EFFECT OF THE SINGLE AND THREE PHASE SWITCHING IN THE TRANSIENT STABILITY OF AN ELECTRIC POWER SYSTEM

USING THE EXTENDED EQUAL AREA CRITERION

C. M. Machado Ferreira(1) J.A. Dias Pinto(') F. P. Maciel Barbosa(2)

(1) Dep. de Engenharia Electrotecnica Instituto Superior de Engenharia de Coimbra Quinta da Nora, 3030 Coimbra, Portugal

E-Mail: cmacfer@isec.pt/jpinto@uc.pt

Abstract In this paper it is studied and analysed the transient

stability of a test power network, when a phase-to-ground fault occurs on a transmission line. A single and three phase reclosure of the tripped circuit breakers poles in the two ends of the faulted line were simulated. It was used the software package TRANsySTEM that the authors developed for transient security assessment of a multimachine power system. These computer programs use the extended equal area criterion. This direct formulation reduces drastically the computing time, since it does not require to solve numerically the differential motion equations of the system.

The results obtained with this direct approach were compared with the solutions produced by the Runge-Kutta method.

1. INTRODUCTION

Transient security assessment is a very important tool in power systems planning [l]. These studies provide necessary information to select the proper set of relays and circuit breakers such that a given fault is cleared in time without losing system stability [2] , [3] .

A great number of the short-circuits that occur on the overhead transmission lines are temporary phase-to-ground faults [4]. In this case, it is a common practice in some countries to trip and to reclose only the faulted phase. This switching technique prevents voltage dips and improves system security [5].

The independent-pole operation requires the use of separate mechanisms for each phase of the circuit-breaker as well as a detailed study of the secondary-arc extinction. The fatigue duty on turbine blades and on turbine-generator shafts should also be analysed [6].

In this paper it is studied the transient stability of a multimachine power system, when a phase-to-ground fault occurs on a transmission line. A single and a three phase

( 2 ) Dep. de Eng. Electrotecnica e de Computadores Faculdade de Engenharia da Universidade do Porto Rua dos Bragas, 4099 Porto Codex, Portugal

E-Mail: fmb@fe.up.pt

0-7803-3879-0 / 98 / $1 0.00 -950 -

reclosure of the tripped circuit breakers poles in the two ends of the faulted line were simulated.

It was used the extended equal area criterion to solve the problem [7], [8]. The results obtained with this direct approach were compared with the solutions produced by the Runge-Kutta method.

In both formulations, the effect of the secondary-arc extinction in the single-pole switching was taken into account [9].

2. FORMULATION OF THE PROBLEM

The extended equal area criterion is a very efficient method that allows to evaluate the transient stability of a multimachine power network without solving numerically the differential motion equations of the system [lo]. The motion of a multimachine power system is described by the following ordinary differential equations [ 11:

with

m

j=1 j+i

Pei =EfGii + Ei Ej(GijcosSij+BijsinS;j ) ( 3 )

where Si - rotor angle of the ith synchronous machine mi - speed of the ith synchronous machine Mi - inertia coefficient of the ith synchronous machine Pmi - mechanical power of the ith synchronous machine Pei - electric power of the ith synchronous machine Ei - voltage behind the direct axis transient reactance of

m - number of machines in the power system the ith synchronous machine

Gij- real part of the ijth element of the nodal admittance

Bij - imaginary part of the ijth element of the nodal

The dot denotes the first order derivative.

matrix

admittance matrix

When a disturbance occurs, the multimachine power system is splitted into the cluster of the critical synchronous machines and the remaining subsystem. The critical cluster is chosen from the most probable critical sets. To specify the synchronous machines of these clusters a selection criterion based on the initial acceleration is applied [ll]. Every one of the two subsystems is then reduced to one equivalent machine. The two equivalent machines can be reduced to one machine connected to an infinite busbar (OMIB):

~6 = pm -[ P, + pmax sin( 6 -U)]

where M - inertia coefficient of the OMIB 6 - difference between the rotor angles of the two

P, - mechanical power of the OMIB P, - constant component of electric power of the

P,, - maximum of electric power of the OMIB U - angular variation The two dots denote the second order derivative.

equivalent machines of the two clusters

OMIB

(4)

Finally, applying the equal area criterion to equation (4), the transient stability margin as well as the critical clearing time and critical clearing angle can be evaluated.

In Fig. 1 it is shown a typical graphic representation of the extended equal area criterion used in this study. The pre-fault, the fault, the tripped and the reclosure circuit breakers situations are specified by "O","D","P" and 'lr" respectively. The accelerating area, the decelerating area and the decelerating area due to the circuit breakers reclosure are denoted by A 1, A2 and A3 respectively. The steady-state curve is only plotted partially. The decelerating areas A2 and A3 are delimited by the rotor angle 6, and 6, respectively. In order to evaluate the area A3, corresponding to the circuit breakers reclosure situation, it is necessary to calculate 6, (Fig. 1). The reclosure angle 6, is obtained from a fourth-order Taylor series [lo].

The transient stability margin can be easily calculated from the acceleration and deceleration areas. The critical clearing angle 6, is obtained considering the stability margin equal to zero.

Pc P I_

1 Pc D

I

Fig. 1. EEAC representation

The: critical clearing time corresponding to a disturbance can be evaluated using the following equation:

where a - corrective factor y - acceleration of the OMIB

During the single phase-to-ground fault situation an effective fault impedance Z,ff should be considered. This impedance, that will be connected to the positive sequence network, is obtained by adding the negative and the zero impedances as viewed from the fault point.

In the case of the single pole switching, it is assumed that the faulted conductor is disconnected at both ends simultaneously. A net effective impedance should be inserted between points X and Y of the positive sequence network (Fig. 2) [6] .

Fig. 2. Three phase schematic diagram of the single-phase switching

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3. APPLICATION EXAMPLE

CTR [SI

The extended equal area criterion was applied to study the transient stability of the electric power system presented in Fig. 3 [12]. It was simulated a single phase-to-ground fault in the transmission lines L 5 and L7. The short-circuit was simulated near the busbars 5 and 7 respectively, considering the two different situations of the circuit breakers switching.

In the first situation the fault was cleared after 0.2 seconds by the simultaneous tripping of the three pole of the two line circuit breakers. In the second one the short-circuit was also cleared after 0.2 seconds by the simultaneous tripping of the single pole of the two line circuit breakers. In both situations the reclosure of the two circuit breakers poles was assumed equal to 0.7 seconds. This setting time value takes into account the secondary arc extinction [9].

Three Pole Single Pole Switching Switching

0.39 --

0 0

Security

Fig. 3. Single line diagram of the analysed network

unstable stable

4. RESULTS AND CONCLUSIONS

The results obtained using the extended equal area criterion are presented in tables 1 and 2. The CTR and TSM denote the critical time to reclosure and the transient stability margin respectively.

1 TSM [p.u. rad] I - 3.40 I 5.47 I

Three Pole Single Pole Switching Switching

CTR [SI TSM [P.u. rad] - 2.23 3.30

Security unstable stable I Table 2 - EEAC results for the short-circuit in line L7.

In figures 4 and 5 are only presented the swing curves corresponding to the two analysed situations when the fault occurs in line L7 near the busbar 7. They were obtained using the Runge-Kutta method, considering the center of angle formulation [lo], [ 131.

150 / /

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0 0 2 5 0 5 0 7 5 1 0 125 1 5 time [SI

Fig. 4. Swing curves considering the three pole switching

In figure 4 “7” and “a” denote the swing curves of the critical machine and all the other machines respectively.

25

7 15 A

-25 0 025 0 5 0 7 5 1 0 125 1 5

time [SI Fig. 5 . Swing curves considering the single pole switching

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From the above results some conclusions can be extracted:

- the solution obtained with the direct formulation used in this study is in accordance with the results calculated with the Runge-Kutta method;

- when a single phase-to-ground fault occurs, the use of the single pole technique in the circuit breakers switching can avoid the unstability of the power network;

- a delay in the single pole reclosure allows a secure secondary arc extinction, without produce system unstability ;

- the extended equal area criterion can be a very important tool during the EPS planning and design stages to specify the most suitable operating times of the protective relaying system, since it allows to evaluate the critical clearing times without solving numerically the differential motion equations of the power network.

REFERENCES

J. A. Dias Pinto, Developments in Power Systems Stability Programs for Microcomputers, Manchester, Department of Electrical Engineering and Electronics, University of Manchester Institute of Science and Technology, U.K., M. Sc. Dissertation, 1983. P. M. Anderson and A. A. Fouad, Power System Control and Stability, Institute of Electrical and Electronics Engineers Press, 1994. J. L. Blackbum, Protective Relaying - Principles and Applications, Second Edition, Marcel Dekker, 1998. J. Esztergalyos, [et al.], IEEE Power System Relaying Committee, "Single Phase Tripping and Auto Reclosing of Transmission Lines", IEEE Transactions on Power Delivery, Vol. PWRD-7, N." 1, pp. 182-192, January 1992. S . H. Horowitz and A. G. Phadke, Power System Relaying, Research Studies Press/John Wiley & Sons, 1993. P. Kundur, Power System Stability and Control, Electric Power Research Institute/McGraw-Hill, 1994. Y . Xue, T. Custem and M. Ribbens-Pavella, "A simple direct method for fast transient stability assessment of large power systems", IEEE Transactions on Power Systems, Vol. PWRS-3,

Y . Xue, [et al.], "Extended equal area criterion revisited", IEEE Transactions on Power Systems,

W. A. Mittelstad, [et al.], "Single-Pole Switching for Stability and Reliability", IEEE Transactions on

pp. 400-412, 1988.

Vol. PWRS-7, N." 3, pp.1012-1022, August 1992.

Power Systems, Vol. PWRS-1, N." 2, pp. 25-36, May 1986.

[lo] M. Pavella and P. G. Murthy, Transient Stability of Power Systems (Theory and Practice), John Wiley & Sons, 1994.

[ l l ] C. M. Machado Ferreira, J. A. Dias Pinto and F. P. Maciel Barbosa, "Effect of the circuit breakers reclosure in the transient stability of an electric power system using the extended equal area cri:terion". In: Record of the Fifth International Middle East Power Conference MEPCON97, vol. 2, pp. 563-567, Alexandria, Egypt, 4-6 January 1997.

[12] F. P. Maciel Barbosa, J. A. PeGas Lopes and J. P. M4arques de Sa, "On Line Transient Stability Assessment and Enhancement by Pattern Recognition Techniques", Electric Machines and Power Systems, New Hemisphere Publishing Company, Vol. 15, pp. 293-310, 1988.

[13] J. Arrillaga and C. P. Amold, Computer Analysis of Power Systems, John Wiley & Sons, 1990.

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