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This paper introduces an algorithm which dramatically reduces the computer effort required for the identification process of the transition matrix used for the fast steady state solution in the time domain on nonlinear power systems by extrapolation to the limit cycle. It is demonstrated that the proposed Enhanced Numerical Differentiation (END) Newton method increases the computer efficiency in at least hundred percent, when compared against the original Numerical Differentiation (ND) method and above 350 times, when compared against a conventional Brute Force (BF) method. The reported results are validated against the response obtained with a digital implementation with Simulink

An Enhanced Process for the Fast Periodic Steady State Solution of Nonlinear Systems by Poincare Map and Extrapolation to the Limit Cycle