Research on Line Loss Calculation Method of Distribution Network Based on Gaussian Mixture Modeling

Line loss is a critical technical indicator for evaluating the energy-saving performance and operational efficiency of distribution systems. With the ongoing advancement of the “dual carbon” goals, the integration of a large number of renewable energy sources—characterized by randomness and intermittency—into distribution networks poses significant challenges to the accuracy and adaptability of traditional line loss calculation methods. This paper proposes a probabilistic line loss calculation method for distribution networks based on the Gaussian Mixture Model (GMM). First, a GMM-based model of node injection current is constructed. Then, by combining the generalized non-central chi-squared distribution, an analytical expression for the theoretical probability distribution of line losses under arbitrary current distributions is derived. For the first time, exact expressions for the mean, variance, and moment-generating function of theoretical line loss are provided. Considering the complexity of direct calculation, a numerical method based on Raphaeli series expansion is developed to compute the probability density function and cumulative distribution function of line loss. Finally, a case study on the IEEE 33-bus distribution system verifies the effectiveness and high accuracy of the proposed method. The results demonstrate that the method enables fast and precise evaluation of the mean and probabilistic characteristics of line losses, offering theoretical support for energy efficiency optimization in distribution networks with high renewable energy penetration.