Robustness Improvement of the AESOPS Algorithm by Means of a Multimachine State-Space based Correction Formula

Abstract

Although the sequential computation methods of obtaining eigenvalues associated with electromechanical modes, such as AESOPS, PEALS and III, may solve some eigenvalue problems of very large power systems, their convergence is very sensitive to both initial estimate of eigenvalues and guess at a machine to be disturbed. The lack of a systematic way of having proper starting conditions and the absence of well justified iteration formulas make these methods too fragile to fully identify critical modes.This paper reveals some inherent similarities between dynamic and transient stabilities, and presents two important improvements to overcome the above fatal weakness. First, analytical ways of providing good initial eigenvalues is proposed based on the “partial center of angles” equivalence concept, and of identifying the relevant machines based on the EEAC (Extended Equal Area Criterion). A second improvement is a reasonable and very simple Newton-Jacobian with analytic scalar formula derived in the multimachine state space to replace a heuristic one which has been followed in literatures with no way out. This significantly relieves the final convergence from its dependence on initial values. Thus the iteration procedure robustly, if not uniquely, converges to the mode in which the disturbed machine group participates most. Simulation results and comparisons are given to verify the effectiveness and robustness of these improvements.