A generalized bus dependency matrix based centrality measures for reactive power compensation

Introduction of deregulation in electricity market and addition of more renewable energy generation plants in distribution end have made electrical power system vulnerable. Increased loads and generation increases the load of individual lines and hence congestion management is required. “Centrality” is the fundamental concept in network and it is based on complex graph theory. “Electrical centrality measures” are used for vulnerability analysis of electrical networks and other issues like analysis of blackouts etc. Voltage control and reactive power management are two important aspects of power system on which reliability of electrical transmission network depends. In this paper, a graph theory based bus dependency matrix is proposed which is used to find out electrical closeness centrality and electrical betweenness centrality for any generalized electrical network in which shortest path between two buses may consist multiple intermediate buses. The proposed algorithm starts with power flow results and the shortest path is searched by using Johnson's algorithm and impedance is used as weights of the paths. The applicability of proposed algorithm is demonstrated for finding centrality indices of different test systems and then centrality index is used as an for managing reactive power at different buses for minimizing losses.