Energy-based stability margin computation incorporating effects of ULTCs

This paper introduces a new definition and computation method for the energy margin as a means to quantify the degree of stability of a dynamic power system model. The method is based on detailed device modeling that spans both transient and midterm time scales and includes effects of under-load tap-changer (ULTC) actions. The energy margin is defined as the minimum distance in potential energy space between the first- and second-kick trajectories, where the latter is chosen to be marginally stable. A generalized second-kick design is proposed. This consists of a combination of a load-step first kick and a three-phase fault second kick, applied at a time instant when the system is "closest" to the boundary of the stability region. The value of the energy margin is tracked through various tap-changer configurations. Thus, situations where ULTC actions are detrimental to stability can be uncovered, and "optimal" tap positions can be found. The concept is first illustrated on a single-machine infinite bus (SMIB); then, results are shown for a ten-bus voltage stability test system and for a modified version of the standard IEEJ 60-Hz test system, where some loads are fed through step-down ULTCs.