Centrality measures for voltage instability analysis in power networks

Graph theoretic methods have been used in network science for the analysis of actors participation and influence over the network. In this paper we use the methods for the analysis of voltage stability profile and critical voltage modes in electrical networks. We model the electric grid as a graph whose Laplacian is based on the Jacobian matrix representation of power flow constraints. Over this model we use newly defined centrality measures to obtain information about voltage-reactive power sensibility of buses and vulnerable zones. The approach is studied with a numerical example, developed over the WSCC-9 bus system. The results obtained from these measures are compared with data obtained from a traditional modal analysis method and electrical centrality measures based on admittance. The results show the designed centrality measures and distance metrics as useful alternatives for the analysis of voltage stability in power networks.