Foundations of the Potential Energy Boundary Surface Method
The potential energy boundary surface (PEBS) method is a fast direct method intended to circumvent the problem of determining the controlling unstable equilibrium point (controlling UEP, or CUEP). For a given fault-on trajectory, the PEBS method uses a rather fast method to find a local approximation of the relevant stability boundary of the original system model and to perform direct transient stability analysis. The PEBS method was first proposed by Kakimoto et al. (1978, 1984) and was later pursued and extended by several researchers (e.g., see Athay et al., 1979; Padiyar and Ghosh, 1989; Sauer et al., 1989).
Unlike the controlling UEP method, the PEBS method cannot consistently give conservative stability assessments. It gives either overestimated or underestimated (i.e., conservative) stability assessments for transient stability analysis. Hence, one critical issue with the PEBS method is whether it provides a good local approximation of the relevant stability boundary (i.e., the stability boundary that the fault-on trajectory is heading towards) or under what conditions it does.
The derivation of the PEBS method was based on heuristic arguments. Theoretical justifications for the PEBS method, except for the one-machine infinite bus, are lacking. In this chapter, we present the theoretical foundation for the PEBS method. Sufficient conditions under which the PEBS method provides a ...