Improved control conguration ofPWM
rectiers based onneuro-fuzzy controller
Hakan Acikgoz
1
, O. Fatih Kececioglu
2
, Ahmet Gani
2
, Ceyhun Yildiz
2
and Mustafa Sekkeli
2*
Background
With advances in power electronics and microprocessors, power electronics technol-
ogy has widely used for many applications. Nowadays, AC/DC converters, which are also
known as rectifiers, are used in adjustable speed drives, uninterruptible power supply sys
-
tems, photovoltaic systems, battery energy storage systems, DC motor drives and com-
munication systems (Singh etal.
2004; Blasko and Kaura 1997). AC to DC conversion has
been performed by an uncontrollable diode rectifier or a phase controlled thyristor recti
-
fier. Although these rectifiers have high reliability, simple structure and low cost, they have
many disadvantages such as low power factor, high THD and unidirectional power flow.
Moreover, these rectifiers that produce high harmonic currents are actually a harmonic
source and have caused harmonic problems (Dannehl etal.
2009; Sekkeli etal. 2015). To
solve these problems, new standards have been introduction by a number of countries
and international organizations to limit harmonics formed in the current drawn from
main supply by rectifiers. During the past 20years, the interest in AC/DC rectifiers has
been growing by day by due to the increasing concern about the harmonic pollution in
the power systems. anks to the rapid development of technology, new rectifier type for
Abstract
It is well-known that rectifiers are used widely in many applications required AC/DC
transformation. With technological advances, many studies are performed for AC/DC
converters and many control methods are proposed in order to improve the perfor-
mance of these rectifiers in recent years. Pulse width modulation (PWM) based rectifi-
ers are one of the most popular rectifier types. PWM rectifiers have lower input current
harmonics and higher power factor compared to classical diode and thyristor rectifiers.
In this study, neuro-fuzzy controller (NFC) which has robust, nonlinear structure and do
not require the mathematical model of the system to be controlled has been proposed
for PWM rectifiers. Three NFCs are used in control scheme of proposed PWM rectifier
in order to control the dq-axis currents and DC voltage of PWM rectifier. Moreover,
simulation studies are carried out to demonstrate the performance of the proposed
control scheme at MATLAB/Simulink environment in terms of rise time, settling time,
overshoot, power factor, total harmonic distortion and power quality.
Keywords: PWM rectifiers, Neuro-fuzzy controller, Total harmonic distortion,
Power quality
Open Access
© 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
(
http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium,
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indicate if changes were made.
RESEARCH
Acikgoz
et al. SpringerPlus (2016) 5:1142
DOI 10.1186/s40064-016-2781-5
*Correspondence:
msekkeli@ksu.edu.tr
2
Department of Electrical
and Electronics,
Faculty of Engineering,
Kahramanmaras Sutcu Imam
University, Kahramanmaras,
Turkey
Full list of author information
is available at the end of the
article
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Acikgoz
et al. SpringerPlus (2016) 5:1142
three-phase AC/DC conversation have been developed such as PWM rectifier (Wu etal.
1991). PWM rectifiers used for AC-DC conversion have many advantages like controllable
DC voltage, fast dynamic response, controllable reactive power, unity power factor, low
harmonic distortion and bidirectional power flow (Bouafia etal.
2010a, b). Generally, the
control techniques of PWM rectifiers can be classified into two types: Voltage oriented
control (VOC) and direct power control (DPC). VOC based on internal current control
loops became very popular method. Another control method is called as DPC which has
not internal current loops and PWM blocks (Malinowski et al.
2001; Malinowski and
Kazmierkowski
2003; Monfared etal. 2010). e main goal of these control techniques is
to eliminate the current harmonics and to regulate the DC bus voltage. In the control of
PWM based rectifiers, DC bus voltage and dq-axis currents are generally controlled by
proportional-integral (PI) controllers due to their simple structure. PI controllers need lin
-
ear mathematical model of system. Moreover, it is known that PI controllers have many
disadvantages such as slow response, large overshoots and oscillations (Cortes etal.
2008;
Blasko and Kaura
1997). To cope with these problems, many control methods have been
proposed by many academics and researchers, namely fuzzy logic controllers (FLC), robust
H∞ controller, linear quadratic regulator (LQR), sliding mode control (SMC) and predic
-
tive control (PC). ese intelligent controllers have used for many industrial applications
and rectifier systems to obtain a good performance in both transient and steady state from
PWM rectifier (Antoniewicz and Kazmierkowski
2006; Yu et al. 2010; Zhao et al. 2011;
Jiabing etal.
2011; Bouafia and Krim 2008; Djerioui etal. 2014). NFC that has nonlinear,
robust structure and based on FLC whose functions are realized by ANN is one of these
intelligent controllers (Zadeh
1965; Jang etal. 1997; Mohagheghi etal. 2007). In this paper,
the robust and nonlinear control strategy based NFC controllers are proposed for DC bus
voltage and dq-axis currents control of PWM rectifier in order to achieve a good dynamic
response. NFC controllers designed for DC voltage and dq-axis currents have two inputs,
single output and six layers. is paper is organized as follows: Power circuit and math
-
ematical model of PWM rectifier is given in first section. e determination of electrical
parameters in PWM rectifier and design of PI controller are presented in second section.
e description of the NFC and its training algorithm are explained in third section. e
simulation results related to proposed controller are comprehensively presented in fourth
section. e final section provides the conclusions of this study.
Mathematical model ofPWM rectier
e three-phase PWM rectifiers are widely used in a wide diversity of applications in
recent years. ese rectifiers have many advantages such as bi-directional power flow,
low harmonic distortion of line current, unity power factor, control of DC bus voltage
(Blasko and Kaura
1997; Kazmierkowski etal. 2002).
e structure of three-phase PWM rectifier is as shown in Fig.
1. e source phase
voltages are expressed as:
(1)
V
a
= V
m
sin θ
(2)
V
b
= V
m
sin(θ − 2π/3)
(3)
V
c
= V
m
sin(θ + 2π/3)
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Acikgoz
et al. SpringerPlus (2016) 5:1142
e mathematical model of PWM rectifier in abc frame can be expressed as: (Blasko
and Kaura
1997).
where, L
s
and R
s
are grid inductance and resistance, respectively. I
a
, I
b
and I
c
are grid
phase currents; V
ra
, V
rb
and V
rc
are the rectifier input voltages. V
ra
, V
rb
and V
rc
voltages
can be found by opening and closing in accordance with the switching elements in the
structure of rectifier to obtain the DC link voltage. Where, S
a
, S
b
and S
c
show switching
functions. ese functions get 0, if the switch is off; if it is on, then they are 1. Clarke’s
matrix in α–β frame can be described as following (Blasko and Kaura
1997):
According to Clake’s transformation, the dynamic model of PWM rectifier can be
defined as:
If Park’s transformation is applied to rectifier system then following equation can be
derived:
(4)
L
s
dI
ra
dt
L
s
dI
rb
dt
L
s
dI
rc
dt
L
s
du
c
dt
=
−R
s
0 00
0 −R
s
00
00−R
s
0
S
a
S
b
S
c
−1
I
ra
I
rb
I
rc
I
L
+
V
a
− V
ra
V
b
− V
rb
V
c
− V
rc
0
(5)
V
ra
V
rb
V
rc
=
2/3 −1/3 −1/3
−1/32/3 −1/3
−
1/3
−
1/32/3
S
a
S
b
S
c
V
dc
(6)
T =
1 −1/2 −1/2
0
√
3/2
−
√
3/2
(7)
V
α
V
β
= L
s
dI
α
dt
dI
β
dt
+
R
s
0
0R
s
I
α
I
β
+
V
rα
V
rβ
Va
Vb
Vc
C
Rs Ls
Rs
Rs
Ls
Ls
S1 S3 S5
S4 S6
S2
RL
I
dc
ra
V
rb
V
rc
V
ra
I
rb
I
rc
I
Fig. 1 Block diagram of three-phase PWM rectifier
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Angle value (θ) required for above transformations can be found with PLL (phase
locked loop) in MATLAB/Simulink or it can be obtain by using abc–αβ transformation.
Determination ofelectrical parameters used inPWM rectier anddesign ofPI
controller
Input inductor must be designed very carefully in order to obtain good performance
from rectifier. Low inductance value causes the increase in current ripple and the perfor
-
mance of rectifier depends on impedance of the grid. e high inductance value reduces
current ripple but it limits the operating range of the rectifier (Wang and Yin
2008).
Consequently, the maximum inductance value can be determined as follows:
where, U
m
is the phase voltage amplitude of the grid, T
s
is the switching period, I
m
is
the amplitude of the grid current, ω is the angular frequency, and ∆I
max
is the allowed
maximal ripple of the grid current. e determination of the value of C is very important
because C has key role in fixed the DC voltage. Also, the value of C should be as small as
possible in order to provide fast tracking of the reference DC voltage. e value of C can
be found as the following equations:
where, ∆U
dc
=(U
dc
−U
dcmin
)/U
dc
, t
r
*
is the rising time for the output voltage and R
L
is
the output load resistance. e choice of U
dc
must meet the load requirement and the
grid current control requirement. Neglecting the high-order harmonics, the limits of the
DC voltage can be determined by the following equations:
where I
1abc
is the rms value of the grid currents and R is the resistance of the filter reactor
and U
1abc
is the rms value of the grid voltages (Wang and Yin
2008). Based on Eqs.(9)–
(
13), the parameters used in simulation study are given in Table2.
(8)
V
d
V
q
= L
s
dI
d
dt
dI
q
dt
+
R
s
−ωL
s
ωL
s
R
s
I
d
I
q
+
V
rd
V
rq
(9)
(2U
dc
−
3U
m
)U
m
T
s
2U
dc
�I
max
≤
L
≤
2U
dc
3I
m
ω
(10)
C
≤
t
∗
r
R
L
ln
6
−
8.27U
m
U
dc
(11)
C
>
1
2R
L
�U
∗
dc
(12)
U
dc
≥
2
√
2U
1abc
(For SPWM)
√
6U
1abc
(For SVPWM)
(13)
SPWM: U
dc
≥ 2
√
2
(
U
1abc
+ RI
1abc
)
2
+
(
ωLI
1abc
)
2
1/2
SVPWM: U
dc
≥
√
6
(
U
1abc
+
RI
1abc
)
2
+
(
ωLI
1abc
)
2
1/2
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e dq-axis currents must be controlled independently in the control of three-phase
PWM rectifiers. e dq-axis currents are usually controlled by PI controllers with fixed
paramteres. A mathematical model of the system to be controlled has been needed to
obtain K
p
and K
i
parameters of PI controller (Blasko and Kaura
1997). e reduced block
diagram is formed for the control of dq-axis currenst given in Fig.
2. e gain values of
PI controller may be easily determined from this reduced block diagram.
In this reduced block diagram; T
s
is sampling and filter delay, K
p
is proportional gain
of PI controller, T
i
is PI controller integral time constant, T
PWM
is time constant of the
PWM block, K
PWM
is rectifier gain K
RL
is gain of system, T
RL
is the system time con-
stant. e smallest time constants in the reduced block diagram are grouped together to
form a single block as a single time constant (Blasko and Kaura
1997).
e integral time constant of the PI controller is obtained by the following equation
according to the dominant pole of the system.
Closed loop transfer function of the system can be obtained by using the reduced
block diagram as below:
To ensure 5 % overshoot, if the damping ratio is selected as (ξ) =
√
2/2
, it can be
obtained by the following equation:
If the damping ratio is written in Eq.
16, Eq.18 is obtained:
e first-order transfer function can be obtained by neglecting the s
2
term because of
the very small product the term T
RL
·T
ei
.
(14)
T
ei
= T
s
+ T
PWM
/2
(15)
T
i
= T
RL
(16)
H
ci
=
1
s
2
T
RL
T
ei
K
p
K
PWM
K
RL
+
s
T
RL
K
p
K
PWM
K
RL
+
1
(17)
ζ
2
=
T
RL
4K
p
K
PWM
K
RL
(18)
K
p
=
T
RL
2T
ei
K
PWM
K
RL
(19)
H
ci
=
1
1 + sT
et
s
sT1
1
+
i
ip
sT
)sT1(K +
2/sT1
K
PWM
PWM
+
RL
RL
sT1
K
+
*
dq
I
dq
I
PWMPI CONTROLLERSAMPLE AND HOLD SYSTEM
d
u
Fig. 2 Reduced block diagram of the current control loop