Improved techniques for reliability evaluation of generation systems

Abstract

This dissertation represents new techniques for evaluating generation capacity reliability. These techniques are based on Fourier transforms and their properties. They permit the use of continuous probability distribution(s) for the probability distribution resulting from the sum of discrete random variables, where each variable is statistically independent of others. It is shown that the well-known Gram-Charlier's expansion is a special case of the first technique. Using the first technique, any continuous distribution can be examined for its suitability for modeling the distribution of the sum of discrete random variables. Using the second technique, a group of continuous distributions can be examined for their suitability for modeling the distribution of the sum of discrete random variables. The aggregate distribution for the generation capacity in a power system is traditionally derived by taking the distribution of a generating unit and combining with it the distribution of another unit until all distributions are processed. Although a recursive algorithm is available for this purpose, the process is computationally very costly. Numerous attempts have been made in the last two decades to develop a continuous distribution for this purpose. Presently, the most widely used continuous technique is the cumulant method, which is most commonly expressed in Gram-Charlier's expansion. Nevertheless, the results are not quite satisfactory. In this dissertation, gamma distribution, specifically that with three parameters, is inserted in the new techniques for evaluating the generation capacity reliability and it is shown that this approach provides superior results than any other methods presently used.