Reliability Analysis of Distribution Networks Using Mathematical Modeling and Topological Methods

The study highlights the importance of understanding the network topology, including radial and mesh configurations, and their impact on fault propagation and system reliability. Mathematical models are developed to simulate the system behavior under various fault scenarios, including probabilistic methods and Markov processes to estimate key reliability metrics such as SAIFI, SAIDI, and CAIDI. Topological methods are applied to identify weak points in the network structure, optimize section switches, and improve load restoration strategies. The integration of these approaches enables a comprehensive analysis that considers both component-level reliability (e.g., transformers, feeders, switches) and system-level performance. Real-world distribution network studies demonstrate the effectiveness of the proposed methods to minimize outages and improve service continuity. The results highlight the practical implications of combining mathematical and topological tools for decision making in network design, maintenance planning, and operational strategies. This work contributes to the field of power system reliability by providing a robust analytical framework that integrates theoretical modeling and practical applications, ensuring a reliable and resilient distribution network capable of meeting growing energy demands.