Enhancement of Voltage Stability by
Coordinated Control
of Multiple FACTS Controllers in Multi

Machine Power
System Environments
Bindeshwar Singh, N. K. Sharma,
and
A. N. Tiwari,
Abstract

This
paper
presents
the implication of adding
various FACTS controllers in multi

machine power system
environment
in coordinated control manner
for
enhancement of voltage stability
requires
an appropriate
m
athematical model of the
power
system and the FACTs
co
ntrollers
such as a Static Var Compensator (SVC) and
Thyristor Controlled Series Capacitor (TCSC)
.
The DAE
(Differential
Algebraic Equation)
methodology for multi

machine system has been
is
used in this paper. Event tough
the SVC model has been incorporated in DAE
model,
TCSC model has not been incorporated. So the purpose of
this paper is to derive a TCSC model such that it ca
n be
incorporated in DAE model
of power system
.
Further in a
l
arge power system there may be more than one FACTS
controllers, therefore it is important to develop a
combination of series and shunt FACTS controllers that
can be incorporated in the DAE model in Modular fashion.
The models developed have been utilized f
or e
i
gen

value
analysis of IEEE 9

bus
3

machine
power systems.
There
are many commercial packages available for transient
simulation and analysis of power systems. The transient
simulation packages (e.g. EMTDC/PSCAD) allow
incorporation of FACTS controller
models. This facility is
however not available in the small signal stability analysis
packages. The objective of this paper is to develop a
methodology to incorporate FACTS controllers in a
modular fashion to facilitate eigen

value and voltage
stability a
nalysis using MATLAB toolbox.
Index Terms

F
lexible
AC
T
ransmission
S
ystems (FACTS)
,
FACTS Controllers,
SVC, TCSC
,
Power Systems
.
I.
INTRODUCTION
HE
DAE (Differential Algebraic Equation) methodology
for multi

machine system has been presented in
[1
]
is
used
in this paper.
Event tough the SVC model has been
incorporated in DAE model [2], TCSC model has not been
incorporated. So the purpose of this paper is to derive a TCSC
model such that it can be incorporated in DAE model. Further
in a large power system there may be more
than one FACTS
controllers, therefore it is important to develop a combination
of series and shunt FACTS controllers that can be
incorporated in the DAE model in Modular fashion. The
models developed have been utilized for egen

value analysis
of IEEE 9

bu
s power systems.
This paper is
organized as follows: Section II
discusses the
DAE model of multi

ma
chine power system without FACTS
controllers
.
Section III
introduces
the
DAE model of multi

machine power system with FACTs controllers.
Section IV
introduce
s
the
results and discussions
.
Section V
presents the
conclusions of the paper
.
II.
DAE MODEL OF MULTI

MACHINE POWER SYSTEM
WITHOUT FACTS CONTROLLERS
T
he methodology given in [1] describes dynamic modeling of
a general m

machine, n

bus system. This mode
l represents
each machine by a two

axis model and the excitation system is
chosen as the IEEE type

I rotating exciter. The transmission
system has been modeled by static equations. The DAE model
utilizes power balance form. The equations are written as:
(1)
(2)
Where
is a vector of state variables
is vec
tor of
algebraic variables and
is a vector of inputs and parameters.
Equation (1) consists of the differential equations of the
mechanical system, field winding, q

axis damper winding, and
the electrical e
quations of the exciter. Equation (2) consists of
the stator algebraic equations and the network power balance
equations. Various vectors are defined as
[1]
(3)
(4)
Based on the methodology described in [1], the linearized
model is given as
(5)
Where
is the load flow Jacobian
and
T
is the algebraic Jacobian.
The vectors
and
are
The system matrix
can be obtained as
Where
(6)
The details of DAE model
are given in [1]. This DAE model
for multi

machine system can be used for studying steady state
stability, voltage stability and low frequency
electro

mechanical oscillations. Based on this methodology, a small
signal stability program has been developed u
sing MATLAB.
The developed program is tested for 9

bus WSCC test system
and its results are corrected with the results published in [1] as
shown below.
III. DAE MODEL OF MULTI

MACHINE POWER
SYSTEM WITH FACTS CONTROLLERS
A.
Case Study(WSCC
9 bus System)
:
In
order to ensure that the developed small signal stability
program gives satisfactory results, eigen

value analysis is
performed for the Western System Coordinating Council
(WSCC) 9

bus system
shown in Fig. 1. This WSCC system
comprises th
r
ee generators
and nine buses. Loads are
connected at buses 5, 6, and 8 as shown in Fig.1. At base case
loading condition of the system, the generator 2 and 3 are
supplying 163 MW and 85MW power respectively. The base
MVA is 100, and system frequency is 60Hz. Table 1 sho
ws
the eigen

values of WSCC system. Column 1 of table 1 shows
the eigen

values reported in [1] while column 2 depicts the
eigen

values obtained from developed MATLAB program. It
is evident that eigen

values obtained from developed
MATLAB program correlate
very well with those reported in
[1]. This validates the developed MATLAB program.
Fig.1. WSCC (9

bus, 3

machine) power system
B.
Mathematical model of SVC :
Static VAR Compensator (SVC) is a shunt connected
FACTS
controller whose main functionality is to
regulate the
voltage
at a given bus by controlling its equivalent reactance.
Basically it consists of a fixed capacitor (FC) and a thyristor
controlled reactor (TCR). Generally they are two
configurations of the SVC.
a)
SVC total susceptance model. A changin
g susceptance
Bsvc represents the fundamental frequency equivalent
susceptance of all shunt modules maki
ng up the SVC as
shown in Fig. 2
(a).
b)
SVC firing angle model. The equivalent reactance
XSVC, which is function of a changing firing angle α, is
made up
of the parallel combination of a thyristor
controlled reactor (TCR) equivalent admittance and a
fixed capacitive reactance
as shown in Fig. 2
(b). This
model provides information on the SVC firing angle
required to achieve a given level of compensation.
Fig.
2
(a)
SVC firing angle model
Fig. 2
(b) SVC total susceptance model
Figure 3
shows the steady

state and dynamic voltage

current
characteristics of the SVC. In the active control range,
current/susceptance and reactive power is varied to regulate
voltage according to a slope (droop) characteristic. The slope
value depends on the desired voltage regulation, the desired
sharing of reactive power production between various sources,
and other
needs of the system. The slope is typically1

5%. At
the capacitive limit, the SVC becomes a shunt capacitor. At
the inductive limit, the SVC becomes a shunt reactor (the
current or reactive power may also be limited).
Fig
.
3.
steady

state and dynamic voltage/current
Characteristics of the SVC
SVC firing angle model is implemented in this paper.
Thus,
the model can be developed with respect to a sinusoidal
voltage, differential and algebraic equations can be written as
The fundamental freq
uency TCR equivalent reactance
Where
And in terms of firing angle
(7)
and
are conduction and firing angles respectively.
At
,
TCR conducts fully and the equivalent reactance
XTCR becomes XL,
while at
,
TCR is blocked and its
equivalent
reactance becomes infinite.
The SVC effective reactance
is determined by the
parallel combination of
and
(8)
Where
(9)
The SVC equivalent reactance is given
above equation
. It is
shown in
Fig.
that the SVC equivalent susceptanc
profile
,
as function of firing angle, does not
present
discontinuities, i.e.,
varies in a continuous,
smooth
fashion in both operative regions. Hence, linearization
of the
SVC power flow equations, based on
with respect
to
firing angle, will exhibit a better
numerical behavior than
the
l
inearized model based on
.
Fig.
4.
SVC equivalent susceptance profile
The initialization of the SVC variables based on the initia
l
values of ac variables and the characteristic of the equivalent
susceptance (Fig.), thus the impedance is initialized at the
resonance point
,
i.e.
=0, corresponding to
firing angle
, for chosen parameters of L and C i.e.
and
.
Proposed SVC power flow model:
The proposed model takes firing angle as the state variable in
power flow formulat
ion. From above equation the SVC
linearized power flow equation can be written as
(10)
At the end of iteration i, the variable firing angle α is updated
according to
SVC
Controller Model
:
Above equation can be written as
(11)
Where
And
`
Incorporation of SVC in multi

machine power systems:
In its simplest form SVC is composed of FC

TCR
configuration as shown in Fig.2. The SVC
is connected to a
coupling transformer that is connected directly to the ac bus
whose voltage is to be regulated. The effective reactance of
the FC

TCR is varied by firing angle control of the thyristors.
The firing angle can be controlled through a PI co
ntroller in
such a way that the voltage of the bus where the SVC is
connected is maintained at the desired reference value.
The SVC can be connected at either the existing load bus or at
a new bus that is created between two buses. As DAE model is
based o
n power

balance, rewriting of the power

balance
equations at the buses with SVC connected in the system
requires modification of
.When SVC is connected at
specified load buses, and
gets
modified as given below
Obtained state
equations
after linearization
of above
equations
(12)
Where
The incorporation of the SVC into DAE model of multi

machine power system is done on the same lines as explained
in [2] given as follows:
Incorporation of (11), (12), and (5) gives DAE model of multi

machine power system with SVC incorporated in the system.
After reordering, final form of DAE model with SVC is given
as
The state equation for th
e system with SVC is then given as
follows:
(13)
The System matrix with SVC given as
(14)
Where
c)
Mathematical model of
TCSC
:
Thyristor Controlled Series Capacitor (TCSC) provides
powerful means of controlling and increasing power transfer
level of a system by varying the apparent impedance of a
specific transmission line.
A TCSC can be utilized in a
planned way for contingencies
to enhance power system
stability. Using TCSC, it is possible to operate stably at power
levels well beyond those for which the system was originally
intended without endangering system stability [3]. Apart from
this, TCSC is also being used to mitigate S
SR (Sub
Synchronous Resonance).
The TCSC
module
shown in Fig.
5.
Fig.
5.
TCSC module
The steady

state impedance of the TCSC is that of a parallel
LC circuit, consisting of
fixed
capacitive impedance,
, and
a variable inductive impedance,
, that is,
(15)
Where
(16)
,
and
is the delay angle measured from the crest
of the capacitor voltage (or, equivalently, the zero crossing of
the line current). The impedance of the
TCSC by delay is
shown in Fig. 6.
Fig.
6
.
TCSC equivalent Reactance as a function of firing
angle
TCSC
Controller Model
:
The structure of the TCSC
is the same as that of a F
C

TCR
type SVC. The equivalent impedance of the TCSC can be
modeled using the following equations [4].
(17)
Where
Firing angle delay (after forward vale voltage)
Conduction angle=
and
TCSC
ratio =
The TCSC can be continuously controlled in the capacitive or
inductive zone by varying firing angle in a predetermined
fashion thus
avoiding steady state resonance region.
Incorporation of TCSC in Multi

machine Power
Systems:
The block diagram representation of TCSC shown in Fig. 7.
Fig.7.Block diagram
representation of TCSC module
Let a TCSC be connected between bus k and bus m as shown
in Fig.
It has been assumed that the controller is lossless. The
power

balance equation and
are given as [4]
Equation (
21) is obtained from (16).
There are number of control strategies for TCSC [4]
Reactance c
ontrol:
Power control:
Current control:
Transmission angle control:
Where the subscript “set” indicates set point.
Any of the above mentioned control strategies can be used to
achieve the objectives of TCSC. In this paper, the power
control strategy has been used, the blo
ck diagram of which is
shown in Fig.
The line power is monitored and compared to desired power
. The error is fed to proportional

integral (PI) controller.
The output of PI controller is fed through a first order block to
get the desir
ed
.
The block diagram representation of TCSC
with PI controller shown in Fig.
8.
Fig.
8.
Block diagram representation of TCSC with PI
controller
The controller equations are given as
( from fig.)
(18)
(19)
(20)
In order to get the linearized model of
TCSC, (
18
), (
19
)
, and
(
20
) are linearized. The linearized TCSC model in matrix
notation can be written as
(21)
Where
(22
)
Inc
orporation of
(
21), (22
), and (5) gives DAE model of multi

machine power system with TCSC incorporated in the system.
After reordering, final form of DAE model with TCSC is
given as
Equation (27) can be written as
(2
3
)
The System matrix with TCSC given as
(2
4
)
Where
C.
Mathematical model of SVC and
TCSC :
Incorporation of
Multiple FACTS controllers (SVC and
TCSC
)
in Multi

machine Power Systems
:
The
matrix
equations given as
(25
)
The System matrix with SVC+TCSC given as
(26
)
Where
IV
.
RESULTS&DISCUSSIONS
After incorporating FACTS controllers individually and in
combination into DAE model of multi

machine system,
voltage stability of 9

bus system is
carried out at various
loading conditions. However results are presented for
maximum loading condition.
Table 3
show
that without any
FACTS controllers the system is unstable, where unstable
eigen

values are highlighte
d
Table 1 Eigen

values of WSCC (9

bus
, 3

machine) power
system
Eigen

values from [1]
Eigen

values from
developed MATLAB
program
Table 2 Eigen

values of WSCC (9

bus,
3

machine) power
system with SVC
Eigen

values from [2]
Eigen

values from
developed MATLAB
program
However the system become stable when
SVC
or TCSC or
SVC
and
TCSC are connected. At maximum loading
condition, there is a need for
a shunt device at bus 5. Table 2
shows e
i
gen

values of the 9

bus system at maximum loading
conditions for three different cases

without any FACTS
device, with an SVC connected at bus 5 a
nd with a TCSC
connected between
lines
(7

5). Whereas TCSC controller
parameters are same as those used for base case loading
condition, the SVC controller
parameters are chosen as
and
.
Table 3 Eigen

values of WS
CC
(9

bus
, 3

machine) power
system with
only
SVC,
or only TCSC, or
SVC
and
TCSC
at
maximum loading condition
.
Without any
FACTS
device
With SVC
With TCSC
With
SVC+TCSC
In the similar fashion multiple FACTS controllers can also be
added to DAE model of multi

machine power systems for
enhancement of voltage stability of the systems
in coordinated
control manner
.
V.CONCLUSIONS
This
paper presents a systematic modular approach to
incorporate series and shunt FACTS controllers
in DAE model
of multi

machine power systems
in coordinated
control
manner
for enhancement of voltage stability of the systems.
This proposed
approach is general and can be ap
plied to any
large power system environments
.
With the proposed
approach it is possible to connect any number and any
type
(
series and shunt) of FACTS cont
rollers. The results of the
proposed modular approach are illustrated for 9

bus
3

machine
WSCC system.
ACKNOWLEDGMENT
The authors would like to thanks Dr. S. C. Srivastava,
and Dr. S. N. Singh,
Indian Institute of Technology, Kanpur,
U.P.,
India,
and Dr. K.S. Verma,
and
Dr. Deependra Singh,
Kamla Nehru Institute of Technology, Sultanpur, U.P.,
India,
for
their valuables
suggestions
in
regarding with
control
coordination
of
multiple
FACTS
controllers
in
multi

machine power systems for enhancement
of
voltage stability
.
REFERENCES
[1]
Peter W. Sauer and M. A. P
ai, Power System Dynamics and Stability,
Prentice Hall, 1998.
[
2
] M. J. Laufenberg, M. A. Pai, and K. R. Padiyar, “ Hopf Bifurcation control
in Power
System with Static Var Compensators, “ Electric Power & Energy Systems, Vol.
19, No.5, pp. 339

347, 1997.
[
3
]
E. V. Larsen, C. Bowl
er, B. Damsky and S. Nilsson, “Benefits
of Thristor
Controlled Series Compensation,
“CIGRE
, 14/37/

04
,
Paris,1992.
[
4
]
C. A. Canizares and Z. T. Faur,
“Analysis of SVC and TCSC controllers in
Voltage Collapse,” IEEE Trans. on Power Systems, Vol 14, No. 1,
, pp.
158

165
,
February 1999.
BIOGRAPHIES
Bindeshwar Singh
received the M.Tech. in electrical engineer
ing from the Indian
Institute of Technology, Roorkee, in 2001.He is now a Ph. D. student at UPTU,
Lucknow, India. His research interests are in Coordination of FACTS controllers in
multi

machine power systems and Power system Engg.. Currently, he is an
Ass
istant Professor with Department of Electrical Engineering, Kamla Nehru
Institute of Technology, Sultanpur,
U.P., India, where he has been since
August’2009.
Mobile: 09473795769, 09453503148
Email
:
bindeshwar_singh2006@rediffmail.com
,
bindeshwar.singh2025@gmail.com
Nikhlesh Kumar Sharma
received the Ph.D. in electrical engineering from the
Indian Institute of Technology, Kanpur, in 2001. Currently, he is a
Prof.&Head
with
, R
aj
K
umar
G
oel
Institute of Technology
, Ghaziabad,
U.P.,
India, where he
has been since June’2009. His interests are in the areas of FACTS control and
Power systems.
Mobile: 09654720667, 09219532281
Email:
drnikhlesh@gmail.com
A.N.Tiwari
received the Ph.D. in electrical engineering from the Indian Institute of
Technology, Roorkee, in 2004. Currently, he is a
n
Asst. Prof. with Department of
Electrical Engineering, M
adan Mohan
M
alviya
E
ngineering
C
ollege
,
Gorakhpur,
U.P.,
India, where he has
been since June’1998. His interests are in the
areas of Electrical Drives and Application of Power Electronics.
Mobile: 09451215400
Email:
amarndee@reffimail.com
APPENDIX
SYSTEM DATA FOR WSCC 3

MACHINES, 9

BUS SYSTEM
Base MVA 100MVA
Machine Data
Parameters
M/C1
M/C2
M/C3
23.6400
6.4000
3.0100
0.14600
0.8958
1.3125
0.06080
0.1198
0.1813
0.09690
0.8645
1.2578
0.09690
0.1969
0.2500
8.96000
6.0000
5.8900
0.31000
0.5350
0.6000
Exciter Data
Parameters
M/C1
M/C2
M/C3
20.0
20.0
20.0
0.20
0.20
0.20
1.0
1.0
1.0
0.314
0.314
0.314
0.063
0.063
0.063
0.35
0.35
0.35
0
0
0
0.0039
0.0039
0.0039
1.555
1.555
1.555
Line Data
Line
number
Bus
Impedance
From
To
R(pu)
X(pu)
Y/2(pu)
1
2
7
0
0.0625
0
2
1
4
0
0.0576
0
3
3
9
0
0.0586
0
4
4
6
0.0170
0.0920
0.0790
5
4
5
0.0100
0.0850
0.0880
6
5
7
0.0320
0.1610
0.1530
7
6
9
0.0390
0.1700
0.1790
8
9
8
0.0119
0.1008
0.1045
9
8
7
0.0085
0.0720
0.0745
Load Flow Results for Base Case of WSCC 9Bus System
Bus
Type
Angles
Voltages
PL
QL
PG
QG
1
SL
0
1.0400
0
0
0.7164
0.2705
2
PV
9.2800
1.0250
0
0
1.6300
0.0665
3
PV
4.6648
1.0250
0
0
0.8500

0.1086
4
PQ

2.2168
1.0258
0
0
0
0
5
PQ

3.9888
0.9956
1.2500
0.5000
0
0
6
PQ

3.6874
1.0127
0,9000
0.3000
0
0
7
PQ
3.7197
1.0258
0
0
0
0
8
PQ
0.7275
1.0159
1.0000
0.3500
0
0
9
PQ
1.9667
1.0324
0
0
0
0
SVC data
K
Tc
Tm
Kp
KI
0.1
0.02
0.02
0.
3
100
TCSC data
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