Probabilistic Power Flow Method for Dc Distribution Systems Based on Gaussian Mixture Model

With the advancement of power electronics technology and the gradual increase of distributed generations, the operation and control of DC distribution systems face increasingly significant challenges, making probabilistic power flow analysis and risk assessment particularly critical. A probabilistic power flow algorithm for DC distribution networks utilizing the Gaussian mixture model is proposed. The approach begins by employing Gaussian mixture modeling to statistically represent the prediction errors of distributed generations, capturing their inherent randomness and correlations. Then, a linear power flow model for DC distribution networks incorporating distributed generations and various VSC control modes is developed. Finally, the sensitivity matrices between node voltages, branch power and forecasting errors of distributed generations have been meticulously derived. By leveraging the linear characteristics of the Gaussian mixture model and sensitivity matrices, the distributions of node voltages and branch powers are efficiently determined. The validity of the proposed method was demonstrated using a modified IEEE-14 bus DC test system.