New continuous distribution method for probabilistic load flow analysis

The probabilistic load flow (PLF) analysis problem can be classified into the following two categories: linearization of the load flow equations of non-linear power system and convolution of the linearized input random variables. Once the load flow equations are linearized, it becomes easier to perform the convolution with either numerical or analytical methods. In PLF, distributions of generation systems and loads are continuous, discrete, or mixture of these. There are a number of techniques for the convolution of these distributions, but most are based on direct manipulation of the convolution integral. Alternative methods have also been presented in the literature. In this paper, a new probability distribution for performing the convolution is proposed. The distribution is a composite of gamma distributions. This proposed generalized multiparameter distribution method is used for the convolution of linear combination of the input random variables. The cumulants of linear combination of random variables are obtained by adding the individual cumulants with weighting factors which are sometimes termed the sensitivity coefficients and are obtained from the given network data. The parameters of the proposed distribution are determined using these cumulants. Studies illustrating the proposed method are described.

New continuous distribution method for probabilistic load flow analysis Conference Paper