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Summary form only given. 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 mid-term 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 3-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 10-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.