Chapter 6
Constructing Analytical Energy Functions for Transient Stability Models
6.1 INTRODUCTION
The task of constructing an energy function for a (postfault) transient stability model is essential to direct methods. The role of the energy function is to make feasible a direct determination of whether a given point (such as the initial point of a postfault power system) lies inside the stability region of a postfault stable equilibrium point (SEP) without performing numerical integration. An energy function is an extension of the Lyapunov function in that it must satisfy the three conditions described in the previous chapter. A Lyapunov function may not be an energy function.
Two different classes of power system models for direct transient stability analysis have been proposed: network-reduction models and network-preserving models. Traditionally, direct methods have been developed for the network-reduction models where all the loads are modeled as constant impedances and the entire network representation is reduced to the generator internal buses. Network-preserving models were proposed in the 1980s to overcome some of the shortcomings of network-reduction models. In each class of model, a model is termed lossless if the nonzero transfer conductance terms are neglected; otherwise, it is termed lossy, such as lossy network-reduction models and lossy network-preserving models.
Practical power system stability models are lossy, where the losses are either from the transmission system ...
