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

基于非线性系统理论的电力系统稳定域分析与观测

• 批准号: 09650317
• 负责人: MITANI Yasunori
• 金额: $ 2.05万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09650317/
• 关键词: power system; nonlinear system; Hopf bifurcation; power system stability; least square fittin; subsynchronou resonance

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.

电力系统是一个大规模的非线性动态系统，电力系统的暂态稳定分析是非线性系统分析的一个实例，其重点是二阶动态分界线的确定，本文的目的是利用Hopf分岔理论分析电力系统的非线性动态，这说明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常规瞬态分析的结果不同。本文应用分岔理论研究了电力系统次同步谐振（SSR）的非线性结构，发现了SSR附近的几种分岔现象;稳定环面和不稳定环面分叉及其壮观的连接。接下来，将分岔理论应用于电力系统稳定性分析，数值分析了非线性系统在一组微分方程作用下的分岔现象，针对多机电力系统中微分方程只能用显式函数表示的问题，提出了一种用最小二乘法从仿真波形中求取近似多项式函数的方法，给出了基于不稳定周期轨道的稳定性边界以及周期轨道存在性和稳定性的判别方法，并将其应用于纵向互联电力系统功率长期振荡的稳定性分析。

项目成果

Yasunori Mitani: "Bifurcations associated with Subsynchronance Resonace" IEEE Transactions on Power Systems. 13(掲載予定). (1998)

Yasunori Mitani：“与子同步共振相关的分叉”IEEE Transactions on Power Systems（即将出版）。

川崎 光喜: "非線形動的システム理論に基づく発電機動揺の動特性解析" 電気学会電力・エネルギー部門大会論文. 論文I. 31-36 (1998)

川崎光希：“基于非线性动力系统理论的发电机振动动态特性分析”IEEJ电力与能源分部会议论文I.31-36（1998）。

Kohki Kawasaki, Tsukasa Imamura, Yasunori Mitani and Kiichiro Tsuji: "A Method for Observing Nonlinear Dynamics in Power Systems by Using Superconducting Magnetic Energy Storage (in Japanese)" Proc.of IEE Japan Technical Meeting. PSE-97-99. 31-36 (1997)

Kohki Kawasaki、Tsukasa Imamura、Yasunori Mitani 和 Kiichiro Tsuji：“使用超导磁能存储观察电力系统非线性动力学的方法（日语）”Proc.of IEE 日本技术会议。

Yasunori Mitani: "Bifurcations associated with Subsynchronance Resonance" IEEE Transactions on Power Systems. 13. 139-144 (1998)

Yasunori Mitani：“与次同步谐振相关的分岔”IEEE Transactions on Power Systems。

川崎 光喜: "Hopf分岐理論を適用した電力系統の過渡安定領域評価" 電気学会電力系統技術研究会資料. PSE-98-79. 13-18 (1998)

Mitsuki Kawasaki：“应用 Hopf 分岔理论评估电力系统的暂态稳定区域”IEEJ 电力系统技术研究组材料。13-18 (1998)。