Evaluation of probabilistic model solving methods for modern power electronic distribution networks with wind power integration

The emergence of more and more power electronic loads and Distributed Generation (DG) presents many challenges to the reliable operation of Distribution Networks (DN). The uncertainties of power electronic loads and DGs have increasingly profound impacts on distribution networks. Currently, probabilistic model solving methods for distribution networks often ignore the power quality and the unbalanced operation of the distribution network. Besides, the traditional Monte Carlo method is accurate, but the heavy calculation burden limits its application in practice. Therefore, the fast and accurate solving of probabilistic models of modern power electronic distribution networks urgently needs to be studied. Therefore, in this paper, a probability solving model for a three-phase unbalanced modern power electronic distribution network with DG integration is developed, and the probability model is solved using Point Estimation Method (PEM) combined with Gram–Charlier expansion and Monte Carlo Simulation (MCS). Besides, this paper presents a detailed analysis comparing the results of PEM and MCS solutions from the perspective of voltage, THD, and line loss. The results prove that the Probability density functions (PDFs) of the parameters obtained by the two methods are almost identical, and the relative errors of the indicators are less than 1%. Moreover, the PEM uses only 1.9% of the time taken by the traditional MCS method in solving modern probabilistic models of distribution networks with power electronic devices integration (wind power, EVC, . etc.). It is shown that the PEM used in this paper, combined with Gram–Charlier expansion, is an accurate and efficient solving method for modern distribution networks, providing a reference for subsequent research.