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The authors describe a novel cumulant method of probabilistic power system simulation using the Laguerre polynomial expansion. In this method, Laguerre polynomials are used for obtaining the equivalent load duration probability density function from cumulants representing the load and generator outage probability density functions. A recursive algorithm is used for calculating moments and cumulants which enables practically any number of cumulants to be used in the simulation. The results of testing the method on the IEEE Reliability Test System are presented. The accuracy and computational efficiency of the method are compared with those of the conventional cumulant method based on the Hermite polynomial expansion.>
Tian et al. (1989) studied this question.