Energy and Power En gi neering, 2011, 3, 285-298
doi:10.4236/epe.2011.33036 Published Online July 2011 (http://www.SciRP.org/journal/epe)
Instantaneous Active and Reactive Power and Current
Strategies for Current Harmonics Cancellation in 3-ph
4-Wire SHAF with Both PI and Fuzzy Controllers
Suresh Mikkili, Anup Kumar Panda
Department of Electrical Engineering, National Institute of Technology, Rourkela, India
Received February 25, 2011; revised March 22, 2011; accepted April 11, 2011
Abstract
Control strategies for extracting the three-phase reference currents for shunt active power filters are com-
pared, evaluating their performance under different source conditions with PI and Fuzzy Controllers in
MATLAB/Simulink environment When the supply voltages are balanced and sinusoidal, the two control
strategies are converge to the same compensation characteristics; However, the supply voltages are distorted
and/or un-balanced sinusoidal, these control strategies result in different degrees of compensation in har-
monics. The compensation capabilities are not equivalent, with p-q control strategy unable to yield an ade-
quate solution when source voltages are not ideal. Extensive simulations are carried out with PI controller
and also with Fuzzy controller for both p-q and id-iq control strategies under different main voltages. Exten-
sive Simulations are carried out with PI as well as fuzzy controller for both p-q and id-iq control strategies by
considering different voltage conditions and adequate results were presented. On owing id-iq method with
fuzzy logic controller gives away an out-standing performance under any voltage conditions (balanced,
un-balanced, balanced and non-sinusoidal).
Keywords: Harmonic Compensation, Shunt Active Filter (SHAF), p-q Control Strategy, id-iq Control
Strategy, PI Controller and Fuzzy Controller
1. Introduction
The power-electronic-based loads such as adjustable
speed drives, rectifier equipment used in telecommunica-
tion networks, power supplies, domestic appliances, etc
offer highly nonlinear characteristics. These nonlinear
loads draw non-sinusoidal [1] currents from ac mains
and cause reactive power burden and excessive neutral
current. They are also responsible for lower efficiency
and interference of distribution system with the nearby
communication networks. To improve the efficiency,
capacitors are employed which also leads to the im-
provement of power factor of the mains. On the other
hand, to reduce the interference with the communication
network due to harmonics in the current flowing in the
distribution system, passive-filters are used. But they
have the limitations of fixed compensation, large size,
and that they can create new system resonance.
Present work mainly focused on two control strategies
p-q and id-iq by using two controllers i.e., fuzzy [2] and
PI. Instantaneous active and reactive theory (p-q theory)
was introduced by H. Akagi, kawakawa, and Nabae in
1984. Since then, many scientists and engineers made
significant contributions to its modifications in three-
phase four-wire circuits and its applications to power
electronic equipment. The p-q theory [3] based on a set
of instantaneous powers defined in the time domain. No
restrictions are imposed on the voltage and current
waveforms, and it can be applied to three phase systems
with or without neutral wire for three phase generic
voltage and current waveforms. Thus it is valid not only
in the steady state but also in the transient state. p-q the-
ory needs additional PLL circuit for synchronization so
p-q method is frequency variant.
In id-iq method [4] angle “θ” is calculated directly from
main voltages and thus enables the method to be fre-
quency independent. Thus large numbers of synchroni-
zation problems with un-balanced and non-sinusoidal
voltages are also avoided.
The PI controller [5] requires precise linear mathe-
matical models, which are difficult to obtain and may not
give satisfactory performance under parameter variations,

S. MIKKILI ET AL. 286
load disturbances, etc. Recently, fuzzy logic controllers
have received a great deal of interests in APF. The ad-
vantages of fuzzy controllers over conventional control-
lers are that they do not need an accurate mathematical
model, can work with imprecise inputs, can handle
non-linearity, and are more robust than conventional
controllers. The Mamdani type of fuzzy controller [6]
used for the control of APF gives better results compared
with the PI controller, but it has the drawback of a larger
number of fuzzy sets and 49 rules. This increases the
complexity of the controller; hence, this demands large
computational time. As a result, it may not be useful for
real-time applications with small sampling time.
When the supply voltages are balanced and sinusoidal,
both p-q and id-iq control strategies are converge to the
same compensation characteristics but when the supply
voltages are distorted and/or un-balanced sinusoidal,
these control strategies result in different degrees of
compensation in harmonics. The p-q control strategy is
unable to yield an adequate solution when source volt-
ages are not ideal. PI controller fails to respond quickly
because of non-linear nature in the system, so we are
developing soft computing techniques to analyze the
performance of system under distorted condition. Fuzzy
supports with outstanding performance under any volt-
age conditions. On observing id-iq method with fuzzy
logic controller gives away an out-standing performance
under any voltage conditions.
2. Shunt Active Filter Configuration
To employ APFs in three-phase four-wire systems, two
types of configurations are possible; one is a three-leg
structure with the neutral conductor being connected to
midpoint of dc-link capacitor (Figure 1); and the other
one is a four-leg structure, where a fourth leg is provided
exclusively for neutral current compensation (Figure 2).
Despite the fact, this topology is seldom preferred owing
to less number of switching devices and lower switching
losses compared to the eight-switch topology [7]. How-
ever, the higher order harmonics generated in the eight
switch configuration due to frequent switching of semi-
conductor devices can be eliminated by the use of RC
high-pass filter as shown in Figure 2 and switching
losses occurring in the VSI can also be minimized by the
use of DC-link voltage regulator [8]. Moreover, the four-
leg APF has simple dc-link voltage controller, requires
small dc-link capacitor, and the control scheme is also
quite simple to implement.
The four-leg eight-switch APF topology is preferred to
be implemented as many researchers have appointed this
configuration as the most proficient alternative to be
used in shunt APF [8]. The three-leg six-switch split-
Figure 1. Three-leg shunt APF wi th non-line ar load.
Figure 2. Four-leg shunt AP F wi th non-linear load.
capacitor configuration of shunt APF suffers from sev-
eral shortcomings viz.
1) Control circuit is somewhat complex;
2) Voltages of the two capacitors of split-capacitor
need to be properly balanced;
3) Large dc-link capacitors are required.
3. Instantaneous Active an d Reactive Power
(p-q) Method
The control algorithm block diagram for p-q method is
depicted in Figure 3. The three-phase source voltages
(vsa, v
sb, v sc) and load currents (iLa, iLb, iLc) in the a-b-c
coordinates are algebraically transformed to the α-β co-
ordinates using Clarke’s transformation as per (1) and (2),
followed by the calculation of the instantaneous active
power (p) and reactive power (q) by following (3).
11
1
222
333
022
a
b
c
v
V
V
v
v





 
 
 

 




(1)

S. MIKKILI ET AL. 287
loss
P

p
0
p
Figure 3. Reference current extraction with conventional p-q method.
αβ α
β βα
v vi
p
i qv -v






  


 
a
α
b
β
c
11v
1
V22
33 V0 - v
22
2v
3




















L
a
α
L
b
L
c
11
1 - -
22
33
0 -
22
i
i2i
i3i





















*
cααβ
c
*
cββα
c
αβ
i*v v-P
1
=22
i*v-vq
v+v

 

 

 


cα
c
1 0
i*
ca i*
13 2
i*=
cb i*
322
i*
cc 13
-
22



 











 
 



Figure 4. Control method for Shunt current compensation based on p-q theory.
11
1
222
333
022
L
a
L
b
L
c
i
ii
ii







 

 

 




(2)
v vi
p
i
qv v
 


 



 
  

(3)
Each of these powers has dc component (1st component)
and ac component (2nd component) as shown in (4).
ppp
qqq



 (4)
For reactive and harmonic compensation, the entire
reactive power and ac component of active power are
utilized as the reference power. The reference currents in
α-β coordinates are calculated by using (5) (Figure 4).
**
*22 *
1
cc
cc
vv
iP
vv
ivv q




 



 



 

 
(4)
*
*
*
*
*
10
13 2
322
13
22
ca
cb
c
cc
ic
i
i i
i









 
 

 
 
 



(5)
In addition PLL (Phase locked loop) employed in

S. MIKKILI ET AL. 288
shunt filter tracks automatically, the system frequency
and fundamental positive-sequence component of three
phase generic input signal. Appropriate design of PLL
allows proper operation under distorted and unbalanced
voltage conditions. Controller includes small changes in
positive sequence detector as harmonic compensation is
mainly concentrated on three phase four wire [9]. As we
know in three-phase three wire, a, b, c are used in
transformations which resemble absence of zero se-
quence component and it is given in Equation (7). Thus
in three phase four wire it was modified as
vvv
v

, v


and
it is given in Equation (8).
10
21 3
32 2
13
22
a
b
c
vv
vv
v





 


 
 
 


  
 



(7)
22
vii
p
1
=
vii
q i+i



 
 

 



 
 (8)
4. Instantaneous Active and Reactive
Current Method (id-iq)
In Figure 5, the entire reference current generation
scheme has been illustrated. The load currents iLa, iLb and
iLc are tracked upon which Park’s transformation is per-
formed to obtain corresponding d-q axes currents iLd and
iLq as given in (9), where  is rotational speed of syn-
chronously rotating d-q frame. According to id-iq control
strategy, only the average value of d-axis component of
load current should be drawn from supply. Here iLd1h and
iLq1h indicate the fundamental frequency component of iLd
and iLq. The oscillating components iLd and iLq, i.e., iLdnh
and iLqnh are filtered out using low-pass filter.
1
112 12
sin cos
cossin 032 32
LdLd hLdnh
LqLqih Lqnh
La
Ld
Lb
Lq
Lc
iii
iii
i
iwt wti
iwt wti

















 

 




(9)
The currents i
Ldnh and iLqnh along with id1h are utilized
to generate reference filter currents icd* and icq* in d-q
coordinates, followed by inverse Park transformation
giving away the compensation currents ica*, icb*, icc* and
icn* in the four wires as described in (10) and (11).


**
**
**
0
sincos 1
sin 2π3cos 2π31
sin 2π3cos 2π31
ca cd
cb cq
cc c
iwt wt
iwt wt
iwt wt
i
i
i







 












(10)
* ***
cnca cb cc
iiii

 (11)
The reference signals thus obtained are compared with
the actual compensating filter currents in a hysteresis
comparator, where the actual current is forced to follow
the reference and provides instantaneous compensation
by the APF [10] on account of its easy implementation
and quick prevail over fast current transitions. This con-
sequently provides switching signals to trigger the
IGBTs inside the inverter. Ultimately, the filter provides
necessary compensation for harmonics in the source cur-
rent and reactive power unbalance in the system. Figure
6 shows voltage and current vectors in stationary and
rotating reference frames. The transformation angle ‘θ’ is
sensible to all voltage harmonics and unbalanced volt-
ages; as a result dθ/dt may not be constant.
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
Figure 5. Reference current extraction with id-iq method.

S. MIKKILI ET AL. 289
Figure 6. Instantaneous voltage and current vectors.
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) [11].
Figures 5 and 6 show the control diagram for shunt
active filter and harmonic injection circuit. On owing
load currents id and iq are obtained from park transforma-
tion 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 alterna-
tive 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 be-
tween the input signal and the filtered one, which is
clearly shown in 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 tran-
sient response can be obtained.
5. Construction of PI Controller
Figure 7 shows the internal structure of the control cir-
cuit. The control scheme consists of PI controller, limiter,
and three phase sine wave generator for reference current
generation and generation of switching signals [12]. The
peak value of reference currents is estimated by regulat-
ing the DC link voltage. The actual capacitor voltage is
compared with a set reference value.
The error signal is then processed through a PI con-
troller, which contributes to zero steady error in tracking
the reference current signal. The output of the PI con-
troller is considered as peak value of the supply current
(Imax), which is composed of two components: a) funda-
mental active power component of load current, and b)
loss component of APF; to maintain the average capaci-
tor voltage to a constant value. Peak value of the current
(Imax) so obtained, is multiplied by the unit sine vectors in
phase with the respective source voltages to obtain the
Figure 7. Conventional PI controller.
reference compensating currents. These estimated refer-
ence currents (Isa*, Isb*, Isc*) and sensed actual currents
(Isa, Isb, Isc) are compared at a hysteresis band, which
gives the error signal for the modulation technique. This
error signal decides the operation of the converter
switches. In this current control circuit configuration, the
source/supply currents Isabc are made to follow the sinu-
soidal reference current Iabc, within a fixed hysteretic
band. The width of hysteresis window determines the
source current pattern, its harmonic spectrum and the
switching frequency of the devices.
The DC link capacitor voltage is kept constant through-
out the operating range of the converter. In this scheme,
each phase of the converter is controlled independently. To
increase the current of a particular phase, the lower switch
of the converter associated with that particular phase is
turned on while to decrease the current the upper switch of
the respective converter phase is turned on. With this one
can realize, potential and feasibility of PI controller.
6. Construction of Fuzzy Controller
Figure 8 shows the internal structure of the control cir-
cuit. The control scheme consists of Fuzzy controller,
limiter, and three phase sine wave generator for reference
current generation and generation of switching signals.
The peak value of reference currents [13] is estimated by
regulating the DC link voltage. The actual capacitor
voltage is compared with a set reference value. The error
signal is then processed through a Fuzzy controller,
which contributes to zero steady error in tracking the
reference current signal.
A fuzzy controller [14] converts a linguistic control
strategy into an automatic control strategy, and fuzzy
rules are constructed by expert experience or knowledge
database. Firstly, input voltage Vdc and the input refer-
ence voltage Vdc-ref have been placed of the angular ve-
locity to be the input variables of the fuzzy logic con-
troller. Then the output variable of the fuzzy logic con-
troller is presented by the control Current Imax. To con-
vert these numerical variables into linguistic variables,
the following seven fuzzy levels or sets are chosen as:

S. MIKKILI ET AL. 290
NB (negative big), NM (negative medium), NS (negative
small), ZE (zero), PS (positive small), PM (positive me-
dium), and PB (positive big) as shown in Figure 9.
The fuzzy controller is characterized as follows:
1) Seven fuzzy sets for each input and output;
2) Fuzzification using continuous universe of dis-
course;
3) Implication using Mamdani's ‘min’ operator;
4) De-fuzzification using the ‘centroid’ method.
Fuzzification: the process of converting a numerical
variable (real number) convert to a linguistic variable
(fuzzy number) is called fuzzification.
Figure 8. Conventional fuzzy controller.
(a)
(b)
(c)
Figure 9. (a) Input Vdc normalized membership function; (b)
Input Vdc-ref Normalized Membership Function; (c) Output
Imax Normalized Membership Function.
De-fuzzification: the rules of FLC generate required
output in a linguistic variable (Fuzzy Number), accord-
ing to real world requirements, linguistic variables have
to be transformed to crisp output (Real number).
Database: the Database stores the definition of the
membership Function required by fuzzifier and defuzzifier.
Rule Base: the elements of this rule base table are de-
termined based on the theory that in the transient state,
large errors need coarse control, which requires coarse in-
put/output variables; in the steady state, small errors need
fine control, 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.
7. Results and Discussions
Figure 10, Figure 11 and Figure 12 illustrate the per-
formance of shunt active power filter under different
main voltages, as load is highly inductive, current draw
by load is integrated with rich harmonics.
Figure 10 illustrates the performance of Shunt active
power filter under balanced sinusoidal voltage condition.
THD for p-q method with PI controller is 2.15%, THD
for p-q method with Fuzzy controller is 1.27%, THD for
id-iq method with PI controller is 1.97% and THD for id-iq
method with Fuzzy Controller is 0.97%.
Figure 11 illustrates the performance of Shunt active
power filter under un-balanced sinusoidal voltage condi-
tion. THD for p-q method with PI controller is 4.16%,
THD for p-q method with Fuzzy controller is 2.98%,
THD for id-iq method with PI controller is 3.11% and
THD for id-iq method with Fuzzy Controller is 1.64%.
Figure 12 illustrates the performance of Shunt active
power filter under balanced non-sinusoidal voltage con-
dition. THD for p-q method with PI controller is 5.31%,
THD for p-q method with Fuzzy controller is 3.85%,
THD for id-iq method with PI controller is 4.92% and
THD for id-iq method with Fuzzy Controller is 3.01%.
Table 1. Rule base.
Vde-ref
Vde NBNMNS Z PS PM PB
NB NBNB NB NB NM NS Z
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

S. MIKKILI ET AL. 291
3ph 4w Bal Sin p-q with PI Controller 3ph 4w Bal Sin p-q with Fuzzy Controller
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
-150
-100
-50
0
50
100
150
Time (Amps)
Filter Current (Amps)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
0
200
400
600
800
1000
Time (Sec)
DC Link Voltage (Volts)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.37 0.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
010 20 3040 50
0
0.2
0.4
0.6
0.8
1
Harmonic order
THD= 2. 15%
Mag (% of Fundamental)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
-40 0
-30 0
-20 0
-10 0
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
-15 0
-10 0
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
-15 0
-10 0
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
0
200
400
600
800
1000
DC Link Voltage (Volts)
Time (Sec)
0.3520.354 0.356 0.3580.360.3620.364 0.3660.3680.370.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
010 2030 40 50
0
0.2
0.4
0.6
0.8
1
Harmonic order
Mag (% of Fundamental)
THD= 1.27%
(a) (b)

S. MIKKILI ET AL. 292
3ph 4w Bal Sin id-iq with PI Controller 3ph 4w Bal Sin id-iq with Fuzzy Controller
0.352 0.354 0.356 0.3580.360.3620.364 0.3660.368 0.37 0.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.3580.36 0.3620.364 0.3660.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.3660.368 0.37 0.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.3660.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.356 0.358 0.360.362 0.364 0.3660.3680.370.372
0
200
400
600
800
1000
Time (Sec)
DC Link Voltage (Volts)
010 20 30 4050
0
0.2
0.4
0.6
0.8
1
Harmonic order
THD= 1. 97 %
Mag (% of Fundamental)
0.3520.354 0.356 0.3580.360.362 0.364 0.3660.3680.370.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.3580.36 0.3620.364 0.366 0.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.3520.354 0.356 0.3580.360.3620.364 0.366 0.3680.37 0.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
0.3520.354 0.356 0.3580.360.3620.364 0.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.356 0.3580.360.3620.364 0.3660.368 0.37 0.372
0
200
400
600
800
1000
Time (sec)
DC Link Voltage (Volts)
01020 30 40 50
0
0.2
0.4
0.6
0.8
1
Harmonic order
THD= 0.97%
Mag (% of Fundamental)
(c) (d)
Figure 10. Shunt ac tive power filte r response unde r balanced sinusoidal voltage c onditions for (a) p-q method with PI; (b) p-q
method with Fuzzy; (c) id-iq method with PI; (d) id-iq method with Fuzzy Contr oller.

S. MIKKILI ET AL.293
3ph 4w Un-bal p-q with PI Controller 3ph 4w Un-bal p-q with Fuzzy Controller
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.366 0.3680.37 0.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.366 0.3680.37 0.372
0
200
400
600
800
1000
Time (Sec)
DC Link Voltage (Volts)
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.366 0.3680.37 0.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
010 20 30 4050
0
1
2
3
4
5
Harmonic order
THD= 4. 16%
Mag (% of Fundamental)
0.352 0.3540.356 0.358 0.36 0.362 0.364 0.366 0.3680.37 0.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.368 0.37 0.372
0
200
400
600
800
1000
Time (Sec)
DC Link Voltage (Volts)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.368 0.37 0.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
01020 3040 50
0
0.2
0.4
0.6
0.8
1
Harmonic order
Mag (% of Fundamental)
THD= 2.98%
(a) (b)

S. MIKKILI ET AL. 294
3ph 4w Un-bal id-iq with PI Controller 3ph 4w Un-bal id-iq with Fuzzy Controller
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.366 0.3680.37 0.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.3580.36 0.362 0.364 0.366 0.3680.37 0.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
0.352 0.354 0.356 0.358 0.36 0.362 0.364 0.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.3560.358 0.36 0.362 0.364 0.366 0.3680.37 0.372
0
200
400
600
800
1000
Time (Sec)
DC Link Voltage (Volts)
010 20304050
0
1
2
3
4
5
Harmonic order
THD= 3.11%
Mag (% of Fundamental)
0.352 0.354 0.356 0.358 0.36 0.362 0.364 0.366 0.3680.37 0.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.358 0.36 0.362 0.364 0.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.358 0.36 0.362 0.364 0.366 0.3680.37 0.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
0.352 0.354 0.356 0.358 0.360.362 0.3640.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.356 0.358 0.36 0.362 0.364 0.366 0.3680.37 0.372
0
200
400
600
800
1000
Time (Sec)
DC Link Voltage (Volts)
010 20 3040 50
0
0.2
0.4
0.6
0.8
1
Harmonic order
Mag (% of Fundamental)
THD= 1.64%
(c) (d)
Figure 11. Shunt active pow er filter re sponse under Un-balanced sinusoidal voltage conditions for (a) p-q method with PI; (b)
p-q method with Fuzzy; (c) id-iq method with PI; (d) id-iq method with Fuzzy Controller.

S. MIKKILI ET AL.295
3ph 4w Non-Sin p-q with PI Controller 3ph 4w Non-Sin p-q with Fuzzy Controller
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.368 0.37 0.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.3560.3580.360.362 0.3640.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.3560.3580.360.362 0.3640.366 0.3680.37 0.372
0
200
400
600
800
1000
Time (Sec)
DC Link Voltage (Volts)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
010 2030 4050
0
1
2
3
4
5
Harmonic order
THD= 3. 85 %
Mag (% of Fundamental)
0.352 0.354 0.356 0.358 0.36 0.362 0.364 0.366 0.368 0.37 0.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.358 0.36 0.362 0.364 0.366 0.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.358 0.36 0.362 0.364 0.366 0.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.356 0.358 0.36 0.362 0.364 0.366 0.368 0.37 0.372
0
200
400
600
800
1000
Time (Sec)
DC Link Voltage (Volts)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.3680.370.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
010 20 30 4050
0
2
4
6
8
10
Harmonic order
Mag (% of Fundamental)
THD= 5.31%
(a) (b)

S. MIKKILI ET AL. 296
3ph 4w Non-Sin id-iq with PI Controller 3ph 4w Non-Sin id-iq with Fuzzy Controller
0.352 0.354 0.356 0.358 0.36 0.3620.364 0.366 0.3680.370.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.356 0.358 0.36 0.3620.364 0.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.358 0.36 0.3620.364 0.366 0.3680.370.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
0.352 0.354 0.356 0.358 0.36 0.3620.364 0.366 0.3680.37 0.372
-150
-100
-50
0
50
100
150
Time
(
Sec
)
Filter Current (Amps)
0.352 0.354 0.356 0.3580.360.3620.364 0.366 0.3680.37 0.372
0
200
400
600
800
1000
Time (Sec)
DC Link Voltage (Volts)
010 20 30 4050
0
1
2
3
4
5
Harmonic order
THD= 4. 92%
Mag (% of Fundamental)
0.352 0.354 0.356 0.358 0.360.362 0.364 0.366 0.368 0.370.372
-400
-300
-200
-100
0
100
200
300
400
Time (Sec)
Source Voltage (Volts)
0.352 0.354 0.3560.3580.360.3620.3640.366 0.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Source Current (Amps)
0.352 0.354 0.356 0.358 0.360.362 0.364 0.366 0.368 0.370.372
-40
-30
-20
-10
0
10
20
30
40
Time (Sec)
Load Current (Amps)
0.352 0.354 0.356 0.3580.360.362 0.364 0.366 0.368 0.37 0.372
-150
-100
-50
0
50
100
150
Time (Sec)
Filter Current (Amps)
0.352 0.354 0.3560.3580.360.362 0.364 0.366 0.368 0.370.372
0
200
400
600
800
1000
Time
(
Sec
)
DC Link Voltage (Volts)
010 2030 40 50
0
0.2
0.4
0.6
0.8
1
Harmonic order
Mag (% of Fundamental)
THD= 3.01%
(c) (d)
Figure 12. Shunt active pow er filter re sponse under balance d non-sinusoidal voltage conditions for (a) p-q method with PI (b)
p-q method with Fuzzy; (c) id-iq method with PI; (d) id-iq method with Fuzzy Controller.

S. MIKKILI ET AL. 297
p-q with PI p-q with Fuzzy i
d
-i
q
with PI i
d
-i
q
with Fuzzy
% THD
Figure 13. THD for p-q and id-iq control me thods with PI and Fu zzy Contr olle rs.
9. References
On observation pi controller fails to respond quickly
because of non-linear nature in the system, but fuzzy
supports with outstanding performance under any volt-
age conditions. Frankly fuzzy is finest controller in all
the controllers, but it too have some drawbacks like re-
dundancy and iteration problems. So one has to choose
the membership function on the bases system complexity.
Extensive simulation is carried out to validate both con-
trollers, on over all with combination of id-iq strategy and
fuzzy controller; there is possibility of building novel
shunt active filter for 3 phase 4 wire system.
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8. Conclusions
In the present paper two control strategies; instantaneous
real active and reactive power control strategy (p-q) and
active and reactive current control strategy (id-iq) are
developed and verified with three phase four wire system
by using two different controllers PI controller as well as
fuzzy controller. Though the two strategies are capable to
compensate current harmonics in the 3 phase 4-wire sys-
tem, but it is observed that instantaneous active and reac-
tive current id-iq control strategy with fuzzy controller
lead always better result under balanced, un-balanced
and non-sinusoidal voltage conditions over remaining
combinations.
[4] V. Soares, et al., “Active Power Filter Control Circuit
Based on the Instantaneous Active and Reactive Current
Id-Iq Method,” IEEE Power Electronics Specialists Con-
ference, Vol. 2, 1997, pp. 1096-1101.
[5] S. Mikkili and A. K. Panda, “Simulation and RTDS
Hardware Implementation of SHAF for Mitigation of
Current Harmonics with p-q and id-iq Control Strategies
Using PI Controller,” International Journal of Engineer-
ing, Technology & Applied Science Research, Vol. 1, No.
3, 2011, pp. 54-62.
[6] S. Mikkili, A. K. Panda and S. Yellasiri, “RTDS Hard-
ware Implementation and Simulation of 3-ph 4-Wire
SHAF for Mitigation of Current Harmonics Using p-q
Control Strategy With Fuzzy Controller,” Journal of
Power Electronics & Power Systems, Vol. 1, No. 1, 2011,
pp. 13-23.
On contrast p-q theory needs additional PLL circuit
for synchronization so p-q method is frequency variant,
where as in id-iq method angle “θ” is calculated directly
from main voltages and thus enables the method to be
frequency independent. Thus large numbers of synchro-
nization 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.
[7] H. Akagi, H. Kanazawa and Y. Nabae, “Instantaneous
Reactive Power Compensators Comprising Switching
Devices without Energy Storage Components,” IEEE
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[8] M. I. M. Montero, et al., “Comparison of Control Strate-
gies for Shunt Active Power Filters in Three-Phase Four-

S. MIKKILI ET AL. 298
Wire Systems,” IEEE Transactions on Power Electronics,
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doi:10.1109/TPEL.2006.886616
[9] H. Akagi, et al., “Instantaneous Power Theory and Ap-
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Hoboken, 2007.
[10] M. Aredes, et al., “Three-Phase Four-Wire Shunt Active
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[11] P. Rodriguez, et al., “Current Harmonics Cancellation in
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Star Filtering Topology,” IEEE Transactions on Power
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doi:10.1109/TPEL.2009.2017810
[12] S. Mikkili and A. K. Panda, “APF for Mitigation of Cur-
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ing PI Controller,” Journal of Trends in Electrical Engi-
neering, Vol. 1, No. 1, 2011, pp. 1-11.
[13] P. Kirawanich and R. M. O’Connell, “Fuzzy Logic Con-
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1574-1585. doi:10.1109/TPEL.2004.836631
[14] S. K. Jain, et al., “Fuzzy Logic Controlled Shunt Active
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