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
mathematical model of the power system and the FACTs
controllers such as a Static Var Compensator (SVC) and
Thyristor Controlled Series Capacitor (TCSC). The DAE
(Differential Algebraic Equation) methodology for multimachine 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 can be
incorporated in DAE model of power system. 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 eigen-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 analysis using MATLAB toolbox.
Index Terms- Flexible AC Transmission Systems (FACTS),
FACTS Controllers, SVC, TCSC, Power Systems.
This paper is organized as follows: Section II discusses the
DAE model of multi-machine power system without FACTS
controllers. Section III introduces the DAE model of multimachine power system with FACTs controllers. Section IV
introduces the results and discussions. Section V presents the
conclusions of the paper.
II. DAE MODEL OF MULTI-MACHINE POWER SYSTEM
WITHOUT FACTS CONTROLLERS
The methodology given in [1] describes dynamic modeling of
a general m-machine, n-bus system. This model 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)
x  f ( x, y, u )
x(0)  xo
0  g ( x, y , u )
(2)
y(0)  yo
Where x is a vector of state variables y is vector of
algebraic variables and u 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 equations of the exciter. Equation (2) consists of
the stator algebraic equations and the network power balance
equations. Various vectors are defined as [1]

 V , , I
xT   i , i , E ' qi , E ' di , E fdi ,VRi , RFi
yT
j
j
di
, I qi


(3)
I.INTRODUCTION
u T  TMi , VREFi , PLi , QLi  i  1,.....m; j  1,.......n (4)
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-bus power systems.
Based on the methodology described in [1], the linearized
model is given as
T
 
 X   A1mod A2 new A3new  X   E 
 0    K2
K1new C4 new   z    0 U (5)



D1new D2 new   v   0 
 0   G1


Where D2 new is the load flow Jacobian J LF and
C4 new 
K
J AE   1new
 is the algebraic Jacobian.
D
D
2 new 
 1new
T
T
The vectors z and v are
z T  1 , V1 ,........., Vm 
 
 
 
v    ,  ,....., 
T
2
3
m
, Vm1 ,........., Vn 
The system matrix Asys can be obtained as

 X  AsysX  EU
Where
1  K 
Asys  A1mod  A2 new A3new 
. J AE  . 2 
 G1 
(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 electromechanical oscillations. Based on this methodology, a small
signal stability program has been developed using 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 three 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 shows
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 changing susceptance
Bsvc represents the fundamental frequency equivalent
susceptance of all shunt modules making 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.
Bus
V
QSVC
jXL
-jXC

Th1
Th2

SVC
Fig. 2(a) SVC firing angle model
V
Bus

BSVC
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
I SVC   jB SVCVk
The fundamental frequency TCR equivalent reactance X TCR
X L
X TCR 
  sin 
Where   2(   ), X L  L
And in terms of firing angle
X L
X TCR 
2(   )  sin 2
(7)
 and  are conduction and firing angles respectively.
At   90 0 , TCR conducts fully and the equivalent reactance
XTCR becomes XL, while at   180 0 , TCR is blocked and its
equivalent reactance becomes infinite.
The SVC effective reactance X SVC is determined by the
parallel combination of X C and X TCR
X SVC ( ) 
X C X L
X C [2(   )  sin 2 ]  X L
(8)
Where X C  1C
2  X [ 2(   )  sin 2 
Qk  Vk  C

X C X L


(9)
The SVC equivalent reactance is given above equation. It is
shown in Fig. that the SVC equivalent susceptanc
( BSVC  1 / X SVC ) profile, as function of firing angle, does not
present discontinuities, i.e., BS VC varies in a continuous,
smooth fashion in both operative regions. Hence, linearization
of the SVC power flow equations, based on BS VC with respect
to firing angle, will exhibit a better numerical behavior than
the linearized model based on X SVC .
Fig.4. SVC equivalent susceptance profile
The initialization of the SVC variables based on the initial
values of ac variables and the characteristic of the equivalent
susceptance (Fig.), thus the impedance is initialized at the
resonance point X TCR  X C , i.e. QS VC =0, corresponding to
firing angle   115 0 , for chosen parameters of L and C i.e.
X L  0.1134  and X C  0.2267  .
Proposed SVC power flow model:
The proposed model takes firing angle as the state variable in
power flow formulation. From above equation the SVC
linearized power flow equation can be written as
(i )
(i )
0
0
  ( i )
 Pk 
2

  k

  0 2Vk [cos 2  1] 

  
Qk 
X L


(10)
At the end of iteration i, the variable firing angle α is updated
according to
 (i )   (i 1)   (i )
SVC Controller Model:
 1
  X 1S VC  
 
  Tm
 X 2 S VC     K I
 
  K
P
 X 3 S VC  
T
 c
0
0
1
Tc
KVS VCo 
Tm   X 1S VC 

0  X 2 S VC  
 1  X
 3 S VC 
Tc 
1

 T (1  KX 3 S VCo) 
 m

0

VS VC 


0




Above equation can be written as

 X SVC  AAVC X SVC  BSVCVSVC
Where
(11)
ASVC
 1
 T
 m
   KI
 KP
 T
 c
0
0
1
Tc
KVSVCo 
Tm 

0 
1 
Tc 
  X   A1 mod
   
 X SVC   P2 SVC

 K
 0   2
 0   G1
P1SVC
A2 new
ASVC
P4 svc
DSVC
P3 svc
K 1new
D1new _ svc
A3 new   X   E 
Bsvcnew  X SVC   0 

    U
C 4 new   z   0 

  
D2 new _ svc   v   0 
The state equation for the system with SVC is then given as
follows:
And

`
BS VC
1

 T (1  KX 3S VCo) 
 m


0



0




 X sys _ svc  Asys _ svcX sys _ svc  E SVCU
(13)
The System matrix with SVC given as
ASYS _ SVC  ASV1  ( ASV 2 * (inv( ASV 4 ) * ASV 3 )
(14)
Where
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 controller 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 on power-balance, rewriting of the power-balance
equations at the buses with SVC connected in the system
requires modification of D2 new .When SVC is connected at
specified load buses, and gets modified as given below
n
PSVCi  PLi (Vi )  ViVk Yik cos( i   k   ik )  0
k 1
i  m  1,......... ......., n
n
QSVCi  QLi (Vi )  ViVk Yik sin( i   k   ik )  0
k 1
i  m  1,......... .......... ...n
Obtained state equations after linearization of above equations
A
AS V1   1 mod
 P2 svc
A
AS V 2   2 new
 P3 svc
A3 new 
Bsvcnew 
P4 svc 
K
AS V 3   2

 G1 DSVC 
C 4 new 
 K 1new
AS V 4  

 D1new _ svc D2 new _ svc 
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 SSR (Sub
Synchronous Resonance).The TCSC module shown in Fig.5.
-jXC
Bus m
C SVCVl  DSVCX SVC  D1Vg  D 2 Vl  0
or
DSVCX SVC  D1Vg  D2 SVCVl  0
P1svc 
ASVC 
Bus k
jXL
Vk

(12)
Where
D2 SVC  CSVC  D2
The incorporation of the SVC into DAE model of multimachine 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 multimachine power system with SVC incorporated in the system.
After reordering, final form of DAE model with SVC is given
as
Th1

Vm
Th2
TCSC
Fig. 5.TCSC module
The steady-state impedance of the TCSC is that of a parallel
LC circuit, consisting of fixed capacitive impedance, X C , and
a variable inductive impedance, X L ( ) , that is,
X TCSC ( ) 
X C X L ( )
X L ( )  X C
(15)
Where
X L ( )  X L

  2  sin 2
, X L  X L ( )  
(16)
X L  L , 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.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 BTCSC are given as [4]
Pk  VkVm BTCSC sin( k   m )
Qk  Vk BTCSC  VkVm BTCSC cos(k  m )
Pm  VkVm BTCSC sin( m   k )
2
Qm  Vm BTCSC  VkVm BTCSC cos(m  k )
2
BTCSC   (k 4  2k 2  1) cos k (   ) /
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 FC-TCR
type SVC. The equivalent impedance of the TCSC can be
modeled using the following equations [4].
k   sin 



1  k 2  1 .



X TCSC  X C  2
2
 4.k . cos ( / 2) .( k tan k  tan  )
  (k 2  1) 2
2
2 

(17)
Where
  Firing angle delay (after forward vale voltage)
  Conduction angle= 2(   ) and
k  TCSC ratio =
XC / XT
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.
 X C (k 4 cos k (   )



  cos k (   ) 

2k 4 cos k (   )



2
 2k cos k (   )

 4

 k sin 2 cos k (   )

 k 2 sin 2 cos k (   )



3
2
 4k cos  sin k (   )

 4k 2 cos  sin  cos k (   )) 


Equation (21) is obtained from (16).
There are number of control strategies for TCSC [4]

Reactance control: Bset  BTCSC  0

Power control:
Pset  P  0
I set  I  0
 Transmission angle control:  set    0
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 block diagram of which is
shown in Fig.
The line power is monitored and compared to desired power
Pset . The error is fed to proportional-integral (PI) controller.
The output of PI controller is fed through a first order block to
get the desired  . The block diagram representation of TCSC
with PI controller shown in Fig.8.

Current control:

Kp
P
Pset
+


+
KI
s

 ref
+
0
A
ATC1   1mod
 P2t csc
 A
ATC 2   2 new
 Bt csc1new
X1TCSC
C.
 X 1TCSC X 2TCSC K P Pset K P P  o




Tc1
Tc1
Tc1
Tc1
Tc1
(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
  k 
 V 

 X TCS C  ATCS CX TCS C  BTCS C  k 
 m 


Vm 
(21)
 X

Where X TCSC   1TCSC 
X 2TCSC 
 Pk 
  k 
 Q 
 V 
 k   C X
 k
TCSC
1TCSC  DTCSC
 Pm 
 m 




Qm 
Vm 
Anew 
Bt cscnew 
Mathematical model of SVC and TCSC :
Incorporation of Multiple FACTS controllers (SVC and
TCSC) in Multi-machine Power Systems:

X 2TCSC  K I Pset  K I P
P1t csc 
ATCSC 
 K P4t csc 
ATC 3   2

 G1 CTCSC 
C 4 new 
 K1new
ATC 4  

D
D
2 new _ t csc 
 1new _ t csc
X 2TCSC
The controller equations are given as( from fig.)
K
X 2TCSC  I ( Pset  P)
s
X 1TCSC 
(24)

1
1  sTC1
Fig.8. Block diagram representation of TCSC with PI
controller

(23)
The System matrix with TCSC given as
ASYS _ TCSC  ATC1  ( ATC 2 * (inv( ATC 4 )) * ATC 3 )
Where

+
 X SYS _ TCSC  ASYS _ TCSCX SYS _ TCSC  ETCSCU
P1svc
  X   A1 mod
 
  P
ASVC
  X SVC   2 svc
 
   P2 t csc
P2 svtc
 X TCSC  
P4 svc
 0   K2
 0   G
D
1
SVC

 
E 
 
0
 0  U
 
0
0
 
The matrix equations given as
P1t csc
P1svtc
ATCSC
P4t csc
CTCSC
A2 new
Bsvc1new
Bt csc1new
K 1new
D1newsvtc
A3new   X 

Bsvcnew   X SVC 
Bt csc new  X TCSC  


C 4 new   0 
D2 newsvtc  0 

 X SVTC  ASVTCX SVTC  ESVTCU
The System matrix with SVC+TCSC given as
ASVTC  ASVTC1  ( ASVTC2 * (inv( ASVTC4 ) * ASVTC3 )
Where
 A1 mod P1svc P1t csc 
ASVTC1   P2 svc ASVC P1svtc 
 P2 t csc P2 svtc ATCSC 
A3 new 
 A2 new

ASVTC2   Bsvc1new Bsvcnew 
 Bt csc1new Bt csc new 
(22)
Incorporation of (21), (22), and (5) gives DAE model of multimachine power system with TCSC incorporated in the system.
After reordering, final form of DAE model with TCSC is
given as
  X   A1 mod P1t csc
P4 svc P4 t csc 
K
A2 new
Anew   X 
ASVTC3   2
 
 
E 



Bt csc new  X TCSC  
 X TCSC   P2t csc ATCSC Bt csc1new
 G1 DSVC CTCSC 


 0 U

 K
P4t csc
K1new
C 4 new   z   
C 4 new 
 K
 0   2

 0
ASVTC4   1new

 0   G1 CTCSC D1new_ t csc D2 new_ t csc   v   


 D1newsvtc D2 newsvtc
Equation (27) can be written as
(25)
(26)
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 highlighted
Table 1 Eigen-values of WSCC (9-bus, 3-machine) power
system
Eigen-values from [1]
Eigen-values
developed
program
from
MATLAB
0.7209 j12.7486
0.7198 j12.7456
0.1908 j8.3672
0.1906 j8.3660
5.4875 j7.9487
5.6867 j7.9663
5.3236 j7.9220
5.3644 j7.9311
5.2218 j7.8161
5.2287 j7.8263
5.1761
5.1779
3.3995
3.3993
0.4445 j1.2104
0.4513 j1.1997
0.4394 j0.7392
0.4481 j0.7291
0.4260 j0.4960
0.4366 j0.4868
0.0000
0.0000
0.0000
0.0000
3.2258
3.2258
conditions for three different cases-without any FACTS
device, with an SVC connected at bus 5 and 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
K P  0.3 and K I  100 .
Table 3 Eigen-values of WSCC (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
73.2762
90.9053
92.8398
46.1753
45.7923
41.2866
13.4003 j 22.7099
45.3014
0.5511 j50.3889
0.7151 j12.3385
0.8122 j12.7828
2.8938 j12.3353
0.5840 j12.6211
10.2041 j 6.9092
8.9940 j 7.6013
10.8806 j5.8904
0.1256 j8.0372
5.4101 j 7.9066
7.1699 j 7.9906
1.2151 j8.8486
9.8966 j 7.0805
1.0760 j 6.7042
5.3159 j 7.9089
6.3982 j 7.4235
7.3482 j 7.9374
7.5342
1.5319 j 7.5468
7.1865
5.2924 j 7.8977
5.4913 j0.1888
6.6072
5.1023
5.3210
4.8011
5.0487
2.1747
3.9843
0.4923 j1.0871
4.7690
1.6763
0.5010 j1.1119
1.9310
0.4599 j 0.9280
0.7284 j 0.3533
0.6142 j 0.6468
0.8733 j0.2529
0.6605 j 0.4841
0.0229 j 0.2268
0.7376 j 0.2042
0.5034
1.0336
0.0000 j 0.0000
0.0000 j 0.0000
0.0000 j 0.0000
0.0000 j 0.0000
3.2258
3.2258
3.2258
0.4012
0.1391
Table 2 Eigen-values of WSCC (9-bus, 3-machine) power
system with SVC
Eigen-values from [2]
Eigen-values
developed
program
from
MATLAB
78.4325
78.4309
10.2417 j 26.2143
10.2421 j 26.2120
0.8432 j12.7698
0.8424 j12.7669
0.2677 j8.4245
4.6918 j1.3196
0.2674 j8.4233
4.6989 j1.3187
3.8082 j1.5021
3.8089 j1.5006
2.6818 j 2.0672
2.6815 j 2.0675
1.7352
1.7356
0.0000
0.0000
0.1365
0.1365
0.8871
0.8867
3.2258
3.2258
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 eigen-values of the 9-bus system at maximum loading
With
SVC+TCSC
3.2258
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 applied 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 controllers. The results of the
proposed modular approach are illustrated for 9-bus 3machine 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.
KA
20.0
20.0
20.0
TA (sec)
0.20
0.20
0.20
Ke
1.0
1.0
1.0
REFERENCES
[1]
Peter W. Sauer and M. A. Pai, Power System Dynamics and Stability,
Prentice Hall, 1998.
Te
0.314
0.314
0.314
[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.
Kf
0.063
0.063
0.063
[3]
E. V. Larsen, C. Bowler, B. Damsky and S. Nilsson, “Benefits of Thristor
Controlled Series Compensation, “CIGRE, 14/37/-04, Paris,1992.
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. 158165,February 1999.
Tf
0.35
0.35
0.35
Rs
0
0
0
Aex
0.0039
0.0039
0.0039
Bex
1.555
1.555
1.555
[4]
BIOGRAPHIES
Bindeshwar Singh received the M.Tech. in electrical engineering 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
Assistant 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, Raj Kumar Goel 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 an Asst. Prof. with Department of
Electrical Engineering, Madan Mohan Malviya Engineering College,
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
Line Data
Line
number
Bus
From
2
1
3
4
4
5
6
9
8
1
2
3
4
5
6
7
8
9
Impedance
R(pu)
0
0
0
0.0170
0.0100
0.0320
0.0390
0.0119
0.0085
To
7
4
9
6
5
7
9
8
7
X(pu)
0.0625
0.0576
0.0586
0.0920
0.0850
0.1610
0.1700
0.1008
0.0720
Y/2(pu)
0
0
0
0.0790
0.0880
0.1530
0.1790
0.1045
0.0745
Load Flow Results for Base Case of WSCC 9Bus System
Bus
1
2
3
4
5
6
7
8
9
Type
SL
PV
PV
PQ
PQ
PQ
PQ
PQ
PQ
Angles
0
9.2800
4.6648
-2.2168
-3.9888
-3.6874
3.7197
0.7275
1.9667
Voltages
1.0400
1.0250
1.0250
1.0258
0.9956
1.0127
1.0258
1.0159
1.0324
PL
0
0
0
0
1.2500
0,9000
0
1.0000
0
QL
0
0
0
0
0.5000
0.3000
0
0.3500
0
PG
0.7164
1.6300
0.8500
0
0
0
0
0
0
Machine Data
Parameters
M/C1
23.6400
M/C2
6.4000
M/C3
3.0100
X d ( pu )
0.14600
0.8958
1.3125
X ' d ( pu )
0.06080
0.1198
0.1813
X q ( pu )
0.09690
0.8645
1.2578
X 'q ( pu)
0.09690
0.1969
0.2500
T 'do (sec)
8.96000
6.0000
5.8900
T 'qo (sec)
0.31000
0.5350
0.6000
M/C1
M/C2
M/C3
H ( pu )
K
0.1
TCSC data
Exciter Data
Parameters
SVC data
Tc
0.02
Tm
0.02
Kp
0.3
KI
100
QG
0.2705
0.0665
-0.1086
0
0
0
0
0
0