Continuous probability distribution for generating capacity reliability evaluation

There are two broad categories of methods for generating capacity reliability evaluation. The traditional approach is based on obtaining generation capacity probability distribution by unit addition algorithms and convolving it with a suitable load model to obtain indices for generation reliability. The alternative approach uses approximation of the discrete probability distribution by a continuous probability distribution. The techniques described in the available literature use some type of infinite expansion based on some well known distributions. Generally the first three or four terms of the expansion are used to improve the accuracy of the solution. Addition of more terms, however, does not ensure higher accuracy of calculated indices and sometimes may even lead to numerical instability. This paper proposes a different approach by using a multi-parameter probability distribution which by itself, without any expansion terms, provides a close approximation to the exact results. The distribution is a composite of gamma distributions. Equations for obtaining the distribution parameters from the unit parameters are derived in this paper. When the number of parameters is increased, the accuracy of indices is enhanced and the results remain stable.

Continuous probability distribution for generating capacity reliability evaluation Conference Paper