Singular sets and surfaces and their implications in power systems

The dynamics of power systems are usually modeled as a set of parameter dependent differential algebraic equations. The stability properties of the DAE model under parameter variations provide a theoretical understanding of voltage stability and voltage collapse. Early investigations have shown that an understanding of voltage stability and the development of practical analysis tools require consideration of bifurcation phenomena. This paper attempts to identify singular surfaces and interpret the associated stability limits using a portable software package, called Voltage Stability Toolbox. Simulation results for the IEEE 14 bus system are illustrated.