On the equilibria of power systems with nonlinear loads

A discussion is presented of various structure-preserving models for power systems along with their differential-algebraic and local-normal-form representations. The different models emanate from a variety of the generator and load damping properties. The equilibria of interest reflect the bus power imbalance after a fault and depend on the nature of the generator and load damping. The classical view of dynamical system equilibria cannot be applied to these models unless an unrealistic assumption about the bus real power balance is made. Transformations of frequency and bus power resolve this difficulty. The results provide a useful basis for the derivation of energy functions of power systems and their justification as Lyapunov functions