Voltage stability of a DAE model for single machine infinite bus system

In this article we study a single machine infinite bus system determined by a static load model. The mathematical model of the power system is a differential algebraic equation (DAE). By using the eigenvalue analysis, the upper branch of the equilibrium curve is stable while the lower branch is stable except for a small section of Q1 between 11. 4108 and 11. 4115. This is different from the results of ordinary differential equation (ODE) model determined by both static load and dynamic load (Walve model). To study the voltage collapse process of the system, we analyze the bifurcation phenomenon near the singular point. By using the singularity theory, the singular point of the DAE system is found to be a limit point. Then by projecting the differential equation on the (V, ω)-plane, a singular ODE is obtained. From the analysis of the phase portrait for the singular ODE, the system is found to collapse by going through the singular surface. A simpler method is given to identify the impasse point of the system and is used to prove that for the phase portrait near bifurcation value Q10, almost every point on the singular surface is an impasse point. This method simplifies previous one by Chua et al., and can be implemented easily in numerical software. This project is supported by National Key Basic Research Special Fund of China (No. G1998020307) and National Natural Science Foundation of China (No. 19990510).