Graph Theory as an Engine for Real-Time Advanced Distribution Management System Enhancements

Graphs could be used to illustrate a wide range of practical challenges. The word network is usually used to denote a graph in which the elements are associated with the vertices and edges, emphasizing its relevance to power systems. This paper focuses on two common graph theory applications in Advanced Distribution Management Systems (ADMS): topology tracing and fast gain matrix computing. Topology tracing is a critical component of any ADMS. Its primary function is to generate a branch-node model by traversing branches and closed switches. The gain matrix is built during each iteration of the weighted least squares (WLS) state estimation method, which utilizes the normal equations technique. The gain matrix is sparse with a nonzero structure that remains unchanged throughout iterations. This study describes a method for predicting the nonzero structure of the gain matrix directly from the network graph and measurement locations. The suggested method for computing the gain matrix is at least seven times faster than the MATLAB built-in implementation, making it suitable for constructing efficient real-time power system state estimation software for ADMS.