Frequency Analysis of Low Frequency Oscillation in Multi-machine System Based on Energy Function and Incomplete Elliptic Integral

MI Xiao; WANG Jie; WANG Rui

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Frequency Analysis of Low Frequency Oscillation in Multi-machine System Based on Energy Function and Incomplete Elliptic Integral

更新时间：2025-12-08

- Frequency Analysis of Low Frequency Oscillation in Multi-machine System Based on Energy Function and Incomplete Elliptic Integral
- Vol. 44, Issue 1, Pages: 321-328(2018)
- 作者机构：
  
  上海交通大学电子信息与电气工程学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published Online：31 January 2018，
  
  Published：2018
- 稿件说明：
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MI Xiao, WANG Jie, WANG Rui. Frequency Analysis of Low Frequency Oscillation in Multi-machine System Based on Energy Function and Incomplete Elliptic Integral[J]. 2018, 44(1): 321-328.
DOI：

MI Xiao, WANG Jie, WANG Rui. Frequency Analysis of Low Frequency Oscillation in Multi-machine System Based on Energy Function and Incomplete Elliptic Integral[J]. 2018, 44(1): 321-328. DOI：

摘要

电力系统是一个存在着诸多扰动的非线性系统

扰动的存在引起了输电线路功率的振荡。为有效抑制低频振荡

研究了低频振荡频率的非线性计算方法及相关应用。基于能量函数及不完全椭圆积分

提出了一种新型振荡频率非线性分析方法:首先建立多机系统模型

通过同调分群法将多机系统等值为单机无穷大系统

然后利用拉格朗日函数法构造对应化简系统的哈密顿能量函数

最后利用椭圆积分的衍生形式求出该状态下发生低频振荡的频率的精确表达式。采用所提方法在MATLAB中对新英格兰10机39节点系统进行低频振荡现象的仿真

并与传统线性化方法在频率计算与分析中进行对比。仿真验证结果表明

此方法在电力系统低频振荡分析中对振荡频率的最大计算误差≤0.04 Hz

且计算速度快。

Abstract

Power system is a nonlinear system with many disturbances

and the presence of the disturbances may cause the oscillation of the transmission capability.In order to effectively suppress low frequency oscillation

we studied the nonlinear calculation method of low frequency oscillation frequency and its application.Moreover

we proposed a new nonlinear approach to analyze the frequency of low frequency oscillation based on energy function and incomplete elliptic integral.Firstly

amulti-machine systems

which is equivalent to a SIMB system according to coherency

was established.Then

the Hamilton energy function of the corresponding simplified system was constructed by using the Lagrange function method.Finally

an exact expression of calculating the frequency of the low frequency oscillation in certain state was obtained by the derived form of the elliptic integral.Furthermore

the proposed method was compared with the traditional linearization method in the New England 10-machine 39-node system for low frequency oscillation simulation analysis and frequency calculation with MATLAB.Simulation results show that the maximum calculation error of the oscillation frequency is ≤0.04 Hz in the analysis of power system low frequency oscillation

and the calculation speed is faster.

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