Transient Stability Probability Assessment and Statistical Estimation

In the paper, a general analytical method for the probabilistic evaluation of power system transient stability is discussed and a new statistical inference approach for this evaluation is proposed. In particular, the transient stability probability (TSP) is defined and evaluated by taking into account the random nature of both the system loads and the fault clearing times (FCT). The paper is focused upon the aspect of statistical estimation of the TSP - a topic generally neglected in literature - on the basis of the obvious consideration that the parameters affecting the TSP (e.g. mean value and variance of loads, FCTs, etc.) are not known, but must be estimated. New properties of point and interval estimations of the TSP are derived and, in particular, an efficient "lower confidence bound" for the TSP estimation is proposed, based upon a suitable Beta probability distribution. In order to show the feasibility of the proposed approach, a numerical application to the Cigre test network is illustrated. Moreover, extensive Monte Carlo simulations to evaluate the estimator efficiency are performed. In the final part of the paper, also a practical example of possible application to the optimization of system design is illustrated. The application of the method is illustrated and performed by using the potential energy boundary surface method, but the estimation results hold their validity irrespective of the method adopted for the transient stability problem formulation and resolution.