Energy and Power En gi neering, 2011, 3, 43-52
doi:10.4236/epe.2011.31007 Published Online February 2011 (http://www.SciRP.org/journal/epe)
Fuzzy Controller Based 3Phase 4Wire Shunt Active Filter
for Mitigation of Current Harmonics with Combined p-q
and Id-Iq Control Strategies
Mikkili Suresh, Anup Kumar Panda, Y. Suresh
Department of Electrical Engineering, National Institute of Technology, Rourkela, India
Received November 14, 2010; revised December 15, 2010; accepted December 16, 2010
Abstract
As more and more variable frequency drives (VFDs), electronic ballasts, battery chargers, and static Var
compensators are installed in facilities, the problems related to harmonics are expected to get worse. As a
result Active power filter (APF) gains much more attention due to excellent harmonic compensation. But
still the performance of the active filter seems to be in contradictions with different control strategies. This
paper presents detailed analysis to compare and elevate the performance of two control strategies for ex-
tracting reference currents of shunt active filters under balanced, un-balanced and non-sinusoidal conditions
by using Fuzzy controller. The well known methods, instantaneous real active and reactive power method
(p-q) and active and reactive current method (id-iq) are two control methods which are extensively used in
active filters. Extensive Simulations are carried out with fuzzy controller for both p-q and Id-Iq methods for
different voltage conditions and adequate results were presented. Simulation results validate the superior per-
formance of active and reactive current control strategy (id-iq) with fuzzy controller over active and reactive
power control strategy (p-q) with fuzzy controller.
Keywords: Harmonic Compensation, Shunt Active Power Filter, p-q Control Strategy, id-iq Control Strategy,
Fuzzy Controller
1. Introduction
Highly automatic electric equipments, in particular, cause
enormous economic loss every year. Owing both power
suppliers and power consumers are concerned about the
power quality problems and compensation techniques. In
recent years, single-phase electronic equipments have
been widely used in domestic, educational and commer-
cial appliances. These equipments include computers,
communication equipments, electronic lighting ballasts
etc. Also, a large number of computers are turned on at
the same time. Each computer and its related devices
have a diode rectifier to convert AC electricity to DC one.
In other words, those equipments draw non- sinusoidal
currents which pollute the utility line due to the current
harmonics generated by the nonlinear loads [1]. It is
noted that non-sinusoidal current results in many prob-
lems for the utility power supply company, such as: low
power factor, low energy efficiency, electromagnetic
interference (EMI), distortion of line voltage etc. and it is
noted that, in three-phase four-wire system, zero line
may be overheated or causes fire disaster as a result of
excessive harmonic current going through the zero line
three times or times that of three. Thus a perfect com-
pensator is necessary to avoid the consequences due to
harmonics [2]. Though several control strategies have
been developed but still two control theories, instanta-
neous active and reactive currents (id-iq) method and in-
stantaneous active and reactive power (p-q) methods are
always dominant. Present paper mainly focused on two
control strategies (p-q and Id-Iq) with fuzzy controller [3].
To validate current observations, Extensive Simulations
are carried out with fuzzy controller for both p-q and Id-Iq
methods for different voltage conditions like sinusoidal,
non-sinusoidal, and un-balanced conditions and adequate
results were presented. On observing the performance of
id-iq control strategy with fuzzy controller is quite good
over p-q control strategy with fuzzy controller.

M. SURESH ET AL. 44
2. Control Strategy
In this section two control strategies are discussed in
detail. Ideal analysis has done in steady state conditions
of the active power filter. Steady state analysis using Fast
Fourier Transform (FFT) for the two control methods
that are presented are now briefly enlightened.
2.1. Instantaneous Real and Reactive Power
Method (p-q)
The active filter currents are achieved from the instanta-
neous active and reactive powers p and q of the
non-linear load. Figure 1 shows the block diagram to
attain reference currents from load. Transformation of
the phase voltages va, vb, and vc and the load currents iLa,
iLb, and iLc into the α - β orthogonal coordinates are given
in Equation (1-2). The compensation objectives of active
power filters [4,5] are the harmonics present in the input
currents. Present architecture represents three phase four
wire and it is realized with constant power controls
strategy [6]. Figure 2 illustrates control block diagram
and Inputs to the system are phase voltages and line cur-
rents of the load. It was recognized that resonance at
relatively high frequency might appear between the
source impedance. So a small high pass filter is incorpo-
rated in the system. The power calculation is given in
detail form in Equation (3).
0
11 1
22 2
211
1
322
33
022
a
b
c
v
v
vv
vv




  

 


 
 
 






(1)
0
11 1
22 2
211
1
322
33
022
a
L
L
b
L
c
i
i
ii
ii





 

 


 
 
 






i


(2)
00 000
0
0
pi v
pvv
qvv
i

 


 




 

 


(3)
From Figure 2 we can observe a high pass filter with
cut off frequency 50 Hz separates the powers p

 from
and a low –
p
Pass filter separates 0 p from 0. The powers current
and 0 of the load, together with q, should be com-
pensated to provide optimal power flow to the source. It
is Important to note that system used is three phase four
wire, so additional neutral currents has to be supplied by
the shunt active power filter thus Ploss is incorporated to
p
p
p
Figure 1. Shows a basic architec tur e of three-phase - four wire shunt active filter.

M. SURESH ET AL.45
K

V

*
i+
Δ
(1- ε)
ca
*
i-
Δ
(1- ε)
ca
















α-β-ο
Transf.
&
p
ower
calcul.
α-β-ο
Transf.
&
p
ower
calcul.
α-β
Volt
R
efer.
P
LL
&
Sine
Gener
i
L
a
i
L
b
i
L
c
50
H
z
50
H
z
p
'
q
p
'
q

α-β
Current
R
efer.
*
icα
*
icβ
α-β-ο
inverse
Transf.
*
ica
*
icb
*
icc
Va
Vb
Vc
iβ

iα

Vdc1
Vdc2
D
C Voltage Regulator
Vref
50Hz
V*
α
V*
β
p
q
i0
20Hz
20Hz
Ploss

p
v
5%Vref
1
ifa
s
1
s
2
s3
s
4
s
5
s
6





ifa
i
f
c
i
f
b
ifa
Figure 2. Control block diagram of shunt active powe r filte r.
correct compensation error due to feed forward network
unable to suppress the zero sequence power. Since active
filter compensates the whole neutral current of the load
in the presence of zero-sequence voltages, the shunt ac-
tive filter eventually supplies po. Consequently if active
filter supplies po to the load, this make changes in dc
voltage regulator, hence additional amount of active
power is added automatically to Ploss which mainly pro-
vide energy to cover all the losses in the power circuit in
the active filter. Thus, with this control strategy shunt
active filter gains additional capability to reduce neutral
currents and there-by supply necessary compensation
when it is most required in the system. Thus the αβ ref-
erence currents can be found with following equation [7].
22
*1
*
c
c
ivv pp
vv iq
vv

 
  


 



 


(4)
0
L
oss
pp p 
where is the ac component / oscillating value of p p

0
p is the dc component of p0
loss
Pis the losses in the active filter
loss
P is the average value of
loss
P
Δ
p Provides energy balance inside the active power
filter and using Equation (5) inverse transformation can
be done.
0
110
2
*211 3
*
322
2*
*
11 3
22
2
ca
cb c
c cc
ii
i
i i







 




 


 





where ica*, icb*, icc* are the instantaneous three-phase
current references
In addition PLL (Phase locked loop) employed in
shunt filter tracks automatically, the system frequency
and fundamental positive–sequence component of three
phase generic input signal [8]. Appropriate design of
PLL allows proper operation under distorted and unbal-
anced voltage conditions. Controller includes small
changes in positive sequence detector as harmonic com-
pensation is mainly concentrated on three phase four
wire. As we know in three- phase three wire, va′, vb′, vc′
are used in transformations which resemble absence of
zero sequence component and it is given in Equation (6).
Thus in three phase four wire it was modified as vα′, vβ′
and it is given in Equation (7).
10
21 3
32 2
13
22
a
b
c
vv
vv
v





 


 
 
 


 

 



(6)
22
1
viip
vii
ii q



 



 

 




  

(7)
DC voltage regulator (p-q):
* i



(5)
The dc capacitor voltages Vdc1 and Vdc2 may be con-
trolled by a dc voltage regulator. A low-pass filter with
cut-off frequency 20 Hz is used to render it insensitive to
the fundamental frequency (50 Hz) voltage variations.
The filtered voltage difference ∆V = Vdc2 − V
dc1 pro-
duces voltage regulation ε according to the following
limit function generator:

M. SURESH ET AL. 46
1; 0.05
; 0.050.05
0.05
1; 0.05
ref
ref ref
ref
ref
VV
VVV V
V
VV



 




where Vref is a pre-defined dc voltage reference and 0.05
Vref was arbitrarily chosen as an acceptable tolerance
margin for voltage variations.
If (Vdc1 + Vdc2) < Vref, the PWM inverter should absorb
energy from the ac network to charge the dc capacitor.
The inverse occur if (Vdc1 + Vdc2) > Vref.
The signal loss P generated in the dc voltage regulator
is useful for correcting voltage variations due to com-
pensation errors that may occur during the transient re-
sponse of shunt active filter.
2.2. Instantaneous Active and Reactive Current
Method (id – iq)
In this method reference currents are obtained through
instantaneous active and reactive currents id and iq of the
non linear load. Calculations follows Similar to the in-
stantaneous power theory, however dq load currents can
be obtained from Equation (8). Two stage transforma-
tions give away relation between the stationary and ro-
tating reference frame with active and reactive current
method [9-11]. Figure 4 shows voltage and current vec-
tors in stationary and rotating reference frames. The
transformation angle ‘θ’ is sensible to all voltage har-
monics and unbalanced voltages; as a result dθ/dt may
not be constant. Arithmetical relations are given in Equa-
tions (8) and (9); finally reference currents can be ob-
tained from Equation (10).
22
1
d
q
ivvi
ivvi
vv





 



 



  (8)
where iα, iβ are the instantaneous α-β axis current refer-
ences
cos sin
sin cos
d
q
ii
ii




 


 






(9)
22
1d
q
ic icv v
ic icv v
vv




 
 
  
(10)
where icd, icq are compensation currents.
One of the advantages of this method is that angle θ is
calculated directly from main voltages and thus makes
this method frequency independent by avoiding the PLL
in the control circuit. Consequently synchronizing prob-
lems with unbalanced and distorted conditions of main
voltages are also evaded. Thus id – iq achieves large fre-
quency operating limit essentially by the cut-off fre-
quency of voltage source inverter (VSI) [12]. Figures 3
and 5 show the control diagram for shunt active filter and
harmonic injection circuit. On owing load currents id and
iq are obtained from park transformation then they are
allowed to pass through the high pass filter to eliminate
dc components in the nonlinear load currents. Filters
used in the circuit are Butterworth type and to reduce the
influence of high pass filter an alternative high pass filter
(AHPF) can be used in the circuit. It can be obtained
through the low pass filter (LPF) of same order and
cut-off frequency simply difference between the input
signal and the filtered one, which is clearly shown in
Figure 3. Active powers filter control circuit.
Figure 4. Instantaneous voltage and current vectors.

M. SURESH ET AL. 47
Figure 5. Park transformation and harmonic current injection circuit.
Figure 5. Butterworth filters used in harmonic injecting
circuit have cut-off frequency equal to one half of the
main frequency (fc = f/2), with this a small phase shift in
harmonics and sufficiently high transient response can be
obtained.
DC Voltage regulator (Id-Iq)
The function of voltage regulator on dc side is per-
formed by proportional — integral (PI) controller, inputs
to the PI controller are, change in dc link voltage (Vdc)
and reference voltage (Vdc*), on regulation of first har-
monic active current of positive sequence id1h
+ it is pos-
sible to control the active power flow in the VSI and thus
the capacitor voltage Vdc.
In similar fashion reactive power flow is controlled by
first harmonic reactive current of positive sequence iq1h
+.
On the contrary the primary end of the active power fil-
ters is just the exclusion of the harmonics caused by
nonlinear loads hence the current iq1h
+ is always set to
zero.
3. Construction of Fuzzy Logic Controller
The concept of Fuzzy Logic (FL) was proposed by Pro-
fessor Lotfi Zadeh in 1965, at first as a way of process-
ing data by allowing partial set membership rather than
crisp membership. Soon after, it was proven to be an
excellent choice for many control system applications
since it mimics human control logic.
Figure 6 shows the internal structure of the control
circuit. The control scheme consists of Fuzzy controller,
limiter, and three phase sine wave generator for reference
current generation and generation of switching signals
[13]. The peak value of reference currents is estimated
by regulating the DC link voltage. The actual capacitor
signal is then processed through a Fuzzy controller,
which contributes to zero steady error in tracking the
reference current signal.
A fuzzy controller conv
voltage is compared with a set reference value. The error
erts a linguistic control strat-
eg
lows:
of dis-
co
ication using Mamdani's ‘min’ operator.
s of this rule base table are determined
ba
a numerical
va
generate required
output in a linguistic variable (Fuzzy Number), accord-
y into an automatic control strategy, and fuzzy rules
are constructed by expert experience or knowledge data-
base. Firstly, input voltage Vdc and the input reference
voltage Vdc-ref have been placed of the angular velocity to
be the input variables of the fuzzy logic controller [14].
Then the output variable of the fuzzy logic controller is
presented by the control Current Imax. To convert these
numerical variables into linguistic variables, the follow-
ing seven fuzzy levels or sets are chosen as: NB (nega-
tive big), NM (negative medium), NS (negative small),
ZE (zero), PS (positive small), PM (positive medium),
and PB (positive big) as shown in Figure 7.
The fuzzy controller is characterized as fol
1) Seven fuzzy sets for each input and output.
2) Fuzzification using continuous universe
urse.
3) Impl
4) De-fuzzification using the 'centroid' method.
Rule Base:
The element
sed on the theory that in the transient state, large errors
need coarse control, which requires coarse input/output
variables; in the steady state, small errors need fine con-
trol, which requires fine input/output variables. Based on
this the elements of the rule table are obtained as shown
in Table 1, with ‘Vdc’ and ‘Vdc-ref’ as inputs.
Fuzzification: The process of converting
riable (real number) convert to a linguistic variable
(fuzzy number) is called fuzzification.
De-fuzzification: The rules of FLC

M. SURESH ET AL. 48
Figure 6. Conventional fuzzy controller.
(a)
(b)
(c)
Figure 7. (a) Input Vdc normalized membership function; (b)
input Vdc-ref normalized mership function; (c) output
istic variables have
be transformed to crisp output (Real number).
fuzzi-
fie
Table 1. Rule base.
mbe
Imax normalized membership function.
ing to real world requirements, lingu
to Database: The Database stores the definition of the
membership Function required by fuzzifier and de
r.
V
de-ref
Vde NBNMNS Z PS PM PB
NB NBNB NB NS Z NB NM
NM NB NB NB NM NS Z PS
NS NBNB NMNS Z PS PM
Z NBNMNS Z PS PM PB
PS NMNS Z PS PM PB PB
PM NS Z PS PM PB PB PB
PB Z PS PM PB PB PB PB
4. System Performance
on 3 phase 4 wire shunt active power
and steady state con-
on AHPF (alternative high
ass filter) were used in Butterworth filter with cut-off
or i-i method with Fuzzy Controller is
1.
In th
re
is sectifilter
sponses are presented in transient
ditions. In the present simulati
p
frequency fc = f/2. Simulation shown here are for differ-
ent voltage conditions like sinusoidal, non-sinusoidal,
unbalanced, and with different main frequencies. Simu-
lation is carried out for both instantaneous power theory
(p-q) and instantaneous active and reactive current theory
(id- iq) with Fuzzy controller.
Figures 8-10 illustrate the performance of shunt active
power filter under different main voltages, as load is
highly inductive, current draw by load is integrated with
rich harmonics.
Figure 8 illustrates the performance of Shunt active
power filter under balanced sinusoidal voltage condition.
THD for p-q method with Fuzzy controller is about
1.45% and THD fdq
14%.
Figure 9 illustrates the performance of Shunt active

M. SURESH ET AL.49
(a) (b)
Figure 8. 3ph 4wire Shunt ative filter re sponse with fuzzy controller under balanced sinuso idal (a) using p-q control strategy
(b) using Id-Iq control strategy.
Fuzzy controller is 3.73%
nd THD for id-iq method with Fuzzy Controller is
D for p-q method with Fuzzy controller is
5.
ditions. So harmonic content seems to very
hi
tion.
Fuzzy controller is finest controller in all the control-
ds with fuzzy controller; on over all with combina-
tio
power filter under un-balanced sinusoidal voltage condi-
tion. THD for p-q method with
id-iq control strategy one can attain perfect compensa-
a
2.27%.
Figure 10 illustrates the performance of Shunt active
power filter under balanced non-sinusoidal voltage con-
dition. TH
11% and THD for id-iq method with Fuzzy Controller is
4.09%.
On observing p-q control strategy fails to deliver ref-
erence currents properly under unbalance and non-sinu-
soidal con
gh in p-q control strategy under these conditions. On
owing id-iq control strategy delivers exact reference cur-
rents under any voltage conditions. As a result with the
lers, but it too has some drawbacks like redundancy and
iteration problems. So one has to choose the membership
function on the bases system complexity Extensive
simulation is carried out to validate both p-q and Id-Iq
metho
n of Id-Iq strategy and fuzzy controller, there is possi-
bility of building novel shunt active filter for 3-phase
4-wire system.
Numerical simulations:
Above simulation is carried out with only AHPF (al-
ternative high pass filter) of 2nd order with cut-off fre-
quency fc = fc/2, it is also assumed that currents are in-

M. SURESH ET AL. 50
(a) (b)
Figure 9. 3ph 4wire Shunt ative filter response with fuzzy controller under un-balanced sinusoidal (a) using p-q control
strategy (b) using Id-Iq control strategy.
dependent of main voltages an
onditions. In addi-
on simulation is also extended to different kinds of fil-
erformance same. Generally
under any voltage conditions.
e and reactive current id-iq
ntroller lead always better result
and non-sinusoidal voltage conditions
ver the instantaneous active and reactive power p-q
method. On contrast p-q theory needs additional PLL
d there is no ripple on the der sinusoidal conditions p
rectifier dc current. Active power filter performance is
analysed under several main voltage c
speaking in all the filters, HPF gives best filtering action
ti
ters like HPF (high pass filter) with 2nd order, AHPF with
4th order and HPF with 4th order. In all those, Alternative
high pass filter shows good performance and it is easy to
obtain with LPF (low pass filter) of same order and
cut-off frequency, simply by difference between the in-
put and filter signal which is shown in Figure 4. Graphs
shown in Figure 11 and Figure 12 summarize the total
performance of the shunt active filter with different fil-
ters. Results presented confirm superior performance of
Id-Iq method with Fuzzy controller. But performance of
shunt active filters with both methods (p-q and Id-Iq) un-
5. Conclusion
In the present paper two control strategies are developed
and verified with three phase four wire system. Though
the two strategies are capable to compensate current
harmonics in the 3 phase 4-wire system, but it is ob-
served that instantaneous activ
method with fuzzy co
under un-balanced
o

M. SURESH ET AL.51
(a) (b)
Figure 10. 3ph 4wire shunt ative filter response with fuzzy controller under balanced non-sinusoidal (a) using p-q control
strategy (b) using Id-Iq control strategy.
Figure 11. THD for p-q method with fuzzy controller. Figure 12. THD for id-iq method with fuzzy controller.

M. SURESH ET AL. 52
Figure 13. THD for p-q and id-iq methods with fuzzy con
troll
circuit for synchronization so p-q method is frequ
variant, where as in id-iq method angle
‘θ’ is calculated directly from main voltages and
enables the method to be frequency independent. T
large numbers of synchronization problems with un-
balanced and non-sinusoidal voltages are also avoided.
Addition to that DC voltage regulation system valid to be
a stable and steady-state error free system was obtained.
Over all, performance of id-iq theory with fuzzy control-
ler is quite good over p-q theory with fuzzy controller.
6. References
[1] H. Akagi, “New Trends in Active Filters for Power Con-
ditioning,” IEEE Transactions on Industry Applications
Vol. 32, No. 6, November-December 1996, pp. 1312-
1322. doi.:10.1109/28.556633
[2] Z. Peng, G. W. Ott and D. J. Adams, “Harmonic and
Reactive Power Compensation Based on the General
Instantaneous Reactive Power Theory for Three-P
Four-Wire Systems,” IEEE Transactions on Power Elec
tronics, Vol. 13, No. 5, November 1998, pp. 1174-1181.
K. Jain, P. Agrawal and H. O. Gupta, “Fuzzy Logic
Controlled Shunt Active Power Filter for Power Quali
Power Filters in Three-Phase Four-Wire Systems,” IEEE
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