Power system stability enhancement via optimal location of SVC is thoroughly investigated in this paper.The performance analysis of SVC has been carried out for IEEE 14 bus system for enhancement of small signal stability and transient stability using Power system analysis tool box (PSAT) software. The effectiveness is demonstrated through the eigen-value analysis and nonlinear time-domain simulation.The results of these studies show that the proposed approach has an excellent capability to enhance the dynamic and transient stability of the power system

1. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
25
OPTIMAL LOCATION OF SVC FOR DYNAMIC
STABILITY ENHANCEMENT BASED ON EIGENVALUE
ANALYSIS
Anju Gupta1
and P R Sharma2
1
Department of Electrical Engineering, YMCA UST, Faridabad
ABSTRACT
Power system stability enhancement via optimal location of SVC is thoroughly investigated in this
paper.The performance analysis of SVC has been carried out for IEEE 14 bus system for enhancement of
small signal stability and transient stability using Power system analysis tool box (PSAT) software. The
effectiveness is demonstrated through the eigen-value analysis and nonlinear time-domain simulation.The
results of these studies show that the proposed approach has an excellent capability to enhance the
dynamic and transient stability of the power system.
KEYWORDS
SVC,,PSAT,dynamic,transient
1. INTRODUCTION
Low frequency oscillations are observed in large power systems when they are interconnected by
relatively weak lines. This may lead to dynamic instability in the absence of adequate damping
[1, 2]. Conventional power system stabilizers (CPSS) are widely used for damping of these
oscillations.[5,6].However whenever there is any fault in the system, machine parameters change,
so at different operating conditions machine behavior is quite different. Hence the stabilizers,
which stabilize the system under a certain operating condition, may no longer yield satisfactory
results when there is a drastic change in power system operating conditions and configurations.
Also when the system is perturbed then the PSSs are not sufficient to damp out the oscillations
leading to system instability. Although PSSs provide supplementary feedback stabilizing signals,
but they cause great variations in the voltage profile and they may even not able to mitigate the
low frequency oscillations and enhance power system stability. Recently, several FACTS devices
have been implemented in power systems for dynamic and transient stability. Some papers
presented the use of PSS and SVC for the damping of low frequency oscillations. [6, 10]. In [7-9]
Designing of SVC has been presented for the dynamic stability.Some papers discussed [11-13]
dynamic stability analysis for small disturbances. However the optimal location of SVC plays a
vital role to enhance dynamic and transient stability.
This paper presents the investigation of best location of SVC to enhance the dynamic and
transient stability for heavy load conditions and disturbances. Time domain simulation is carried
out to show the effectiveness of proposed controller.

2. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
26
2. SMALL SIGNAL STABILITY
The system used is shown by differential algebraic equation (DAE) set, in the form:
2.1. Damping Ratio and Linear frequency
The eigen-values λ of A matrices can be obtained by solving the root of the following
characteristic equation:
det (λI-A) =0 (4)
The eigen-values determine the system stability. A negative eigen value increases the system
stability and a positive eigen value decreases the stability.
As for any obtained eigen-values λi=σi+jωi the damping ratio and oscillation frequency f can be
defined as follows:
fi = ωi/ 2π
The above parameters σi and ωi can be used to evaluate the damping effects of the power system
stabilizers on the power oscillation.Damping of the system is dependent on the damping ratio and
oscillation frequency. More the damping ratio, the system will provide more damping to the
oscillations and hence will be more dynamically stable. It is advisable to install the stabilizers for
each machine of the system but this will increase the investment cost, hence the optimal
arrangement of stabilizers and FACTS devices have to be made with the consideration of
economical factors.
2.2. Participation Factor
If λi is an eigen value of A, vi and wi are non zero column and row vectors respectively such that
the following relations hold:
Avi = λi vi i=1,2 ……………..n

3. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
27
WiA= λi wi i=1,2,……n
Where, the vectors vi and wi are known as right and left eigenvectors of matrix A. And they are
henceforth considered normalized such that
wi vi=1
Then the participation factor pki (the kth state variable xk in the ith eigen-value λi) can be given
as
Pki = vki wki
Where wki and vik are the ith elements of wk and vk respectively
3. THE PROPOSED APPROACH
The simulations are done in PSAT software which allows computing and plotting the eigen
values and the participation factors of the system, once the power flow has been solved. Fig 2
shows the algorithm to determine the optimal location of SVC for dynamic stability analysis
based on eigen values analysis The eigen values can be computed for the state matrix of the
dynamic system, and for the power flow Jacobian matrix (sensitivity analysis).Unlike other
software, such as PST and Simulink based tools, eigen values are computed using analytical
Jacobian matrices, thus ensuring high-precision results.
3.1 Dynamic Analysis
The Jacobian matrix of a dynamic system is defined by:
Then the state matrix As is obtained by eliminating ∆y, and thus implicitly assuming that JFLV is
nonsingular (i.e., no singularity-induced bifurcations)
It is lengthy to compute the all eigen-values if the dynamic order of the system is high.PSAT
allows computing a reduced number of eigen-values based on sparse matrix properties and eigen-
value relative values (e.g. largest or smallest magnitude, etc.). PSAT also computes participation
factors using right and left eigenvector matrices.

4. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
28
3.2. QV Sensitivity Analysis
The sensitivity analysis is computed on a reduced matrix. Let us assume that the power flow
Jacobian matrix JFLV is divided into four sub-matrices
Then the reduced matrix used for QV sensitivity analysis is defined as follows:
Where it is assumed that Jpθ is nonsingular. Observe that the power flow Jacobian matrix used in
PSAT takes into account all static and dynamic components, e.g. tap changers etc.
4. STUDY SYSTEM
The system under consideration is an IEEE 14 bus system shown in Figure 1.with 20
transmission lines, 5 generators and loads.
Figure 1. IEEE 14 bus system for dynamic stability analysis

5. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
29
Figure 2. Dynamic Stability Determination Algorithm
5. SIMULATION RESULTS
5.1. Rotor angle Stability analysis
Case 1. Small Signal stability analysis
The simulations are carried out for an IEEE 14 bus system in PSAT software for disturbances and
loading conditions specified as three phase fault applied at bus 2 and 140%loading at each bus
applied to the system and Eigen value analysis has been done without SVC and with SVC at
different locations. Complete data is given in Appendix..
Table 1.shows the eigen value of the associated states without SVC and Table 2. gives the eigen
value report with and without SVC .Table 3 gives the eigen values at different locations of

6. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
30
SVC.SVC increases the dynamic order of the system and also the negative eigen values increase
leading to dynamic system stability. It is concluded from Table 3. that with SVC at different
locations eigen-values are shifted to negative side on real axis providing more damping to the
system leading to dynamic stability of the system. Table 4 shows the best location of SVC for the
different associated states.
Table 1. Eigen- values for different states without SVC
Table 2. Eigen value report with and without SVC

7. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
31
Table 3. Comparison of Eigen value at different locations of SVC for heavy loading
Table 4. Best location of SVC for particular states
Case 2 Time Domain Simulation
The time domain simulations have been carried out at disturbances and loading conditions
specified above.SVC is located at the location determined from the eigen value analysis .Figure2-
4 shows the relative angular plots with and without SVC at bus 4.It can be seen that optimal

8. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
32
placement of SVC provides the best damping characteristics and enhance greatly the transient
stability of the system by reducing the settling time. Figure 5-10 shows the generators angular
speeds without SVC and with SVC at optimal location. It is clear that damping has increased
considerably enhancing the transient stability of system
Figure 2. Relative Rotor angle plots delta21
Figure 3. Relative Rotor angle plots delta42

9. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
33
Figure 4. Relative rotor angle plots delta52
Figure 5. Angular speed of generator 2 with SVC

10. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
34
Figure 6.Angular speed of generator 2 without SVC
Figure 7. Angular speed omega 4 without SVC

11. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
35
Figure 8. Angular speed omega 4 with SVC
Figure 9.Angular speed omega 5 without SVC

12. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
36
Figure 10. Angular speed omega 5 with SVC
Figure 11. Lowest three voltages with SVC

13. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
37
Figure 12. Voltages without SVC
Figure 11.and Figure 12.shows the voltages graphs with and without SVC. It has been observed
that oscillations are considerably reduced and system voltages become stable with the insertion of
SVC at optimal location.
6. CONCLUSIONS
The determination of optimal location of SVC for dynamic stability enhancement of a power
system is done with eigen value analysis followed by time domain simulations. The simulations
are done on IEEE 14 bus system using PSAT software. It has found that by optimally placing
SVC,eigen values are shifted to negative real axis providing more damping to the system making
the system stable.
REFERENCES
[1] Yu Yn Electric power System Dyanmics.New Yirk:Academic Press:1983.
[2] Suuer Pw,Pai MA,Power ssytem dynamics and stability,Englewood Cliffs,NJ,USA : Prentice
Hall;1998.
[3] Nwohu, Mark Ndubuka,” Low frequency power oscillation damping enhancement and voltage
improvement using unified power flow controller(UPFC) in multi-machine power system,”Journal of
Electrical and Electronics Engineering Research,Vol 3(5),pp 87-100,july 2011.
[4] Ferdrico Milano,2004, “Power system Analysis Toolbox Documentation for PSAT, version 2.1.6.
[5] Kundur P,Klein MRogers GJ Zymno MS applications of Power system Stabilizers for enhancement
of overall system stability,IEEE Tran PWRS 1989,4(2): 614-626.
[6] M.A Adibo,Y.L Abdel –Magid ,”Cordinated design of PSS and SVC based controller to enhance
power system stsbility,” Electrical Power and energy systems,2003,pp 695-704.
[7] Padiyar KR ,Verma RK ,Damping torque analysis of static VAR system oscillations,” IEEE
Tran.PWRS 1991;6(2);458-465.
[8] Hammad AE Analysis of Power System stsbility enhancement by Static VAR compenssators,IEEE
Tran PWRS 1986:1(4),222-227.
[9] Therattil, J.P, Panda, P.C.,” Dynamic stability enhancement using self-tuning Static Var
Compensator,”IEEE INDICOB,2012,pp1-5.

14. Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014
38
[10] M.A. Al-Biati, M.A. El-Kady,A.A. Al-Ohaly,” Dynamic stability improvement via coordination of
static var compensator and power system stabilizer control actions,”Electric Power system Research,
Volume 58, Issue 1, 21 May 2001, Pages 37–44.
[11] Haque, M.H., Pothula, M.R., “Evaluation of dynamic voltage stability of a power system,” IEEE
powercon 2004, Vol 2,1139 – 1143.
[12] Haque,M.H,” Use of series and shunt FACTS devices to improve first swing stability limit,”IEEE
Power Engineering Conference,2005.
[13] Haque,“Improvement of first swing stability limit by utilizing full benefit of shunt FACTS devices,”
Power Systems, IEEE Transactions on , Volume:19, Issue: 4 ,pp1894-1902.
Authors’ Information
Ms Anju Gupta was born in 1975 in India, completed B.Tech in Electrical Engineering
from N.I.T Kurukshetra in 1997 and M.Tech in Control Systems form same institution in
1999.Presently pursuing Ph.D from M.D University Rohtak in Electrical Engineering
(Power System).She is currently working as Associate Professor in Electrical Engineering
Department in YMCA Uviversity of Science and Technology,Faridabad..She has
publications in various IEEE conferences and international journals on Power Systems. Her areas of interest
are Power System stability and FACTS, Power System Optimization using AI tools, Location of FACTS
devices.
Dr. P.R. Sharma was born in 1966 in India. He is currently working as Professor in the department of
electrical Engineering in YMCA university of Science & Technology, Faridabad. He received his B.E
Electrical Engineering in 1988 from Punjab University Chandigarh, M.Tech in Electrical Engineering
(Power System) from Regional Engineering College Kurukshetra in 1990 and Ph.D from M.D.University,
Rohtak in 2005. He started his carrier from industry. He has vast experience in the industry and teaching.
His area of interest is Power System Stability, Congestion Management, Optimal location and coordinated
control of FACTS devices,