This article describes the proportional integral (PI), proportional integral derivative (PID) and fuzzy logic controller (FLC) based three phase shunt active power line conditioners (APLC) for the power-quality improvement such as reactive power and harmonic current compensation generated due to nonlinear loads. PI, PID controller requires precise linear mathematical model and FLC needs linguistic description of the system. The controller is capable of controlling dc capacitor voltage and generating reference source currents. Hysteresis current controller is used for current control in PWM voltage source inverter. Extensive simulation studies under transient and steady states are conducted, the simulation result analysis reveal that the APLC performs perfectly in conjunction with PI, PID and FLC. A comparative assessment of the three different controllers is brought out.

1. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
PI, PID and Fuzzy logic controller for Reactive
Power and Harmonic Compensation
Karuppanan P and Kamala Kanta Mahapatra
Dept of ECE, National Institute of Technology-Rourkela, India-769008
Email: karuppanan1982@gmail.com, kmaha2@rediffmail.com
Abstract— This article describes the proportional integral under both steady state and transient conditions. The
(PI), proportional integral derivative (PID) and fuzzy logic operation of APLC is demonstrated in details. The methods
controller (FLC) based three phase shunt active power line of extracting reference current(s) and dc capacitor voltage
conditioners (APLC) for the power-quality improvement such is also presented. The results are also presented that
as reactive power and harmonic current compensation validates the concept and a comparative assessment is
generated due to nonlinear loads. PI, PID controller requires
precise linear mathematical model and FLC needs linguistic
done.
description of the system. The controller is capable of
controlling dc capacitor voltage and generating reference II. DESIGN OF SHUNT APLC
source currents. Hysteresis current controller is used for
The active power line conditioner comprises of six
current control in PWM voltage source inverter. Extensive
simulation studies under transient and steady states are power transistors six power diodes, a dc capacitor , three
conducted, the simulation result analysis reveal that the filter inductor. Reduction of current harmonics is achieved
APLC performs perfectly in conjunction with PI, PID and by injecting equal but opposite current harmonic
FLC. A comparative assessment of the three different components at the point of common coupling (PCC), this
controllers is brought out. facilitates improving the power quality on the connected
power system. The APLC additionally supplies the reactive
Index Terms—Proportional Integral (PI) controller, current component of the load current. The block diagram
Proportional Integral Derivative (PID) controller Fuzzy logic of APLC is shown in fig 1. The output voltage of the
controller (FLC), Hysteresis current controller (HCC), Active
inverter is controlled with respect to the voltage at the point
power line conditioners (APLC).
of common coupling. The design of the DC side capacitor
is based on the principle of instantaneous power flow. The
I. INTRODUCTION
selection of C DC can be governed by reducing the voltage
AC power supply feeds different kind of linear and ripple.
non-linear loads in utilities and industrial applications. The The instantaneous current can be written as [4]
non-linear loads produce harmonics. The harmonic and is (t ) = iL (t ) − ic (t ) (1)
reactive power cause poor power factor and distort the
Source voltage is given by
supply voltage at the common coupling point or customer
vs (t ) = Vm sin ωt ( 2)
service point [1-3]. Passive L-C filters are used to
compensate the lagging power factor of the reactive load, If a nonlinear load is applied, then the load current will
but there are drawbacks such as resonance, large size, have a fundamental component and harmonic components,
weight, etc., the alternative solution, are an active power which can be represented as
∞
line conditioner (APLC) that provides an effective solution
for harmonics elimination and reactive power iL (t ) = ∑I
n =1
n sin( nωt + Φ n )
compensation. The controller is the most important part of
the APLC and currently lot of research is being conducted ⎛ ∞ ⎞
in this area. PI and PID controllers have been used to = I1 sin(ωt + Φ1 ) + ⎜
⎜ ∑
I n sin( nωt + Φ n ) ⎟
⎟
(3)
extract the fundamental component of the load current(s) ⎝ n=2 ⎠
and simultaneously control dc capacitor voltage of the The instantaneous load power can be given as
shunt APLC [1-2]. Recently, fuzzy logic controllers (FLC) p L (t ) = is (t ) * vs (t )
are used in power electronic system [3-5] as it can handle = Vm sin 2 ωt * cos φ1 + Vm I1 sin ωt * cos ωt * sin φ1
nonlinearity, and it is more robust than conventional
nonlinear controllers. ⎛ ∞ ⎞
This paper explores the potential and feasibility of PI,
+ Vm sin ωt * ⎜
⎜∑ I n sin(nωt + Φ n ) ⎟
⎟
PID and FLC schemes that are suitable for extracting the ⎝ n=2 ⎠
fundamental component of the load current(s) and = p f (t ) + pr (t ) + p h (t ) (4)
simultaneously controlling dc capacitor voltage of the From the equation the real (fundamental) power drawn by
shunt APLC. The performance of APLC with different the load is
controllers are evaluated through computer simulations
54
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2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
3-Phase Source isa,isb, isc Non-Linear Load
A ILa,iLb, iLc A
B RL
B
C C LL
Ica,icb, icc
vsa,vsb, vsc Rs,Ls
Rc,Lc Active Power Filter
A
B VDC
C
G PWM-VSI inverter
g1 g2 g3 g4 g5 g6
Active Power Controller
isa* Proportional Integral
Hysteresis Current isb* Reference current (Or) VDC
Controller Generator Proportional-Integral
Derivative
isc* (Or)
Fuzzy Logic Controller VDC ref
isc isb isa vsc vsb vsa
Fig 1 Block diagram of the Proposed APLC based on Fuzzy logic controller or Proportional-Integral controller
p f (t ) = Vm I1 sin 2 ωt * cos φ1 = vs (t ) * is (t ) (5)
PID-Controller
From this equation the source current supplied by the PI-Controller
source, after compensation is
Gain
p f (t ) Vdc,ref
is (t ) = = I1 cosφ1 sin ωt = I sm sin ωt (6)
vs (t ) Integrator Gain
Saturation
where,
I sm = I1 cos φ1 (7) Derivative Gain
Vdc
The total peak current supplied by the source is
LPF isa*
I sp = I sm + I sl (8) Vs Gain
X
If the active filter provides the total reactive and harmonic isb*
power, then is(t) will be in phase with the utility voltage Vs Gain
X
and purely sinusoidal. At this time, the active filter must isc*
provide the following compensation current: Vs X
Gain
ic (t ) = iL (t ) − is (t ) (9)
The desired source currents, after compensation, can be Fig 2 PI and PID- controller for reference current generator
given
Its transfer function can be represented as
isa * = I sp sin ωt (10)
K
isb * = I sp sin(ωt − 1200 ) (11) H ( s) = K P + I (13)
s
isc * = I sp sin(ωt + 1200 ) (12) where, K P is the proportional constant that determines the
dynamic response of the DC-bus voltage control and K I is
Where I sp = I sm + I sl is the amplitude of the desired
the integration constant that determines it’s settling time. PI
source current. controller to eliminate the steady state error in dc voltage.
A. Proportional Integral (PI) Controller: The proportional gain [ K P =0.3] and integral gain [ K I =9]
Figure 2 shows the block diagram of the proposed PI are set such way that Vdc across capacitor is nearly equal to
control scheme of an APLC. The DC side capacitor voltage the reference value of Vdc .
is sensed and then compared with a reference value. The
obtained error e = Vdc ,ref − Vdc at the nth sampling instant is B. Proportional Integral Derivative (PID) Controller:
used as input for PI controller. PI controller used to control The PID controller works on the principle of the PI
the DC-bus voltage. controller(refer fig 2), its control gain is a linear
combination of the error itself representing the present, the
integral of the error representing the past and the derivative
of the error representing the future/trend.
55
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3. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
KI D. Hysteresis Band Current Control:
H ( s) = K P + + K D ( s) (14)
s emax +Vdc/2
The controller is tuned with proper gain parameters iactual(t) vout
e (t) L
[ K P =0.7, K I =23, K D =0.01]. iout
C. Fuzzy Logic Controller (FLC):
Fuzzy logic control is derived from fuzzy set theory, emin -Vdc/2
iref (t)
the transition between membership and non-membership
can be gradual. Therefore, boundaries of fuzzy sets can be
vague and ambiguous, making it useful for approximate Fig 4 Block diagram of hysteresis current controller
systems [4-5]. In fig.1 shows the APLC compensation
system with fuzzy control scheme. In order to implement A hysteresis current controller (Fig. 4) is implemented
the control algorithm of a shunt active power line to control the switches in the inverter [6-8] to control the
conditioner in a closed loop, the dc capacitor voltage current within the inverter.
VDC is sensed and then compared with the reference III. SIMULATION RESULT AND ANALYSIS
value VDC , ref .
The results of the proposed PI, PID and fuzzy logic
controlled shunt APLC is investigated using SIMULINK/
Rule Base
MATLAB. The system parameters values are; source
voltage (Vs) is 230 Vrms, System frequency (f) is 50 Hz,
e(n) Source impedance of RS, LS is 1 Ω; 0.1mH respectively,
Vdc,ref Rule Evaluator Filter impedance of Rc, Lc is 1 Ω; 2.7 mH, Load impedance
+ Fuzzification
(Decision Defuzzification
of RL, LL of diode rectifier RL load in Steady state: 20 Ω;
- making)
ce(n) 200 mH and Transient: 10 Ω; 100 mH respectively, DC
Vdc link capacitance (CDC) is 1600 μF, Reference Voltage
(VDC) is 400 V and Power devices used are IGBT/Diode.
Data Base
Case 1: Proportional Integral controller:
Fig 3 Fuzzy logic controller
PI-controlled APLC system comprises of a three-phase
Table 1 Rule base table source, a nonlinear load (six pulse diode rectifier bridge
feeding an RL load) and a PWM voltage source inverter
ce(n) NB NM NS ZE PS PM PB
e(n)
with a dc capacitor input. The simulation time T=0 to
T=0.5s with diode rectifier and R L load parameter values
NB NB NB NB NB NM NS ZE
of 20 ohms and 200 mH respectively. The source current
NM NB NB NB NM NS ZE PS after compensation is presented in fig. 5 (a) that indicates
NS NB NB MN NS ZE PS PM the current becomes sinusoidal. The load current is shown
ZE NB NM NS ZE PS PM PB in (b) for a particular phase (phase a). The actual reference
PS NM NS ZE PS PM PB PB currents for phase (a) are shown in fig. 5(c). This wave is
obtained from our proposed PI controller. The APLC
PM NS ZE PS PM PB PB PB
supplies the compensating current that is shown in Fig.
PB ZE PS PM PB PB PB PB 5(d). The current after compensation is as shown in (a)
which would have taken a shape as shown in (b) without
In case of a fuzzy logic control scheme, the error
( )
e = VDC , ref − VDC and integration of error signal
APLC. It is clearly visible that this waveform is sinusoidal
with some high frequency ripples. We have additionally
(∫ e) are used as inputs for fuzzy processing shown in fig achieved power factor correction as shown in Fig. 5(e),
phase (a) voltage and current are in phase. The time
3. The output of the fuzzy controller after a limit is domain response of the PI controller is shown in Fig. 5(f)
considered as the magnitude of peak reference current I max . that clearly indicates the controller output settles after a
few cycles.
The switching signals for the PWM inverter are obtained 100
Isa
by comparing the actual source currents (isa , isb , isc ) with
80
60
40
(a)
20
0
-20
(isa *, isb *, isc *) in
-40
-60
-80
the reference current templates the
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
50
iLa
40
30
(b)
20
hysteresis current controller. The output pulses are then
10
0
-10
-20
given to the switching devices of the PWM converter.The
-30
-40
-50
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
rules used in this paper are shown in table 1.
80
Isaref
60
40
(c) 20
-20
0
-40
-60
-80
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
56
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4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
The real and reactive power measured using PID
80
Ica
60
40
20
(d) -20
-40
-60
0
controller, shown in fig 9.
9000
-80
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
8000
7000
200 Isa
6000
Real Power
Vsa
150 Reactive Power
5000
100
(e)
50 4000
0 3000
-50 2000
-100
1000
-150
0
-200
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -1000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fig 9 Active and Reactive power at diode rectifier RL load under the
700
Vdc
600
500
(f)
400
300
200
100
steady state condition (P=7.34 KW, Q=0.034 KW)
0
-100
Total Harmonic distortion measurement (THD) of the
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Fig.5 Simulation results for PI-controlled three-phase APLC under the
APLC in the transient condition by proportional-integral
steady state condition (a) Source current after APLC, (b) Load currents,
(c)Reference currents by the Proportional-integral algorithm, (d) derivative controller, shown in fig 10.
Compensation current by APLC, (e) source voltage per current for unity
20
Mg it d b s do " a eP a "-P r mt r
aa ee
18
16
power factor and (f) DC capacitor voltage 14
a nu e a e n Bs e k
(a)
12
10
8
The active power P and reactive power Q associated 6
4
2
with a periodic voltage-current pair that can contain
0
0 2 4 6 8 10 12 14 16 18
Order of Harmonic
30
harmonics. P and Q are calculated by averaging the
Mg it d b s do " a e e k -Pr mt r
a nu e a e n Bs Pa " aa e e
25
20
voltage-current product with a running average window (b) 15
10
over one cycle of the fundamental frequency (refer fig 6). 5
0
0 2 4 6 8 10
Order of Harmonic
12 14 16 18
t
1
∫ V (ωt ) × I (ωt )dt
Fig 10 PID-controlled under the Transient condition (a) FFT analys of
P= (15) Source current without APLC(THD=24.96%) (b) with
T
t −T APLC(THD=2.96%).
t
1
Q=
T ∫ v(ωt ) × i(ωt − π / 2)dt (16) Case 3: Fuzzy logic controller:
t −T Simulation time T=0 to T=0.5s with load of rectifier
with RL parameter values of 20 ohms and 200mH
9000
8000
7000
6000 Real Power
5000 Reactive Power
respectively in the steady state and the load with R L value
4000
3000
2000
1000
of 10 ohms and 100 mH under transient condition. The
0
-1000
0 0.1 0 .2 0.3 0 .4 0.5 0 .6 0.7 0 .8 0.9 1
Fig 6 Active and Reactive power at diode rectifier RL load under the simulated waveforms are presented in figures 11, 12 and
steady state condition (P=7.34 KW, Q=0.04 KW) 13.
100
Isa
80
Total Harmonic distortion (THD) is measured of the
60
40
(a)
20
0
APLC in the PI controller, shown in fig 7.
-20
-40
-60
-80
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
16
M iu b eo"a Pk- amr
a e
a t d a dn s e " P e
r t
50
14
iLa
40
12
30
Be a
10 20
(a)
10
8
(b)
0
g e s
6
-10
4 -20
n
-30
2
-40
0
0 2 4 6 8 10 12 14 16 18 -50
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Order of Harmonic
30
80
a e
e a - r tr
M iu be n a Pk P m
a td ad " s e" a e
Ica
25
60
20
(b)
40
g e s oB
15
20
10
(c)
0
n
5
0
-20
0 2 4 6 8 10 12 14 16 18
Order of Harmonic
-40
-60
Fig 7 PI-controlled under the steady state (a) FFT analys of Source current
-80
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
600
without APLC (THD=25.58%) (b) with APLC(THD=1.98%).
Vdc
500
400
300
(d)
200
Case 2: Proportional Integral Derivative controller: 100
-100
0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
ID controlled simulation waveforms are verified
Fig.11 Simulation results for Fuzzy Logic Controlled 3-phase APLC
similarly PI-controller, PID controller waveform presented under the steady state condition (a) Source current after APLC, (b) Load
in figures 8, 9 and 10. currents, (c) Compensation current by APLC, and (d) DC capacitor
voltage
100
Isa
80
60
40
(a) The summarized DC voltage settling time compared
20
0
-20
-40
PI, PID and Fuzzy logic controller, shown in table 2
-60
-80
-100
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
50
iLa
40
30
20
Table 2 comparison of PI, PID and FLC for DC voltage settling time
10
(b)
0
-1 0
-2 0
-3 0
-4 0
-5 0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
80
Ica
Diode VDC settling time in seconds
60
40
(c)
20
rectifier
0
-20
-40
PI PID Fuzzy logic
RL load
-60
-80
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
700
vdc
controller
controller controller
600
500
(d)
400
300
200
Steady State 0.37s 0.26s 0.22s
100
0
-100
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Fig.8 Simulation results for PID controlled 3-phase APLC under the Transient 0.39s 0.28s 0.23s
steady state condition (a) Source current after APLC, (b) Load currents,
(c) Compensation current by APLC, and (d) DC capacitor voltage
The real and reactive power measured using fuzzy
logic controller, shown in fig 12.
57
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5. ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010
9000
8000
7000
CONCLUSIONS
6000
Real Power
PI, PID and fuzzy logic controllers are implemented for
5000 Reactive Power
4000
3000
three phase shunt active power line conditioner to obtain dc
2000
1000
0
capacitor voltage and the reference currents. This facilitates
-1000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fig 12 Active and Reactive power at diode rectifier RL load under the to improve the power quality parameters such as reactive
steady state condition (P=7.33 KW, Q=0.04 KW) power and harmonic compensation due to nonlinear load.
The summarized Real (P) and Reactive (Q) power The performance of a PI, PID and fuzzy logic controlled
calculation compared with PI, PID and Fuzzy logic APLC is verified and compared under steady state and
controller, shown in table 3. transient in various disciplines. The fuzzy logic controller
reduces ripples in the dc capacitor voltage and needs less
Table 3 comparison of PI, PID and FLC for Real and Reactive power settling time compared to PI and PID-controller. The THD
Controller Condition Real (P) and Reactive (Q) power of the source current after compensation is less than 5% in
measurement case of all the controllers, the harmonic limit imposed by
Without APLC With APLC the IEEE-519 standard. Apparently it seems that the fuzzy
PI Steady state P=3.90 KW P=7.34 KW
Q=0.12 KW Q=0.04 KW
logic controller is an effective candidate for active power
Transient P=4.85 KW P=7.34 KW line conditioner to solve power quality issues as this would
Q=0.16 KW Q=0.07 KW also facilitate easy implementation.
PID Steady state P=3.90 KW P=7.34 KW
Q=0.12 KW Q=0.03 KW
ACKNOWLEDGEMENTS
Transient P=4.85 KW P=7.34 KW
Q=0.16 KW Q=0.07 KW The authors would like to acknowledge to Ministry of
Fuzzy logic Steady state P=3.91 KW P=7.33 KW
Q=0.13 KW Q=0.04 KW
Communication and Information Technology, Govt. of
Transient P=4.83 KW P=7.35 KW India for the financial support.
Q=0.17 KW Q=0.08 KW
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an d ae n Bs ek
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5
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Order of Harmonic
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58
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