An Approximate Method for Probabilistic Assessment of Transient Stability

Power-system transient-stability evaluation deals with the performance of the system when subjected to aperiodic disturbances such as faults, sudden loss of load or generation, and line switching. Under these conditions stability is lost when one or more generators fall out of synchronism with the rest of the system. Numerous disturbances can lead to system instability and the probabilities of their occurrences are quite different. Most system-design criteria require system survival under specific fault conditions in the normal system state. Systems are therefore designed with a set of severe criteria which may be extremely unlikely. In some cases the initial criteria become too expensive to maintain and they are modified or relaxed. The probabilities of occurrences of the disturbances should be included in the assessment to develop a realistic appraisal of system adequacy. Probabilistic considerations in the stability of simple single and multi-machine systems involves simulating the system dynamics during the disturbance. In large-scale systems, such a simulation can be computationally expensive. Approximate methods of stability evaluation are quite adequate in initial system planning to identify the critical areas. This paper deals with an approximate method using Lyapunov functions to obtain a transient stability risk index which is useful in initial system planning and design studies. The procedure for considering the probabilities associated with the type, location, and clearance of faults is illustrated for a simple multimachine system. The effect of system load on the risk index is also demonstrated.