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

电力系统是一个大范围的非线性动态系统。电力系统的暂态稳定分析是非线性系统分析领域的一个例子，重点放在二阶动态的分离线上。本研究的目的是用Hopf分叉理论分析电力系统的非线性动力学，它揭示了由不稳定周期轨道形成的稳定边界的存在。稳定域的结果可能与传统的暂态分析结果不同。首先，本研究将分叉理论应用于检测与次同步谐振(SSR)相关的电力系统的非线性结构。我们在SSR附近发现了几种类型的分叉。Hopf、稳定环面和不稳定环面分支及其壮观联系。其次，将分支理论应用于电力系统稳定性分析。当一组微分方程组仅用显式函数表示时，数值分析了非线性系统的分叉。然而，描述多机电力系统的微分方程式的函数没有显式表示。因此，提出了一种用最小二乘法从仿真波形中获得逼近多项式函数的方法。基于不稳定周期轨道的稳定性边界以及周期轨道的存在性和稳定性的检测，该方法已被应用于纵向互联电力系统长期电力振荡的稳定性分析。

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.