Derivation of an Accurate Polynomial Representation of the Transient Stability Boundary

This paper presents an efficient method to estimate a transient stability boundary (TSB) as a nonlinear function of power system variables. The proposed method exploits the computational efficiency of linear estimation methods to determine an accurate nonlinear function. The novelty of the proposed method is that a nonlinear transformation is applied to the original variables, voltage magnitudes, and phase angles, so that the TSB is approximately linear in terms of the transformed variables. The linear function obtained using the transformed variables is indeed nonlinear in terms of original variables. The attractiveness of this method is that the estimated function is not a linearized approximation, although a linear estimation method is used. The potential of the proposed method is demonstrated using the New England 39-bus system and a larger power system with 470 buses