Analysis and Observation of Power System Stability Region Based on Nonlinear System Theory

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Power system is a large scale nonlinear dynamic system.The transient stability analysis of power system is an example placed in the area of the nonlinear system analysis, where the emphasis has been placed on the separatrix of second-order dynamics.The purpose of this research is to analyze the nonlinear dynamics of power system using Hopf bifurcation theory, which tells us the existence of stability boundary formed by the unstable periodic orbit.The results of stability region are possibly different from those by the conventional transient analysis.First, in this research the bifurcation theory has been applied to inspect the nonlinear structure of power system associated with subsynchronous resonance (SSR).We detected several kinds of bifurcations around SSR ; Hopf, stable torus and unstable torus bifurcations and their spectacular connections.Next, the bifurcation theory has been applied to the analysis of power system stability.The bifurcations of nonlinear system are numerically analyzed when a set of differential equations represented only by explicit functions.The functions of differential equation expressing a multi-machine power system, however, are not explicitly represented.Therefore, a method to obtain approximated polynnomial functions from simulated waveforms by a least square method, is proposed.Stability boundary based on the unstable periodic orbit as well as the detection of existence and stability of periodic orbit, have been quantitatively observed by the proposed method.It has been applied to the stability analysis of long term power oscillation in a longitudinally interconnected power system.