Efficient Eigen-Analysis for Large Delayed Cyber-Physical Power System Using Explicit Infinitesimal Generator Discretization
Efficient Eigen-Analysis for Large Delayed Cyber-Physical Power System Using Explicit Infinitesimal Generator Discretization
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DOI：
10.1109/tpwrs.2015.2463109
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发表时间：
2016-05
影响因子：
6.6
通讯作者：
Hua Ye;Yutian Liu;Peng Zhang
中科院分区：
文献类型：
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作者：
Hua Ye;Yutian Liu;Peng Zhang
时延对广域测控系统的性能有很大的影响，从而可能危及电力系统的稳定性。时滞CPPS（DCPPS）具有超越特征方程，导致无穷多个特征值基本上无法用传统的特征值分析方法求解。本文提出了一种显式无穷小生成元离散化（EIGD）方法，以解决传统的棘手问题。首先，利用无穷小生成元将DCPPS的时滞微分方程转化为常微分方程。然后，该算子被最佳离散化，从而产生一个高度结构化的，稀疏的和显式的近似矩阵。通过利用矩阵和系统矩阵的稀疏性，可以精确地计算原始DCPPS的最右特征值。EIGD方法的主要贡献在于：1）为精确获得多时滞CPPS的临界特征值提供了理论基础; 2）充分利用稀疏技术，构造了一个高度结构化的近似矩阵，使大规模DCPPS的特征分析成为可能; 3）将平移-反演变换、Arnoldi算法、Newton校正和特征灵敏度相结合，形成了一个分析大型DCPPS的计算框架。EIGD的准确性、效率和可扩展性在两区四机试验系统和实际大电网上得到了广泛的研究和充分的验证。
Time delays significantly compromise the performance of wide-area measurement and control system and thus may jeopardize the stability of cyber-physical power systems (CPPS). A delayed CPPS (DCPPS) has a transcendental characteristic equation, leading to an infinite number of eigenvalues basically unsolvable by traditional eigen-analysis methods. In this paper, an explicit infinitesimal generator discretization (EIGD) approach is presented to tackle the traditionally intractable problem. First, the delayed differential equation of DCPPS is transformed to an ordinary differential equation by using an operator called infinitesimal generator. The operator is then optimally discretized, resulting in a highly structured, sparse and explicit approximant matrix. By exploiting the sparsity of the matrix and that of system matrices, the rightmost eigenvalues of the original DCPPS can be accurately computed. The contributions of the EIGD approach lie in the following: 1) it forms a theoretical foundation for accurately obtaining the critical eigenvalues of a CPPS with multiple delays; 2) it constructs a highly structured approximant matrix that enables efficient eigen-analysis of a large DCPPS by making full use of sparsity techniques; and 3) it integrates the shift-invert transformation, Arnoldi algorithm, Newton correction and eigen-sensitivity to form a computational framework for the analysis of large DCPPS. The accuracy, efficiency and scalability of EIGD have been extensively studied and thoroughly validated on the two-area four-machine test system and a practical large transmission grid.