平衡格莱姆方法在电力系统线性模型降阶中的应用

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摘要通过近似求解线性系统的可控格莱姆矩阵和可观格莱姆矩阵,结合平衡实现理论,详细研究了高阶电力系统动态线性模型的截断降阶和残差降阶。首先,利用交替方向隐方法（ADI）迭代求解李亚谱诺夫（Lyapunov）方程,得到系统可控格莱姆矩阵和可观格莱姆矩阵的Cholesky因子,计算平衡转换矩阵和平衡系统的Hankel奇异值；然后,分别使用截断和残差降阶方法得到系统的平衡降阶模型；最后,通过对4机系统和50机系统的降阶研究,获得不同阶数的电力系统降阶模型,并进行动态仿真,分析原系统及降阶系统的动态行为,结果表明上述降阶方法是可行有效的。

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关键词 ：电力系统, 模型降阶, 平衡实现, 交替方向隐方法

Abstract：This paper studies a large-scale linear power system model reduction problem using the balanced truncation and residualization method. The process of model reduction is based on an approximations solution of the Lyapunov equation. First,the Lyapunov equation is solved by the alternating direction implicit (ADI) method; then,using the Cholesky factors of the controllability and observability gramians,the balancing transformation matrix and the Hankel singular values of power system dynamic model. Next,the reduction models of power system are obtained by the above proposed method are calculnted. Finally,the four-generator test power system and IEEE 50-generator test power system are analyzed for model reduction by the proposed method,and some simulating curves are given on the Dymola platform. The results of simulation show that the proposed method is very efficient.

Key words： Power system model reduction balanced realization alternating direction implicit

收稿日期: 2011-06-20 出版日期: 2013-12-11

PACS:

TM744

基金资助:国家自然科学基金资助项目（51077054）。

引用本文:

赵洪山，李志为，兰晓明，时宁. 平衡格莱姆方法在电力系统线性模型降阶中的应用[J]. 电工技术学报, 2013, 28(7): 201-207. Zhang Zhe,Zhao Hongshan,Li Zhiwei,Lan Xiaoming,Shi Ning. Power System Linear Model Reduction Based on the Balanced Gramian Method. Transactions of China Electrotechnical Society, 2013, 28(7): 201-207.

链接本文:

http://dgjsxb.ces-transaction.com/CN/Y2013/V28/I7/201

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