A New Approach to the Determination of Transient Stability of Large Power Systems

Abstract

The determination of transient stability of multimachine power systems is important from the point of view of power system planning and Control. Numerical integration algorithms for the multimachine case give accurate results but are time consuming. The direct method of Liapunov has been used for the determination of critical clearing time. This method gives quicker but conservative answers. The conservativeness of the Liapunov method has prevented its wide acceptance by the practising engineers. Even though the Liapunov méthod gives conservative answers for the critical clearing time based on the values of V-functions along the trajectory of the faulted system, the method gives other useful information. For example, the V-Functions can be evaluated at the unstable equilibrium points of the postfault system and the critical unstable equilibrium point determined corresponding to the minimum of the V-function values at. various u.e.p.s. The critical u.e.p. corresponds to one particular machine losing synchronism or a particular group of machines losing synchronism. Once the particular critical machine or group is spotted out by the use of V-functions, the system may be reduced into two or three sets of machines (depending upon the critical u.e.p.) each of which may be combined to yield an equivalent machine (or zone). The resulting two or three machine system may be solved rigorously to get all information pertaining to transient stability. This approach combines the simplicity of the Liapunov method and the accuracy of the numerical integration techniques. The results obtained by this method are compared with those obtained by other methods for the case of a single machine going out of step.