Probability Distribution Functions for Generation Reliability Indices - Analytical Approach

The primary objective of this research is to analytically develop probability density functions (p.d.f.) for the widely used power generation reliability indices, Loss of Load and Unserved Energy. The equations to calculate the parameters of the distributions of these indices upon a prescribed load plan are derived. In order to develop the theoretical structure for the problem stated, classical and decision theoretic (Bayesian) statistical inference are used as major tools along with the univariate and multivariate asymptotic theory. Consequently, an approximate numerical multiple integration scheme is employed to compute the parameters of the asymptotic normal densities of the reliability indices for the sample power networks. The authors believe that this statistical approach offers a more realistic alternative to the conventional reliability evaluation in generation systems; that is, to the calculation of an averaged valtie for the Loss of Load and Unserved Energy where outage data is traditionally assumed to be deterministic with certainty.