Transient stability evaluation of multimachine power systems: a probabilistic approach based upon the extended equal area criterion

The probabilistic aspects of transient stability evaluation of electrical power systems are discussed. The stability properties of the system after a given fault are characterised by means of the instability probability, which is defined in terms of the critical clearing time and the fault clearing time. Particular attention is devoted to the probabilistic description of the load demand, characterised by a random vector, and its effect on the critical clearing time. The instability probability is evaluated by using an analytical approach, already proved satisfactory in the single-machine case, as shown in a previous paper by the authors. The method is illustrated with reference to a simple system: the critical clearing time is calculated, for each value of the random inputs, by means of the extended equal area criterion. Its probability distribution is then evaluated, by means of a regression technique, in terms of the load demand distribution. Such distribution is then used to calculate the instability probability as a function of the basic statistical parameters of the system. The proposed method allows a straightforward analytical determination of the influence of the system parameters on the instability probability. A peculiar aspect regarding a multinode system, which is also analysed in the paper, is the effect of the statistical correlation among the loads on the stability