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American Journal of Sustainable Cities and Society
available online on http://www.rspublication.com/ajscs/ajsas.html
Issue 1 vol 1 July 2012
Enhancement of Voltage Stability through Optimal
Placement of Facts Controllers in Power Systems
1
KIRAN KUMAR KUTHADI
Head of the Department
Electrical & Electronics Engineering
Sree Vahini Institute of Science & Technology, TIRUVURU, Krishna Dist, Andhra Pradesh, INDIA
Email.id: [email protected]
****
2
N. SURESH J.E.,
MAHArashtra state power GENEration CO. Ltd,
Nagapur, Maharashtra, INDIA
ABSTRACT: The loss minimization is a major role in Power System (PS) research. Transmission line losses in a
Power System can be reduced by Var compensation. After the establishment of power markets with transmission
open access, the significance and use of Flexible AC Transmission Systems (FACTS) devices for manipulating line
power flows to relieve congestion and maximize the overall grid operation have been increased. Proper placement
of Static VAR compensator (SVC) and Thyristor Controlled Series compensator (TCSC) reduces transmission
losses, increases the available capacity, and improves the voltage profile. This paper presents an optimal placement
of SVC and TCSC to determine SVC and TCSC locations and control parameters for minimization of transmission
loss. Optimal location methods utilize the sensitivity of total real power transmission loss with respect to the control
parameters of devices. The location of SVC & TCSC is placed based on VSI. The results have been obtained on
IEEE 5bus and IEEE 14bus test system. Test result shows that both SVC and TCSC can determine optimal
placement.
Index Terms: Flexible AC Transmission Systems (FACTS), Static VAR compensator (SVC), Thyristor Controlled
Series compensator (TCSC), Voltage Stability Index (VSI).
1.INTRODUCTION
Most of the large power system blackouts, which occurred worldwide over the last twenty years, which are caused
by heavily stressed system with
large amount of real and reactive power demand and low voltage condition. When the voltages at power system
buses are low, the losses will also to be increased. This study is devoted to develop a technique for improving the
voltage and minimizing the losses and hence eliminate voltage instability in a power system. Application of FACTS
devices are currently pursued very intensively to achieve better control over the transmission lines for manipulating
power flows. There are several kinds of FACTS devices. Thyristor-Controlled Series Capacitors (TCSC), Thyristor
Controlled Phase Shifting Transformer (TCPST) and Static Var Compensator (SVC) can exert a voltage in series
with the line and, therefore, can control the active power through a transmission line. The optimal operation of the
power system networks have been based on economic criterion. Now other criterion such as: improving voltage
profile, minimizing power loss of transmission line, and etc. have been concerned. An optimal power flow program
(OPF) has been solved an optimization problem where the objective function, equality and inequality constraints are
nonlinear equation [1]. The Flexible AC Transmission System (FACTS) have been considered to maximize the use
of existing transmission facilities. In this paper FACTS devices have been considered as additional control variables
in power flow. Two of FACTS devices consisting of static var compensator (SVC) and thyristor controlled series
compensator (TCSC) have been used in this paper. Minimization of transmission loss is solved by using the
nonlinear interior point methods [2] to finding values of SVC and TCSC along with other control parameter such as
transformer tap that was present in [3]. Due to high cost of SVC and TCSC, it is important to decide their optimal
placement.
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Issue 1 vol 1 July 2012
This paper presents the method of the optimal location utilizes the sensitivity of total real power transmission
loss with respect to the control parameters of devices, the new equation of SVC is the sum of reactive power flow
that has relationship with bus and the new equation of TCSC is sum of real power loss that has relationship with
transmission line. The IEEE standard tested power system has been considered as tested system to investigate the
effect of considering TCSC and SVC on power loss minimization and system stability.
2. MATHEMATICAL MODEL OF FACT’S
i.
Static VAR compensator (SVC)
The SVC is taken to be a continuous, variable susceptance, which is adjusted in order to achieve a specified
voltage magnitude while satisfying constraint conditions. SVC total susceptance model represents a changing
susceptance. 𝐵𝑆𝑉𝐶 represents the fundamental frequency equivalent susceptance of all shunt modules making up the
SVC. This model is an improved version of SVC models [2]. SVC’s normally include a combination of
mechanically controlled and thyristor controlled shunt capacitors and reactors. The most popular configuration for
continuously controlled SVC’s is the combination of either fix capacitor and thyristor controlled reactor [3].
Fig. 1 Basic Structure of SVC
As far as steady state analysis is concerned, both configurations can modeled along similar lines, The SVC
structure shown in Fig. 1 is used to derive a SVC model that considers the Thyristor Controlled Reactor (TCR)
firing angle as state variable. This is a new and more advanced SVC representation than those currently available.
The SVC is treated as a generator behind an inductive reactance when the SVC is operating within the limits. The
reactance represents the SVC voltage regulation characteristic, i.e., SVC’s slope, 𝑋𝑠𝑡 [4]. The reason for including
the SVC voltage current slope in power flow studies is compelling. The slope can be represented by connecting the
SVC models to an auxiliary bus coupled to the high voltage bus by an inductive reactance consisting of the
transformer reactance and the SVC slope, in per unit (p.u) on the SVC base. A simpler representation assumes that
the SVC slope, accounting for voltage regulation is zero. This assumption may be acceptable as long as the SVC is
operating within the limits, but may lead to gross errors if the SVC is operating close to its reactive limits.
The linearized equation of the SVC is given by the following Eqns. (i) and (ii) where the total susceptance
𝐵𝑆𝑉𝐶 is taken to be the state variable.
𝑖
∇𝜃𝑘
∇𝐵𝑆𝑉𝐶
(𝑖)
𝐵𝑆𝑉𝐶
at the end of iteration i, the variable shunt susceptance 𝐵𝑆𝑉𝐶 up dated according to the Eqn. (ii) given below
∇𝐵𝑆𝑉𝐶 𝑖 𝑖
𝑖+1
𝑖
𝐵𝑆𝑉𝐶
= 𝐵𝑆𝑉𝐶
+
𝐵𝑆𝑉𝐶
(𝑖𝑖)
𝐵𝑆𝑉𝐶
∇𝑃𝑘
∇𝑄𝑘
𝑖
0 0
=
0 𝑄𝑘
𝑖
In this paper, the SVC Susceptance model is used for incorporation into an existing power flow algorithm.
Here, the SVC state variables are incorporated inside the Jacobian and mismatch equations, leading to very robust
iterative solutions.
ii.Thyristor Controlled Series Compensator (TCSC)
The effect of TCSC on network can be seen as a controllable reactance inserted in the related transmission
line. The model of the network with TCSC is show in Fig. 2 [6].
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Issue 1 vol 1 July 2012
Fig. 2 A Model of TCSC
The TCSC consist of a capacitor bank and a thyristor controlled inductive branch connected in parallel and
series connected to the transmission line. The equivalent reactance of TCR, XLeq, at fundamental frequency, is
show in Eqn (iii). The controllable reactance, XTCSC, is directly used as the control variable that can be
determined by
𝑋𝐶 𝑋𝐿
𝑋𝐶
2 𝜋 − 𝛼 + sin 2𝛼 − 𝑋𝐿
𝜋
The power flow equation of the branch can be derived as follows
𝑃𝑖𝑗 = 𝑉𝑖2 𝑔𝑖𝑗 − 𝑉𝑖 𝑉𝑗 (𝑔𝑖𝑗 cos 𝛿𝑖 − 𝛿𝑗 + 𝑏𝑖𝑗 sin(𝛿𝑖 − 𝛿𝑗 ))
𝑋𝑇𝐶𝑆𝐶 =
(𝑖𝑖𝑖)
𝑄𝑖𝑗 = −𝑉𝑖2 𝑏𝑖𝑗 − 𝑉𝑖 𝑉𝑗 (𝑔𝑖𝑗 sin 𝛿𝑖 − 𝛿𝑗 − 𝑏𝑖𝑗 cos (𝛿𝑖 − 𝛿𝑗 ))
Where
3. VOLTAGE STABILITY INDEX
Voltage stability is becoming an increasing source of concern in secure operating of present-day power systems.
The problem of voltage instability is mainly considered as the inability of the network to meet the load demand
imposed in terms of inadequate reactive power support or active power transmission capability or both. It is mainly
concerned with the analysis and the enhancement of steady state voltage stability based on L-index.
Consider an 𝑛-bus system having1, 2, 3, … 𝑛, generator buses(𝑔), and 𝑔 + 1, 𝑔 + 2, … 𝑛, the load buses(𝑟 = 𝑛 −
𝑔 − 𝑠). The transmission system can be represented by using a hybrid representation, by the following set of
equations
𝑉𝐿
𝐼
𝑍
= 𝐻 𝐿 = 𝐿𝐿
𝐼𝐺
𝑉𝐿
𝐾𝐺𝐿
𝐹𝐿𝐺
𝑌𝐺𝐺
𝐼𝐿
𝑉𝐺
It can be seen that when a load bus approaches a steady state voltage collapse situation, the index 𝐿
approaches the numerical value 1.0. Hence for an overall system stability condition, the index evaluated at any of
the buses must be less than unity. Thus the index value 𝐿 gives an indication of how far the system is from voltage
collapse. The 𝐿 − indices for a given load condition are computed for all load buses. The equation for the 𝐿 −index
for 𝑗𝑡ℎ node can be written as,
𝑖=𝑔
𝐿𝑗 = 1 −
𝐹𝑗𝑖
𝑖=1
𝑉𝑖
𝑉𝑗
𝑖=𝑔
𝐹𝑗𝑖𝑟
+ 𝑗𝐹𝑗𝑖𝑚
1−
𝐹𝑗𝑖
𝑖=1
𝑉𝑖
𝑉𝑗
∠𝜃𝑗𝑖 + 𝛿𝑖 − 𝛿𝑗
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𝑖=𝑔
𝐿𝑗 = 1 −
𝐹𝑗𝑖
𝑖=1
𝑉𝑖
𝑉𝑗
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𝐹𝑗𝑖𝑟 + 𝑗𝐹𝑗𝑖𝑚
𝐹𝑗𝑖𝑟 = ⃒𝐹𝑗𝑖 ⃒cos⁡
(𝜃𝑗𝑖 + 𝛿𝑖 − 𝛿𝑗 )
𝐹𝑗𝑖𝑚 = ⃒𝐹𝑗𝑖 ⃒sin⁡
(𝜃𝑗𝑖 + 𝛿𝑖 − 𝛿𝑗 )
It can be seen that when a load bus approaches a steady state voltage collapse situation, the index 𝐿
approaches the numerical value 1.0. Hence for an overall system voltage stability condition, the index evaluated at
any of the buses must be less than unity. Thus the index value 𝐿 gives an indication of how far the system is from
voltage collapse.
4. SIMULATION RESULTS
For the validation of the proposed FACT’s devices, both SVC and TCSC have been tested on the following IEEE
5-Bus and IEEE 14-Bus test System. A MATLAB code for both techniques was developed for simulation purpose.
IEEE 5-Bus Test System
i. Location of TCSC:
The solution for optimal location of FACT’s devices to minimize the installation cost of FACT’s devices
and overloads for IEEE 5-bus test system were obtained and discussed in this section.
Fig. 3 IEEE 5 Bus Test System without TCSC & SVC
Voltage stability indices are calculated for the IEEE 5 bus system without any FACTS devices as shown in
Fig. 3.
Fig. 4 IEEE 5 Bus Test System with TCSC
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By considering the Voltage stability index (Lj) value, it is observed that bus Elm is more sensitive towards
system security. Therefore bus Elm is more suitable location for TCSC to improve power system security/stability.
An additional node is termed as node Elmfa, is used to connect the TCSC. The modified original networks to
include a TCSC between nodes Elm and Elmfa as shown in Fig. 4.
Table 1: Voltage Stability Index (VSI) Before & After Placement of TCSC
Name of
the Bus
VSI Before TCSC
VSI After TCSC
Lake
Main
Elm
Elmfa
0.0354
0.0358
0.0391
----
0.0279
0.0357
0.0253
0.0226
Table 2: Analysis of Voltage magnitudes, Phase Angles for
IEEE 5-bus test system with & without TCSC
Name of
the Bus
North
South
Lake
Main
Elm
Elmfa
Before Placement of
TCSC
VM (p.u)
VA (deg)
1.060
1.000
0.987
0.984
0.972
---
0.000
-2.061
-4.637
-4.957
-5.765
----
After Placement of
TCSC
VM(p.u)
VA(deg)
1.060
1.000
0.998
0.970
0.968
0.970
0.000
-2.346
-3.697
-6.544
-6.530
-6.534
Table 3: Analysis of Sending, Receiving Active & Reactive Power for
IEEE 5-Bus test system with TCSC
Branch
Sending Active &
Receiving Active &
Reactive Power
Reactive Power
MW
Mvar
MW
Mvar
89.4993
73.9459
87.0094
72.8471
1-2
1-3
2-3
2-4
2-5
3-4
6-5
41.6199
24.2002
27.3698
55.4394
18.9641
5.8462
16.7018
2.6449
1.8850
5.9579
2.6872
0.2227
40.1156
23.8485
26.9204
54.1878
18.9259
5.8122
17.4362
0.2510
0.7055
5.1170
4.5173
4.9135
ii. Location of SVC
The solution for optimal location of FACT’s devices to minimize the installation cost of FACT’s devices
and overloads for IEEE 5-bus test system were obtained and discussed in this section. By considering the Voltage
stability index (Lj) value, it is observed that bus Elm is more sensitive towards system security. Therefore bus Elm is
more suitable location for SVC to improve power system security/stability as shown in Fig. 5. After placement of
SVC voltage stability index is improved and system losses are reduced as shown in Table 4, Table 5 and Table 6.
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Fig. 5 IEEE 5 Bus Test System with SVC
Table 4: VSI Before & After Placement of SVC
Name of the
VSI Before
VSI After
Bus
SVC
SVC
0.0299
0.0298
Lake
0.0304
0.0286
Main
0.0099
Elm
0.0328
Table 5: Analysis of Voltage magnitudes, Phase Angles for
IEEE 5-bus test system without and with SVC
Name of
Before Placement of
After Placement of
the Bus
SVC
SVC
VM (p.u)
VA (deg)
VM(p.u)
VA(deg)
1.060
0.000
1.060
0.000
North
1.000
-2.057
1.000
-2.063
South
0.993
-4.716
0.993
-4.713
Lake
0.989
-5.034
0.991
-5.058
Main
0.978
-5.849
1.000
-6.215
Elm
Table 6: Analysis of Sending, Receiving Active & Reactive Power for
IEEE 5-Bus test system with SVC
Branch
Sending Active &
Receiving Active &
Reactive Power
Reactive Power
MW
Mvar
MW
Mvar
89.38
73.97
86.90
72.89
1-2
41.79
14.49
40.34
15.40
1-3
24.35
05.43
23.99
02.55
2-3
27.60
05.47
27.14
02.91
2-4
54.95
17.63
53.64
18.57
2-5
19.32
02.15
19.29
00.30
3-4
06.42
08.20
06.36
03.43
4-5
IEEE 14-Bus Test System
i. Location of TCSC
By considering the Voltage stability index (Lj) value, it is observed that 14-bus is more sensitive towards system
security. Therefore 14-Bus is more suitable location for TCSC to improve power system security/stability and
improvement of voltage stability as shown in Table 7 and Table 8. An additional node is termed as 15-Bus, is used
to connect the TCSC.
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Table 7: Analysis Voltage magnitudes, Phase Angles for IEEE 14-bus test system without and with TCSC
Name of
the Bus
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
Before Placement of
TCSC
VM (p.u)
VA (deg)
1.060
0.000
1.000
-4.551
0.906
-12.809
0.918
-9.872
0.934
-8.261
0.848
-16.041
0.857
-14.320
0.845
-14.320
0.836
-16.888
0.828
-17.199
0.834
-16.831
0.829
-17.390
0.823
-17.506
0.807
-18.785
-----
After Placement of
TCSC
VM(p.u)
VA(deg)
1.060
0.000
1.000
-4.411
1.000
-13.252
0.982
-10.272
0.990
-8.758
1.000
-15.316
0.976
-13.754
1.000
-13.754
0.959
-15.630
0.958
-15.901
0.975
-15.742
0.982
-16.271
0.975
-16.293
0.946
-17.190
0.947
-17.009
Table 8: Analysis of Sending, Receiving Active & Reactive Power for IEEE 14 Bus test system with TCSC
Branch
1-2
2-3
2-4
1-5
2-5
3-4
4-5
5-6
4-7
7-8
4-9
7-9
9-10
6-11
6-12
6-13
9-14
10-11
12-13
13-14
Sending Active &
Reactive Power
MW
Mvar
157.80
59.63
74.84
12.86
55.19
6.04
76.52
18.74
41.13
7.04
22.06
19.04
60.67
0.77
44.88
1.28
27.83
3.91
0.00
13.54
15.80
4.93
27.83
15.74
4.78
0.92
7.92
8.96
7.94
3.20
17.82
9.96
9.35
0.49
4.23
6.74
1.75
1.41
5.78
5.02
Receiving Active &
Reactive Power
MW
Mvar
152.86
47.35
72.14
22.03
53.40
9.62
73.51
8.90
40.14
8.37
22.65
19.23
61.18
0.22
44.88
6.46
27.83
2.20
0.00
13.88
15.80
3.35
27.83
14.56
4.77
0.94
7.78
8.67
7.85
3.01
17.55
9.41
9.22
0.23
4.28
6.87
1.74
1.40
5.68
4.80
ii. Location of SVC
The solution for optimal location of FACT’s devices to minimize the installation cost of FACT’s devices
and overloads for IEEE 14-bus test system were obtained and discussed in this section. By considering the Voltage
stability index (Lj) value, it is observed that 14-Bus is more sensitive towards system security. Therefore 14-Bus is
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more suitable location for SVC to improve power system security/stability and improve voltage stability as show in
Table 9 and Table 10.
Table 9: Analysis of Voltage magnitudes, Phase Angles for IEEE 14-bus test system without and with SVC
Name of
the Bus
01
02
03
04
05
06
07
08
09
10
11
12
13
14
Before Placement of
SVC
VM (p.u)
VA (deg)
1.060
0.000
1.000
-4.551
0.906
-12.809
0.918
-9.872
0.934
-8.261
0.848
-16.041
0.857
-14.320
0.845
-14.320
0.836
-16.888
0.828
-17.199
0.834
-16.831
0.829
-17.390
0.823
-17.506
0.807
-18.785
After Placement of
SVC
VM(p.u)
VA(deg)
1.060
0.000
1.000
-4.411
1.000
-13.242
0.985
-10.324
0.992
-8.774
1.000
-15.172
0.984
-13.846
1.000
-13.846
0.976
-15.714
0.972
-15.945
0.982
-15.702
0.989
-16.225
0.987
-16.495
1.000
-18.236
Table 10: Analysis of Sending, Receiving Active & Reactive Power for IEEE 14 Bus test system with SVC
Branch
1-2
2-3
2-4
1-5
2-5
3-4
4-5
5-6
4-7
7-8
4-9
7-9
9-10
6-11
6-12
6-13
9-14
10-11
12-13
13-14
Sending Active &
Reactive Power
MW
Mvar
157.79
59.63
74.76
12.85
55.35
7.57
76.58
17.90
41.05
8.04
22.13
17.46
61.65
3.18
43.87
0.70
28.48
1.05
0.00
8.72
16.23
2.32
28.48
8.01
5.40
2.32
7.21
5.53
7.53
0.90
17.93
0.86
9.80
12.93
3.61
3.51
1.36
0.85
5.57
6.21
Receiving Active &
Reactive Power
MW
Mvar
152.86
47.35
72.07
22.00
53.55
11.20
73.58
8.12
40.06
9.37
22.69
17.75
62.17
2.15
43.87
5.63
28.48
0.71
0.00
8.85
16.23
0.78
28.48
7.02
5.39
2.29
7.13
5.36
7.46
0.75
17.71
0.44
9.45
13.68
3.63
3.56
1.36
0.85
5.45
6.46
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5.CONCLUSION
In this paper, a new method for optimal placement and parameters settings of SVC and TCSC has been
proposed for improving voltage profile in a power system. The proposed approach has been implemented on IEEE
5-bus and IEEE 14-Bus system. The criteria for selection of optimal placement of SVC and TCSC were to maintain
the voltage profile, minimize the voltage deviations and to reduce the power losses using VSI. Simulations
performed on the test system shows that the optimally placed SVC and TCSC maintains the voltage profile,
minimizes the deviations and also reduces the real and reactive power losses.
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