An extended energy function for voltage collapse analysis considering voltage dependent load models

It is well known that the role played by the loads on the voltage collapse mechanism is very important. In spite of that, a Lyapunov function that includes the ZIP load model for the purpose of voltage collapse analysis has never been determined. This paper presents an energy function that includes this voltage dependent load model. From the assumption that the parameters of the power system change slowly, the power system can be modeled by its load flow equations. In order to calculate the desired Lyapunov function, an auxiliary dynamic system is used. It is shown that all equilibrium points of this dynamic system are solutions of the load flow equations of the power system. Thus, it is possible to infer from the voltage stability margin of a power system, calculating the equilibrium points of the proposed auxiliary dynamic system. Based on the extension of LaSalle´s invariance principle, an energy function associated with the auxiliary dynamic system is proposed. It is demonstrated that this energy function is an extended Lyapunov function and it is suitable for voltage collapse analyses. This methodology is applied to a simple two bus test system and the results are presented.