An Improved Analytical Probabilistic Load Flow Method with GMM Models of Correlated DER Generation

The increasing penetration of distributed resources (DER) intensifies the volatility in the distribution network. The accurate and efficient method of probabilistic load flow (PLF) becomes a necessity due to the uncertainty and intermittence of DER. Therefore, we propose an improved analytical PLF method to meet the needs of accuracy and efficiency simultaneously. Specifically, the Gaussian mixture model (GMM) is adopted to deal with the uncertainty of the output of DG. Using Taylor expansion, we can obtain the quadratic function to approximate the power flow solution space considering the nonlinearity of the power flow equation. Unlike the previous studies, a set of quadratic functions can be obtained by choosing the mean of each GMM component as the expansion point (EP). Then, the analytical component-based expression of the bus voltage or the branch power flow can be derived according to the spectral theorem and Cholesky decomposition. Eventually, we can acquire the overall probability distribution of the concerned bus voltage by assembling all the component-based distributions. A case study on a 33-bus distribution test system illustrates the efficacy of the proposed method.