An Improved Double Fuzzy PI Controller For Shunt Active Power Filter DC Bus Regulation

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 6, No. 2, June 2015, pp. 337~347
ISSN: 2088-8694  337
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
An Improved Double Fuzzy PI Controller For Shunt Active
Power Filter DC Bus Regulation
Nabil Elhaj*, Moulay Brahim Sedra*, Tarik Jarou*, Hind Djeghloud**
* Laboratory of High Energies, Engineering Sciences, and Reactors, Ibn Tofail University, Kenitra, Morocco
** Laboratory of Electrical Engineering, Constantine 1 University, Constantine, Algeria
Article Info ABSTRACT
Article history:
Received Jan 30, 2015
Revised May 16, 2015
Accepted May 25, 2015
This paper targets to demonstrate the importance of the choice of the
algorithm references detection to be applied with a double fuzzy PI corrector
(DFPI) for the control and the regulation of a shunt active power filter
(SAPF) DC bus voltage. In a previous work, the synchronous reference
frame (SRF) algorithm was applied and gave satisfactory results. In the
present paper, the SRF is compared to the positive sequence of the
fundamental of the source voltage algorithm (PSF) which offered better
results regarding the power quality of the considered main utility feeding a
variable DC RL load throughout a diode bridge. The results were carried out
using computer simulation performed under MATLAB/Simulink
environment. To make the obtained results more convenient, a comparison
between the couples (SRF, PI), (PSF, PI), (SRF, DFPI), (PSF, DFPI) is added
to prove the effectiveness of the couple (PSF, DFPI) in satisfying the
compromise between a good regulation of the SAPF DC bus voltage and a
good quality of filtering resulting in an improved quality of power.
Keyword:
Harmonics
SAPF
SRF & PSF algorithms
DFPI DC voltage controller
Comparisons
Copyright © 2015 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Nabil elhaj,
Laboratory of High Energies, Engineering Sciences and Reactors,
Ibn Tofail University,
Kenitra, Morocco.
Email: Nabilmaill@yahoo.fr
1. INTRODUCTION
Recently, improving the quality of energy in electrical distribution power utilities becomes a subject
of great interest. The power quality of these utilities is mainly related to the voltage and current waveforms
that should be sinusoidal and in phase each other. However, the power quality can be affected by the
influence of many disturbances, these disturbances are found under different forms (harmonics, sags,
unbalance, flickers and swells) [1]-[2].
To minimize the effect of disturbances on power quality several solutions are proposed as effective
remediation namely active power filters (APFs) based on voltage source (VSIs) or current source (CSIs)
inverters that can be connected in parallel, series or both of them between the power utility and the disturbing
load [3]-[4]. The principle of these topologies is to provide the opposite disturbance that counters the existing
disturbance, so that it can’t attain the power utility.
To be effective in its operation the active power filtering system needs to be well supplied with a
sufficient and non fluctuating DC voltage in its DC bus terminals and well controlled to provide the desired
output signals. To achieve these conditions, the control circuit is designed on the basis of three main blocks:
the algorithm that detects the reference signals, the corrector that compensates the fluctuations of the DC bus
voltage and the modulator that generates the switching signals to be launched to the inverter switches gates.
These three blocks work together to output the compensating signals. Thus, they must be carefully conceived

 ISSN: 2088-8694
IJPEDS Vol. 6, No. 2, June 2015 : 337 – 347
338
to avoid failing in operation of the APF system. Several kinds of theses blocks can be found in the literature
[5]-[6], [7]-[8], [9]-[10].
In this paper two algorithms of reference currents detection are considered to be associated with the
DFPI controller introduced in [11]. It’s a matter of the synchronous referential frame (SRF) algorithm and the
positive sequence of voltage source fundamental (PSF) algorithm. The objective is to conclude about the
most suitable algorithm to be applied with the DFPI controller intended to regulate the DC bus voltage of a
shunt APF system. The pulses generator is a hysteresis modulator and the validation of the presented studies
is based on simulation works performed under MATLAB/Simulink.
This work is summarized in five sections. Section 2 concerns the description of the considered
topology and control technique. Section 3 presents the algorithms SRF and PSF. Section 4 recalls the
principle of the introduced DFPI [11]. Section 5 is consecrated to the verification by computer simulation and
to the comparative studies.
2. DESCRIPTION OF THE CONSIDERED TOPOLOGY AND CONTROL TECHNIQUE
Figure 1 shows the studied system that consists of a three phase power supply and its internal
impedance (RsLs), a nonlinear load (diode rectifier) and a shunt active power filter. The rectifier loaded by a
passive circuit (RLLL). The SAPF comprises a three-phase voltage inverter and an output filter (Rf Lf). This
inverter is formed by a three half-bridges (T1-T4, T2-T5, T3-T6) based on IGBTs with anti-parallel diodes. The
inverter legs are fed by a DC voltage Vdc. To generate the IGBTs pulses a hysteresis current controller is
used. The reference currents are achieved first by the SRF algorithm, then by the PSF algorithm. The
regulation of the DC voltage of SAPF is based on a Double Fuzzy logic PI controller [11]-[12]. A resistor Rdc
is added to the system which is connected in parallel to the capacitor Cdc feeding the SAPF through the
regulating loop. The role of this resistor is to minimize Vdc ripples by controlling the constant time  as
explained in (1).
R 
C (1)
Where Cdc is dimensioned in [11] and  takes as value few alternances of the fundamental frequency [13].
The other passive elements and Vdc are also dimensioned in [11].
Figure 1. Schematic diagram of the studied system
3. SRF & PSF ALGORITHMS FOR REFERENCE DETECTION
a. SRF Algorithm
The principle of this algorithm is to force the source current to have the same angular frequency as
that of the source voltage (i.e. source voltage and current waves are in synchronism each other), in this way

IJPEDS ISSN: 2088-8694 
An Improved Double Fuzzy PI Controller for Shunt Active Power Filter DC Bus Regulation (Nabil Elhaj)
339
the power factor is forced to remain near the unity. The extraction of the reference currents is based on the
Park transformation applied to the load three-phase currents so that the angle is procured from source three-
phase voltages angular frequency through a three-phase PLL. Then from the obtained diphase load currents,
fundamental part is removed using a 2nd
order low-pass filter tuned on the fundamental frequency and which
remains are the desired diphase reference currents as expressed in (2). Finally by using the inverse Park
transformation, the three-phase reference currents are carried out. All these steps are summarized in the set of
equations (2)-(4) and illustrated in the synoptic scheme of Figure 2 [14].
∗
. ∗
(2)
Where [P]-1
is the inverse of the Park transformation [P] [15], ∗
are the diphase reference currents given
by (3).
∗
(3)
With:
. (4)
And are outputs of the second order low-pass filter tuned on the fundamental frequency.
Figure 2. Synoptic scheme of the SRF algorithm (neglecting the zero sequence)
b. PSF Algorithm
The objective of this algorithm is also to keep the power factor around the unity but this time by
forcing the source current to have the same argument as that of the positive sequence of the source voltage
fundamental component. Thus the first step of the algorithm is to extract fundamental components from the
source voltages using a second order band-pass filter. Then, the obtained instantaneous signals are converted
into complex signals with help of Fourier block. Afterward, positive sequence of these complex signals is
extorted through the Fortescue transformation. From this positive sequence component, the module will serve
together with load active power to compute the module of the fundamental component of the source current
as expressed in (5), whereas the argument will be the angle of this current. Then, from the total load current,
the new current is removed; as a result a pure harmonic reference current is produced. The algorithm is
illustrated in Figure 3 [16].
. (5)
The demonstration of this equation is given in [16]. The reference currents are then expressed by (6):
∗
∗
∗
.
sin
sin 2 3⁄
sin 2 3⁄
(6)

 ISSN: 2088-8694
340
Figure 3. Synoptic scheme of the PSF algorithm
4. THE DFPI CONTROLLER
a. Principle of Vdc regulation
Fuzzy logic controller is used for complicated systems and allows translating knowledge and human
reasoning to simple rules that a computer can use, while artificial intelligence and PI Control are used to
achieve this objective. The diagram of Figure 4 shows the control algorithm of the capacitor voltage of the
SAPF DC, this control is based on a double fuzzy PI controller. The DC bus voltage capacitor is compared
with the reference to obtain the error ‘e’ given by the following equation:
e t V∗
t V t (7)
The reference voltage Vdc
*
corresponds to the charge of the capacitor Cdc, these quantities are dimensioned in
[11]. The derivative of the error is given by (8).
∆e t e t e t 1 (8)
Figure 4. The proposed DFPI Controller for Vdc regulation
b. Structural construction of the fuzzy controller
The structural diagram of a fuzzy controller is shown in Fig.5. It consists of four distinct blocks
[17]:
Figure 5. The structural diagram of the fuzzy controller

341
1. Base of rules
It consists on the establishment of the fuzzy rules based on the direction of variation of the error ‘e’, and the
algebraic sign of the error ‘e’ and its derivative ‘Δe’.
2. Fuzzification interface
In this step the membership functions of the input/output for each fuzzy partition of the universe of discourse
are defined (Figure 6).
3. Inference mechanism
It is the process of designing fuzzy rules like: If e is ... & e is ... So ... the command is.
4. Defuzzification interface
In this step real value assigned to the variables of fuzzy output (several methods are available and most of
them use the centroid or the bisector methods).
(a)
(b)
(c)
Figure 6. Membership function used in fuzzification for a) input variable e, b) input variable e,
and c) output variable Vdc
As shown in Figure 6 the fuzzification consists in using triangular membership functions for ‘e’ and
its derivative ‘e’. The inference mechanism describes 49 fuzzy rules summarized in Table 1, The linguistic
values are defined as follows: {Positive Big (PB), Positive Medium (PM), Positive Small (PS), Zero (ZO),
Negative Small (NS), Negative Medium (NM), Negative Big (NB)}. For defuzzification, the bisector method
is applied.
Table 1. Fuzzy rules table
Δe/e NB NM NS Z PS PB
NB NB NB NB NB NM NS
NM NB NB NB NM NS Z
NS NB NB NS NS Z PS
Z NB NM Z Z PS PM
PS NM NS PS PS PM PB
PM NS Z PM PM PB PB

 ISSN: 2088-8694
342
c. Dimensioning of the PI controller
The harmonic currents influence on the stability of the capacitor voltage and causes a corrugation of
this latter. To reduce the ripples of DC voltage, a PI controller is used. The dimensioning of coefficients Kp
and Ki of the PI can be achieved starting from the following diagram (Figure 8) which leads to the transfer
function of the corrected system in the open loop expressed by (9).
Figure 7. Coefficients Dimensioning of PI controller
. (9)
Where,
and (10)
Where iF and VF are active components of the SAPF output current and voltage.
The passing band of the voltage loop is inferior to that of the current loop, consequently the pole of
TFi(p) will not intervene in the voltage loop stability, so one can consider that 1 [18]. By
neglecting the switching losses in the active filter and in the output filter, the energy is the same in both
DC and AC sides. Thus:
. ∗
. . . (11)
Where,
3. .
√
. . (12)
Therefore,
.
√ . . ∗ . .
(13)
With,
√ . . ∗
.
(14)
Now by introducing the PI controller, the transfer function for the open loop becomes:
.
.
.
.
(15)
Where,
and (16)
In the periodical state, is expressed as:
.
(17)
So that,

343
and (18)
According to Bode diagram of , and can be deduced from the cutting frequency
2. . for which the gain of 1 is null and its phase  equals atan ω ω⁄ .
Finally,

and
√
(19)
Generally, the cutting frequency is set at 20 Hz [18].
5. VERIFICATION BY COMPUTER SIMULATION
In this section simulation works about the previous study are provided. They were carried out using
MATLAB/Simulink software and considering the parameters reported in Table 2.
Table 2. Simulation Parameters
Parameter Value
AC supply voltage and frequency 380V-50Hz
Supply impedance Rs = 0.07 Ω, Ls = 0.25 mH
Rectifier load RL = 10 Ω, LL = 50 mH
Output filter impedance RF = 10 mΩ, LF = 0.95 mH
Upstream filter impedance Rc = 0.387 Ω, Lc = 0.3 mH
DC link capacitor
DC Résistance
Cdc = 3.1 mF
Rdc = 64.5 Ω
DC link reference voltage ∗
= 550 V
PI angle, coefficients and saturation 60°, Kp = 0.1, Ki = 7.28, ±5V
The simulations models concern for pairs of (algorithm of references, V controller) considering
(SRF, PI), (SRF, DFPI), (PSF, PI) and (PSF, DFPI). The obtained results are presented in the figures 8 to 13,
note that only results of phase a are presented since there is similarity with the other phases shifted by 120°
from a.
Figure 8 presents the source current before performing the filtering operation. A nonsinusoidal wave
can be seen in Figure 8.a. The harmonic spectrum of this wave gives a THD% of 25.48% which is not
conform to the standards IEEE 519 and IEC 61000-3-2. Besides, the current is not in phase with the source
voltage which means that the PF is not close to the unity.
Figure 8. Results before starting the operation of the SAPF (a). Waveforms of V and i (b) Harmonic
spectrum of i
0.8 0.85 0.9 0.95 1
-50
0
50
isa(A)
0 5 10 15 20 25 30
0
10
20
30
40
50
60
Harmonic order
Harmonicmagnitude
0.8 0.85 0.9 0.95 1
-500
0
500
Time (s)
Amp(A,V)
isa
(a) (b)
THDis % = 25.48%
Duration = 1s
Vsa

 ISSN: 2088-8694
344
Figure 9 shows the results after putting the SAPF under operation but without inserting the
controller of V . The upper plot of Figure 9.a illustrates V with its refrence V∗
, it is obvious that V is
inferior to V∗
(the deviation is around 6%). However the two other plots of Figure 9.b demonstrate a good
quality of filtering in both current and source voltage as well as a good compensation of the power factor
since no delay is noticed between the two signals. The THD% of the source current is 4.79% as depicted in
Figure 9.c which agrees with the standards restrictions.
Figure 9. Results before inserting the V controller (case of PSF algorithm).
(a) V and V∗
(b) i and i with V (c) Harmonic spectrum of i
Figure 10 shows the obtained results after inserting the PI controller and using the SRF as algorithm
for detecting the references of the SAPF currents. The first curve (Figure 10.a) mentions that V follows
perfectly its reference after a transient state of more than 0.3s. Concerning the filtering quality and the power
factor compensation. Figure 10.b describes sinusoidal waveforms for both current and voltage in the source,
moreover they are in phase which means a satisfactory value of the PF. Figure 10.c gives the THD% of i
which is also conform to norms (2.79%).
Figure 10. Results after inserting the PI controller associated to the SRF algorithm
(a) V and V∗
0 0.2 0.4 0.6 0.8 1
-100
0
100
isa(A)
0 0.2 0.4 0.6 0.8 1
-500
0
500
Amp(A,V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
500
550
600
Amp(V)
vdc* vdc
0 10 20 30
0
20
40
60
80
Harmonic order
Harmonicmagnitude
Time (s)
(a)
THD is % = 4.79 %
Duration = 1sVsa isa
(c)
Time (s)
(b)
0 10 20 30
0
20
40
60
80
Harmonic order
Harmonicmagnitude
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
500
550
600
Amp(V)
vdc* vdc
0 0.2 0.4 0.6 0.8 1
-100
0
100
isa(A)
0 0.2 0.4 0.6 0.8 1
-500
0
500
Time (s)
Amp(A,V)
(c)
Time (s)
(a)
(b)
isa
THD is % = 2.79 %
Duration = 1s
Vsa

345
Figure 11 provides the results of the DFPI associated to the SRF algorithm. As shown in Figure
11.a, less transient state occurs (less than 0.1s), then V reaches V∗
and evolves with it. The impact of the
DFPI in reducing the transient state duration is very clear. Figure 11.b demonstrates the synchronism
between source voltage and current whereas Figure 11.c indicates an acceptable THD% of isa. Which mean
that the improvement introduced in V regulation hasn’t influenced the power factor and the filtering
quality.
Figure 11. Results after inserting the DFPI controller associated to the SRF algorithm
(a) V and V∗
Now, results concerning the couples (PSF algorithm, PI controller), (PSF algorithm, DFPI
controller) will be dressed. The objective is to carry out better results than those of the precedent couples
(SRF algorithm, PI controller) and (SRF algorithm, DFPI controller). Fig.12 shows the results of the couple
(PSF algorithm, PI controller). One can see better result in V regulation comparing to that shown in Figure
11.a, the transient state in Figure 12.a describes an exceeding value of 25V, while Figure 11.a indicated a
lack of 50V in the transient state. Although the obtained THD% of i (3.89%) is greater than that of Figure
11.c (3.07%), but it remains conform to norms (< 5 %).
Figure 12. Results after inserting the PI controller associated to the PSF algorithm
(a) V and V∗
0 10 20 30
0
20
40
60
80
Harmonic order
Harmonicmagnitude
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
500
550
600
Amp(V)
vdc* vdc
0 0.2 0.4 0.6 0.8 1
-100
0
100
isa(A)
0 0.2 0.4 0.6 0.8 1
-500
0
500
Time (s)
Amp(A,V)
(c)
Time (s)
(a)
(b)
Vsa isa
THD is % = 3.07 %
Duration = 1s
0 10 20 30
0
20
40
60
80
Harmonic order
Harmonicmagnitude
0 0.2 0.4 0.6 0.8 1
-100
0
100
isa(A)
0 0.2 0.4 0.6 0.8 1
-500
0
500
Amp(A,V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
500
550
600
Amp(V)
vdc* vdc
(c)
isaVsa
Time (s)
(a)
(b)
Time (s)
THD is % = 3.89 %
Duration = 1s

 ISSN: 2088-8694
346
Finally Figure 13 gives the results of the last couple (PSF algorithm, DFPI controller).
Figure 13. Results after inserting the DFPI controller associated to the PSF algorithm
(a) V and V∗
(b) i and isa with Vsa (c) Harmonic spectrum of i
Obviously the regulation of V is the best for this latest couple. In fact as depicted in Figure 13.a
V describes less exceeding value (< 25V) in the transient state comparing to Figure 12.a. Furtheremore the
THD% of Figure 13.c (3.62%) is less than that of Figure 12.c. Consequently, one can conclude that the
couple (PSF algorithm, DFPI controller) is the best in regulating V , correcting the power factor and
improving i waveform.
6. CONCLUSION
In the objective of improving the results carried out in a former work, the present article has focused
on changing the algorithm of detection of the reference currents of a SAPF to obtain better response
simultaneously in regulating the DC voltage V of the SAPF, maintaining the power factor at a satisfactory
level and improving the filtering quality (obtaining a conform THD% of the source current). In the previous
work, the SRF algorithm was used, it was associated to the DFPI V controller. In this study, the SRF is
compared to the PSF algorithm since it is based on the principle of forcing the fundamental source current to
have the same angle as that of the positive sequence of the fundamental source voltage. Thus, the main
feature of the PSF is to ensure a unity power factor in the source side. After presenting the considered
algorithms and controllers, a verification through simulations were performed under MATLAB/Simulink
environment which concerned four couples of algorithm/controller (SRF/PI, SRF/DFPI, PSF/PI, PSF/DFPI).
The results indicated that the best couple satisfying the targets (less transient state and less exceeding value
of V , a unique PF and a conform THD% of i ) is the couple (PSF/DFPI). The continuation of the study
concerns the application of a DFPI controller for regulating the SAPF current.
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0 10 20 30
0
20
40
60
80
Harmonic order
Harmonicmagnitude
0 0.2 0.4 0.6 0.8 1
-100
0
100
isa(A)
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Time (s)
Amp(A,V)
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Vsa

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