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1
ABSTRACT
A Shunt Active Power Filter(APF) is a device that is connected in parallel to group
of loads.APF cancels the reactive and harmonic currents drawn by the load so as to make
supply current sinusoidal. Active Power Filter play a vital role in present day liberalized
energy market. Active Power Filter are explored for executing different power conditioning
function simultaneously along with harmonic elimination due to increase in nonlinear and
unbalanced load, at the point of common coupling. The aim of present dissertation is to
study different control strategies for Active Power Filter. More importantly to study
instantaneous power theory based Shunt Active Power Filter which is predominantly used in
present scenario. The shunt active power filter is investigated through Matlab/Simulink
simulation under different load conditions. Simulation results are discussed in depth. Then
the design issues of Active Power Filter for different load conditions are also discussed.
2
CHAPTER 6
SIMULATION DESIGN
The p-q theory based shunt APF is implemented for Harmonic compensation and power
factor correction. Logic utilized for shunt APF is discussed in chapter 5 and is summarized
in fig.5.2
6.1 Specification of the design:
Simulation is performed on 2 types of Three phase Balanced Non –Linear Load as
fallows:
System Parameters
Source Voltage 220 (line- line)
System Frequency 60 Hz
APF
Dc-link voltage 800V
Dc side capacitance C 1100
Ac side inductance 3.75mH
Ac side resistance 0.01 Ω
(Rating of APF is generally decided by peak voltage and RMS Current)
Load 1 Thyristor Rectifier (of rating 4 KVA)supplying to DC motor equivalent of 2.5KW
AC side inductance 1mH
AC side resistance 0.01 Ω
3
DC side Resistance 18 Ω
DC side Inductance 85mH
Load2 Diode rectifier (of rating around 3KVA) supplying to purely resistive load
AC side inductance NA
AC side resistance NA
DC side Resistance 18 Ω
DC side Inductance NA
(NOTE: Rating of APF is generally decided by peak voltage and RMS Current[14]
APF rating for Load1 is will result in rating of
.Thus in practical cases can be assumed to be around 1-1.5KVA}.
4
220
V rm
s L-L
3-ph
ase
Sour
ce
PI c
ontro
ller
Low
Pass
FIlt
er
Curre
nt m
easu
rem
ent
Volta
ge m
easu
rem
ent
RcLc
Cont
inuo
us
pow
ergu
i
A B C non-
linea
r loa
d curre
nt m
easu
rem
ent1
v+-
v+-
VcVbVa
Valp
ha
Vbet
a
pdc
plos
s
Isal
fa
Isbe
taIn
1
In2O
ut1
Load
Cur
rent
mea
sure
men
t
Isal
pha
Isbe
ta
Ia*
Ib*
Ic*
Inve
rse T
rans
form
atio
n
Isa*
Isb*
Isc*
Isa
Isb
Isc
A1 A2 B1 B2 C1
C2
Hyste
risis
Band
Cur
rent
Con
trolle
r
[Vdc
]G
oto7
[isc]
[Vsc
][V
sb]
[isb]
[isa]
[Vsa
]
[Vdc
]
[isc]
[isb]
[isb][isa]
[isc]
[Vsb
]
[Vsa
]
[Vsc
]
[isa]
i+
- i+
-
i+
-
i+
-
i+
-
i+
-
i+
-i+
-i+
-
800
g11
g12
g21
g22
g31
g32
Vdc
a b c
Com
pens
ator
Vsa
Vsb
Vsc
Isa
Isb
Isc
Valp
ha
Vbet
a p
Clar
ke T
rans
form
atio
n
Capa
cito
r vol
tage
butte
r
v+-
Fig 6.1 p-q theory based control block diagram of three-phase shunt APF system.
5
6.2 Clark Transformation:
is done in accordance with section 4.2.2
Fig 6.2 Block Diagram for Clark Transformation and p calculation
Fig 6.3 Clark transformation block diagram for both
3
p
2
Vbeta
1
Valpha
Vbeta
Ibeta
Valpha
Ialpha
p
Subsystem5
a
b
c
alpha
beta
Subsystem2
a
b
c
alpha
beta
Subsystem1
6
Isc
5
Isb
4
Isa
3
Vsc
2
Vsb
1
Vsa
2
beta
1
alpha
Sum of
Elements1
Sum of
Elements
-K-
K=sqrt(2/3)
-K-
K=sqrt(2/3)
-K-
K=-1/2
-1
1
1
-K-
K=-1/2
3
c
2
b
1
a
6
6.3 Calculation of
According p-q theory real and imaginary power can be separated into two parts:
Real power:
Imaginary power: (from eq)
and are average power due to component respectively
and are oscillating power due to components respectively.
And will produces a purely sinusoidal waveform. But in order to
achieve unity power factor APF must compensate for from component . Thus,
will produce purely sinusoidal waveform with unity power factor.
Thus, inverse transformation will produce reference current for each
phase. can deduced from which is filtered out using low pass filter from p.
Fig 6.4 Block diagram for calculation of p
1
p
Product1
Product
4
Ialpha
3
Valpha
2
Ibeta
1
Vbeta
7
Fig 6.5 from using Low Pass filter
6.4 DC-Bus Voltage Control
Under a loss free situation, the shunt APF need not provide any active power
to cancel the reactive and harmonic currents from the load. These currents show up as
reactive power. Thus, it is indeed possible to make the DC-bus capacitor delivers the
reactive power demanded by the proposed shunt APF. As the reactive power comes from the
DC-bus capacitor and this reactive energy transfers between the load and the DC-bus
capacitor (charging anddischarging of the DC-bus capacitor), the average DC-bus voltage
can be maintained at a prescribed value.
However, due to switching loss, capacitor leakage current, etc., the distribution
source must provide not only the active power required by the load but also the additional
power required by the VSI to maintain the DC-bus voltage constant. Unless these losses are
regulated, the DC-bus voltage will drop steadily.
A PI controller used to control the DC-bus voltage is shown in Figure6.6. Its transfer
function can be represented as
where is the proportional constant that determines the dynamic response of the
DC-bus voltage control, and is the integration constant that determines its settling time.
Fig 6.6 PI controller for DC-bus voltage control
(Note: )
It can be noted that if and are large, the DC-bus voltage regulation is dominant, and
the steady-state DC-bus voltage error is low. On the hand, if and are small, the real
1
ploss
Subtract
PID
PID Controller
2
constant
1
Vdc
8
power unbalance give little effect to the transient performance. Therefore, the proper
selection of and is essentially important to satisfy above mentioned two control
performances.
6.5Reference Current Calculation:
Reference Currents are calculated from inverse clark transformation.
Fig 6.7 Block diagram for calculation of
Fig 6.8 Reference Current calculation
2
Isbeta
1
Isalfa
Product3
Product2
Product1
Product
Divide1
Divide
4
ploss
3
pdc
2
Vbeta
1
Valpha
3
Ic*
2
Ib*
1
Ia*
Subtract
-K-
Gain3
-K-
Gain2
-K-
Gain1
-K-
Gain
2
Isbeta
1
Isalpha
9
6.6 Hysteresis Band Current Controller:
It is introduced in chapter 3 section 3.5.2
Fig 6.9 Hysteresis Band Current Controller
Actual source currents ( ) are compared with the reference currents
generated by the control algorithm in the hysteresis-band current controller. Three
hysteresis-band current controllers generate the switching pattern of the VSI. The switching
logic is formulated as follows
If < ( HB) higher switch is OFF and lower switch is ON for leg “A” (QA=1)
If > ( + HB) higher switch is ON and lower switch is OFF for leg “A” (QA=0).
The switching functions of QB and QC for legs „„B‟‟ and „„C‟‟ are determined similarly,
using corresponding reference and measured currents and hysteresis bandwidth (HB). The
hysteresis-band current control is the fastest control method with minimum hardware and
software but variable switching frequency is its main drawback
6
C2
5
C1
4
B2
3
B1
2
A2
1
A1
Subtract3
Subtract2
Subtract1
Relay3
Relay2
Relay1
NOT
Logical
Operator2
NOT
Logical
Operator1
NOT
Logical
Operator
6 Isc
5 Isb
4 Isa
3
Isc*
2
Isb*
1
Isa*
10
6.7 Compensator:
Switching is done according to gating signals from Hysteresis Band Current Controller.
Capacitor Voltage is continuously measured and fed to PI controller as explained earlier.
Fig 6.10 Compensator
1
Vdc
3
c
2
b
1
a
v+-
Voltage Measurement3
gm
12
gm
12
gm
12
gm
12
gm
12
gm
12
C
6 g32
5 g31
4 g22
3 g21
2 g12
1 g11
11
6.8 Non-Linear Loads
Case:1 Thyristor Converter Supplying to DC motor equivalent
Fig6.11 Block Diagram for Thyristor Converter controlled DC motor
Using PI controller DC motor current value is maintained at 20 Amps. PI controller varies
alpha of thyristor until motor current matches reference current. Pulse width is takes as .
Synchronization Voltages
DC motor equivalent circuit
PI Curent Regulator
LlacRlac
3 C
2 B
1 A
v+-
Vca
v+-
Vbc
v+-
Vab
g
A
B
C
+
-
Thyristor Converter
alpha_deg
AB
BC
CA
Block
pulses
Synchronized
6-Pulse Generator
1
s
Id_Refence
i+
-
Id
5
100
90
0
12
case2:Diode Rectifier supplying to pure resistive load
Fig 6.12 Block diagram for Diode rectifier supplying to pure Resistive Load
A pure resistive load is taken in order to APF performance. As in this load phase current
varies in abrupt manner on the contrary to RL load where load phase current is smooth
varying curve.
3 C
2 B
1 A
Diode5
Diode4
Diode3
Diode2
Diode1
Diode
13
CHAPTER 7
SIMULATION RESULTS
7.1 Case 1: Thyristor converter supplying to DC motor Equivalent(R-L Type Load)
FiFig 7.1 Source Voltages and Load Currents with APF(Case 1)
14
Fig 7.2 Harmonic Analysis of Load Current with APF(Case 1)
Fig 7.3 Reference Current (Case 1)
15
Fig 7.4 Source Current with APF(Case 1)
Fig 7.5 Compensating Current and Load Current(Case 1)
16
Fig 7.6 Source Voltage and Source Current with APF(Case 1)
17
Fig7.7 Harmonic Analysis of Source Current (Case 1)
18
Fig7.8 DC Capacitor Voltage for three-phase APF(Case 1)
19
7.2 Case 2: Diode Rectifier supplying to pure resistive
Fig 7.9 load Source Voltage & Load Current with APF
20
Fig 7.10 Harmonic Analysis of Load Current
21
Fig 7.11 Source Current after Compensation(Case 2)
Fig 7.12 Compensating Current and Load Current(Case 2)
22
Fig 7.13 Source Voltages and Source Current(Case 2)
23
Fig 7.14 Harmonic analysis of Source Current(Case 2)
24
Fig 7.15 DC Capacitor voltage for three-phase APF(Case 2)
25
7.3 Simulation Result Discussion:
As the source current and voltage are in phase,also the source current is almost
sinusoidal(very low THD) it can be said that source is providing only active power required
by the circuit. In instantaneous power theory view, source current is providing only average
real power component( ) while remaining components i.e real oscillating power( ),
imaginary average power( ) and imaginary oscillating power( ), is being provided by
Shunt APF.(see Discussion in section 6.3 )
From source currents and THD in case1 (RL load) and case 2 (purely resistive load
)it can be said that the effectiveness of the active filter in compensating for harmonic
components of the load current depends on the specific load current waveform involved.
Two different waveforms may have the same rms harmonic content but the active filter may
do a better job of compensating for one of the waveforms because of the waveshapes
involved. Source current has very less THD in case of RL load compared to purely resistive
one. Thus it can be inferred performance of shunt APF with RL load is much better than
purely resistive load.
In general, the current waveform of an ac regulator with resistive load is an example
of the waveshape that poses the severest challenge for an active filter. The problem is the
high di/dt that is required of the filter to compensate for the high di/dt at turn on of the
regulator. The problem is most severe when the regulator is turned on with a firing angle
close to 90 degrees because this is when the available driving voltage stored on the dc
capacitor is at a minimum. The output di/dt capability can be raised either by increasing the
dc voltage setting or by reducing the size of the interfacing inductance. The limiting factor
for increasing the dc voltage is the voltage withstand capability of the IGBT devices. The
limiting factors for reducing the interfacing inductance include the IGBT di/dt withstand
capability, control requirements, the interface passive filter requirement, and overall system
stability. If the interfacing inductance becomes too small, the dc voltage cannot be kept
constant for normal operation.
From harmonics analysis of Source Current it can be seen due to uneven switching
of compensator large number of interharmonics are introduced. But,it should be noted that
26
those components have very less magnitude.(Maximum magnitude of interharmonic is 0.11
% in case 1)
Using PI Controller DC capacitor is maintained at reference value. It was seen that
Settling time improved drastically using PI controller.
It is worth to also to note that p-q based APF can be used for complete harmonic
elimination not selective harmonic elimination.
7.4 Future Scope
As p-q theory can be implemented in three-phase with excellent results in terms of
THD, transient response, reference current generation. The work on extending use of p-q
theory in single phase APF is being done[13].
Switching required in APF is very high in order of 10 kHz. Resulting in appreciable
amount of power. Thus, one can further work on to reduce switching frequency and to
switching losses.
One can also work on linear control technique to replace hysteresis band controller
.So, that irregular switching in compensator can be removed.
Study of Control system of APF is also a possibility n order to get lesser steady state
error and improved settling time. Most importantly to study various APF techniques and
comparing them in terms of dynamic response, performance under various type of load, total
harmonic compensation is to be done.
27
CHAPTER 8
CONCLUSION
The validity in terms of eliminating p-q theory in terms of eliminating harmonics and power
factor improvement is confirmed from low THD source current which is in phase with source
voltage. But p-q theory utilizes large number of sensors and reference current calculation block.
Large number of calculation in p-q theory demands higher processing power. Resulting in utility to
be complex and expensive. The p-q theory base APF is predominantly utilized in three phase circuits
thus can not be used at remote single phase customer. As a result, Harmonics are present in large part
of system. From source currents of the both cases (i.e. RL Load and purely resistive load) it can be
inferred that APF is most effective when the load current waveform does not have abrupt changes.
The overall filtering effectiveness depends significantly on the types of loads being compensated. As
a result, it is very effective for most voltage source inverter-type loads, even when the distortion is
high.
From comparing reference current and source waveforms it can be concluded that hysteresis
band current controller done the compensation at the cost of high switching frequency. Which can
result in high switching losses in practical high power APF applications. PI controller performance is
also validated from the DC-bus capacitor voltage which shows decreased settling time.
In theoretical view p-q theory has some shortcomings which need to be addressed. Like
mathematical expression of instantaneous power does not fallow power conservation and real and
imaginary power needed to be more accurately defined as zero sequence instantaneous power can
not be defined by the theory. In practical approach also it can be noted that p-q theory is incapable of
providing selective harmonic elimination and specific power factor compensation.
28
References
1.H. Akagi, Y. Kanazawa and A. Nabae, "Generalized Theory of Instantaneous Reactive
Power and Its Applications," Transactions of he lEE-Japan, Part B, vol. 103, no.7, 1983, pp.
483-490
2.Power Quality C.Sankaran
3.H. Akagi. “New trends in active filters for power conditioning”, IEEE Trans. on Industry
Applications, vol. 32, pp. 1312-1322, (1996).
4. Das, J. C. Passive Filters – Potentialities and Limitations. IEEE Trans. On Industry
Applications. 2004. 40(1): 232-241.
5. Power Electronics Handbook CRC PRESS
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IEE Electric Power Applications. 2000. 147(5): 403-413.
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Portugal: IEEE. 1997. 302-307.
8.Chen, C. L., Chen, E. L., and Huang, C. L. An Active Filter for Unbalanced
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the Power Electronics Specialist Conference (PESC). June 20-25, 1994.
Taipei, Taiwan: IEEE. 1994. 1451-1455.
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10.Textook of “Modern Power Electronics and AC Drives”, B.K.Bose
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IEEE
29
12.Instanteneous Power Theory and applications to power conditioning, IEEE Press, H.
Akagi, E. H. Watanabe, M. Aredes.
13. M. Tarafdar Haque “SINGLE-PHASE PQ THEORY”, IEEE Trans.
14 “Active filter design and specification for control of harmonics in industrial and
commercial facilities”, Mark McGranaghan Electrotek Concepts, Inc.
30