The Impact of Line Resistance on the Performance of Controllable Series Compensator for Improving Voltage Stability

Journal of Advanced Computing and Communication Technologies (ISSN: 2347 - 2804)
Volume No.5 Issue No.2, April 2017
16
The Impact of Line Resistance on the Performance of Controllable
Series Compensator for Improving Voltage Stability
By
1st
Punit Verma, 2nd
Pradeep Singh, 3rd
Jyotsna Singh, 4th
Rajive Tiwari, 5th
M. R. Farooqi
1st
Dept. of Electrical Engineering, MNIT Jaipur, India
2nd
3rd
4th
5th
1st
2015pes5122@mnit.ac.in, 2nd
psn121988@gmail.com,
3rd
sjyotsna04@gmail.com, 4th
rajivetiwari72@gmail.com
ABSTRACT
In recent years controllable FACTS devices are increasingly
integrated into the transmission system. FACTS devices that
provide series control such as Controllable Series Compensator
(CSC) has significant effect on the voltage stability of Electric
Power system. In this work impact of line resistance on the
performance of CSC in a single-load infinitive-bus (SLIB)
model is investigated. The proposed framework is applied to
SLIB model and obtained results demonstrates that line
resistance has considerable effect on voltage stability limits and
performance of CSC.
Keywords
FACTS,CSC,Voltage stability limit, PV curves
1.INTRODUCTION
Power system voltage stability analysis has become very
important for secure power system operation and satisfactory
design as power industry’s is undergoing revolutionary
restructuring and a deregulation of electricity market [1, 2].
Renewable energy sources are increasingly in integrated into
distribution system to enhance security and stability. But
presence on non-conventional resources has significant impact
on line capacity of distribution network [3-5].
Flexible Alternating Current Transmission System (FACTS)
devices are installed in power system network to improve the
voltage stability as well as increase the power transfer [7]. It can
be stated that the maximum power transmission over long lines
is limited by the series reactive impedance of the line. [7] Series
capacitive compensation results in reduced reactive line
impedance and increased transmitted power. But with advent of
FACTS technology, controllable series line compensation can be
achieved power electronic devices for full utilization of
transmission assets by altering the power flow in the lines.
FACTS devices can be classified by their response time and
possibility to alter the circuit parameters like network admittance
and voltage phasors. FACTS devices can also be classified on
the basis of connection i.e. as parallel or series connection [7,
8].Application of series controllable FACTS device CSC is
discussed in this paper.
Series FACTS devices can increase the maximum power
transfer capability of the line and can also damp out the
oscillations. In this paper we see that the voltage stability of the
system is improved by the application of CSC and also effect of
line resistance is studied on the performance of CSC.
When the system is heavily loaded or the power transfer
capability is reduced due to disturbances, in that case the lack of
reactive power support makes the system voltage unstable which
leads to voltage instability [11]. A system is said to be in voltage
stable if at a given operating condition, for every bus in the
system, the bus voltage magnitude enhances when supplied with
additional reactive power .A system is voltage unstable if for at
least one bus in the system, the bus voltage magnitude reduces
as the reactive power injection at the same bus is reduced [11].
Voltage stability can be classified on the basis of extremity
of the disturbance and also its duration. The application of the
FACTS devices in transmission line plays very important role in
the disturbances which occurs due to induction motors and
HVDC converters [12]. Voltage stability analysis is done using
continuation power flow (CPF) method is discussed in [13].
Voltage stability analysis can be done by using analytical and
probabilistic methods [14].Short term voltage instability
phenomenon is discussed in paper [15], which shows that short
term voltage instability occurs when the consumers have
electrical motors and electronic controlled devices.
Authors in [16] studied the effect of a serial FACTS device
on the voltage stability with the help of CPF. The understanding
of the logical equations of FACTS devices (series) connected in
single load infinitive bus (SLIB) is discussed in [17]. Logical
solutions to asses voltage of load bus connected in the SLIB
model with an application of a CSC is discussed in [6].All the
aforementioned work neglected the effect of line resistance
while analyzing voltage stability of system in presence of
FACTS devices.
In this paper the line resistance has been considered for the
analysis which results in reduction in the performance of CSC
on the SLIB model. Mathematical model of SLIB is developed
including CSC and line resistance and. Analytical equations are
formulated to outline voltage instability. In order to analyze
voltage stability upper and lower nose curves are plotted for
different values of compensation parameter. Also the

17
comparison of the PV curves with and without resistance is
presented for considered SLIB model.
This paper is organized as follows: Section II discusses
Controllable Series Compensator and section III discusses
mathematical modeling of CSC and Finally in section IV results
are shown and discussed in detail.
2.CONTROLLABLE SERIES COMPENSATOR
A. Concept of controllable series compensator
The basic idea of series compensator is to decrease and
increase the overall effective series transmission
impedance from the sending end to receiving end
depending upon the requirement.
AC
XXc
Z = R
Vs Vr
Fig – 1 Radial Transmission Line With Series Compensation
P(p.u.)
Vr
(p.u)
1 20
0.5
1
3
Xc = 0 Xc = 0.5X Xc = 0.75X
Fig – 2 Transmittable Power and Voltage Stability Limit of A Radial
Transmission Line
Fig 1shows a basic radial system with line reactance X, series
compensating reactance Xc and load impedance Z [8]. The
corresponding terminal voltage Vr versus power P plots,with
unity power factor load at 0,50 and 75% series compensation are
shown in Fig 2 [8]. The nose point at each plot given for a
specific compensation level represents the corresponding voltage
instability.
B. The SLIB model with the CSC
The application, connection and working principle of CSC is
described in [9, 10]. The CSC works as a continuously
controlled reactance Xc. The SLIB model with the CSC is
presented in Fig 3, which is represented by the π model of the
transmission line with the line parameters. After the addition of
CSC the two bus system becomes four bus system. The SLIB
model with the CSC provides the simple approach for voltage
stability assessment.
I1 I1
I10 Ia0 Ib0
jBa0 jBb0
jXc I2 I2
I20
V2,δ2
P2
Q2=P2*K
jB20
R2+jX2Va Vb
R1+jX1
jB10
V1=1pu δ1=0
Fig – 3 The SLIB Model With The CSC
In large electric power system damping and load flow can be
controlled by CSC.
C. Operating modes of CSC
1. Capacitivemode:In this mode the CSC delivers the
reactive power to the system hence the voltage profile of the
system can be improved. In that mode the values of the
series reactance is negative i.e. Xc< 0
2. Inductive mode: In this mode the CSC absorbs the
reactive power from the system hence the voltage profile of
the system has been worsen. In that mode the values of the
series reactance is positive i.e. Xc> 0
D. Approaches to Controllable Series Compensation
The series compensator can be used as a controlled voltage
source which controls the current of the transmission line
and is connected in series with the transmission line [8]. The
series compensator can be used either as a variable reactive
impedance or as a controlled voltage source in series with
the transmission line. In case of series compensation the
basic reference parameter is the line current. So the working
of the series compensator is seen from the perspective of the
line current. The series compensator can be approached in
the following ways:
1. Variable Impedance Type Series Compensators-
Variable impedance type series compensators make use
of thyristor controlled-capacitors or thyristor controlled
reactors. GTO Thyristor-controlled series capacitor
(GCSC), Thyristor-switched series capacitor (TSSC),
Thyristor-controlled series capacitor (TCSC) falls under
this category.
2. Switching Converter Type Series Compensator –
Voltage source converter based series compensator
whichuses the converter based technology for series and
shunt compensation [8]. A voltage-sourced converter with
its internal control can be considered as a synchronous
voltage source. It can produce sinusoidal voltage with
controllable amplitude and phase angle, generate or absorb a
reactive power. Static Synchronous Series Compensator
(SSSC) is good example.
3.MATHEMATICAL MODELLING OF CSC
Voltage stability assessment is done using SLIB with CSC
connected in series (Fig.3). The CSC is connected through the
π model of the transmission line with the
parameters , , , , and .
The SLIB model shown in Fig.3 is suitable for voltage-
instability studies because relation between load bus and its

18
voltage can be analyzed depending on the load flows and the
characteristics of the loads, which can be voltage dependent or
voltage independent. In order to understand, how the CSC affect
the voltage , the CSC is placed at random distance from the
slack bus, the parameters and , and , and as
shown in Fig.3 have different values. Two bus SLIB model is
converted to four bus model when series device connected
between the buses A and B. On the buses A and B the
suceptances and are connented as shown in figure for the
model with the CSC.
The analytical equation for the voltage with the CSC (Fig.3)
using the Kirchhoff current and voltage laws are formulated as
follows:
= + + + + (1)
= -( +j ( + + + )-j ( + + )-
+j )( + ) (2)
Currents expressions (1) and (2) can be expressed in terms of
known variables , , , with the parameters
, , , , , , and of the network and with the
unknown variable-voltage [6]. After the introduction of the
new denotations , , and [6] the voltage is written
as:-
( -1)+ . (cos -jsin )+ +j =0 (3)
Where , , and are given as follows:
= ( ( ( + )-1+ ( - . . ))+ ( . -
1+ ( . . )))+ ( .( .( + )- . )-
- - + ( -1)+ ( + - . . ))) (4)
= .( . ( + )- . - -
+ .( ( . -1)+ .( + - . . )))+ ( (1-
( + )+ . .( . -1))+ (1- . + .( .
( . -1)- ))) (5)
= .( + )+ .( . . )+ ( + + + ( .
. ( + ) .( -1)+ .( + -
. . )))(6)
= ( .( . -1)- )+ ( .( .( + )-1+ ( -
. . ))+ (1- . + .( . ( . -1)- ))) (7)
The analytical solution of (3) consists of four roots, of which
those two with positive values of the voltage are interesting.
These two solutions form the so-called upper and lower nose
curve ( ) for the SLIB model with a CSC [6].
4.SIMULATION RESULTS
Simulations for the proposed SLIB model are carried out on
MATLAB to investigate the impact of CSC on the SLIB model.
The impact of the operation of the CSC on the maximum
power can be seen from the table 1. A negative value of the
reactance means that the CSC operates in the capacitive
mode and a positive value of the means that the CSC
operates in the inductive mode. It can be seen that the voltage
stability is improved when we operate the CSC in capacitive
mode.The table shows the results when the line resistance is
neglected.
Table 1 : Maximum Power for Different Values of The Parameter for
= =0
S.NO Series
Compensation
( in pu)
Maximum Power
(
Line
Resistances
( & in
pu)
1. 0.16 1.133 0
2. 0.04 1.677 0
3. 0 2.002 0
4. -0.04 2.489 0
5. -0.08 3.299 0
6. -0.12 4.908 0
Fig – 4 Power Variation on The Different Values Of The Compensation
Parameter Xcfor = = 0
It can be observed from Fig.4 and Table 1that when we apply the
compensation in capacitive mode, the maximum power that can
be transferred through the transmission line increases and when
we apply the compensation in inductive mode, the maxmimum
power that can be transferred through the transmission line
reduces. As the line resistance is neglected so it can be
concluded that the performance of the CSC is not affected by the
resistance of the transmission line.
Simulation results for load voltage and in presence of CSC
are shown in Fig 5 where each PV curve represents a specific
value of the parameter . The curves represent the voltage
stability of the system and the point at which the voltage
collapse occurs represent the point at which the maximum power
is transferred.
Fig – 5 PV curves for different values of the parameter for SLIB with
the CSC at = 1 pu
Effect of line resistance can be observed from Fig.6. It can be
seen from the Fig 6 and Table 2 that the maximum power that
can be transferred through line is reduced considerably.
Also it can be seen that after adding the compensation, the
maximum power that can be transferred through the
transmission line is increased slightly. So the performance of
CSC is inferior when line resistance of line is considered.
0
1
2
3
4
5
6
0.16 0.04 0 -0.04 -0.08 -0.12
Power(inpu)
Series Compensation (Xc in pu)
Power variation
when R1=R2=0

19
Table 2 : Maximum Power for Different Values of The Parameter for
= =0.1pu
S.NO Series
Compensation
( in pu)
Maximum Power
(
Line
Resistances
( & in
pu)
1. 0.16 0.589 0.1
2. 0.04 0.881 0.1
3. 0 0.943 0.1
4. -0.04 1.009 0.1
5. -0.08 1.077 0.1
6. -0.12 1.141 0.1
Fig – 6Power Variation on The Different Values Of The Compensation
Parameter Xc for = = 0.
The results of the simulation ( ) in presence of CSC while
the line resistance has taken into consideration is shown in fig 7.
Fig–7 PV curves for different values of the parameter for SLIB with
the CSC at = 1 pu when = =0.1 pu
Fig 8 shows the comparison of power with the different
values of resistances.
Fig – 8Comparision of The Power Variation Curve for Different Values
of The Resistances
5.CONCLUSION
Improvement of voltage stability is highly desirable for reliable
electrical power system. FACTS is one of the best and
promising solution available for reactive power compensation
and improvement of voltage stability.
This paper investigates the performance of FACTS device CSC,
when the resistance of the transmission line is taken into
consideration. SLIB model is used for the analysis. The voltage
stability and maximum power that can be transferred through the
transmission line is calculated with and without considering the
line resistances. It is found that when the line resistance is
considered the voltage stability and maximum power transferred
is reduced considerably. It can also be seen that performance of
CSC is reduced. Hence it can be concluded that line resistance is
the significant parameter for the analysis of voltage stability
improvement through the FACTS devices.
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0
0.2
0.4
0.6
0.8
1
1.2
0.16
0.04
0
-0.04
-0.08
-0.12
Power(inpu)
Power variation
when R1=R2=0.1
0
2
4
6
0.16
0.04
0
-0.04
-0.08
-0.12
Power(inpu)
R1=R2=0
R1=R2=0.1

20
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The Impact of Line Resistance on the Performance of Controllable Series Compensator for Improving Voltage Stability

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The Impact of Line Resistance on the Performance of Controllable Series Compensator for Improving Voltage Stability