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

8/12/2019 OPTIMAL LOCATION OF SVC FOR DYNAMIC STABILITY ENHANCEMENT BASED ON EIGENVALUE ANALYSIS

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

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O PTIMAL LOCATION OF SVC FOR D YNAMIC

S TABILITY ENHANCEMENT BASED ON EIGENVALUE ANALYSIS

Anju Gupta 1 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 ofsmall 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.Theresults of these studies show that the proposed approach has an excellent capability to enhance thedynamic 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 byrelatively 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 theseoscillations.[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 satisfactoryresults 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 oscillationsleading 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 thelow frequency oscillations and enhance power system stability. Recently, several FACTS deviceshave been implemented in power systems for dynamic and transient stability. Some paperspresented 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 avital role to enhance dynamic and transient stability.

This paper presents the investigation of best location of SVC to enhance the dynamic andtransient stability for heavy load conditions and disturbances. Time domain simulation is carriedout 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 of A matrices can be obtained by solving the root of the followingcharacteristic equation:

det ( I-A) =0 (4)

The eigen-values determine the system stability. A negative eigen value increases the systemstability and a positive eigen value decreases the stability.

As for any obtained eigen-values i= i+j i the damping ratio and oscillation frequency f can bedefined as follows:

fi = i/ 2

The above parameters i and i can be used to evaluate the damping effects of the power systemstabilizers on the power oscillation.Damping of the system is dependent on the damping ratio andoscillation frequency. More the damping ratio, the system will provide more damping to theoscillations and hence will be more dynamically stable. It is advisable to install the stabilizers foreach machine of the system but this will increase the investment cost, hence the optimalarrangement of stabilizers and FACTS devices have to be made with the consideration ofeconomical factors.

2.2. Participation Factor

If i is an eigen value of A, v i and wi are non zero column and row vectors respectively such thatthe following relations hold:

Av i = i v i i=1,2 ..n


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W iA= i w i i=1,2,n

Where, the vectors v i and w i are known as right and left eigenvectors of matrix A. And they arehenceforth considered normalized such that

w i v i=1

Then the participation factor pki (the kth state variable xk in the ith eigen-value i) can be givenas

Pki = v ki wki

Where w ki and v ik 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 eigenvalues and the participation factors of the system, once the power flow has been solved. Fig 2shows the algorithm to determine the optimal location of SVC for dynamic stability analysisbased on eigen values analysis The eigen values can be computed for the state matrix of thedynamic system, and for the power flow Jacobian matrix (sensitivity analysis).Unlike othersoftware, such as PST and Simulink based tools, eigen values are computed using analyticalJacobian 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 isnonsingular (i.e., no singularity-induced bifurcations)

It is lengthy to compute the all eigen-values if the dynamic order of the system is high.PSATallows 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 participationfactors 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 flowJacobian 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 Jp is nonsingular. Observe that the power flow Jacobian matrix used inPSAT 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 20transmission lines, 5 generators and loads.

Figure 1. IEEE 14 bus system for dynamic stability analysis


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SVC.SVC increases the dynamic order of the system and also the negative eigen values increaseleading to dynamic system stability. It is concluded from Table 3. that with SVC at differentlocations eigen-values are shifted to negative side on real axis providing more damping to thesystem leading to dynamic stability of the system. Table 4 shows the best location of SVC for thedifferent 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 conditionsspecified 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 transientstability of the system by reducing the settling time. Figure 5-10 shows the generators angularspeeds without SVC and with SVC at optimal location. It is clear that damping has increasedconsiderably 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 observedthat oscillations are considerably reduced and system voltages become stable with the insertion ofSVC at optimal location.

6. CONCLUSIONS

The determination of optimal location of SVC for dynamic stability enhancement of a powersystem is done with eigen value analysis followed by time domain simulations. The simulationsare done on IEEE 14 bus system using PSAT software. It has found that by optimally placingSVC,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 ofElectrical 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 ofstatic var compensator and power system stabilizer control actions,Electric Power system Research,Volume 58, Issue 1, 21 May 2001, Pages 3744.

[11] Haque, M.H., Pothula, M.R., Evaluation of dynamic voltage stability of a power system, IEEEpowercon 2004, Vol 2,1139 1143.

[12] Haque,M.H, Use of series and shunt FACTS devices to improve first swing stability limit,IEEEPower 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 Engineeringfrom N.I.T Kurukshetra in 1997 and M.Tech in Control Systems form same institution in1999.Presently pursuing Ph.D from M.D University Rohtak in Electrical Engineering(Power System).She is currently working as Associate Professor in Electrical EngineeringDepartment in YMCA Uviversity of Science and Technology,Faridabad..She haspublications 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 FACTSdevices.

Dr. P.R. Sharma was born in 1966 in India. He is currently working as Professor in the department ofelectrical Engineering in YMCA university of Science & Technology, Faridabad. He received his B.EElectrical 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 coordinatedcontrol of FACTS devices,

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

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