Voltage collapse analysis in a graph theoretical framework

Voltage collapse is a type of failure with major influence in blackouts. Blackouts, although infrequent, are costly to society. For the Smart grid, integration of new technologies, new policies, and increasing power demand makes the power system becoming more disturbed, which increases the possibility of voltage collapses of all size. Hence, its complexity requires new approaches for modeling and analysis that captures the power network structure. This work presents a graph theory-based analysis of the voltage collapse problem. We present a review of voltage stability and collapse to identify its basic characteristics. We model the power system as an undirected weighted graph whose weights are voltage coupling magnitude between nodes. A steady state analysis is developed over the model to obtain properties of branches, and buses. The obtained graph properties are closely related with results obtained from Q-V modal analysis in the example. Also a dynamical system behavior is determined with the nonlinear differential equations of elements that govern the direction of network dynamics over a voltage collapse mechanism in time.