The application of decision theory to contingency selection

This paper presents the theory and method for systematically finding the performance index (PI) which is used in Automatic Contingency Selection (ACS) algorithms. Since the ACS problem is a binary decision problem, then the choice of the PI is equivalent to the selection of a decision function which measures the impact of each contingency on the system performance in terms of giving out-of-limit conditions. This paper shows how to select the set of weighting coefficients in the currently used PI´s for analyzing either the real power flow or node voltage magnitude problems in order to circumvent some of the contingency ranking problems. Even more important, it is shown how to select the threshold values of the PI which guarantee proper classification of the contingencies in terms of minimizing the probabilities of missing critical contingencies and false alarms. The approach taken is a set theoretic one which allows us to develop a method for finding the PI as a volume maximization problem which can be solved using standard SUMT methods. One such algorithm is given together with an illustrative example.