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Transcript
26
ACTA ELECTROTEHNICA
Performance Evaluation of Fuzzy-Logic
Controller Applied to a Transmission
System with STATCOM
A. ABDERRAHMANI, A. CHAKER and A. LAOUFI
ABSTRACT - This paper proposes and validates the models to accurately represent the STATCOM in voltage stability studies of
power systems and the development of a fuzzy logic controller for damping oscillations in FACTS. The ability of fuzzy logic to
handle rough and unpredictable real world data made it suitable for a wide variety of applications, especially, when the models or
processes are too complex to be analyzed by classical methods. These models are first validated by means of MATLAB simulations
on a test system, and then are implemented into two different methods used to study voltage in the system.
Keywords: FACTS, STATCOM, Modeling, Reactive compensation, Controls Method, Fuzzy-Logic controller.
1.
INTRODUCTION
As power demand grows rapidly and expansion in
transmission and generation is restricted by the limited
availability of resources and the strict environmental
constraints, power systems are today much more loaded
than before. This causes the power systems to be
operated near their stability limits. The development and
use of FACTS controllers in power transmission systems
has led to many applications of these controllers to
improve the stability of power networks.
The STATic synchronous shunts COMpensators
(STATCOM) is one of the most versatile flexible AC
transmission system devices, which can be used to
control the reactive power flows in a transmission line
by injecting a variable reactive current. The STATCOM
is a power electronics-based Synchronous Voltage
Generator (SVG) that generates a three-phase voltage
from a DC capacitor in synchronism with the
transmission line voltage. The basic STATCOM model
consists of a step-down transformer with leakage
reactance, a three-phase GTO VSI, and a DC side
capacitor shown in Figure 1. The AC voltage difference
across this transformer leakage reactance produces
reactive power exchange between the STATCOM and
the power system at the point of interface. The voltage
can be regulated to improve the voltage profile of the
interconnected power system, which is the primary duty
of the STATCOM. A secondary damping function can
be added to the STATCOM for enhancing power system
dynamic stability.
The STATCOM main function is to regulate key
bus voltage magnitude by dynamically absorbing or
generating reactive power to the AC grid network, like a
thyristor static compensator. This reactive power

Fig. 1. STATCOM configuration.
transfer is done through the leakage reactance of the
coupling transformer by using a secondary transformer
voltage in phase with the primary voltage (network
side). This voltage is provided by a voltage-source
PWM inverter and is always in quadrature to the
STATCOM current [01].The operation and control
fundamentals of the STATCOM have been extensively
discussed in [1], [5] and [12].
The control system is based on a decoupled
strategy or d-q transformation that makes it possible to
control the reactive current flow between the
STATCOM and the transmission system. Until now, the
most frequently used strategy has been the conventional
property and integrates (PI). Proposed a fuzzy-logic
controller as the substitution of the traditional controller.
The results reveal that the fuzzy-logic controller
proposed in this paper is very effective.
The operation of the full STATCOM model is fully
studied in both capacitive and inductive modes in a
power transmission system and load excursion.
Manuscript received December 6, 2012.
© 2013 – Mediamira Science Publisher. All rights reserved.
27
Volume 54, Number 1, 2013
2.
commands to alter the modulation index and phase angle
in equation 2.
STATCOM MODELS
Due to the nature of the inverter switching, the
dynamic models of FACTS devices are nonlinear and
non-constant. In addition, the dynamics of the inverter
switches are much faster than the power System
dynamics of interest. Therefore, it is desirable to develop
a set of simplified state-based models for the FACTS
devices that are sufficiently detailed to provide accurate
representation of the real hardware System, yet simple
enough for implementation in a power System
simulation [13].
By injecting a current of variable magnitude in
quadrature with the line voltage, the STATCOM can
inject reactive power into the power system. The
STATCOM does not employ a capacitor or reactor
banks to produce reactive power as does the SVC, but
instead uses a capacitor to maintain a constant the
voltage for the inverter operation. An equivalent circuit
for the STATCOM is shown in Figure 2.
3.
DECOUPLED CONTROL METHOD
The new decoupled control system is based on a
full dq decoupled current control strategy using both
direct and quadrature current components of the
STATCOM AC current [01].
It can be shown that with line resistance included,
the mathematical model for the response of a Voltage
Sourced Converter to an. applied voltage V=Vd into a
synchronously rotating orthogonal system can be given
as
 R sh


  I
 sh _ d  1 V1 _ d  Vsh _ d 
d I sh _ d   L sh
.





dt I sh _ q      R sh  I sh _ q  L sh V1 _ q  Vsh _ q 

L sh 
For the purposes of further derivation of the new
control system, the classical decoupled watt-var
algorithm was studied. By interdicting two new
variables Xl and X2
1

X1  L .(V1 _ d  Vsh _ d )

sh

1
X  .(V  V )
 2 L sh 1 _ q sh _ q
 dI sh _ d
R
R
  sh . I sh _ d  . I sh _ q  X1   sh . I sh _ d  U1

L sh
L sh
 dt
 dI
R
R
sh
_
q

  sh . I sh _ q  .I sh _ d  X 2   sh . I sh _ q  U 2
 dt
L sh
L sh
Fig. 2. 2 Equivalent circuit of the STATCOM.
 R sh

0
0 

L
I sh _ a   sh
V1 _ a  Vsh _ a  (1)
 I sh _ a 
 
R sh
d
.I   1 V  V 
I

0

0
 sh _ b  
  sh _ b  L  1 _ b sh _ b 
dt 
L sh
 

 sh V  V 
I
sh
_
c
R  I sh _ c 

 
 1 _ c sh _ c 
0
0
 sh 
L sh 

Where:
 Rsh and Lsh represent the STATCOM transformer
losses;
 Vsh_abc
are the inverter ac side phase voltages;
 V1_abc are the System side three phase voltage.
The output of the STATCOM is given by:
Ea  k.VDC . cos(.t  )
(2)
Where:
 VDC is the voltage across the capacitor;

is the injected voltage phase angle;
 k is the PWM modulation gain.
The control objectives for the STATCOM are to
provide independent reactive power support and to
maintain constant the capacitor voltage. This is best
accomplished by regulating the PWM switching
(4)
(5)
(6)
U1  . I sh _ q  X 1
Thus we see that if we have 
U 2  . I sh _ d  X 2
as control variables.
Thus it is seen from equation (06) that by
controlling U1 and U2 one can independently regulate
Ish_d and Ish_q thereby controlling the real (Psh) and the
reactive power flow (Qsh).
By controlling U1 the real power flow (Psh) and
hence the DC link capacitor voltage (VDC) can be
regulated. By controlling U2 the reactive power flow
(Qsh) can be regulated [01]. To close the feedback loop,
the auxiliary variables U1 and U2 are controlled by
proportional-integral (PI) controllers as given below in
equation 7. The D-axis current Ish_d is controlled by u1
and the Q-axis current Ish_q is controlled by U2.
K i3

I shd_ ref  (K p3  s ).(VCD _ ref  VCD )

K
 I shq_ ref  (K p 4  i 4 ).(Vm _ ref  Vm )
s

(7)
The decoupled control system is implemented as
shown in Figure 3. A phase locked loop (PLL)
synchronizes on the positive sequence component of the
three-phase terminal voltage at interface Bus 2. The
output of the PLL is the angle (θ) that's used to measure
the direct axis and quadrature axis component of the AC
28
ACTA ELECTROTEHNICA
Fig. 3. Decoupled control diagram of STATCOM: ①References ②Measured ③Control ④Impulses.
three-phase voltage and current. The outer regulation
loop comprising the AC voltage regulator provides the
reference current (Ishq_ref) for the current regulator that
is always in quadrature with the terminal voltage to
control the reactive power [01].
4.
NB
NB
Shunt The disadvantage of PI controller is its
inability to react to abrupt changes in the error signal, e,
because it is only capable of determining the
instantaneous value of the error signal without
considering the change of the rise and fall of the error,
which in mathematical terms is the derivative of the
error signal, denoted as Δe. To solve this problem,
Fuzzy logic control as it is shown in Fig.5 is proposed.
Each of the two linguistic variables is defined over
a universe of discourse namely Ue and Ue respectively.
Let the universe of discourse for each of the input
linguistic variable be divided into 5 fuzzy sets namely,
Positive Big (PB), Positive Medium (PM), Zero (ZE),
Negative Medium (NM), and Negative Big (NB). Each
of the fuzzy set has a definite support. Each fuzzy set
can be triangular, or trapezoidal or sigmoid. In this case,
triangular fuzzy sets are used. Let the universe of
PB
PM
U n i v e r s e o f d i s c o u r se
FUZZY LOGIC CONTROLLER (FLC)
DESIGN METHODOLOGY
Fig. 4. Sample fuzzy logic controller.
ZE
NM
NM
ZE
PM
PB
-0,6
-0,6
Fig. 5. Five fuzzy sets of the inputs/output.
discourse for the error be {-0.02 0.02}. Let the universe
of discourse for the rate of change of error be {-0.006
0.006}.
The expert knowledge is generally given in the
following format.
"IF (e set of conditions) THEN (u set of consequent
can be inferred)".
These statements contain a set of conditions and a
set of decisions to be inferred. The set of decisions could
be fuzzy sets.
Table 1. A Fuzzy knowledge base.
e
e
NB
NM
ZE
PM
PB
NB
NM
ZE
PM
PB
NB
NM
NM
NM
NM
NM
NM
ZE
ZE
ZE
PM
PM
PM
PB
PM
PM
PB
29
Volume 54, Number 1, 2013
Fig. 6. Single Line Diagram Representing STATCOM.
DIGITAL SIMULATION RESULTS
PI controller
Fuzzy logic controller
1.01
V-bus (pu)
1.005
1
0.995
0.99
0.985
0.98
0
0.05
0.1
0.15
0.2
0.25
Time
0.3
0.35
0.4
0.45
0.5
Fig. 7. Terminal voltage of STATCOM (Qc=1pu, QL=1pu).
Without STATCOM
PI controller
Fuzzy logic controller
1
0.5
0
Ish (pu)
To verify the validity and effectiveness of the
proposed strategy, we conducted a simulation research
and then offered the simulation waveform. The
STATCOM is designed to control the voltage at Bus 2,
and thus regulate the load bus voltage at Bus 3. The
STATCOM is rated at 100 Mvar with the coupling
transformer ration of 500/4kV/15kV.
In the process, Load variations are simulated on
Bus 4 to depict the behavior of the reduced model in
steady state, thus validating the proposed model for
small voltage variations (less than 10%).
The following load excursion sequence is tested, to
validate and test the limits of the proposed reduced
model for large system disturbances.
The STATCOM is connected to the power system
at t=0 Sec with only load 1 in the system. The DC
voltage is 19.28 kV.
Step 1- at t=0.1 the capacitive load Qc=1pu is
connected by switching CB1. Therefore, the DC voltage
has increased to 20.79 kV, the voltage is suddenly
decreased by 1.8% (0.982 pu of nominal voltage without
STATCOM). The STATCOM reacts by generating
reactive power (Q=+70 Mvar) to keep voltage at 1 pu.
The 100% settling time is approximately 63 ms. At this
point.
Step 2- at t=0.2 this time, both the capacitive is
removed from Bus 4. !Unexpected End of Formula
Step 3- at t=0.3 the inductive load QL=1 pu is
connected by switching CB2. The DC capacitor voltage
has been lowered to 17.87 kV. The capacitive load has a
compensative effect so the STATCOM absorbs about
0.7 p.u. of reactive power into the AC system at bus
2.The regulated bus voltage is now about 1 p.u (without
STATCOM 1.017 pu +1.7%).
Step 4- Finally, at t=0.4 s the source voltage in set
back to its nominal value and the STATCOM operating
point comes back to zero Mvar.
The STATCOM responds to any changes in the AC
system voltage within two control methods. Figures 7, 8
and 8. shows the simulation results in the case of a
Without STATCOM
1.015
-0.5
-1
-1.5
-2
0
0.05
0.1
0.15
0.2
0.25
Time
0.3
0.35
0.4
0.45
0.5
Fig. 8. Current of STATCOM (Qc=1pu, QL=1pu).
Without STATCOM
0.8
PI controller
Fuzzy logic controller
0.6
0.4
0.2
Q-inj(pu)
5.
0
-0.2
-0.4
-0.6
-0.8
0
0.1
0.2
0.3
Time
0.4
0.5
0.6
Fig. 9. Injected reactive power (Qc=1pu, QL=1pu).
0.7
30
ACTA ELECTROTEHNICA
Without STATCOM
25.6
PI controller
settle & reach the final steady state value. Therefore, the
power system strength greatly affects the response time
and stability of the STATCOM. If the PI controller is set
to provide a fast response for a strong system, it may
lead to possible instability for a weak power system. But
the fuzzy logic controller is set to provide a suitable
response for power system.
Iq-Measured
1
Iq-reference
0.8
0.6
(a)
Ish-q (pu)
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.45
0.5
Time
Iq-Measured
1
Iq-reference
0.8
0.6
0.4
(b)
Ish-q (pu)
capacitive and inductive mode using the sample power
transmission system. The digital simulation is carried
out for the two controllers (PI and fuzzy). Both novel
controllers' schemes are validated under this condition in
order to show their capability in keeping the STATCOM
stable for a power system.
The digital simulation for the study system shown
in Fig. 6 is carried out again under the same load
excursions but using the Fuzzy logic controller. This
new controller shows the elevated level of the stability
of the power transmission system and provides a smooth
transition from the capacitive to full inductive
compensation level. The digital simulation results of this
comparison are depicted in Fig. 7, 8 and 9.
To check the effect of the power system strength
on the STATCOM stability, the digital simulation is
carried out again in the proposed system shown in
Figure 2. In this case, the loads of this power system are
replaced with new loads, which are Load1 (Qc=1.7pu)
and load2 (QL=1.7pu). Both control schemes were
validated in order to show the effects of the control
methods based on PWM.
The comparative response curves controller pi and
fuzzy logic controller both are shown in the Fig. 7, 8 9
and 10. The response measured and reference quadrature
current is obtained without & with the fuzzy logic
controller and is shown in the Figs. 11. It is clearly
observed from the simulation results that with the fuzzy
logic controller, the dynamic performance of the power
system is quite improved with the incorporation of the
fuzzy logic controller. It is also observed that with the
controller, the oscillations are also damped out in a
lesser time. The response characteristics take less time to
0.2
0
-0.2
-0.4
-0.6
-0.8
0
0.05
0.1
0.15
0.2
0.25
Time
0.3
0.35
0.4
Fig. 12. Measured and reference quadrature current:
(a): PI controller (b): Fuzzy logic controller.
Without STATCOM
1.03
Fuzzy logic controller
PI controller
Fuzzy logic controller
1.02
25.4
V-bus (pu)
Line reactive power (pu)
1.01
25.2
25
24.8
1
0.99
24.6
0.98
24.4
24.2
24
0.97
0
0
0.05
0.1
0.15
0.2
0.25
Time
0.3
0.35
0.4
0.45
0.05
0.1
0.15
0.2
0.3
0.35
0.4
0.45
0.5
Fig. 13. Terminal voltage of STATCOM
(Qc=1.7pu, QL=1.7pu).
Time
Fig. 10. Line reactive power (Qc=1pu, QL=1pu).
Without STATCOM
x 10
0.25
0.5
PI controller
Fuzzy logic controller
4
PI controller
Fuzzy logic controller
1
3
0.5
Vdc (pu)
Ish (pu)
2.5
2
0
-0.5
1.5
-1
1
0
0.05
0.1
0.15
0.2
0.25
Time
0.3
0.35
0.4
0.45
Fig. 11. Capacitor DC voltage (Qc=1pu, QL=1pu).
0.5
0
0.05
0.1
0.15
0.2
0.25
Time
0.3
0.35
0.4
0.45
Fig. 14. Current of STATCOM (Qc=1.7pu, QL=1.7pu).
0.5
31
Volume 54, Number 1, 2013
7.
Without STATCOM
PI controller
Fuzzy logic controller
1
8.
Q-inj(pu)
0.5
0
9.
-0.5
10.
-1
-1.5
0
0.05
0.1
0.15
0.2
0.25
Time
0.3
0.35
0.4
0.45
0.5
Fig. 15. Injected reactive power (Qc=1.7pu, QL=1.7pu).
6.
11.
CONCLUSION
12.
The system has been modeled and simulated by
Simulink/Matlab software to analyze and compare the
performance of the STATCOM with the two controllers.
The simulation results show that the program has
been successfully used at 'DECOUPLED CONTROL
METHOD'. The developed control strategy decoupled is
not only simple, reliable, and may be easy to implement
in real time applications. The performance of the
developed method in this paper thus demonstrates the
damping of the power system oscillations using the
effectiveness of fuzzy logic controller for different
system load power.
It is shown that the STATCOM with fuzzy logic
controller provides better performance in the
enhancement of dynamic and transient stability.
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Abdesselam ABDERRAHMANI
Prof. Abdellah LAOUFI
Faculty of the Sciences and Technology
Bechar University
B.P 417 BECHAR (08000), ALGERIA
E-mail: [email protected],
[email protected]
Prof. Abdelkader CHAKER
Department of Electrical Engineering
Networks Laboratory, ENSET Oran
E-mail: [email protected]
Abdesselam ABDERRAHMANI was born on 14.12.1970. In
1994 he graduated at the Electrotechnical Department of the Faculty of
Electrical Engineering at University Tiaret in Algeria. He defended his
“Magister” in the field of optimal power flow problems in 2008 at
university Bechar Algeria; his thesis title was "Optimal design of
power system using ant colony". His scientific research is focusing a
control and command of power systems, and study of the Dynamic
stability of the networks electrical supply.
Abdelkader CHAKER is a Professor in the Department of
Electrical Engineering at the ENSET, in Oran Algeria. He received a
Ph.D. degree in Engineering Systems from the University of SaintPetersburg. His research activities include the control of large power
systems, multi-machine multi-converter systems, and the unified
power flow controller. His teaching includes neural process control
and real time simulation of power systems.
Abdellah LAOUFI received the state engineer degree in
electrical engineering from the University of Sciences and Technology
of Oran (USTO), Algeria, the M.Sc. degree from the Electrical
Engineering Institute of the University of Djillali Liabes, Algeria, and
the Ph.D. degree from the Electrical Engineering Institute of the
University of Djillali Liabes. He is currently professor of electrical
engineering at Bechar University.