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The Application of Lyapunov function to power systme stability analysis and control Vongsuriya, Khien

Abstract

Lyapunov functions are applied to the power system studies. Three types of power system problems are investigated, namely, the determination of asymptotic stability regions of a nonlinear power system for fault and switching transient stability studies, the systematic optimum parameter setting of power system controllers, and the determination of linear and nonlinear optimum stabilising signals as functions of state variables for both nonlinear and linearized power systems. To investigate and construct the transient stability region of a synchronous machine connected to infinite bus through a transmission system after fault and switching, high degree Lyapunov function series generated by Zubov's method is applied. For the optimum parameter setting of a power system, a computation technique based on the method of gradient has been developed to adjust the system parameters simultaneously so as to minimise a system performance function which is evaluated from a Lyapunov function of the second degree. For the computation of the second degree Lyapunov function a method based on the concept of similarity transformation has been developed and applied so that the simultaneous solution of a large number of algebraic equations can be avoided. To determine the optimum stabilizing signals for a power system, the concept of the Lyapunov function of the optimum system is applied. To compute the Lyapunov function of the optimum nonlinear power system, a general iterative scheme and algorithm have been developed.

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