OPTIMAL LOCATION OF SVC FOR DYNAMIC STABILITY ENHANCEMENT BASED ON EIGENVALUE ANALYSIS

Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 3, No 1, February 2014

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OPTIMAL LOCATION OF SVC FOR DYNAMIC

STABILITY ENHANCEMENT BASED ON EIGENVALUE

ANALYSIS

Anju Gupta1 and P R Sharma

2

1Department 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.


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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


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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.


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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


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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


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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


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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


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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


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Figure 4. Relative rotor angle plots delta52

Figure 5. Angular speed of generator 2 with SVC


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Figure 6.Angular speed of generator 2 without SVC

Figure 7. Angular speed omega 4 without SVC


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Figure 8. Angular speed omega 4 with SVC

Figure 9.Angular speed omega 5 without SVC


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Figure 10. Angular speed omega 5 with SVC

Figure 11. Lowest three voltages with SVC


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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.


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[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,

OPTIMAL LOCATION OF SVC FOR DYNAMIC STABILITY ENHANCEMENT BASED ON EIGENVALUE ANALYSIS

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