A Matrix-Based Analytical Approach for Reliability Assessment of Mesh Distribution Networks

To address the limitations of conventional reliability assessment methods in handling mesh distribution networks with flexible operation characteristics and complex topologies, namely their poor adaptability and low computational efficiency, this paper proposes a matrix-based analytical approach for reliability assessment of mesh distribution networks. First, a network configuration centered on the soft open points (SOP) is established. Through multi-feeder interconnection and flexible power flow control, a topology capable of fast fault transfer and service restoration is formed. Second, based on the restoration modes of load nodes under fault scenarios, three types of fault incidence matrices (FIM) are proposed. By means of matrix algebra, explicit analytical expressions are derived for the relationships among equipment failure probability, duration, impact range, and reliability indices. This overcomes the drawbacks of iterative search in conventional reliability assessments, significantly improving efficiency while ensuring accuracy. Finally, a modified 44 bus Taiwan test system is used for reliability assessment to verify the effectiveness of the proposed method. The results demonstrate that the proposed matrix-based analytical reliability assessment method enables explicit analytical calculation of both system-level and load-level reliability indices in mesh distribution networks, providing effective support for planning and operational optimization to enhance reliability.