Chapter 9
Foundation of the Closest UEP Method
9.1 INTRODUCTION
The closest unstable equilibrium point (UEP) method is a classical tool for problems associated with power system dynamic security assessment (Chiang and Thorp, 1989a; Cook and Eskicioglu, 1983; El-Abiad and Nagappan, 1966). In this chapter, we study the closest UEP method from both theoretical and computational points of view. The robustness of the closest UEP with respect to changes in different parameters of a power system will be shown. This robustness property of the closest UEP heightens the practical applicability of the closest UEP method to power system dynamic security assessment (Lee and Chiang, 2004; Pavella et al., 2000; Qiu et al., 1989; Ribbens-Pavella and Evans, 1985).
An improved closest UEP method with a solid theoretical foundation is proposed. This improved closest UEP method explores the model structure to develop a reduced-state method to compute the closest UEP of a reduced-state model. It will be shown that the improved closest UEP method is optimal in the sense that the estimated stability region characterized by the corresponding energy function is the largest one within the entire stability region. Issues regarding the existence and uniqueness of the closest UEP are investigated. Topological and dynamic characterizations of the closest UEP will be derived.
9.2 A STRUCTURE-PRESERVING MODEL
The structure-preserving model of power systems will be used in this chapter. Consider a power system consisting ...
