Multi-area generation system reliability calculations

This paper presents the results of an investigation of a technique for the evaluation of the reliability of supplying power in a system with a number of interconnected load-generation areas. There is no restriction as to how the areas may be interconnected. Most previous techniques using analytical methods (as opposed to Monte Carlo simulations) have been limited to systems with a maximum of three interconnected areas. Systems with more areas have been analyzed assuming that the interconnecting electrical network did not contain any loops. The application of straightforward enumerative methods to systems with more complex interconnections than these can result in an improbably large number of computations. The method of analysis described in this paper is based upon the use of a linear flow network to model the transmission interconnections and makes use of an efficient graph theory algorithm to segregate the failure states by finding critical minimal cuts in the network. The probabilities of failure to supply the various loads are computed by evaluating the various combined event probabilities associated with these critical minimal cuts. For the cases tested, the technique reduces the number of probability evaluations required by about one to two orders of magnitude in comparison with complete state enumeration methods. The tested method provides reliability measures (i.e., the probability of failure to meet the load) for each individual area and the total system, and also allows the computation of the probability that each "link" (transmission line or source) is a member of a critical minimal cut. The latter will facilitate the application of the method to the design of systems and specifically to the problem of evaluating the reliability benefits of increased transmission capacity versus added generation.