An analytical method for probabilistic load flow using Gaussian mixture model

Stochastic power injections may over load transmission lines. Probabilistic load flow (PLF) is a good methodology to assess these possible risks in the presence of uncertainty and stochasticity. With the help of Gaussian Mixture Model (GMM), this paper proves two important properties of GMM, and proposes a completely analytical method to compute the probabilistic density distribution (PDF) of active power on transmission lines in consideration of correlation of stochasticity. This method is free of any cumulants based series expansion. In order to efficiently construct the corresponding cumulative distribution function (CDF), a fast algorithm is adopted to avoid integral operation. Test results in the modified IEEE system verify that this method is both accurate and efficient.