Canadian Journal of Basic and Applied Sciences
©PEARL publication, 2015
ISSN 2292-3381
CJBAS Vol. 03(02), 67-77, February 2015
Transient Stability Enhancement of Single Machine Infinite Bus (SMIB) System
using TCSC based Controller
Neha Maithil a, Rahul Agrawal a, Sourabh Kothari b
a
b
Assistant Professor, Vindhya Institute of Technology & Science, Indore (M.P.), India.
Assistant Professor, Chameli Devi Group Of Institutions, Indore (M.P.), India.
Keywords:
Abstract
Transient Stability,
Single Machine Infinite
Bus (SMIB) System,
FACTS,
Power System Stabilizer
(PSS),
TCSC Controller
In present scenario, the major concern of the power engineers is to increase the power
transfer capability of the existing system and power system stability for increasing
system performance and reliable operation. This led to the development of FACTS
technology. FACTS controllers enhance power transfer capability as well as power
system stability. This paper presents modeling and simulation of single machine
infinite bus (SMIB) system with PSS incorporated with TCSC controller. Thyristor
Controlled Series Capacitor (TCSC) controller is used to improve transient stability of
the SMIB system. Design of PSS and TCSC controller is proposed. The model of
SMIB with both PSS and TCSC is developed in MATLAB for simulation purpose.
Three phase symmetrical faults are introduced in the study. The simulation results show
that the stability of the power system is being improved by TCSC controller and it
effectively damp out the power system oscillations.
Nomenclature
∆ωr
dB
Sm
Smo
H
D
d / dt
Tm
Te
Pm
Pe
Efd
Eb
T’do
T’qo
Xd
X’d
Xq
X’q
Efdo
Xc

Rotor angle deviation of synchronous generator in radians
Rotor speed deviation in radian / sec
Generator Slip in per unit
Initial operating slip in p.u.
Inertia constant
Damping co-efficient
Differential operator
Mechanical torque input in N-M
Electrical torque in N-M
Mechanical power input to the generator
Electrical power output of the generator
Excitation system voltage in per unit
Voltage of infinite bus in per unit
Open circuit d-axis time constant in second
Open circuit q-axis time constant in second
d-axis synchronous reactance in p.u.
d-axis transient reactance in p.u.
q-axis synchronous reactance in p.u.
q-axis transient reactance in p.u
Initial value of Efd
Nominal reactance of the fixed capacitor C
Corresponding Author :
E-mail, nehamaithil@gmail.com – Tel, (+91) 9826173619
Neha Maithil et al. - Can. J. Basic Appl. Sci. Vol. 03(02), 67-77, February 2015
Xp
σ
α
k
Ke
Te
XTCSC
XL
Inductive reactance of inductor L connected in parallel with C
Conduction angle of TCSC
Firing angle of TCSC
Compensation ratio
Exciter Gain
Time Constant of Exciter
Reactance of TCSC
Reactance of Transmission Line
1. Introduction
Modern power systems, are growing in size and complexity, are characterized by long distance
bulk power transmissions and wide area interconnections. To meet the load demand and satisfy the
reliability and stability criteria in a complex modern interconnected power system, either it is
required to utilize the existing transmission lines more efficiently, or newly constructed lines should
be added to the system. With the increase of electric power demand, the power stations are remotely
located in dispersed areas. Therefore, it has become inescapable to establish new long transmission
lines and using new technologies. On the other hand, this scheme is very expensive and
environmental issues should be considered. One of the solutions to this problem is the utilization of
the existing transmission lines more effectively and with a higher loading capacity. To realize a
smart and fault tolerant grid a new technology Flexible AC transmission system (FACTS) was
proposed. FACTS devices are solid state converters that have the capability of controlling various
electrical parameters in transmission circuits. The devices of FACTS family such as Thyristor
controlled series compensator (TCSC), static synchronous series compensator (SSSC), Static VAR
Compensator (SVC), Thyristor controlled phase angle regulator (TCPST), Static compensator
(STATCOM), Unified power flow controller (UPFC) etc [4, 8]. FACTS devices can be connected
to a transmission line in various ways, such as in the series, shunt or a combination of series and
shunt.
Today the stability of power system has been become a major concern in system operation.
Several disturbances involve a large excursion of generator rotor angles, power flows, bus voltages
and other system variables. In recent years, considerable efforts have been made to improve or
enhance the power system stability [1, 2, 8]. Fast acting, high gain Automatic Voltage Regulators
(AVR) are being employed to the synchronous generators to maintain the distantly located
interconnected power systems at constant operating voltage. Though AVRs can enhance the overall
transient stability, they are responsible for low frequency generator rotor angle oscillations (0.1-3
Hz). They may further grow in magnitude affecting the small signal stability. In order to produce
positive damping on these small frequency oscillations, Power System Stabilizers (PSS) are
employed [14]. The purpose of the PSS is to introduce supplementary signals in the feedback loop
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of the voltage regulator. To damp the power system oscillations, PSS controllers are used [15]. But
in the same cases the PSS are not able to suitably damp inter-area oscillations modes. In such cases,
the simultaneous use of both controller types (PSS and FACTS damping controllers) is required to
guarantee a good closed loop system performance. This paper proposes a design of PSS and TCSC
supplementary damping controllers. With the advent of FACTS devices, the model of SMIB power
system is incorporated with FACTS controllers.
2. Test Power System (SMIB System with TCSC)
This paper focuses attention on the single machine infinite bus (SMIB) power systems. Since
SMIB system is relatively simple to study, it is extremely useful in describing the general concepts
of power system stability, the influence of various factors upon stability, and alternative controller
concepts. The SMIB installed with TCSC is shown in figure 1. Vt and Eb are the generator terminal
and infinite bus voltage respectively. XT, XL and XTH represent the reactance of the transformer,
transmission line per circuit and the Thevenin’s impedance of the receiving end system
respectively.
Figure 1. SMIB Power system with TCSC.
3. Modeling of Power System Components
In this paper, the modeling of power system components includes the modeling of single
synchronous generator connected to infinite bus and modeling of excitation system with power
system stabilizer (PSS) [11,12].
3.1 Modeling the Synchronous Generator Infinite-bus Power System
This paper presents a dynamic model of synchronous generator represented by model 1.1, i.e.
with field circuit and one equivalent damper winding on q-axis.
The non-linear equations of machine are given by [9]:
d
 B (Sm - Smo )
dt
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Neha Maithil et al. - Can. J. Basic Appl. Sci. Vol. 03(02), 67-77, February 2015
dS m
1

[ D( S m - Smo )  Tm - Te ]
dt
2H
dE ' q
1

[ E ' q  (x d - x' d ) i d  E fd ]
dt
T'do
dE ' d
1

[ E ' d  (x q - x' q ) i q ]
dt
T'qo
The electrical torque Te is expressed in terms of variables E’d,E' q,id and iq as:
Te  E' d i d  E' q i q  (x' d - x' q ) i d iq
The stator algebraic equations and the network equations for a lossless network are expressed as:
E' q  x' d i d  v q
E' d - x' q i q  v d
vq  - x e i d  E b cos
vd  x e i q - E b sin
On solving above equations, the variables id and iq can be obtained as:
id 
iq 
E b cos  - E' q
x e  x' d
E b sin  - E' q
x e  x' q
3.2.Excitation System Modeling with PSS
In the paper, the simplified IEEE type-ST1A excitation system is considered shown in figure 2.
The inputs of the excitation system are the terminal voltage VT and reference voltage VR. KA and TA
represents the gain and time constants of the excitation system respectively [1].
Figure 2. IEEE type ST1A excitation system
The method of incorporating these models into a transient stability program by considering the
excitation system model shown in figure 3. It represents a bus-fed thyristor excitation system (IEEE
type STIA) with an automatic voltage regulator (AVR) and a power system stabilizer (PSS).
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Neha Maithil et al. - Can. J. Basic Appl. Sci. Vol. 03(02), 67-77, February 2015
Figure 3. Thyristor excitation system with AVR and PSS
Figure 4 shows PSS and IEEE type-ST1A excitation system excluding terminal voltage
transducer. Both figures 3 and 4 represent the same system.
Figure 4. PSS and IEEE Type-ST1A Excitation system
4. Modeling of TCSC controller structure
TCSC is defined as “A capacitive reactance compensator which consists of a series capacitor
bank shunted by a thyristor-controlled reactor in order to provide a smoothly variable series
capacitive reactance” [4,5,6]. TCSC is most important and best known series controllers which has
been employed for many years to enhance power transfer capability of line as well enhance the
system stability. The TCSC has three main components: capacitor bank C, bypass inductor L and
bidirectional Thyristors T1 and T2 as shown in figure 5. To adjust the reactance of TCSC according
to the system control algorithm and to response some system parameter variations, the firing angles
of thyristors are controlled. The basic scheme is shown in figure 5. iC and iL are the instantaneous
values of the currents in the capacitor banks and inductor, respectively; iS the instantaneous current
of the controlled transmission line; v is the instantaneous voltage across the TCSC.
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Neha Maithil et al. - Can. J. Basic Appl. Sci. Vol. 03(02), 67-77, February 2015
A Simplified TCSC circuit is shown in figure 6 for the purpose of mathematical analysis.
Transmission line current is assumed to be the independent input variable and is represented as a
variable current source, iS(t). Here the sinusoidal line current is assumed for the sake of analysis [9].
The equivalent TCSC reactance XTCSC is the ratio of VCF to Im.
Figure 5. Basic scheme of TCSC
Figure 6. A Simplified TCSC Equivalent Circuit
The equivalent TCSC reactance is given by:
X TCSC 
2
VCF
X C
2  sin2
4X 2 C cos 2  (k tan k - tan )
 XC 
Im
(X C - XP )

(X C - X P ) (k 2 - 1)

Or
X TCSC 
2
VCF
X C   sin
4X 2 C cos 2 ( / 2) (k tan(k / 2) - tan( / 2))
 XC 
Im
(X C - XP )

(X C - X P ) (k 2 - 1)

Where
VCF = Fundamental component of the capacitor voltage.
XC = Nominal reactance of the fixed capacitor only.
XP = Inductive reactance of inductor connected in parallel with fixed capacitor.
Β = Angle of advance
σ = 2 (π – α), the conduction angle of TCSC
The variation of per unit TCSC reactance as a function of firing angle α for different values of
the compensation ratio k= √ (XC / XP is accounted. If the value of XC is changed then the maximum
value of XTCSC also changes and hence the initial value of compensation can be changed [9]. In this
paper, the TCSC controller is assumed to modeled here only as a variable capacitive reactance
within the operating region defined by the limits imposed by α [13]. Thus XTCSCmin ≤ XTCSC ≤
XTCSCmax, with XTCSCmax = XTCSC(αmin) and XTCSCmin = XTCSC(180°) = XC.
In the capacitive region, i.e., αmin> αr where αr denotes to the resonant point, as the inductive
region associated with 90° < α < αr induce high harmonics that cannot be properly modeled in
stability studies.
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5. Simulation Results
5.1. SMIB with PSS and without TCSC
In this section, the simulation results of SMIB with PSS are discussed (i.e. without including
TCSC controller). SMIB with PSS controller presents results under two operating conditions which
are explained below. First condition, without three phase fault and second condition, with three
phase fault. The three phase fault that we consider here is a dead short circuit of all the three lines
not involving the ground.
Case 1. Without three phase fault
Figure 7 shows the excitation voltage with respect to time. Figure 8 shows the variations in
parameters (a) rotor speed deviation (b) output active power (c) voltage stability (d) output reactive
power. Figure 9 shows the effect of PSS on (a) load angle (b) rotor angle deviation (c) electric
power (d) rotor speed.
Figure 7. Excitation voltage of SMIB with PSS
without fault
Figure 8. SMIB with PSS without fault (a) Rotor speed
deviation (b) Output active power(c) Voltage stability (d)
Output reactive power
Figure 9. SMIB with PSS without fault (a) Load angle (b) Rotor angle deviation (c) Electrical power (d) Rotor speed
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Neha Maithil et al. - Can. J. Basic Appl. Sci. Vol. 03(02), 67-77, February 2015
Case 2. With three phase fault
This case shows the variations in parameters when we applied symmetrical three phase fault to
the SMIB system with PSS controller. The results are shown from figure 10 to figure 12.
Figure 10. Excitation voltage of SMIB with PSS
with fault
Figure 11. SMIB with PSS with fault (a) Rotor speed
deviation (b) Output active power(c) Voltage stability (d)
Output reactive power
Figure 12. SMIB with PSS with fault (a) Load angle (b) Rotor angle deviation (c) Electrical power (d) Rotor speed
5.2. SMIB with PSS and with TCSC Controller
To show the advantages of TCSC controller incorporated with PSS in SMIB power system,
simulation results are carried out in this section. Same as above, SMIB with TCSC presents results
under two cases i.e. with and without three phase fault.
Case 1. Without three phase fault
Figure 13 shows the excitation voltage with respect to time. Figure 14 shows the variations in
parameters (a) rotor speed deviation (b) output active power (c) voltage stability (d) output reactive
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power. Figure 15 shows the effect of TCSC on (a) load angle (b) rotor angle deviation (c) electric
power (d) rotor speed. Figure 16 shows the three phase voltage and current of the generator.
Figure 13. Excitation voltage of SMIB with PSS- TCSC
without fault
Figure 14. SMIB with PSS- TCSC without fault (a)
Rotor speed deviation (b) Output active power(c)
Voltage stability (d) Output reactive power
Figure 15. SMIB with PSS-TCSC without fault (a)
Load angle (b) Rotor angle deviation(c) Electrical power
(d) Rotor speed
Figure 16. Three phase voltage and current of generator
without fault
Case 2. With three phase fault
Results are shown in figure 17 to figure 20.
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Figure 17. Excitation voltage of SMIB with PSS- TCSC
with fault
Figure 18. SMIB with PSS- TCSC with fault (a) Rotor
speed deviation (b) Output active power (c) Voltage
stability (d) Output reactive power
Figure 19. SMIB with PSS-TCSC with fault (a) Load
angle (b) Rotor angle deviation (c) Electrical power (d)
Rotor speed
Figure 20. Three phase voltage and current of generator
with fault
Various simulation results shown above with and without fault have been explored and results
validate the superior performance of the proposed system. Results show that SMIB with both PSS
and TCSC controllers is more effective than SMIB with PSS controller only.
6. Conclusion
This paper investigates that the FACTS controllers, when equipped with PSS can effectively damp
out power system oscillations. This paper deals with modeling and simulation of TCSC controllers
for SSR mitigation and enhancing power system stability. A SMIB is considered for this study.
Comparative study is done by simulating the simple SMIB system with PSS and then SMIB system
is simulated with PSS and TCSC controller both and thus simulations studies are carried out.
Simulation results clearly indicate the effect of TCSC in improving transient performance of SMIB
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Neha Maithil et al. - Can. J. Basic Appl. Sci. Vol. 03(02), 67-77, February 2015
under symmetrical three phase fault. Rotor angle deviation (ω or ωr), electric power (Pe), rotor
speed deviation and load angle with PSS-TCSC and without TCSC (i.e. with PSS only) is observed.
This observation is helpful to examine stability improvement in both the cases. This work can be
extended to multi-machine system by using other types of FACTS controllers like SVC, UPFC etc.
Intelligent controllers such as Fuzzy Logic, Neural Network, Hybrid Fuzzy PI based controllers,
Big bang controllers etc. can be designed for more effective results. In this study soft computing
techniques like GA, PSO may be employed in the future to optimize the parameters of TCSC.
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