Applied mathematics in Engineering, Management and Technology 3(1) 2015:72-79
www.amiemt-journal.com
Investigating the static synchronous series compensator performance
under adaptive controller
Alireza Farzaneh, Ali Safari
Sama Technical and Vocational Training College, Islamic Azad University, Islamshahr Branch, Islamshahr, Iran
E-mail: farzaneh@iiau.ac.ir, safari_ee@hotmail.com
Abstract
In this paper, the performance of static synchronous series compensator (SSSC) is
studied under an adaptive controller. The proposed adaptive controller is designed
based on the model reference adaptive control strategy. The control strategy is to
damp out the low frequency oscillations and the SSSC role is as a stabilizer. A multi
machine power system with nine buses is considered as case study. Simulation
results demonstrate the effectiveness and validity of the proposed method.
Keywords: Low Frequency Oscillations; Model Reference Adaptive Control; Multi Machine
Power System; Stabilizer; Static Synchronous Series Compensator
1. Introduction
Static synchronous series compensator (SSSC) is a series type flexible AC transmission systems (FACTS)
devise which can be used for power flow control, stability improvement and power transfer control [1-5]. Many
researchers have been proposed to study and analyze the SSSC in electric power systems [1-5]. Paper [6]
presents the impact of static series synchronous compensator (SSSC) and static compensator (STATCOM) on
power system predictability. Paper [6] explains that in power systems with the high penetration of renewable
energies such as wind powers, accuracy in predicting power system state is really important, especially in
bidding strategies, risk management and operational decisions. paper [6] utilizes the predictability indices and
clarifies some important questions and concerns about power system such as; do the STATCOM and SSSC
improve or impair the predictability of system state? Also, this paper warns the operator of system about
ignoring the predictability concept in FACTS included power systems. Moreover, the necessity of utilizing
predictability indices in optimization problems beside conventional objectives, such as losses, is discussed. The
results are discussed on IEEE 14 and 57 bus test systems. Paper [7] presents a new robust decentralized
frequency stabilizers design of Static Synchronous Series Compensators (SSSCs) by taking system uncertainties
into consideration. As an interconnected power system is subjected to load disturbances with changing
frequency in the vicinity of the inter-area oscillation mode, system frequency may be severely disturbed and
oscillate. To compensate for such load disturbances and stabilize frequency oscillations, the dynamic power
flow control by an SSSC installed in series with a tie line between interconnected systems can be applied. The
proposed decentralized design translates SSSCs installed in interconnected power systems into a Multi-Input
Multi-Output (MIMO) system. The overlapping decompositions is used to extract the decoupled Single-Input
Single-Output (SISO) subsystem embedded with the inter-area mode of interest from an MIMO system. As a
result, each frequency stabilizer of SSSC can be independently designed to enhance the damping of the interarea mode in the decoupled subsystem. In addition, by incorporating the multiplicative uncertainty model in the
decoupled subsystem, the robust stability margin of system against uncertainties such as various load changes,
system parameters variations etc., can be guaranteed in terms of the multiplicative stability margin (MSM). In
this study, the configuration of frequency stabilizer is practically based on a second-order lead/lag compensator.
Without trial and error, the control parameters of the frequency stabilizer are automatically optimized by a
micro genetic algorithm, so that the desired damping ratio of the inter-area mode and the best MSM are
acquired. Simulation study shows the high robustness of the decentralized frequency stabilizers against various
load disturbances and system parameter variations in the three-area loop interconnected power system.
Paper [8] presents the enhancement of load frequency stabilization effect of superconducting magnetic energy
storage by static synchronous series compensator based on H∞ control. This paper explains it is well known that
the load frequency stabilization effect of superconducting magnetic energy storage (SMES) in an interconnected
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A. Farzaneh et al
power system is restricted to its located area. The SMES almost has no frequency stabilization effect in another
interconnected area. To enhance the frequency stabilization effect of SMES, the static synchronous series
compensator (SSSC) can be applied as an auxiliary device. The SSSC can be used as an energy transfer device
of the SMES to stabilize the frequency in another interconnected area. The proposed technique not only
introduces a sophisticated frequency stabilization in deregulated power systems but also offers a smart energy
management control of SMES. In addition, to take the robust stability of the controlled power system against
system uncertainties into account, the H∞ control is used to design robust frequency stabilizers of the SMES
and SSSC. Simulation results in a two area interconnected power system confirm the high robustness of the
frequency stabilizers SMES and SSSC against load disturbances and system uncertainties.
This paper studies the performance of SSSC as a stabilizer in electric power systems; where, the SSSC
stabilizer is designed based on the model reference adaptive control theory. A 9-bus power system is considered
as case study. Simulation results show the ability of the proposed method in damping power system oscillations.
2. Test systems
In this paper, a 9-bus power system installed with SSSC is considered as cases study. Figure 1 shows the
proposed test system. Where, the SSSC is installed between bus 8 and bus 9. The system data can be found in
[9].
Figure 1: Nine bus power system installed with SSSC between bus 8 and bus 9
3. Model reference adaptive control
In order to introduce the model reference adaptive control strategy, a plant model is considered as (1).
y
k p s  b0 
s  a1s  a 0
2
(1)
u
Where, u shows the control signal, y is output and model reference is defined as (2).
ym 
km
uc
s  am
(2)
In this case, the control signal is defined as (3).
up (t)=θ1(t) w1(t)+ θ2(t) w2(t)+ θ3(t) y+ θ4(t) uc
where;
(3)
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A. Farzaneh et al
dw 1
 Fw1  gu
dt
dw 1
 Fw 2  gy
dt
u  θT w

θ  θ1

T
w  w1
θ2
T
T
w2
θ3
T
θ4
y

uc

In addition, the θ adaptive rule is obtained as (4).
dθ
 Γ e w
dt
(4)
The Γ can be chosen as (5) and afterward, the θ adaptive rule is obtained as (6).
Γ  diag γ i 
dθ i
 γ i e w i
dt
(5)
(6)
4. SSSC stabilizer based on the Model reference adaptive control
In order to controller design, in first, the power system transfer function is derived and then the model reference
is defined. The suitable reference model for a system is chosen based on the desired settling time, overshoot,
rise time and such characteristics. In this paper, the reference model is defined as (7).
y
110-3 s(s  1.05)
u
s 2  2.1s  2.2
(7)
5. Simulation results
In order to study the system under different loading conditions, three loading conditions are defined as Table 1.
The system responses following disconnection of line between bus 4 and bus 6 are depicted in Figures 2 to 7. It
is clear the system without stabilizer does not show suitable responses and large oscillations are seen, while, in
the system with stabilizer, the oscillations are suitably damped out.
In order to more analysis, the system Eigen-values are compared for the both the proposed cases. It is clear that
the system with stabilizer provides more damping.
Table 1: System loading conditions
Operating condition
Parameters (p.u.)
nominal
Nominal values
20% increasing the parameter from the
heavy
nominal values
20% reducing the parameter from the nominal
light
values
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A. Farzaneh et al
1.0018
1.0016
1.0014
Speed G1 (p.u.)
1.0012
1.001
1.0008
1.0006
1.0004
1.0002
1
0.9998
0
5
10
15
Time (s)
20
25
30
Figure 2: Speed G1 at the nominal loading condition following disturbance
(Solid: with stabilizer, Dashed: without stabilizer)
1.0016
1.0014
1.0012
Speed G2 (p.u.)
1.001
1.0008
1.0006
1.0004
1.0002
1
0.9998
0
5
10
15
Time (s)
20
25
30
Figure 3: Speed G2 at the nominal loading condition following disturbance
(Solid: with stabilizer, Dashed: without stabilizer)
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A. Farzaneh et al
1.0018
1.0016
1.0014
Speed G3 (p.u.)
1.0012
1.001
1.0008
1.0006
1.0004
1.0002
1
0.9998
0
5
10
15
Time (s)
20
25
30
Figure 4: Speed G3 at the nominal loading condition following disturbance
(Solid: with stabilizer, Dashed: without stabilizer)
1.88
1.86
V9 (p.u.)
1.84
1.82
1.8
1.78
1.76
1.74
0
5
10
15
Time (s)
20
25
30
Figure 5: Voltage of bus 9 at the nominal loading condition following disturbance
(Solid: with stabilizer, Dashed: without stabilizer)
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A. Farzaneh et al
1.0005
1
0.9995
Speed G1 (p.u.)
0.999
0.9985
0.998
0.9975
0.997
0.9965
0.996
0
10
20
30
Time (s)
40
50
60
Figure 6: Speed G1 at the heavy loading condition following disturbance
(Solid: with stabilizer, Dashed: without stabilizer)
1.94
1.92
V9 (p.u.)
1.9
1.88
1.86
1.84
1.82
0
10
20
30
Time (s)
40
50
60
Figure 7: Voltage of bus 9 at the heavy loading condition following disturbance
(Solid: with stabilizer, Dashed: without stabilizer)
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Table 2: System Eigen-values for two cases
With stabilizer
Without stabilizer
-0.1
-0.1
-1000
-1000
-1000
-1000
-1000
-1000
-1.4277+11.741i
-5.6834+17.136i
-1.4277-11.741i
-5.6834-17.136i
-0.23817+7.6918i
-5.3193+17.053i
-0.23817-7.6918i
-5.3193-17.053i
-5.4123+5.7922i
-5.4758+17.108i
-5.4123-5.7922i
-5.4758-17.108i
-5.1509+5.6968i
-1.2985+11.761i
-5.1509-5.6968i
-1.2985-11.761i
-5.2246+5.7752i
-0.21944+7.7037i
-5.2246-5.7752i
-0.21944-7.7037i
-5.1284
-5.1327
-3.6397
-3.6361
-0.55582+0.8498i
-0.40127+1.2902i
-0.55582-0.8498i
-0.40127-1.2902i
-0.11182+0.39525i
-0.31736+0.9136i
-0.11182-0.39525i
-0.31736-0.9136i
0
0
-0.56064+0.3156i
-0.11777+0.33856i
-0.56064-0.3156i
-0.11777-0.33856i
-0.56471+0.54949i
-0.2753+0.64716i
-0.56471-0.54949i
-0.2753-0.64716i
-3.2258
-3.2258
-200
-200
6. Conclusions
This paper investigated the performance of static synchronous series compensator (SSSC) under model
reference adaptive stabilizer. The SSSC control strategy was assumed to damp out the low frequency
oscillations such as a classical stabilizer. A nine-bus multi machine power system was considered as case study.
Simulation results demonstrated the effectiveness and validity of the proposed method to damp out oscillations
and stability improvement.
Acknowledgement
This paper is extracted from an approved research project in Sama Technical and Vocational Training College,
Islamic Azad University, Islamshahr Branch, Islamshahr, Iran . Therefore, The authors gratefully acknowledge
the financial and other support of this research, provided by this academic unit.
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