Voltage stability of power systems: links between static and dynamic approaches

Higher utilization of electric power systems has renewed researchers' interest on voltage stability, which has been analyzed under different approaches that can be generally classified into static and dynamic methods. While the former ones are based on the power flow equations, the latter use system algebraic and differential equations; there might be a correlation between the two forms if linearized models are examined. In this paper, several load flow Jacobians are defined and correlated to the linearized system state matrix to show under which conditions there might be contemporaneous singularity. Several cases related to simple electrical systems including elements (static loads under LTC transformers, induction motors and aggregate dynamic loads) that may prove critical for system voltage stability are analytically considered, evidencing how these relationships can be achieved.