Lyapunov function for robust voltage stability analysis considering perturbation location

In this paper, a method to analyze the small-perturbation voltage stability of power systems with varying load by means of the quadratic Lyapunov function is presented. By using the quadratic Lyapunov function, the voltage stability is analyzed algebraically as a result of this analysis, and a voltage stability index is proposed. Numerical tests are carried out on a 3-bus system and a single machine to verify the performance of these indices as well as verification of computation bound of varying ratio of reactive power and voltage from its operating condition which force the system to maintain its stability. In this paper, by considering the location of uncertainties in the Jacobian matrix, a robust stability analysis is also presented.