Performance Investigation of Shunt Active Power Filter Using Hysteresis Current Control Method

Performance Investigation of Shunt Active Power Filter Using Hysteresis
Current Control Method
VIKASH ANAND
M.Tech. (Power Electronics & Drives)
Electrical Engineering Department
Madan Mohan Malviya Engineering College
Gorakhpur-273010(U.P), India
Dr. S. K. SRIVASTAVA
Associate Professor
Electrical Engineering Department
Madan Mohan Malviya Engineering College
Gorakhpur-273010 (U.P),India
ABSTRACT
The simulation study of PI Controlled, three phase
shunt active power filter to improve power quality by
compensating harmonics and reactive power required
by a non-linear load is presented. The shunt active
filter employs a simple method for the reference
compensation current based on Fast Fourier
Transform. Classic filters may not have satisfactory
performance in fast varying conditions. But auto
tuned active power filters give better results for
harmonics minimization, reactive power
compensation and power factor improvement. This
paper has proposed an auto tuned shunt active filter,
which maintains the THD well within the IEEE-519
standards. The results are found to be quite
satisfactory to mitigate harmonic distortion, reactive
power compensation and power factor improvement.
KEYWORDS
Power System, Shunt Active Filter, PI Controller,
Hysteresis Current Pulse Width Modulation.
1. INTRODUCTION
Harmonics contamination is a serious and a harmful
problem in Electric Power System. Active Power
filtering constitutes one of the most effective proposed
solutions. A shunt active power filter that achieves low
current total harmonic distortion (THD), reactive power
compensation and power factor correction is presented.
Hence, it is necessary to reduce the dominant
harmonics below 5% as specified in IEEE-519-1992
harmonic standard [1].
Harmonic Amplification is one the most serious
problem. It is caused by harmonic resonance between
line inductance and power factor correction (PFC)
capacitors installed by consumers. Active filters for
damping out harmonic resonance in industrial and
utility power distribution systems have been researched
[1]-[5].
Traditionally based, passive L-C filters were used to
eliminate line harmonics in [2]-[4]. However, the
passive filters have the demerits of fixed compensation,
bulkiness and occurrence of resonance with other
elements. The recent advances in power semiconductor
devices have resulted in the development of Active
Power Filters (APF) for harmonic suppression. Various
topologies of active filters have been proposed for
harmonic mitigation. The shunt APF based on Voltage
Source Inverter (VSI) structure is an attractive solution
to harmonic current problems. The SAF is a pulse width
modulated (PWM) VSI that is connected in parallel
with the load. It has the capability to inject harmonic
current into the AC system with the same amplitude but
opposite phase than that of the load [1]-[2]. The
principal components of the APF are the VSI, a DC
energy storage device that in this case is capacitor, a
coupling transformer and the associated control circuits.
The performance of an active filter depends mainly on
the technique used to compute the reference current and
the control method used to inject the desired
compensation current into the line.
There are two major approaches that have emerged for
the harmonic detection [2], namely, time domain and
the frequency domain methods. The frequency domain
methods include, Discrete Fourier Transform (DFT),
Fast Fourier Transform (FFT), and Recursive Discrete
Fourier Transform (RDFT) based methods. The
frequency domain methods require large memory,
computation power and the results provided during the
transient condition may be imprecise [4]. On the other
hand, the time domain methods require less calculation
and are widely followed for computing the reference
current.
International Journal of Engineering Research & Technology (IJERT)
Vol. 1 Issue 4, June - 2012
ISSN: 2278-0181
1www.ijert.org

There are several current control strategies proposed in
the literature [5]-[7], [8]-[9], namely, PI control,
Average Current Mode Control (ACMC), Sliding Mode
Control (SMC) and hysteresis control. Among the
various current control techniques, hysteresis control is
the most popular one for active power filter
applications. Hysteresis current control [6] is a method
of controlling a voltage source inverter so that the
output current is generated which follows a reference
current waveform in this paper. Generally, PI controller
[7] is used to control the DC bus voltage of SAF. The
PI controller based approach requires precise linear
mathematical model.
This chapter basically deals with the modeling and
design of shunt active power filter for compensation of
harmonics and reactive power. Designs of different
parameters like power circuit, control circuit, control
strategies, EMI/ Ripple factor are discussed.
2. Basic Compensation Principle
Fig.1 shows the basic compensation principle of shunt
active power filter. A voltage source inverter (VSI) is
used as the shunt active power filter. This is controlled
so as to draw or supply a compensating current Ic from
or to the utility, such that it cancels current harmonics
on the AC side i.e. this active power filter (APF)
generates the nonlinearities opposite to the load
nonlinearities [3].
Fig.1 Basic compensation principle
Fig.2 Waveform for actual load current (A), desired source
current (B) and the compensating filter current (C).
Fig.3 Single line diagram of the shunt active power filter
showing power flow
Total instantaneous power drawn by the nonlinear load
can be represented as:-
pL(t) = fp ( )t + rp ( )t + hp ( )t
Where,
pf(t) - instantaneous fundamental (real) power absorbed
by the load,
pr(t) – instantaneous reactive power drawn by the load,
and
ph(t) – instantaneous harmonic power drawn by the
load.
In order to achieve unity power factor operation and
drawing sinusoidal currents from the utility, active
power filter must supply all the reactive and harmonics
power demand of the load. At the same time, active
filter will draw real component of power (PLoss) from
the utility, to supply switching losses and to maintain
the DC link voltage unchanged.
Power components (reactive and the harmonic) should
be supplied by the active power filters i.e.
cp ( )t = rp ( )t + hp ( )t
2.1 Estimation of Reference Source Current
From the single line diagram shown in fig.3
is(t) = iL(t) - ic(t) (1)
Where,
is(t), iL(t), ic(t) are the instantaneous value of source
current, load current and the filter current.
And the utility voltage is given by
vs(t) = mV sinωt (2)
Where,
vs(t) – is the instantaneous value of the source voltage,
Vm - is the peak value of the source voltage.
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If non-linear load is connected then the load current will
have a fundamental component and the harmonic
components which can be represented as –
iL(t) = n n
n=1
I sin(nωt + )


1 1I sin(ωt + ) + n n
n=2
I sin(nωt + )

 (3)
Where, I1 and  1 are the amplitude of the fundamental
current and its angle with respect to the fundamental
voltage, and
In and n are the amplitude of the nth harmonic current
and its angle.
Instantaneous load power Lp (t) can be expressed as–
L Lsp (t) = v (t) i (t)
= mV sinωt 1 1I sin(ωt + ) +
mV sinωt n n
n=2
I sin(nωt + )


= fp ( )t + rp ( )t + hp ( )t (4)
= fp ( )t + cp ( )t (5)
In the equation (4) and (5)
fp ( )t is the real power (fundamental),
rp ( )t represents the reactive power and
hp ( )t represents the harmonic power drawn by the load.
For ideal compensation only the real power
(fundamental) should by supplied by the source while all
other power components (reactive and the harmonic)
should be supplied by the active power filters i.e.
cp ( )t = rp ( )t + hp ( )t
.
The total peak current supplied by the source
Imax = Ism + IsL (6)
Where, Ism = I1 1cos
and IsL is the loss component of current drawn from the
source.
If active power filter provide the total reactive and
harmonic power, then is(t) will be in phase with the
utility and pure sinusoidal. At this time, the active filter
must provide the following compensation current:
Ic(t) = IL(t) – is(t) (7)
Hence, for the accurate and instantaneous compensation
of reactive and harmonic power it is very necessary to
calculate the accurate value of the instantaneous current
supplied by the source.
Is(t) = Imax sinωt (8)
Where, Imax (= I1 1cos + IsL) is the amplitude of the
desired source currents. The phase angles can be
obtained from the source voltages. Hence, the
waveform and phases of the source currents are known
and only the magnitude of the source currents needs to
be determined.
The peak value or the reference current Imax is
estimated by regulating the DC link voltage of the
inverter. This DC link voltage is compared by a
reference value and the error is processed in a PI
controller. The output of the PI controller is
considered as the amplitude of the desired source
currents and the reference currents are estimated by
multiplying this peak value with the unit sine vectors
in phase with the source voltages.
2.2 Design of Shunt Active Power Filter
The shunt active power filter mainly consists of DC
link capacitor, filter inductor, PI controller and the
hysteresis controller.
2.2.1 DC Link Capacitor
The DC link capacitor mainly serves two purposes-
(a) It maintains almost a constant DC voltage.
(b) It serves as an energy storage element to supply
real power difference between load and source during
transients.
In this scheme the role of the DC link capacitor is to
absorb/supply real power demand of the load during
transient. Hence the design of the DC link capacitor is
based on the principle of instantaneous power flow.
Equalizing the instantaneous power flow on the DC
and AC side of the inverter considering only
fundamental component [3].
Vdc Idc = vca(t) ica(t)+ vcb(t) icb(t)+vcc(t) icc(t) (9)
Assuming that three phase quantities are displaced by
1200
with respect to each other,  is the phase angle
by which the phase current lags the inverter phase
voltage, and 2 Vc and 2 Ic are the amplitudes of
the phase voltage and current, respectively of the input
side of the inverter.
Vdc Idc = 2Vca Ica sin ω1t sin (ω1t-  a) + 2Vcb Icb sin
(ω1t-1200
) sin (ω1t -1200
-  b) + 2Vcc Icc sin (ω1t
+1200
) sin (ω1t +1200
-  c) (10)
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Case I: If the three phase system is balanced-
Then, Vca = Vcb = Vcc = Vc
Ica = Icb = Icc = Ic, and
 a =  b =  c = 
Hence,
Vdc Idc = 3 Vc Ic cos (11)
i.e. the DC side capacitor voltage is a DC quantity and
ripple free.
Case II: If the three phase system is unbalanced-
Vdc Idc =(Vca Ica cos a + Vcb Icb cos b + Vcc Icc cos c) -
[Vca Ica cos (2ω1t- a) + Vcb Icb cos (2ω1t - 2400
-  b) +
Vcc Icc cos (2ω1t + 2400
-  c)] (12)
The above equation shows that the first term is a dc
component, which is responsible for the power transfer
from dc side to the AC side. Here it is responsible for
the loss component of the inverter and to maintain the
DC side capacitor voltage constant.
The peak to peak ripple voltage is given by–
Vpp = π * Ipp * Xc = (π * Ipp) / (ω * Cf) (13)
Where, Ipp is the peak to peak second harmonic ripple
of the DC side current. Assuming that Vpp is much less
than Vdc then using equations (14) and (15) the
maximum value of the Vpp can be obtained as-
Vpp = (π * Ic1, rated) / ( 3 ω * Cf) (14)
Case III: Since the total load power is sum of the
source power and compensator power (i.e. PL = Pc +
Ps), so that when load change takes place, the changed
load power must be absorbed by the active power filter
and the utility i.e.
 PL =  Pc +  Ps (15)
Hence, selection of capacitor value Cf can be governed
by reducing the voltage ripple. As per the specification
of Vpp, max and Ic1, rated the value of the capacitor can be
found from the following equation –
Cf = (π * Ic1, rated) / ( 3 ω * Vpp, max) (16)
It is observed that the value of Cf depends on the
maximum possible variation in load and not on the
steady state value of the load current. Hence, proper
forecasting in the load variation reduces the value of Cf.
2.2.2 Selection of Lc and Reference Capacitor
Voltage (Vdc,ref)
The design of these components is based on the
following assumptions:
(a) The AC source voltage is sinusoidal.
(b) For Lc, the AC side line current distortion is
assumed to be 5%.
(c) Reactive power compensation capability of the
active filter.
(d) The PWM converter is assumed to operate in the
linear modulation mode (i.e 0  ma  1).
For satisfactory operation the magnitude of Vdc,ref
should be higher than the magnitude of the source
voltage Vs. By suitable operation of switches a voltage
Vc having fundamental component Vc1 is generated at
the ac side of the inverter. This results in flow of
fundamental frequency component Is1, as shown in
fig.4.The phasor diagram for Vc1>Vs representing the
reactive power flow is also shown in this figure. In this
Is1 represent fundamental component [3]-[11].
Fig.4 Single line and vector diagrams for shunt APF
As per the compensation principle active power filter
adjusts the current Ic1 to compensate the reactive power
of the load. In order to maintain Is1 in phase with Vs,
active filter should compensate all the fundamental
reactive power of the load. The vector diagram
represents the reactive power flow in which Is1 is in
phase with Vs and Ic1 is orthogonal to it.
Form the vector diagram,
Vc1 = Vs + jω Lf Ic1 (17)
i.e. to know Vc1 it is necessary to know Ic1
Ic1 =
c1 s
f
V - V
ωL
=
c1 s
f c1
V V
1-
ωL V
 
 
 
(18)
Now the three phase reactive power delivered from the
active power filter can be calculated from the vector
diagram as –
Qc1 = QL1 = 3 Vs Ic1 = 3 Vs
c1 s
f c1
V V
1-
ωL V
 
 
 
(19)
From these equations
If Vc1 > Vs, Qc1 is positive.
If Vc1 < Vs, Qc1 is negative.
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i.e. active power filter can compensate the lagging
reactive power from utility only whenVc1>Vs.
From[11], If the inverter is assumed to operate in the
linear modulation mode i.e. modulation index varies
between 0 and 1, then the amplitude modulation index
is given by-
ma =
c1
dc
2 2V
V
(where, Vm= 2 Vc ) (20)
And the value of Vdc is taken as
Vdc = 2 2 c1V (for ma =1) (21)
The filter inductor Lf is also used to filter the ripples of
the inverter current,and hence the design of Lf is based
on the principle of harmonic current reduction.The
ripple current of the inverter can be given in terms of
the maximum harmonic voltage, which occurs at the
frequency mfω.
Ich(mfω) = (22)
Where,mf is the frequency modulation ratio of PWM
converter.
On solving (19) and (22) simultaneously, the value of
Lf and Vc1(i.e Vdc) can be calculated. Vc1 and Vdc ref,
must be set according to the capacity requirement of the
system (i.e Vs< Vc1  2Vs ).As the switching frequency
is not fixed with the hysteresis controller, a practically
feasible value of 10kHz has been assumed.
2.3 PI Controller
The controller used is the discrete PI controller that
takes in the reference voltage and the actual voltage and
gives the maximum value of the reference current
depending on the error in the reference and the actual
values. The mathematical equations for the discrete PI
controller are:
The voltage error V (n) is given as:
V (n) =V*(n) - V (n)
The output of the PI controller at the nth instant is given
as:
I(n)=I(n-1) + Kp[V(n)-V(n-1)] + Ki V(n)
2.4 Hysteresis Current Controller
With the hysteresis control, limit bands are set on either
side of a signal representing the desired output
waveform. The inverter switches are operated as the
generated signals within limits. Hysteresis-band PWM
is basically an instantaneous feedback control method
of PWM where the actual signal continually tracks the
command signal within a hysteresis band [10].
Fig.5 Basic principle of hysteresis band control
The rate of change of inductor current is then given by
(23)
Making assumption that the ac supply does not change
during a cycle of switch operations, the time taken t
m
taken to cross a dead band is
(24)
The switching frequency f
sw
is, therefore variable.
Combining above two equations (23) and (24) to obtain
the switching period, and inverting, gives
3. Simulation And Performance
Investigation Of Shunt APF
In this section the simulation analysis of shunt APF is
described, first for R-L load and then for DC machine
load and the FFT analysis has been carried out
simultaneously.
3.1 Operation of Simulation Model
The operation of the simulation model shown below is
described as – first the capacitor voltage is sensed which is
compared with the reference voltage and the error signal is
given to the PI controller for processing to obtain the
maximum value (Im) of the reference current which is
multiplied with the unit vector template i.e. sinωt to get the
reference current Im sinωt for phase a. This signal is now
delayed by 1200
for getting the reference current for phase
b, which is further delayed by 1200
to get the reference
current for the phase c. these reference currents are now
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compared with the actual source currents and the error is
processed in the hysteresis controller to generate the firing
pulses for the switches of the inverter. And the switches
are turned on and off in such a way that if the reference
current is more than the actual source current then the
lower switch is turned on and the upper switch is turned off
and if the reference current is less than the actual source
current then the upper switch of the same leg is turned on
and the lower switch is turned off. The output of the shunt
active power filter is such that the source current is purely
sinusoidal and the harmonic current is drawn or supplied
by the filter.
Fig.6 MATLAB model for Shunt active power filter
3.2 Simulation Result And Discussion
Fig.7 Three phase supply voltages
The waveform shown in fig.7 demonstrates that supply
voltage is almost sinusoidal of Vpeak=100 volt in phase 0,-
120 and +120 degree of a, b and c phase respectively.
Fig.8 Load current
The waveform shown in fig.8 demonstrates that load
current is in sinusoidal nature with containing small
amount harmonic .
Fig.9 Source current before and after compensation
The waveform shown in fig.9 demonstrates that source
current before compensation (i.e from 0 to 0.1 sec.) and
after compensation (i.e from 0.1 sec.), it is almost
sinusoidal with reduced harmonic content.
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Fig.10 Source voltage, source current and filter current for
phase A
The waveform shown in fig.10 demonstrates that source
voltage, source current before and after compensation
and filter current for phase A.
Fig.11 Capacitor voltage and capacitor current
The waveform shown in fig.11 demonstrates that
capacitor voltage settles at nearly constant value of Vdc
ref. and capacitor current settles at almost equal to the
value of filter current.
Fig.12 FFT Analysis for load current
Fig.13 FFT Analysis for source current
The waveform shown in fig.12 and fig.13 demonstrates
that source current is reduced THD from 21.83% to
0.89%.
THD analysis of shunt active power filter for RL-Load
is shown in table 1.
Load type
THD(%) (
Load Current
THD(%)
Source Current
R-L Load
21.83 % 0.89 %
Table 1
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4. Conclusion
The performance of the system improves and the THD is
reduced up to very large extent. Also, it is seen from the
simulation results that the source current and the source
voltages are in same phase i.e. the input power factor is
unity and there is no reactive power from the source.
References
[1] Roger C.Dugan, Mark F. McGranaghan, Surya
Santoso and H.Wayne Beaty, Electrical Power System
Quality, McGraw –Hill.
[2] Bhim Singh, Kamal Al Haddad and Ambrish
Chandra, A Review of Active Filters for Power
QualityImprovement, IEEE Trans on Industrial
Electronics, Vol.46, No.5, October 1999, pp. 960-970.
[3] S.K.Jain, P.Agrawal and H.O.Gupta, Fuzzy Logic
controlled shunt active power filter for power quality
improvement, IEE proceedings in Electrical Power
Applications, Vol 149, No.5, September 2002.
[4] Y.Sato, T.Kawase, M.Akiyama, and T.Kataoka, A
control strategy for general – purpose active filters based
on voltage detection, IEEE Trans. Ind. Appl., vol. 36,
no.5, pp.1405–1412, Sep / Oct.2000.
[5] M. Kazmierkowsi, L.Malesani,Current Control
Techniques for Three Phase Voltage Source PWM
converters: A survey, IEEE Trans on Industrial
Electronics, vol.45, no.5, pp.691- 703, October 1998.
[6] S. Buso, L. Malesani, P. Mattavelli, Comparison of
current control Techniques for Active power Filter
Applications, IEEE Transactions on Industrial
Electronics, Vol.45, no.5, pp.722-729, Oct 1998.
[7] E.E.EL-Khoy, A. EL-Sabbe, A.El-Hefnawy, and
Hamdy M.Mharous, Three phase active power filter
based on current controlled voltage source inverter,
Electrical Power and Energy Systems, 28 (2006), 537-
547.
[8] V. Agelidis, M. Calais, Application specific
harmonic performance evaluation of multicarrier PWM
techniques, IEEEPESC’ 98 Conference Record, pp. 172-
178, 1998.
[9] G. Carrara, S. Gardelta, M. Marchesoni, A new
multilevel PWM method: theoretical analysis, IEEE
Trans. On power electronics Vol. 7. No. 3, July, pp.497-
505,1992.
[10] PENG, F.Z., AKAGI, H., and NABAE, A,: ‘A
study of active power filters using quad series voltage
sourcc PWM convcrtcrs for harmonic compensation’,
IEEE Trans.Power Electron, 1990. 5, (I). pp. 915.
[11] LEE, C.C.: ‘Fuzzy logic in control system: fuzzy
logic controller-part 1’. IEEE Trans. Syst. Man Cybern,
1990, 20, (2). pp. 404-415.
Appendix
The values of the different parameters used for
shunt active power filter.
 Source voltage:3-phase, 100V, 50Hz
 Proportional gain Kp: 0.5
 Integral gain Ki : 10
 Capacitor reference voltage: 300V
 RL load parameters: 10 Ω, 100mH
 line parameters : 0.2 Ω, 1.5mH
 Filter inductor : 5mH
 Hysteresis band gap : -0.01 to 0.01
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Performance Investigation of Shunt Active Power Filter Using Hysteresis Current Control Method

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