Figure 2 Thedetails of system data and initial operating point are givenin [34] The proposed controller can be applied to a UPFCconnected between any two buses of the power system (with119899 bus) regardless of the interaction between these two busesand other buses Only local measurements information is
required for the implementation of the proposed algorithmThe simulation results of the proposed controller (SNC)are compared with conventional Proportional Integral (PI)controllers used for power flow control UPFC sending-endbus voltage control and DC-link voltage control These clas-sical controllers are tuned using optimal control techniquesand the parameters obtained are given in the Appendix Toevaluate the performance of the proposed controller four setsof simulations have been performed In all simulations theuncertainty factor is set at +10 That is the parameters ofthe system under simulation are set at 110 compared to thesame parameters introduced in the controller
41 Step Changes in Transmission Line Real and ReactivePower Flow References In this case study the initial complexpower flow (119875B3 + 119895119876B3) at the receiving end of the trans-mission line is found as (18 + 11989500) pu A step change inactive power reference from 18 to 22 pu and reactive powerreference from00 to 05 pu of the transmission line take placeat 119905 = 002 s and 032 s respectively The simulation resultsfor this case study are depicted in Figures 3 and 4 It can beseen from these figures that the active and reactive power flowthrough the transmission line the UPFC DC-link voltage
8 Advances in Electrical Engineering
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03
(ii)
0 005 01 015 02 025 03095
1
VB2
(pu)
(iii)
09
1
11
VDC
(pu)
(iv)
REFSNC
18
2
22
PB3
(pu)
0020406
QB3
(pu)
005 01 015 02 025 030Time (s)
(a)
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03minus01
minus005
0
Vq_S
H (p
u)
(ii)
0 005 01 015 02 025 030
01
Vd_S
E (p
u)
(iii)
(iv)
02
025
Vq_S
E (p
u)
05
1
15
Vd_S
H (p
u)005 01 015 02 025 030
Time (s)
(b)
Figure 6 Control response to measurement noise (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at busB2 (iv) UPFC DC-link voltage (a) (i) 119863-axis voltage of shunt converter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of seriesconverter (iv) 119876-axis voltage of series converter
and the voltagemagnitude at bus B2 are controlled effectivelyThe results also clearly show that the response speed andtransient conditions are further improved with the proposedcontroller as compared to the conventional PI controllersFigure 4 clearly shows the excellent performance of theUPFCin power flow control under the influence of the proposedcontroller
42 Load Variation In practice the references values of thecontrol power system remain constant and the quantitiesbeing controlled vary under the effect of load variationdisturbance and other perturbations In this case studythe load increases by 20 of its nominal value from 119905 =002 s The simulation results are depicted in Figure 5 Itcan be noticed in these figures that the active and reac-tive power flow through the transmission line the DC-link voltage and the voltage magnitude at bus B2 areall regulated to their respective reference values Figure 5shows that the excess active and reactive power requestedby the load is supplied only by generator G2 The figurealso demonstrates once more the excellent performance ofthe proposed controller in terms of overshot and settlingtime
43 Robustness to Measurement Noise In practice it is notpossible to measure a signal accurately due to the presence
of noise For this reason the third case study investigatesthe robustness of the proposed nonlinear controller withrespect to measurement noise (uncertainties) In this casestudy all simulations are conducted under noise condi-tions in the measured line currents with the magnitudeof the noise reaching about 4 of the maximum valueof the measurable line currents A step change in reac-tive power under the same conditions as in the first casestudy is used to evaluate the robustness of the systemThe simulation results for this case study are depicted inFigure 6 From these results it can be seen that the activeand reactive power flow through the transmission line theUPFC DC-link voltage and the voltage magnitude at busB2 are all regulated to their respective reference valuesdespite the presence of measurement noise Hence it canbe concluded that the controller exhibits an excellent noiseresistance
44 Three-Phase-to-Ground Fault Test In this case study athree-phase-to-ground fault is applied on bus-5 and the faultis cleared after 100ms Simulation results for this case studyare shown in Figure 7 From these results it can be seenthat the proposed controller rapidly steers the system to itsprefault steady state and satisfactorily improves the transientstability of the power system as compared to the conventionalPI controllers
Figure 7 Control response to three-phase fault (a) All generator rotor angle in COI (b) All terminal generator voltage
5 Conclusion
In this paper a new hybrid approach which combines RadialBasis Function (RBF) neural network with the sliding modetechnique has been used to design a Unified Power FlowController (UPFC) for power flow control UPFC sending-end voltage control and DC voltage regulation of an electricpower transmission system The RBF neurosliding modecontrol technique uses online training to get its optimalparameter valuesThe proposed technique is robust and doesnot need the knowledge of the perturbation bounds nor thefull state of the nonlinear system The performance of theproposed controller has been evaluated through simulationson a Kundur power system and compared with a classicalPI controller Simulation results have shown the effectivenessand satisfactory performance of the proposed controller indealing with the perturbations considered Future worksshould be targeted towards the extension of the proposed
hybrid approach to a wide area interconnected power systemfor power oscillation damping
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1(ii) PI controllers parameters are as follows
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
Figure 1 UPFC in power system (a) Schematic diagram of the UPFC system (b) Single-phase representation of the UPFC system
the transmission system operating conditions Howeverlarge memory and long computation time are required forits proper functioning and in addition the controller isdesigned under the assumption that the upper bound ofthe disturbance is known A comparative study of transientstability and reactive power compensation issues in anautonomous wind-diesel-photovoltaic based hybrid systemusing robust fuzzy-sliding mode based Unified Power FlowController has been presented in [12] but it has the limitationthat a linearized small-signal model of the hybrid systemis considered for the transient stability analysis Hence thesystem will suffer from performance degeneracy when theoperating condition changes In [22] the recently proposed119867infin-learning method for updating the parameter of a singleneuron radial basis function neural network has been usedas a control scheme for the UPFC to improve the transientstability performance of amultimachine power system How-ever the updating control parameters are optimized for eachperturbation using a generic algorithm which increases thecomputational burden and makes the control implementa-tion less feasible A neural network predictive controller forthe UPFC has been designed in [23] to improve the transientstability performance of the power system Neverthelessthe neural network controller is implemented only on theseries branch of the UPFC which limits the performanceof the device In [17] a neural network controller basedon a feedback linearization autoregression average modelis used to design an adaptive-supplementary unified powerflow control for two interconnected areas of a power systemHowever in this paper andmany others the bounds of systemuncertainty and disturbances are assumed to be known Butin practice it is always difficult to determine the exact upperlimit of system uncertainty and disturbances Hence theabove controllers cannot provide satisfactory results
From the above drawbacks in this paper a new hybridapproach which combines RBF neural network with thesliding mode technique to design a UPFC controller forpower flow control and DC voltage regulation of an electricpower transmission system with unknown bounds of systemuncertainty and disturbances is proposed The advantagesof this design philosophy are that the controller is suitablefor practical implementation and it makes the design usefulfor the real world complex power system The remainingsections of this paper are organized as follows In Section 2
the mathematical model of a UPFC in 119889119902 reference frameis described The design of the RBF neurosliding modecontroller is developed in Section 3 In Section 4 simulationresults in a Kundur two-area four-machine power system arepresented Finally in Section 5 some concluding remarks endthe paper
2 System Modeling
Figure 1(a) shows a schematic diagram of a UPFC systemwhile Figure 1(b) shows a single-phase representation of thepower circuit of the UPFC which consists of two back-to-back self-commutated voltage source converters connectedthrough a common DC-link [24 25] The series converter iscoupled to the AC system through a series transformer andthe shunt converter is coupled through a shunt transformerIn Figure 1(b) the series and shunt converters are representedby the voltage sources Vse and Vsh respectivelyThe subscriptsldquo119904rdquo ldquo119903rdquo and ldquo119901rdquo are used to represent the sending-end busreceiving end bus and the three-phase quantities (phases119886 119887 119888) respectively Also119877 and 119871 represent the resistance andleakage inductance of series converter respectively 119894se is theline current 119877sh 119871 sh and 119894sh are the resistance inductanceand current of the shunt converter respectively The seriesand shunt branch currents of the circuit in Figure 1(b) can beexpressed by the following three-phase system of differentialequations [24ndash26]
119889119894se119901119889119905 = 1119871 (minus119877119894se119901 + Vse119901 + V119904119901 minus V119903119901) 119889119894sh119901119889119905 = 1119871 (minus119877119894sh119901 + Vsh119901 minus V119904119901)
(1)
Using Parkrsquos transformation and assuming that theinstantaneous power is kept invariant and the sending-endvoltage vector V119904 is in the 119889-axis (ie V119904 = (V119904119889 + 119895V119904119902) =(V119904119889 + 1198950)) the three-phase system of differential equations(1) can be transformed into an equivalent two-phase (119889 119902)system of equations as follows
119889119894sh119902119889119905 = minus119908119894sh119889 minus 119877sh119871 sh
119894se119902 + 1119871 sh
(Vsh119902) (5)
where 119908119887 = 2120587119891119887 is the fundamental angular frequency ofthe supply voltage and 119908 = 2120587119891 is the angular frequency ofsynchronous reference frame (rads)
Since the series and shunt converters of the UPFC arecoupled through a common DC-link if the losses in theconverters are neglected then the dynamic of the DC-linkvoltage can be expressed as [27]
119889Vdc119889119905 = minus 1Vdc119862dc
(119875se + 119875sh) (6)
where 119875se and 119875sh are the active power supplied by the seriesand shunt converters respectively and Vdc is the voltage of theDC capacitor of capacitance 119862dc
It is clear from (6) that Vdc decreases when 119875se + 119875sh gt0 and it increases when 119875se + 119875sh lt 0 Note that (6) is anonlinear differential equation and has to be investigated atan operating point However the derivative of V2dc can bewritten as
Using (6) and (7) the derivative of V2dc can be expressed as
119889V2dc119889119905 = minus 2119862 (119875se + 119875sh) (8)
Maintaining constant DC-link voltage is very important forthe UPFC control system [1 28 29] The DC-link voltagevaries when 119875se + 119875sh = 0 Since (8) does not containa direct control signal like (4) we will consider 119875sh as anauxiliary input that can be used to maintain the DC-linkvoltage constant
3 UPFC RBF Neurosliding ModeController Design
In this section the method proposed in [30 31] for time-varying parameter estimation will be modified and appliedto design a robust adaptive controller for the UPFC using theRBF neural network
Let us consider the SISO first-order nonlinear system inthe following form
where 119909 isin 119877 119906 isin 119877 and 119910 isin 119877 are state variables systeminput and system output respectively 119891(119909 119905) and 119892(119909 119905) areunknown smooth functions 119891(119909 119905) represents the nominalpart of the system which does not depend upon the controlinput while the uncertainties and external disturbance are
concentrated in the term 119889(119905) assumed to be bounded by anunknown constant 1198890 gt 0 Since all physical plants operate inbounded regions we study the control problem of system (9)whose state 119909 belongs to a compact subsetΩ sub 119877
Let the desired smooth signal 119910lowast = 119909lowast the tracking error119890119909 and augmented item 119878119909 be defined as
119890119909 = 119909 minus 119909lowast119878119909 = 119890119909 + 119862119909 int 119890119909119889119905 (10)
where 119862119909 gt 0 is a design parameter The integral term isincluded in the sliding manifold 119878119909 so as to ensure that thesystem trajectories start on the slidingmanifold from the firstinstant of time From (10) we have
with 120583119909 = 119862119909119890119909 minus lowast(11)
From 119878119909 if the desired sliding mode controller is chosen as[31]
119906lowast119909 = minus 1119892 (119909 119905) (119891 (119909 119905) + 120583119909 + 119889 (119905)) minus
119878119909120598119909 (12)
where 0 lt 120598119909 lt 1 is a design parameter then 119878119909 = 119878119909120598119909 and119878119909 will converge exponentially to 0The above desired controller (12) is not implementable
in practice since the functions 119891(119909 119905) and 119892(119909 119905) and theterms 120583119909 and 119889(119905) are assumed to be unknown Hence inthis work a RBF neural network combined with the slidingmode technique will be applied to approximate the unknowncontroller 119906lowast119909
The control signal (12) can be approximated by the neuralcontroller proposed in [31] as
119908lowast119895 120601 (10038171003817100381710038171003817120594119909 minus 11986211989510038171003817100381710038171003817 ]119895) (13)
where 120601(sdot) denotes a nonlinear function 119862119895 and ]119895 119895 =1 119873 are the center and the width of the 119895th hidden unitrespectively119873 is the number of hidden nodes or Radial BasisFunction (RBF) units 119908lowast is the optimal weight vector andsatisfies 119908lowast le 119877120596 120594119879119909 = (119909 119878119909 119878119909120598119909) is the input vector ofthe RBF network 119890119891(120594119909) is the optimal approximation errorwhich is unknown and bounded forall120594119909 isin Ω119909119862119895 and ]119895 119895 = 1 119873 are chosen respectively using theClustering algorithm [32] as follows
119862119895 = 120594119909min+ 2119895 minus 12 ]119895
(14)
4 Advances in Electrical Engineering
Phasors
Clockt
ABC
ABC
Area 1 B1 Area 2B4B5Line 1a Line 1b(110 km)
Line 2a(110 km)
Line 2B(110 km)
(110 km)
A B CFault
UPFC
Pref (pu)
Qref (pu)
[m]
[m]
TripBy passVdqrefPQrefUPFCA1
A2
B1
B2
C1C2
m
Bypass[PQref]
[PQref]
[Vdqref]
[Vdqref]Vdqref
P Pref (pu)Q Qref (pu)
Vdqref
UPFCmeasurements
measurementsV P Q
B2 B3Series 100MVA 10 injection
Shunt 230 kv 100 MVA
Vconv_phase (deg)
Vpos seq B1 B2 B3 B4P B1 B2 B3 B4 (MW)
Q B1 B2 B3 B4 (MVar)
Vconv_mag (pu)
Scope
Scope 1
d_thetad_theta (deg)
Vt (pu)Machines
Machinesignals
Pa (pu)w (pu)w
Pa
VtStop
Stop
Stop simulationif there is loss of synchronism
++
+ +
Figure 2 Kundur power system test
where 120594119909minand 120594119909max
are the lower and upper bounds ofthe 119894th element of the RBF input vector 120594119879119909 = (119909 119878119909 119878119909120598119909)respectively
Note that the term 120575119906119909(119905) is time-varying and cannot beapproximated by a static neural network In the followinganalysis sliding robust termswill be used in the identificationscheme to compensate the effect of this uncertainty time-varying term The controller 119906lowast119909(120594119909 119905) will be approximatedassuming that the terms 119890119891(120594119909) and 120575119906119909(119905) are bounded byunknown positive constants
For this purpose the following neural controller is pro-posed in order to approximate the control signal 119906lowast119909(120594119909 119905)
where the term 119887119909(119905) is introduced in order to improve theconvergence rate of the neural network in the presence of theuncertainties terms
Consider the systems described by (9) the sliding-neuralnetwork controller (15) and Assumptions 1 and 2 given in[31] If the bias term 119887119909(119905) the learning rule of the weight 119908and the adaptation law for the unknown bound 120582119909 are chosenas
1003816100381610038161003816100381610038161003816100381610038161003816119908119895=119908119895 if 1003816100381610038161003816100381611990811989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909 = 120572119909 if 119878119909 = 00 if 119878119909 = 0
(16)
with120572119909 gt 0 119909(0) = 0 and Proj(sdot) the well-known projectionfunction [33] on the compact set Ω120596 = 120596 120596 le 119877120596then the neural network controller error 119878119909 will convergein finite time to the origin The proof of the convergenceof above neural network controller to zero can be found in[31]
In order to apply the neurosliding controller describedabove to power flow control UPFC sending-end bus voltagecontrol and DC-link voltage control the dynamic equationsof the UPFC completely described by (2) to (5) and (8) can berewritten as
Advances in Electrical Engineering 5
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
REFPINSC
0 01 02 03 04 05 06
(i)
18
2
22
PB3
(pu)
002040608
QB3
(pu)
097098099
1101
VB2
(pu)
099
1
101
VDC
(pu)
01 02 03 04 05 060Time (s)
(a)
0 01 02 03 04 05 06
(iii)
0 01 02 03 04 05 06
(iii)
(vi)
SNCPI
0 01 02 03 04 05 06
(i)
01015
02025
Id_S
H (p
u)
minus04minus02
00204
Iq_S
H (p
u)16
18
2
22
Id_S
E (p
u)
minus020
020406
Iq_S
E (p
u)
01 02 03 04 05 060Time (s)
(b)
Figure 3 Control response to step changes in real and reactive power flow references in the transmission line (a) (i) Active power at busB3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2 (iv) UPFC DC-link voltage (b) (i)119863-axis current of shunt converter (ii)119876-axis current of shunt converter (iii)119863-axis current of series converter (iv) 119876-axis current of series converter
1199063 = Vsh119889 minus V1199041198891199094 = 119894sh119902
1198914 (119909 119905) = minus119908119894sh119889 minus 119877sh119871 sh
1198924 (119909 119905) = 1119871 sh
1199064 = Vsh119902
6 Advances in Electrical Engineering
0 01 02 03 04 05 0608
1
Vd_S
H (p
u)(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus008minus006minus004minus002
0
Vq_S
H (p
u)
minus0050
00501
Vd_S
E (p
u)
01502
02503
Vq_S
E (p
u)
01 02 03 04 05 060Time (s)
(a)
0 01 02 03 04 05 06
(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus240minus220minus200minus180
PB2
(Mw
)
minus125minus120minus115minus110minus105
PB5
(Mw
)
0102030
QB2
(Mva
r)
121416182022
QB5
(Mva
r)
01 02 03 04 050 06Time (s)
(b)
Figure 4 Control response to step changes in real and reactive power flow references in the transmission line (a) (i)119863-axis voltage of shuntconverter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of series converter (iv) 119876-axis voltage of series converter (b) (i) Activepower at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power at bus B5
1199095 = V2dc1198915 (119909 119905) = minus 2119862119875se1198925 (119909 119905) = minus 2119862
1199065 = 119875sh(18)
where 1198891(119905) to 1198895(119905) represent system uncertaintiesThe reference values of the state variables are obtained as
where 119875lowast119903 and119876lowast119903 are the active and reactive power referencesat the receiving end bus of the transmission line respectively
We can design the neurosliding controller lowast119896 using theUPFC dynamics given in (17) as (for 119896 = 1 5)
Figure 5 Control response to load variation (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2(iv) UPFC DC-link voltage (b) (i) Active power at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power atbus B5
1003816100381610038161003816100381610038161003816100381610038161003816119908119896119895=119908119896119895 if 1003816100381610038161003816100381611990811989611989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909119896 = 120572119909119896 if 119878119909119896 = 00 if 119878119909119896 = 0
(20)
4 Simulation Results
The performance of the proposed nonlinear controlleris evaluated through digital simulations using MATLABSIMULINK software The power system used is a Kundurtwo-area four-machine power system shown in Figure 2 Thedetails of system data and initial operating point are givenin [34] The proposed controller can be applied to a UPFCconnected between any two buses of the power system (with119899 bus) regardless of the interaction between these two busesand other buses Only local measurements information is
required for the implementation of the proposed algorithmThe simulation results of the proposed controller (SNC)are compared with conventional Proportional Integral (PI)controllers used for power flow control UPFC sending-endbus voltage control and DC-link voltage control These clas-sical controllers are tuned using optimal control techniquesand the parameters obtained are given in the Appendix Toevaluate the performance of the proposed controller four setsof simulations have been performed In all simulations theuncertainty factor is set at +10 That is the parameters ofthe system under simulation are set at 110 compared to thesame parameters introduced in the controller
41 Step Changes in Transmission Line Real and ReactivePower Flow References In this case study the initial complexpower flow (119875B3 + 119895119876B3) at the receiving end of the trans-mission line is found as (18 + 11989500) pu A step change inactive power reference from 18 to 22 pu and reactive powerreference from00 to 05 pu of the transmission line take placeat 119905 = 002 s and 032 s respectively The simulation resultsfor this case study are depicted in Figures 3 and 4 It can beseen from these figures that the active and reactive power flowthrough the transmission line the UPFC DC-link voltage
8 Advances in Electrical Engineering
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03
(ii)
0 005 01 015 02 025 03095
1
VB2
(pu)
(iii)
09
1
11
VDC
(pu)
(iv)
REFSNC
18
2
22
PB3
(pu)
0020406
QB3
(pu)
005 01 015 02 025 030Time (s)
(a)
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03minus01
minus005
0
Vq_S
H (p
u)
(ii)
0 005 01 015 02 025 030
01
Vd_S
E (p
u)
(iii)
(iv)
02
025
Vq_S
E (p
u)
05
1
15
Vd_S
H (p
u)005 01 015 02 025 030
Time (s)
(b)
Figure 6 Control response to measurement noise (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at busB2 (iv) UPFC DC-link voltage (a) (i) 119863-axis voltage of shunt converter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of seriesconverter (iv) 119876-axis voltage of series converter
and the voltagemagnitude at bus B2 are controlled effectivelyThe results also clearly show that the response speed andtransient conditions are further improved with the proposedcontroller as compared to the conventional PI controllersFigure 4 clearly shows the excellent performance of theUPFCin power flow control under the influence of the proposedcontroller
42 Load Variation In practice the references values of thecontrol power system remain constant and the quantitiesbeing controlled vary under the effect of load variationdisturbance and other perturbations In this case studythe load increases by 20 of its nominal value from 119905 =002 s The simulation results are depicted in Figure 5 Itcan be noticed in these figures that the active and reac-tive power flow through the transmission line the DC-link voltage and the voltage magnitude at bus B2 areall regulated to their respective reference values Figure 5shows that the excess active and reactive power requestedby the load is supplied only by generator G2 The figurealso demonstrates once more the excellent performance ofthe proposed controller in terms of overshot and settlingtime
43 Robustness to Measurement Noise In practice it is notpossible to measure a signal accurately due to the presence
of noise For this reason the third case study investigatesthe robustness of the proposed nonlinear controller withrespect to measurement noise (uncertainties) In this casestudy all simulations are conducted under noise condi-tions in the measured line currents with the magnitudeof the noise reaching about 4 of the maximum valueof the measurable line currents A step change in reac-tive power under the same conditions as in the first casestudy is used to evaluate the robustness of the systemThe simulation results for this case study are depicted inFigure 6 From these results it can be seen that the activeand reactive power flow through the transmission line theUPFC DC-link voltage and the voltage magnitude at busB2 are all regulated to their respective reference valuesdespite the presence of measurement noise Hence it canbe concluded that the controller exhibits an excellent noiseresistance
44 Three-Phase-to-Ground Fault Test In this case study athree-phase-to-ground fault is applied on bus-5 and the faultis cleared after 100ms Simulation results for this case studyare shown in Figure 7 From these results it can be seenthat the proposed controller rapidly steers the system to itsprefault steady state and satisfactorily improves the transientstability of the power system as compared to the conventionalPI controllers
Figure 7 Control response to three-phase fault (a) All generator rotor angle in COI (b) All terminal generator voltage
5 Conclusion
In this paper a new hybrid approach which combines RadialBasis Function (RBF) neural network with the sliding modetechnique has been used to design a Unified Power FlowController (UPFC) for power flow control UPFC sending-end voltage control and DC voltage regulation of an electricpower transmission system The RBF neurosliding modecontrol technique uses online training to get its optimalparameter valuesThe proposed technique is robust and doesnot need the knowledge of the perturbation bounds nor thefull state of the nonlinear system The performance of theproposed controller has been evaluated through simulationson a Kundur power system and compared with a classicalPI controller Simulation results have shown the effectivenessand satisfactory performance of the proposed controller indealing with the perturbations considered Future worksshould be targeted towards the extension of the proposed
hybrid approach to a wide area interconnected power systemfor power oscillation damping
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1(ii) PI controllers parameters are as follows
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
119889119894sh119902119889119905 = minus119908119894sh119889 minus 119877sh119871 sh
119894se119902 + 1119871 sh
(Vsh119902) (5)
where 119908119887 = 2120587119891119887 is the fundamental angular frequency ofthe supply voltage and 119908 = 2120587119891 is the angular frequency ofsynchronous reference frame (rads)
Since the series and shunt converters of the UPFC arecoupled through a common DC-link if the losses in theconverters are neglected then the dynamic of the DC-linkvoltage can be expressed as [27]
119889Vdc119889119905 = minus 1Vdc119862dc
(119875se + 119875sh) (6)
where 119875se and 119875sh are the active power supplied by the seriesand shunt converters respectively and Vdc is the voltage of theDC capacitor of capacitance 119862dc
It is clear from (6) that Vdc decreases when 119875se + 119875sh gt0 and it increases when 119875se + 119875sh lt 0 Note that (6) is anonlinear differential equation and has to be investigated atan operating point However the derivative of V2dc can bewritten as
Using (6) and (7) the derivative of V2dc can be expressed as
119889V2dc119889119905 = minus 2119862 (119875se + 119875sh) (8)
Maintaining constant DC-link voltage is very important forthe UPFC control system [1 28 29] The DC-link voltagevaries when 119875se + 119875sh = 0 Since (8) does not containa direct control signal like (4) we will consider 119875sh as anauxiliary input that can be used to maintain the DC-linkvoltage constant
3 UPFC RBF Neurosliding ModeController Design
In this section the method proposed in [30 31] for time-varying parameter estimation will be modified and appliedto design a robust adaptive controller for the UPFC using theRBF neural network
Let us consider the SISO first-order nonlinear system inthe following form
where 119909 isin 119877 119906 isin 119877 and 119910 isin 119877 are state variables systeminput and system output respectively 119891(119909 119905) and 119892(119909 119905) areunknown smooth functions 119891(119909 119905) represents the nominalpart of the system which does not depend upon the controlinput while the uncertainties and external disturbance are
concentrated in the term 119889(119905) assumed to be bounded by anunknown constant 1198890 gt 0 Since all physical plants operate inbounded regions we study the control problem of system (9)whose state 119909 belongs to a compact subsetΩ sub 119877
Let the desired smooth signal 119910lowast = 119909lowast the tracking error119890119909 and augmented item 119878119909 be defined as
119890119909 = 119909 minus 119909lowast119878119909 = 119890119909 + 119862119909 int 119890119909119889119905 (10)
where 119862119909 gt 0 is a design parameter The integral term isincluded in the sliding manifold 119878119909 so as to ensure that thesystem trajectories start on the slidingmanifold from the firstinstant of time From (10) we have
with 120583119909 = 119862119909119890119909 minus lowast(11)
From 119878119909 if the desired sliding mode controller is chosen as[31]
119906lowast119909 = minus 1119892 (119909 119905) (119891 (119909 119905) + 120583119909 + 119889 (119905)) minus
119878119909120598119909 (12)
where 0 lt 120598119909 lt 1 is a design parameter then 119878119909 = 119878119909120598119909 and119878119909 will converge exponentially to 0The above desired controller (12) is not implementable
in practice since the functions 119891(119909 119905) and 119892(119909 119905) and theterms 120583119909 and 119889(119905) are assumed to be unknown Hence inthis work a RBF neural network combined with the slidingmode technique will be applied to approximate the unknowncontroller 119906lowast119909
The control signal (12) can be approximated by the neuralcontroller proposed in [31] as
119908lowast119895 120601 (10038171003817100381710038171003817120594119909 minus 11986211989510038171003817100381710038171003817 ]119895) (13)
where 120601(sdot) denotes a nonlinear function 119862119895 and ]119895 119895 =1 119873 are the center and the width of the 119895th hidden unitrespectively119873 is the number of hidden nodes or Radial BasisFunction (RBF) units 119908lowast is the optimal weight vector andsatisfies 119908lowast le 119877120596 120594119879119909 = (119909 119878119909 119878119909120598119909) is the input vector ofthe RBF network 119890119891(120594119909) is the optimal approximation errorwhich is unknown and bounded forall120594119909 isin Ω119909119862119895 and ]119895 119895 = 1 119873 are chosen respectively using theClustering algorithm [32] as follows
119862119895 = 120594119909min+ 2119895 minus 12 ]119895
(14)
4 Advances in Electrical Engineering
Phasors
Clockt
ABC
ABC
Area 1 B1 Area 2B4B5Line 1a Line 1b(110 km)
Line 2a(110 km)
Line 2B(110 km)
(110 km)
A B CFault
UPFC
Pref (pu)
Qref (pu)
[m]
[m]
TripBy passVdqrefPQrefUPFCA1
A2
B1
B2
C1C2
m
Bypass[PQref]
[PQref]
[Vdqref]
[Vdqref]Vdqref
P Pref (pu)Q Qref (pu)
Vdqref
UPFCmeasurements
measurementsV P Q
B2 B3Series 100MVA 10 injection
Shunt 230 kv 100 MVA
Vconv_phase (deg)
Vpos seq B1 B2 B3 B4P B1 B2 B3 B4 (MW)
Q B1 B2 B3 B4 (MVar)
Vconv_mag (pu)
Scope
Scope 1
d_thetad_theta (deg)
Vt (pu)Machines
Machinesignals
Pa (pu)w (pu)w
Pa
VtStop
Stop
Stop simulationif there is loss of synchronism
++
+ +
Figure 2 Kundur power system test
where 120594119909minand 120594119909max
are the lower and upper bounds ofthe 119894th element of the RBF input vector 120594119879119909 = (119909 119878119909 119878119909120598119909)respectively
Note that the term 120575119906119909(119905) is time-varying and cannot beapproximated by a static neural network In the followinganalysis sliding robust termswill be used in the identificationscheme to compensate the effect of this uncertainty time-varying term The controller 119906lowast119909(120594119909 119905) will be approximatedassuming that the terms 119890119891(120594119909) and 120575119906119909(119905) are bounded byunknown positive constants
For this purpose the following neural controller is pro-posed in order to approximate the control signal 119906lowast119909(120594119909 119905)
where the term 119887119909(119905) is introduced in order to improve theconvergence rate of the neural network in the presence of theuncertainties terms
Consider the systems described by (9) the sliding-neuralnetwork controller (15) and Assumptions 1 and 2 given in[31] If the bias term 119887119909(119905) the learning rule of the weight 119908and the adaptation law for the unknown bound 120582119909 are chosenas
1003816100381610038161003816100381610038161003816100381610038161003816119908119895=119908119895 if 1003816100381610038161003816100381611990811989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909 = 120572119909 if 119878119909 = 00 if 119878119909 = 0
(16)
with120572119909 gt 0 119909(0) = 0 and Proj(sdot) the well-known projectionfunction [33] on the compact set Ω120596 = 120596 120596 le 119877120596then the neural network controller error 119878119909 will convergein finite time to the origin The proof of the convergenceof above neural network controller to zero can be found in[31]
In order to apply the neurosliding controller describedabove to power flow control UPFC sending-end bus voltagecontrol and DC-link voltage control the dynamic equationsof the UPFC completely described by (2) to (5) and (8) can berewritten as
Advances in Electrical Engineering 5
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
REFPINSC
0 01 02 03 04 05 06
(i)
18
2
22
PB3
(pu)
002040608
QB3
(pu)
097098099
1101
VB2
(pu)
099
1
101
VDC
(pu)
01 02 03 04 05 060Time (s)
(a)
0 01 02 03 04 05 06
(iii)
0 01 02 03 04 05 06
(iii)
(vi)
SNCPI
0 01 02 03 04 05 06
(i)
01015
02025
Id_S
H (p
u)
minus04minus02
00204
Iq_S
H (p
u)16
18
2
22
Id_S
E (p
u)
minus020
020406
Iq_S
E (p
u)
01 02 03 04 05 060Time (s)
(b)
Figure 3 Control response to step changes in real and reactive power flow references in the transmission line (a) (i) Active power at busB3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2 (iv) UPFC DC-link voltage (b) (i)119863-axis current of shunt converter (ii)119876-axis current of shunt converter (iii)119863-axis current of series converter (iv) 119876-axis current of series converter
1199063 = Vsh119889 minus V1199041198891199094 = 119894sh119902
1198914 (119909 119905) = minus119908119894sh119889 minus 119877sh119871 sh
1198924 (119909 119905) = 1119871 sh
1199064 = Vsh119902
6 Advances in Electrical Engineering
0 01 02 03 04 05 0608
1
Vd_S
H (p
u)(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus008minus006minus004minus002
0
Vq_S
H (p
u)
minus0050
00501
Vd_S
E (p
u)
01502
02503
Vq_S
E (p
u)
01 02 03 04 05 060Time (s)
(a)
0 01 02 03 04 05 06
(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus240minus220minus200minus180
PB2
(Mw
)
minus125minus120minus115minus110minus105
PB5
(Mw
)
0102030
QB2
(Mva
r)
121416182022
QB5
(Mva
r)
01 02 03 04 050 06Time (s)
(b)
Figure 4 Control response to step changes in real and reactive power flow references in the transmission line (a) (i)119863-axis voltage of shuntconverter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of series converter (iv) 119876-axis voltage of series converter (b) (i) Activepower at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power at bus B5
1199095 = V2dc1198915 (119909 119905) = minus 2119862119875se1198925 (119909 119905) = minus 2119862
1199065 = 119875sh(18)
where 1198891(119905) to 1198895(119905) represent system uncertaintiesThe reference values of the state variables are obtained as
where 119875lowast119903 and119876lowast119903 are the active and reactive power referencesat the receiving end bus of the transmission line respectively
We can design the neurosliding controller lowast119896 using theUPFC dynamics given in (17) as (for 119896 = 1 5)
Figure 5 Control response to load variation (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2(iv) UPFC DC-link voltage (b) (i) Active power at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power atbus B5
1003816100381610038161003816100381610038161003816100381610038161003816119908119896119895=119908119896119895 if 1003816100381610038161003816100381611990811989611989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909119896 = 120572119909119896 if 119878119909119896 = 00 if 119878119909119896 = 0
(20)
4 Simulation Results
The performance of the proposed nonlinear controlleris evaluated through digital simulations using MATLABSIMULINK software The power system used is a Kundurtwo-area four-machine power system shown in Figure 2 Thedetails of system data and initial operating point are givenin [34] The proposed controller can be applied to a UPFCconnected between any two buses of the power system (with119899 bus) regardless of the interaction between these two busesand other buses Only local measurements information is
required for the implementation of the proposed algorithmThe simulation results of the proposed controller (SNC)are compared with conventional Proportional Integral (PI)controllers used for power flow control UPFC sending-endbus voltage control and DC-link voltage control These clas-sical controllers are tuned using optimal control techniquesand the parameters obtained are given in the Appendix Toevaluate the performance of the proposed controller four setsof simulations have been performed In all simulations theuncertainty factor is set at +10 That is the parameters ofthe system under simulation are set at 110 compared to thesame parameters introduced in the controller
41 Step Changes in Transmission Line Real and ReactivePower Flow References In this case study the initial complexpower flow (119875B3 + 119895119876B3) at the receiving end of the trans-mission line is found as (18 + 11989500) pu A step change inactive power reference from 18 to 22 pu and reactive powerreference from00 to 05 pu of the transmission line take placeat 119905 = 002 s and 032 s respectively The simulation resultsfor this case study are depicted in Figures 3 and 4 It can beseen from these figures that the active and reactive power flowthrough the transmission line the UPFC DC-link voltage
8 Advances in Electrical Engineering
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03
(ii)
0 005 01 015 02 025 03095
1
VB2
(pu)
(iii)
09
1
11
VDC
(pu)
(iv)
REFSNC
18
2
22
PB3
(pu)
0020406
QB3
(pu)
005 01 015 02 025 030Time (s)
(a)
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03minus01
minus005
0
Vq_S
H (p
u)
(ii)
0 005 01 015 02 025 030
01
Vd_S
E (p
u)
(iii)
(iv)
02
025
Vq_S
E (p
u)
05
1
15
Vd_S
H (p
u)005 01 015 02 025 030
Time (s)
(b)
Figure 6 Control response to measurement noise (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at busB2 (iv) UPFC DC-link voltage (a) (i) 119863-axis voltage of shunt converter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of seriesconverter (iv) 119876-axis voltage of series converter
and the voltagemagnitude at bus B2 are controlled effectivelyThe results also clearly show that the response speed andtransient conditions are further improved with the proposedcontroller as compared to the conventional PI controllersFigure 4 clearly shows the excellent performance of theUPFCin power flow control under the influence of the proposedcontroller
42 Load Variation In practice the references values of thecontrol power system remain constant and the quantitiesbeing controlled vary under the effect of load variationdisturbance and other perturbations In this case studythe load increases by 20 of its nominal value from 119905 =002 s The simulation results are depicted in Figure 5 Itcan be noticed in these figures that the active and reac-tive power flow through the transmission line the DC-link voltage and the voltage magnitude at bus B2 areall regulated to their respective reference values Figure 5shows that the excess active and reactive power requestedby the load is supplied only by generator G2 The figurealso demonstrates once more the excellent performance ofthe proposed controller in terms of overshot and settlingtime
43 Robustness to Measurement Noise In practice it is notpossible to measure a signal accurately due to the presence
of noise For this reason the third case study investigatesthe robustness of the proposed nonlinear controller withrespect to measurement noise (uncertainties) In this casestudy all simulations are conducted under noise condi-tions in the measured line currents with the magnitudeof the noise reaching about 4 of the maximum valueof the measurable line currents A step change in reac-tive power under the same conditions as in the first casestudy is used to evaluate the robustness of the systemThe simulation results for this case study are depicted inFigure 6 From these results it can be seen that the activeand reactive power flow through the transmission line theUPFC DC-link voltage and the voltage magnitude at busB2 are all regulated to their respective reference valuesdespite the presence of measurement noise Hence it canbe concluded that the controller exhibits an excellent noiseresistance
44 Three-Phase-to-Ground Fault Test In this case study athree-phase-to-ground fault is applied on bus-5 and the faultis cleared after 100ms Simulation results for this case studyare shown in Figure 7 From these results it can be seenthat the proposed controller rapidly steers the system to itsprefault steady state and satisfactorily improves the transientstability of the power system as compared to the conventionalPI controllers
Figure 7 Control response to three-phase fault (a) All generator rotor angle in COI (b) All terminal generator voltage
5 Conclusion
In this paper a new hybrid approach which combines RadialBasis Function (RBF) neural network with the sliding modetechnique has been used to design a Unified Power FlowController (UPFC) for power flow control UPFC sending-end voltage control and DC voltage regulation of an electricpower transmission system The RBF neurosliding modecontrol technique uses online training to get its optimalparameter valuesThe proposed technique is robust and doesnot need the knowledge of the perturbation bounds nor thefull state of the nonlinear system The performance of theproposed controller has been evaluated through simulationson a Kundur power system and compared with a classicalPI controller Simulation results have shown the effectivenessand satisfactory performance of the proposed controller indealing with the perturbations considered Future worksshould be targeted towards the extension of the proposed
hybrid approach to a wide area interconnected power systemfor power oscillation damping
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1(ii) PI controllers parameters are as follows
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
are the lower and upper bounds ofthe 119894th element of the RBF input vector 120594119879119909 = (119909 119878119909 119878119909120598119909)respectively
Note that the term 120575119906119909(119905) is time-varying and cannot beapproximated by a static neural network In the followinganalysis sliding robust termswill be used in the identificationscheme to compensate the effect of this uncertainty time-varying term The controller 119906lowast119909(120594119909 119905) will be approximatedassuming that the terms 119890119891(120594119909) and 120575119906119909(119905) are bounded byunknown positive constants
For this purpose the following neural controller is pro-posed in order to approximate the control signal 119906lowast119909(120594119909 119905)
where the term 119887119909(119905) is introduced in order to improve theconvergence rate of the neural network in the presence of theuncertainties terms
Consider the systems described by (9) the sliding-neuralnetwork controller (15) and Assumptions 1 and 2 given in[31] If the bias term 119887119909(119905) the learning rule of the weight 119908and the adaptation law for the unknown bound 120582119909 are chosenas
1003816100381610038161003816100381610038161003816100381610038161003816119908119895=119908119895 if 1003816100381610038161003816100381611990811989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909 = 120572119909 if 119878119909 = 00 if 119878119909 = 0
(16)
with120572119909 gt 0 119909(0) = 0 and Proj(sdot) the well-known projectionfunction [33] on the compact set Ω120596 = 120596 120596 le 119877120596then the neural network controller error 119878119909 will convergein finite time to the origin The proof of the convergenceof above neural network controller to zero can be found in[31]
In order to apply the neurosliding controller describedabove to power flow control UPFC sending-end bus voltagecontrol and DC-link voltage control the dynamic equationsof the UPFC completely described by (2) to (5) and (8) can berewritten as
Advances in Electrical Engineering 5
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
REFPINSC
0 01 02 03 04 05 06
(i)
18
2
22
PB3
(pu)
002040608
QB3
(pu)
097098099
1101
VB2
(pu)
099
1
101
VDC
(pu)
01 02 03 04 05 060Time (s)
(a)
0 01 02 03 04 05 06
(iii)
0 01 02 03 04 05 06
(iii)
(vi)
SNCPI
0 01 02 03 04 05 06
(i)
01015
02025
Id_S
H (p
u)
minus04minus02
00204
Iq_S
H (p
u)16
18
2
22
Id_S
E (p
u)
minus020
020406
Iq_S
E (p
u)
01 02 03 04 05 060Time (s)
(b)
Figure 3 Control response to step changes in real and reactive power flow references in the transmission line (a) (i) Active power at busB3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2 (iv) UPFC DC-link voltage (b) (i)119863-axis current of shunt converter (ii)119876-axis current of shunt converter (iii)119863-axis current of series converter (iv) 119876-axis current of series converter
1199063 = Vsh119889 minus V1199041198891199094 = 119894sh119902
1198914 (119909 119905) = minus119908119894sh119889 minus 119877sh119871 sh
1198924 (119909 119905) = 1119871 sh
1199064 = Vsh119902
6 Advances in Electrical Engineering
0 01 02 03 04 05 0608
1
Vd_S
H (p
u)(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus008minus006minus004minus002
0
Vq_S
H (p
u)
minus0050
00501
Vd_S
E (p
u)
01502
02503
Vq_S
E (p
u)
01 02 03 04 05 060Time (s)
(a)
0 01 02 03 04 05 06
(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus240minus220minus200minus180
PB2
(Mw
)
minus125minus120minus115minus110minus105
PB5
(Mw
)
0102030
QB2
(Mva
r)
121416182022
QB5
(Mva
r)
01 02 03 04 050 06Time (s)
(b)
Figure 4 Control response to step changes in real and reactive power flow references in the transmission line (a) (i)119863-axis voltage of shuntconverter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of series converter (iv) 119876-axis voltage of series converter (b) (i) Activepower at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power at bus B5
1199095 = V2dc1198915 (119909 119905) = minus 2119862119875se1198925 (119909 119905) = minus 2119862
1199065 = 119875sh(18)
where 1198891(119905) to 1198895(119905) represent system uncertaintiesThe reference values of the state variables are obtained as
where 119875lowast119903 and119876lowast119903 are the active and reactive power referencesat the receiving end bus of the transmission line respectively
We can design the neurosliding controller lowast119896 using theUPFC dynamics given in (17) as (for 119896 = 1 5)
Figure 5 Control response to load variation (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2(iv) UPFC DC-link voltage (b) (i) Active power at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power atbus B5
1003816100381610038161003816100381610038161003816100381610038161003816119908119896119895=119908119896119895 if 1003816100381610038161003816100381611990811989611989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909119896 = 120572119909119896 if 119878119909119896 = 00 if 119878119909119896 = 0
(20)
4 Simulation Results
The performance of the proposed nonlinear controlleris evaluated through digital simulations using MATLABSIMULINK software The power system used is a Kundurtwo-area four-machine power system shown in Figure 2 Thedetails of system data and initial operating point are givenin [34] The proposed controller can be applied to a UPFCconnected between any two buses of the power system (with119899 bus) regardless of the interaction between these two busesand other buses Only local measurements information is
required for the implementation of the proposed algorithmThe simulation results of the proposed controller (SNC)are compared with conventional Proportional Integral (PI)controllers used for power flow control UPFC sending-endbus voltage control and DC-link voltage control These clas-sical controllers are tuned using optimal control techniquesand the parameters obtained are given in the Appendix Toevaluate the performance of the proposed controller four setsof simulations have been performed In all simulations theuncertainty factor is set at +10 That is the parameters ofthe system under simulation are set at 110 compared to thesame parameters introduced in the controller
41 Step Changes in Transmission Line Real and ReactivePower Flow References In this case study the initial complexpower flow (119875B3 + 119895119876B3) at the receiving end of the trans-mission line is found as (18 + 11989500) pu A step change inactive power reference from 18 to 22 pu and reactive powerreference from00 to 05 pu of the transmission line take placeat 119905 = 002 s and 032 s respectively The simulation resultsfor this case study are depicted in Figures 3 and 4 It can beseen from these figures that the active and reactive power flowthrough the transmission line the UPFC DC-link voltage
8 Advances in Electrical Engineering
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03
(ii)
0 005 01 015 02 025 03095
1
VB2
(pu)
(iii)
09
1
11
VDC
(pu)
(iv)
REFSNC
18
2
22
PB3
(pu)
0020406
QB3
(pu)
005 01 015 02 025 030Time (s)
(a)
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03minus01
minus005
0
Vq_S
H (p
u)
(ii)
0 005 01 015 02 025 030
01
Vd_S
E (p
u)
(iii)
(iv)
02
025
Vq_S
E (p
u)
05
1
15
Vd_S
H (p
u)005 01 015 02 025 030
Time (s)
(b)
Figure 6 Control response to measurement noise (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at busB2 (iv) UPFC DC-link voltage (a) (i) 119863-axis voltage of shunt converter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of seriesconverter (iv) 119876-axis voltage of series converter
and the voltagemagnitude at bus B2 are controlled effectivelyThe results also clearly show that the response speed andtransient conditions are further improved with the proposedcontroller as compared to the conventional PI controllersFigure 4 clearly shows the excellent performance of theUPFCin power flow control under the influence of the proposedcontroller
42 Load Variation In practice the references values of thecontrol power system remain constant and the quantitiesbeing controlled vary under the effect of load variationdisturbance and other perturbations In this case studythe load increases by 20 of its nominal value from 119905 =002 s The simulation results are depicted in Figure 5 Itcan be noticed in these figures that the active and reac-tive power flow through the transmission line the DC-link voltage and the voltage magnitude at bus B2 areall regulated to their respective reference values Figure 5shows that the excess active and reactive power requestedby the load is supplied only by generator G2 The figurealso demonstrates once more the excellent performance ofthe proposed controller in terms of overshot and settlingtime
43 Robustness to Measurement Noise In practice it is notpossible to measure a signal accurately due to the presence
of noise For this reason the third case study investigatesthe robustness of the proposed nonlinear controller withrespect to measurement noise (uncertainties) In this casestudy all simulations are conducted under noise condi-tions in the measured line currents with the magnitudeof the noise reaching about 4 of the maximum valueof the measurable line currents A step change in reac-tive power under the same conditions as in the first casestudy is used to evaluate the robustness of the systemThe simulation results for this case study are depicted inFigure 6 From these results it can be seen that the activeand reactive power flow through the transmission line theUPFC DC-link voltage and the voltage magnitude at busB2 are all regulated to their respective reference valuesdespite the presence of measurement noise Hence it canbe concluded that the controller exhibits an excellent noiseresistance
44 Three-Phase-to-Ground Fault Test In this case study athree-phase-to-ground fault is applied on bus-5 and the faultis cleared after 100ms Simulation results for this case studyare shown in Figure 7 From these results it can be seenthat the proposed controller rapidly steers the system to itsprefault steady state and satisfactorily improves the transientstability of the power system as compared to the conventionalPI controllers
Figure 7 Control response to three-phase fault (a) All generator rotor angle in COI (b) All terminal generator voltage
5 Conclusion
In this paper a new hybrid approach which combines RadialBasis Function (RBF) neural network with the sliding modetechnique has been used to design a Unified Power FlowController (UPFC) for power flow control UPFC sending-end voltage control and DC voltage regulation of an electricpower transmission system The RBF neurosliding modecontrol technique uses online training to get its optimalparameter valuesThe proposed technique is robust and doesnot need the knowledge of the perturbation bounds nor thefull state of the nonlinear system The performance of theproposed controller has been evaluated through simulationson a Kundur power system and compared with a classicalPI controller Simulation results have shown the effectivenessand satisfactory performance of the proposed controller indealing with the perturbations considered Future worksshould be targeted towards the extension of the proposed
hybrid approach to a wide area interconnected power systemfor power oscillation damping
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1(ii) PI controllers parameters are as follows
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
Figure 3 Control response to step changes in real and reactive power flow references in the transmission line (a) (i) Active power at busB3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2 (iv) UPFC DC-link voltage (b) (i)119863-axis current of shunt converter (ii)119876-axis current of shunt converter (iii)119863-axis current of series converter (iv) 119876-axis current of series converter
1199063 = Vsh119889 minus V1199041198891199094 = 119894sh119902
1198914 (119909 119905) = minus119908119894sh119889 minus 119877sh119871 sh
1198924 (119909 119905) = 1119871 sh
1199064 = Vsh119902
6 Advances in Electrical Engineering
0 01 02 03 04 05 0608
1
Vd_S
H (p
u)(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus008minus006minus004minus002
0
Vq_S
H (p
u)
minus0050
00501
Vd_S
E (p
u)
01502
02503
Vq_S
E (p
u)
01 02 03 04 05 060Time (s)
(a)
0 01 02 03 04 05 06
(i)
0 01 02 03 04 05 06
(ii)
0 01 02 03 04 05 06
(iii)
(iv)
PISNC
minus240minus220minus200minus180
PB2
(Mw
)
minus125minus120minus115minus110minus105
PB5
(Mw
)
0102030
QB2
(Mva
r)
121416182022
QB5
(Mva
r)
01 02 03 04 050 06Time (s)
(b)
Figure 4 Control response to step changes in real and reactive power flow references in the transmission line (a) (i)119863-axis voltage of shuntconverter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of series converter (iv) 119876-axis voltage of series converter (b) (i) Activepower at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power at bus B5
1199095 = V2dc1198915 (119909 119905) = minus 2119862119875se1198925 (119909 119905) = minus 2119862
1199065 = 119875sh(18)
where 1198891(119905) to 1198895(119905) represent system uncertaintiesThe reference values of the state variables are obtained as
where 119875lowast119903 and119876lowast119903 are the active and reactive power referencesat the receiving end bus of the transmission line respectively
We can design the neurosliding controller lowast119896 using theUPFC dynamics given in (17) as (for 119896 = 1 5)
Figure 5 Control response to load variation (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2(iv) UPFC DC-link voltage (b) (i) Active power at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power atbus B5
1003816100381610038161003816100381610038161003816100381610038161003816119908119896119895=119908119896119895 if 1003816100381610038161003816100381611990811989611989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909119896 = 120572119909119896 if 119878119909119896 = 00 if 119878119909119896 = 0
(20)
4 Simulation Results
The performance of the proposed nonlinear controlleris evaluated through digital simulations using MATLABSIMULINK software The power system used is a Kundurtwo-area four-machine power system shown in Figure 2 Thedetails of system data and initial operating point are givenin [34] The proposed controller can be applied to a UPFCconnected between any two buses of the power system (with119899 bus) regardless of the interaction between these two busesand other buses Only local measurements information is
required for the implementation of the proposed algorithmThe simulation results of the proposed controller (SNC)are compared with conventional Proportional Integral (PI)controllers used for power flow control UPFC sending-endbus voltage control and DC-link voltage control These clas-sical controllers are tuned using optimal control techniquesand the parameters obtained are given in the Appendix Toevaluate the performance of the proposed controller four setsof simulations have been performed In all simulations theuncertainty factor is set at +10 That is the parameters ofthe system under simulation are set at 110 compared to thesame parameters introduced in the controller
41 Step Changes in Transmission Line Real and ReactivePower Flow References In this case study the initial complexpower flow (119875B3 + 119895119876B3) at the receiving end of the trans-mission line is found as (18 + 11989500) pu A step change inactive power reference from 18 to 22 pu and reactive powerreference from00 to 05 pu of the transmission line take placeat 119905 = 002 s and 032 s respectively The simulation resultsfor this case study are depicted in Figures 3 and 4 It can beseen from these figures that the active and reactive power flowthrough the transmission line the UPFC DC-link voltage
8 Advances in Electrical Engineering
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03
(ii)
0 005 01 015 02 025 03095
1
VB2
(pu)
(iii)
09
1
11
VDC
(pu)
(iv)
REFSNC
18
2
22
PB3
(pu)
0020406
QB3
(pu)
005 01 015 02 025 030Time (s)
(a)
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03minus01
minus005
0
Vq_S
H (p
u)
(ii)
0 005 01 015 02 025 030
01
Vd_S
E (p
u)
(iii)
(iv)
02
025
Vq_S
E (p
u)
05
1
15
Vd_S
H (p
u)005 01 015 02 025 030
Time (s)
(b)
Figure 6 Control response to measurement noise (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at busB2 (iv) UPFC DC-link voltage (a) (i) 119863-axis voltage of shunt converter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of seriesconverter (iv) 119876-axis voltage of series converter
and the voltagemagnitude at bus B2 are controlled effectivelyThe results also clearly show that the response speed andtransient conditions are further improved with the proposedcontroller as compared to the conventional PI controllersFigure 4 clearly shows the excellent performance of theUPFCin power flow control under the influence of the proposedcontroller
42 Load Variation In practice the references values of thecontrol power system remain constant and the quantitiesbeing controlled vary under the effect of load variationdisturbance and other perturbations In this case studythe load increases by 20 of its nominal value from 119905 =002 s The simulation results are depicted in Figure 5 Itcan be noticed in these figures that the active and reac-tive power flow through the transmission line the DC-link voltage and the voltage magnitude at bus B2 areall regulated to their respective reference values Figure 5shows that the excess active and reactive power requestedby the load is supplied only by generator G2 The figurealso demonstrates once more the excellent performance ofthe proposed controller in terms of overshot and settlingtime
43 Robustness to Measurement Noise In practice it is notpossible to measure a signal accurately due to the presence
of noise For this reason the third case study investigatesthe robustness of the proposed nonlinear controller withrespect to measurement noise (uncertainties) In this casestudy all simulations are conducted under noise condi-tions in the measured line currents with the magnitudeof the noise reaching about 4 of the maximum valueof the measurable line currents A step change in reac-tive power under the same conditions as in the first casestudy is used to evaluate the robustness of the systemThe simulation results for this case study are depicted inFigure 6 From these results it can be seen that the activeand reactive power flow through the transmission line theUPFC DC-link voltage and the voltage magnitude at busB2 are all regulated to their respective reference valuesdespite the presence of measurement noise Hence it canbe concluded that the controller exhibits an excellent noiseresistance
44 Three-Phase-to-Ground Fault Test In this case study athree-phase-to-ground fault is applied on bus-5 and the faultis cleared after 100ms Simulation results for this case studyare shown in Figure 7 From these results it can be seenthat the proposed controller rapidly steers the system to itsprefault steady state and satisfactorily improves the transientstability of the power system as compared to the conventionalPI controllers
Figure 7 Control response to three-phase fault (a) All generator rotor angle in COI (b) All terminal generator voltage
5 Conclusion
In this paper a new hybrid approach which combines RadialBasis Function (RBF) neural network with the sliding modetechnique has been used to design a Unified Power FlowController (UPFC) for power flow control UPFC sending-end voltage control and DC voltage regulation of an electricpower transmission system The RBF neurosliding modecontrol technique uses online training to get its optimalparameter valuesThe proposed technique is robust and doesnot need the knowledge of the perturbation bounds nor thefull state of the nonlinear system The performance of theproposed controller has been evaluated through simulationson a Kundur power system and compared with a classicalPI controller Simulation results have shown the effectivenessand satisfactory performance of the proposed controller indealing with the perturbations considered Future worksshould be targeted towards the extension of the proposed
hybrid approach to a wide area interconnected power systemfor power oscillation damping
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1(ii) PI controllers parameters are as follows
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
Figure 4 Control response to step changes in real and reactive power flow references in the transmission line (a) (i)119863-axis voltage of shuntconverter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of series converter (iv) 119876-axis voltage of series converter (b) (i) Activepower at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power at bus B5
1199095 = V2dc1198915 (119909 119905) = minus 2119862119875se1198925 (119909 119905) = minus 2119862
1199065 = 119875sh(18)
where 1198891(119905) to 1198895(119905) represent system uncertaintiesThe reference values of the state variables are obtained as
where 119875lowast119903 and119876lowast119903 are the active and reactive power referencesat the receiving end bus of the transmission line respectively
We can design the neurosliding controller lowast119896 using theUPFC dynamics given in (17) as (for 119896 = 1 5)
Figure 5 Control response to load variation (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2(iv) UPFC DC-link voltage (b) (i) Active power at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power atbus B5
1003816100381610038161003816100381610038161003816100381610038161003816119908119896119895=119908119896119895 if 1003816100381610038161003816100381611990811989611989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909119896 = 120572119909119896 if 119878119909119896 = 00 if 119878119909119896 = 0
(20)
4 Simulation Results
The performance of the proposed nonlinear controlleris evaluated through digital simulations using MATLABSIMULINK software The power system used is a Kundurtwo-area four-machine power system shown in Figure 2 Thedetails of system data and initial operating point are givenin [34] The proposed controller can be applied to a UPFCconnected between any two buses of the power system (with119899 bus) regardless of the interaction between these two busesand other buses Only local measurements information is
required for the implementation of the proposed algorithmThe simulation results of the proposed controller (SNC)are compared with conventional Proportional Integral (PI)controllers used for power flow control UPFC sending-endbus voltage control and DC-link voltage control These clas-sical controllers are tuned using optimal control techniquesand the parameters obtained are given in the Appendix Toevaluate the performance of the proposed controller four setsof simulations have been performed In all simulations theuncertainty factor is set at +10 That is the parameters ofthe system under simulation are set at 110 compared to thesame parameters introduced in the controller
41 Step Changes in Transmission Line Real and ReactivePower Flow References In this case study the initial complexpower flow (119875B3 + 119895119876B3) at the receiving end of the trans-mission line is found as (18 + 11989500) pu A step change inactive power reference from 18 to 22 pu and reactive powerreference from00 to 05 pu of the transmission line take placeat 119905 = 002 s and 032 s respectively The simulation resultsfor this case study are depicted in Figures 3 and 4 It can beseen from these figures that the active and reactive power flowthrough the transmission line the UPFC DC-link voltage
8 Advances in Electrical Engineering
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03
(ii)
0 005 01 015 02 025 03095
1
VB2
(pu)
(iii)
09
1
11
VDC
(pu)
(iv)
REFSNC
18
2
22
PB3
(pu)
0020406
QB3
(pu)
005 01 015 02 025 030Time (s)
(a)
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03minus01
minus005
0
Vq_S
H (p
u)
(ii)
0 005 01 015 02 025 030
01
Vd_S
E (p
u)
(iii)
(iv)
02
025
Vq_S
E (p
u)
05
1
15
Vd_S
H (p
u)005 01 015 02 025 030
Time (s)
(b)
Figure 6 Control response to measurement noise (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at busB2 (iv) UPFC DC-link voltage (a) (i) 119863-axis voltage of shunt converter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of seriesconverter (iv) 119876-axis voltage of series converter
and the voltagemagnitude at bus B2 are controlled effectivelyThe results also clearly show that the response speed andtransient conditions are further improved with the proposedcontroller as compared to the conventional PI controllersFigure 4 clearly shows the excellent performance of theUPFCin power flow control under the influence of the proposedcontroller
42 Load Variation In practice the references values of thecontrol power system remain constant and the quantitiesbeing controlled vary under the effect of load variationdisturbance and other perturbations In this case studythe load increases by 20 of its nominal value from 119905 =002 s The simulation results are depicted in Figure 5 Itcan be noticed in these figures that the active and reac-tive power flow through the transmission line the DC-link voltage and the voltage magnitude at bus B2 areall regulated to their respective reference values Figure 5shows that the excess active and reactive power requestedby the load is supplied only by generator G2 The figurealso demonstrates once more the excellent performance ofthe proposed controller in terms of overshot and settlingtime
43 Robustness to Measurement Noise In practice it is notpossible to measure a signal accurately due to the presence
of noise For this reason the third case study investigatesthe robustness of the proposed nonlinear controller withrespect to measurement noise (uncertainties) In this casestudy all simulations are conducted under noise condi-tions in the measured line currents with the magnitudeof the noise reaching about 4 of the maximum valueof the measurable line currents A step change in reac-tive power under the same conditions as in the first casestudy is used to evaluate the robustness of the systemThe simulation results for this case study are depicted inFigure 6 From these results it can be seen that the activeand reactive power flow through the transmission line theUPFC DC-link voltage and the voltage magnitude at busB2 are all regulated to their respective reference valuesdespite the presence of measurement noise Hence it canbe concluded that the controller exhibits an excellent noiseresistance
44 Three-Phase-to-Ground Fault Test In this case study athree-phase-to-ground fault is applied on bus-5 and the faultis cleared after 100ms Simulation results for this case studyare shown in Figure 7 From these results it can be seenthat the proposed controller rapidly steers the system to itsprefault steady state and satisfactorily improves the transientstability of the power system as compared to the conventionalPI controllers
Figure 7 Control response to three-phase fault (a) All generator rotor angle in COI (b) All terminal generator voltage
5 Conclusion
In this paper a new hybrid approach which combines RadialBasis Function (RBF) neural network with the sliding modetechnique has been used to design a Unified Power FlowController (UPFC) for power flow control UPFC sending-end voltage control and DC voltage regulation of an electricpower transmission system The RBF neurosliding modecontrol technique uses online training to get its optimalparameter valuesThe proposed technique is robust and doesnot need the knowledge of the perturbation bounds nor thefull state of the nonlinear system The performance of theproposed controller has been evaluated through simulationson a Kundur power system and compared with a classicalPI controller Simulation results have shown the effectivenessand satisfactory performance of the proposed controller indealing with the perturbations considered Future worksshould be targeted towards the extension of the proposed
hybrid approach to a wide area interconnected power systemfor power oscillation damping
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1(ii) PI controllers parameters are as follows
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
Figure 5 Control response to load variation (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at bus B2(iv) UPFC DC-link voltage (b) (i) Active power at bus B2 (ii) Active power at bus B5 (iii) Reactive power at bus B2 (iv) Reactive power atbus B5
1003816100381610038161003816100381610038161003816100381610038161003816119908119896119895=119908119896119895 if 1003816100381610038161003816100381611990811989611989510038161003816100381610038161003816 lt 119877119908
0 otherwise119895 = 1 119873
120582119909119896 = 120572119909119896 if 119878119909119896 = 00 if 119878119909119896 = 0
(20)
4 Simulation Results
The performance of the proposed nonlinear controlleris evaluated through digital simulations using MATLABSIMULINK software The power system used is a Kundurtwo-area four-machine power system shown in Figure 2 Thedetails of system data and initial operating point are givenin [34] The proposed controller can be applied to a UPFCconnected between any two buses of the power system (with119899 bus) regardless of the interaction between these two busesand other buses Only local measurements information is
required for the implementation of the proposed algorithmThe simulation results of the proposed controller (SNC)are compared with conventional Proportional Integral (PI)controllers used for power flow control UPFC sending-endbus voltage control and DC-link voltage control These clas-sical controllers are tuned using optimal control techniquesand the parameters obtained are given in the Appendix Toevaluate the performance of the proposed controller four setsof simulations have been performed In all simulations theuncertainty factor is set at +10 That is the parameters ofthe system under simulation are set at 110 compared to thesame parameters introduced in the controller
41 Step Changes in Transmission Line Real and ReactivePower Flow References In this case study the initial complexpower flow (119875B3 + 119895119876B3) at the receiving end of the trans-mission line is found as (18 + 11989500) pu A step change inactive power reference from 18 to 22 pu and reactive powerreference from00 to 05 pu of the transmission line take placeat 119905 = 002 s and 032 s respectively The simulation resultsfor this case study are depicted in Figures 3 and 4 It can beseen from these figures that the active and reactive power flowthrough the transmission line the UPFC DC-link voltage
8 Advances in Electrical Engineering
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03
(ii)
0 005 01 015 02 025 03095
1
VB2
(pu)
(iii)
09
1
11
VDC
(pu)
(iv)
REFSNC
18
2
22
PB3
(pu)
0020406
QB3
(pu)
005 01 015 02 025 030Time (s)
(a)
0 005 01 015 02 025 03
(i)
0 005 01 015 02 025 03minus01
minus005
0
Vq_S
H (p
u)
(ii)
0 005 01 015 02 025 030
01
Vd_S
E (p
u)
(iii)
(iv)
02
025
Vq_S
E (p
u)
05
1
15
Vd_S
H (p
u)005 01 015 02 025 030
Time (s)
(b)
Figure 6 Control response to measurement noise (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at busB2 (iv) UPFC DC-link voltage (a) (i) 119863-axis voltage of shunt converter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of seriesconverter (iv) 119876-axis voltage of series converter
and the voltagemagnitude at bus B2 are controlled effectivelyThe results also clearly show that the response speed andtransient conditions are further improved with the proposedcontroller as compared to the conventional PI controllersFigure 4 clearly shows the excellent performance of theUPFCin power flow control under the influence of the proposedcontroller
42 Load Variation In practice the references values of thecontrol power system remain constant and the quantitiesbeing controlled vary under the effect of load variationdisturbance and other perturbations In this case studythe load increases by 20 of its nominal value from 119905 =002 s The simulation results are depicted in Figure 5 Itcan be noticed in these figures that the active and reac-tive power flow through the transmission line the DC-link voltage and the voltage magnitude at bus B2 areall regulated to their respective reference values Figure 5shows that the excess active and reactive power requestedby the load is supplied only by generator G2 The figurealso demonstrates once more the excellent performance ofthe proposed controller in terms of overshot and settlingtime
43 Robustness to Measurement Noise In practice it is notpossible to measure a signal accurately due to the presence
of noise For this reason the third case study investigatesthe robustness of the proposed nonlinear controller withrespect to measurement noise (uncertainties) In this casestudy all simulations are conducted under noise condi-tions in the measured line currents with the magnitudeof the noise reaching about 4 of the maximum valueof the measurable line currents A step change in reac-tive power under the same conditions as in the first casestudy is used to evaluate the robustness of the systemThe simulation results for this case study are depicted inFigure 6 From these results it can be seen that the activeand reactive power flow through the transmission line theUPFC DC-link voltage and the voltage magnitude at busB2 are all regulated to their respective reference valuesdespite the presence of measurement noise Hence it canbe concluded that the controller exhibits an excellent noiseresistance
44 Three-Phase-to-Ground Fault Test In this case study athree-phase-to-ground fault is applied on bus-5 and the faultis cleared after 100ms Simulation results for this case studyare shown in Figure 7 From these results it can be seenthat the proposed controller rapidly steers the system to itsprefault steady state and satisfactorily improves the transientstability of the power system as compared to the conventionalPI controllers
Figure 7 Control response to three-phase fault (a) All generator rotor angle in COI (b) All terminal generator voltage
5 Conclusion
In this paper a new hybrid approach which combines RadialBasis Function (RBF) neural network with the sliding modetechnique has been used to design a Unified Power FlowController (UPFC) for power flow control UPFC sending-end voltage control and DC voltage regulation of an electricpower transmission system The RBF neurosliding modecontrol technique uses online training to get its optimalparameter valuesThe proposed technique is robust and doesnot need the knowledge of the perturbation bounds nor thefull state of the nonlinear system The performance of theproposed controller has been evaluated through simulationson a Kundur power system and compared with a classicalPI controller Simulation results have shown the effectivenessand satisfactory performance of the proposed controller indealing with the perturbations considered Future worksshould be targeted towards the extension of the proposed
hybrid approach to a wide area interconnected power systemfor power oscillation damping
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1(ii) PI controllers parameters are as follows
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
Figure 6 Control response to measurement noise (a) (i) Active power at bus B3 (ii) Reactive power at bus B3 (iii) Voltage magnitude at busB2 (iv) UPFC DC-link voltage (a) (i) 119863-axis voltage of shunt converter (ii) 119876-axis voltage of shunt converter (iii) 119863-axis voltage of seriesconverter (iv) 119876-axis voltage of series converter
and the voltagemagnitude at bus B2 are controlled effectivelyThe results also clearly show that the response speed andtransient conditions are further improved with the proposedcontroller as compared to the conventional PI controllersFigure 4 clearly shows the excellent performance of theUPFCin power flow control under the influence of the proposedcontroller
42 Load Variation In practice the references values of thecontrol power system remain constant and the quantitiesbeing controlled vary under the effect of load variationdisturbance and other perturbations In this case studythe load increases by 20 of its nominal value from 119905 =002 s The simulation results are depicted in Figure 5 Itcan be noticed in these figures that the active and reac-tive power flow through the transmission line the DC-link voltage and the voltage magnitude at bus B2 areall regulated to their respective reference values Figure 5shows that the excess active and reactive power requestedby the load is supplied only by generator G2 The figurealso demonstrates once more the excellent performance ofthe proposed controller in terms of overshot and settlingtime
43 Robustness to Measurement Noise In practice it is notpossible to measure a signal accurately due to the presence
of noise For this reason the third case study investigatesthe robustness of the proposed nonlinear controller withrespect to measurement noise (uncertainties) In this casestudy all simulations are conducted under noise condi-tions in the measured line currents with the magnitudeof the noise reaching about 4 of the maximum valueof the measurable line currents A step change in reac-tive power under the same conditions as in the first casestudy is used to evaluate the robustness of the systemThe simulation results for this case study are depicted inFigure 6 From these results it can be seen that the activeand reactive power flow through the transmission line theUPFC DC-link voltage and the voltage magnitude at busB2 are all regulated to their respective reference valuesdespite the presence of measurement noise Hence it canbe concluded that the controller exhibits an excellent noiseresistance
44 Three-Phase-to-Ground Fault Test In this case study athree-phase-to-ground fault is applied on bus-5 and the faultis cleared after 100ms Simulation results for this case studyare shown in Figure 7 From these results it can be seenthat the proposed controller rapidly steers the system to itsprefault steady state and satisfactorily improves the transientstability of the power system as compared to the conventionalPI controllers
Figure 7 Control response to three-phase fault (a) All generator rotor angle in COI (b) All terminal generator voltage
5 Conclusion
In this paper a new hybrid approach which combines RadialBasis Function (RBF) neural network with the sliding modetechnique has been used to design a Unified Power FlowController (UPFC) for power flow control UPFC sending-end voltage control and DC voltage regulation of an electricpower transmission system The RBF neurosliding modecontrol technique uses online training to get its optimalparameter valuesThe proposed technique is robust and doesnot need the knowledge of the perturbation bounds nor thefull state of the nonlinear system The performance of theproposed controller has been evaluated through simulationson a Kundur power system and compared with a classicalPI controller Simulation results have shown the effectivenessand satisfactory performance of the proposed controller indealing with the perturbations considered Future worksshould be targeted towards the extension of the proposed
hybrid approach to a wide area interconnected power systemfor power oscillation damping
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1(ii) PI controllers parameters are as follows
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
Figure 7 Control response to three-phase fault (a) All generator rotor angle in COI (b) All terminal generator voltage
5 Conclusion
In this paper a new hybrid approach which combines RadialBasis Function (RBF) neural network with the sliding modetechnique has been used to design a Unified Power FlowController (UPFC) for power flow control UPFC sending-end voltage control and DC voltage regulation of an electricpower transmission system The RBF neurosliding modecontrol technique uses online training to get its optimalparameter valuesThe proposed technique is robust and doesnot need the knowledge of the perturbation bounds nor thefull state of the nonlinear system The performance of theproposed controller has been evaluated through simulationson a Kundur power system and compared with a classicalPI controller Simulation results have shown the effectivenessand satisfactory performance of the proposed controller indealing with the perturbations considered Future worksshould be targeted towards the extension of the proposed
hybrid approach to a wide area interconnected power systemfor power oscillation damping
Appendix
Simulation Parameters
(i) The parameters of the UPFC are shown in Table 1(ii) PI controllers parameters are as follows
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
The values of 119908119895 are randomly initialized
Conflicts of Interest
The authors declare that they have no conflicts of interest
References
[1] I Papic P Zunko D Povh and M Weinhold ldquoBasic controlof unified power flow controllerrdquo IEEE Transactions on PowerSystems vol 12 no 4 pp 1734ndash1739 1997
[2] S Kannan S Jayaram andM M A Salama ldquoReal and reactivepower coordination for a unified power flow controllerrdquo IEEETransactions on Power Systems vol 19 no 3 pp 1454ndash14612004
[3] B Lu and B-T Ooi ldquoNonlinear control of voltage-sourceconverter systemsrdquo IEEE Transactions on Power Electronics vol22 no 4 pp 1186ndash1195 2007
[4] A Zangeneh A Kazemi M Hajatipour and S Jadid ldquoA Lya-punov theory based UPFC controller for power flow controlrdquoInternational Journal of Electrical Power amp Energy Systems vol31 no 7-8 pp 302ndash308 2009
[5] B Lei and S Fei ldquoA brand new nonlinear robust control designof SSSC for transient stability and damping improvement ofmulti-machine power systems via pseudo-generalized Hamil-tonian theoryrdquoControl Engineering Practice vol 29 pp 147ndash1572014
[6] J D D Nguimfack-Ndongmo G Kenne R Kuate-Fochie ACheukem H B Fotsin and F Lamnabhi-Lagarrigue ldquoA simpli-fied nonlinear controller for transient stability enhancement ofmultimachine power systems using SSSC devicerdquo InternationalJournal of Electrical Power amp Energy Systems vol 54 pp 650ndash657 2014
[7] A Ajami S H Hosseini S Khanmohammadi and G BGharehpetian ldquoModeling and control of C-UPFC for powersystem transient studiesrdquo Simulation Modelling Practice andTheory vol 14 no 5 pp 564ndash576 2006
[8] A Hamache M O Bensidhoum and H Chekireb ldquoRoRobustsliding mode control of unified power flow controllerfor powerflow trackingrdquo in Proceedings of the 8th International Conferenceon Modelling Identification and Control (ICMIC rsquo16) pp 412ndash417 Algiers Algeria November 2016
[9] A Khodabakhshian M R Esmaili and M Bornapour ldquoOpti-mal coordinated design of UPFC and PSS for improvingpower system performance by usingmulti-objective water cyclealgorithmrdquo International Journal of Electrical Power amp EnergySystems vol 83 pp 124ndash133 2016
[10] S K Routray R K Patnaik and P K Dash ldquoAdaptive non-linear control of UPFC for stability enhancement in a multima-chine power system operating with a DFIG based wind farmrdquoAsian Journal of Control vol 19 no 5 pp 1ndash20 2017
[11] L Saribulut A Teke and M Tumay ldquoDynamic control ofunified power flow controller under unbalanced network con-ditionsrdquo Simulation Modelling Practice and Theory vol 19 no2 pp 817ndash836 2011
[12] A Mohanty S Patra and P K Ray ldquoRobust fuzzy-slidingmode based UPFC controller for transient stability analysis inautonomous wind-diesel-PV hybrid systemrdquo IET GenerationTransmission amp Distribution vol 10 no 5 pp 1248ndash1257 2016
[13] M Fadi A Shameem M Saad A Ibrahim and A H MohdFairuz ldquoPower flow control using fuzzy based UPFC underdifferent operating conditionsrdquo Journal of Electrical Systems vol13 no 2 pp 398ndash414 2017
[14] F M Albatsh S Mekhilef S Ahmad and H Mokhlis ldquoFuzzylogic based UPFC and laboratory prototype validation fordynamic power flow control in transmission linesrdquo IEEE Trans-actions on Industrial Electronics 2017
[15] M Khaksar A Rezvani and M H Moradi ldquoSimulation ofnovel hybrid method to improve dynamic responses with PSSand UPFC by fuzzy logic controllerrdquo Neural Computing andApplications 2016
[16] M E A Farrag and G Putrus ldquoAn on-line training radial basisfunction neural network for optimum operation of the UPFCrdquoEuropean Transactions on Electrical Power vol 21 no 1 pp 27ndash39 2011
[17] N Zeb B Khan S M Ali et al ldquoAdaptive controller basedunified power flow control for low power oscillation dampingrdquoAsian Journal of Control vol 20 no 1 pp 1ndash10 2017
[18] M J Rana M S Shahriar and M Shafiullah ldquoLevenbergndashMarquardt neural network to estimate UPFC-coordinated PSSparameters to enhance power system stabilityrdquoNeural Comput-ing and Applications 2017
[19] Q Zhu S Fei T Zhang and T Li ldquoAdaptive RBF neural-networks control for a class of time-delay nonlinear systemsrdquoNeurocomputing vol 71 no 16ndash18 pp 3617ndash3624 2008
[20] J Liu Radial Basis Function (RBF) Neural Network Control forMechanical Systems Design Analysis and Matlab SimulationSpringer Heidelberg Germany 2013
[21] C C Hua C X Yu and X P Guan ldquoNeural network observer-based networked control for a class of nonlinear systemsrdquoNeurocomputing vol 133 pp 103ndash110 2014
[22] S Mishra ldquoNeural-network-based adaptive UPFC for improv-ing transient stability performance of power systemrdquo IEEETransactions on Neural Networks and Learning Systems vol 17no 2 pp 461ndash470 2006
[23] S Tiwari R Naresh and R Jha ldquoNeural network predictivecontrol of UPFC for improving transient stability performanceof power systemrdquo Applied Soft Computing vol 11 no 8 pp4581ndash4590 2011
[24] C M Yam andM H Haque ldquoA SVD based controller of UPFCfor power flow controlrdquo Electric Power Systems Research vol 70no 1 pp 76ndash84 2004
[25] M A Sayed and T Takeshita ldquoAll nodes voltage regulationand line loss minimization in loop distribution systems usingUPFCrdquo IEEE Transactions on Power Electronics vol 26 no 6pp 1694ndash1703 2011
[26] M E Elgamal A Lotfy and G E M Ali ldquoVoltage profileenhancement by fuzzy controlled MLI UPFCrdquo InternationalJournal of Electrical Power amp Energy Systems vol 34 no 1 pp10ndash18 2012
Advances in Electrical Engineering 11
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
[27] H Chen Y Wang and R Zhou ldquoTransient stability enhance-ment via coordinated excitation and UPFC controlrdquo Interna-tional Journal of Electrical Power amp Energy Systems vol 24 no1 pp 19ndash29 2002
[28] H Fujita Y Watanabe and H Akagi ldquoTransient analysis of aunified power flow controller and its application to design ofthe dc-link capacitorrdquo IEEE Transactions on Power Electronicsvol 16 no 5 pp 735ndash740 2001
[29] I AxenteM Basu andM F Conlon ldquoDc link voltage control ofUPQC for better dynamic performancerdquo Electric Power SystemsResearch vol 81 no 9 pp 1815ndash1824 2011
[30] T Ahmed-Ali G Kenne and F Lamnabhi-Lagarrigue ldquoIden-tification of nonlinear systems with time-varying parametersusing a sliding-neural network observerrdquo Neurocomputing vol72 no 7-9 pp 1611ndash1620 2009
[31] G Kenne A S Fotso and F Lamnabhi-Lagarrigue ldquoA newadaptive control strategy for a class of nonlinear system usingRBF neuro-sliding-mode technique application to SEIG windturbine control systemrdquo International Journal of Control vol 90no 4 pp 855ndash872 2017
[32] A K Jain and R C Dubes Algorithms for Clustering DataPrentice Hall 1988
[33] D Luenberger Linear and Nonlinear Programming Addison-Wesley Publishing Company Reading Mass USA 1984
[34] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994
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