Two spectral discretization methods based on linear multistep and implicit Runge-Kutta discretization of infinitesimal generator (IGD-LMS/IRK) are presented in this paper for eigen-analysis of large delayed cyber-physical power system (DCPPS) with large time delays. First, the whole delay interval is partitioned into several sub-intervals by time delays in the system. The piecewise partitioning allows the avoidance of interpolations in evaluating system states at the delay points. Second, two time integration methods, i.e., LMS and IRK, are utilized to discretize infinitesimal generator on each sub-interval, resulting in highly structured and sparse discretization matrices. Third, IGD-LMS/IRK are efficiently implemented to compute the system's electromechanical oscillation modes. The shift-invert preconditioning technique is used and the sparsity in augmented system state matrices is exploited to guarantee the efficiency and scalability of IGD-LMS/IRK in dealing with large DCPPS. Numerical results on the two-area four-machine test system and a real-life large transmission grid validate the improved efficiency and accuracy of the proposed methods in analyzing DCPPS with large time delays.

中文翻译：

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基于时间积分的大型延迟信息物理电力系统特征分析的IGD方法

本文提出了两种基于线性多步和无穷小发生器隐式Runge-Kutta离散化(IGD-LMS/IRK)的谱离散化方法，用于具有大时延的大型延迟信息物理电力系统(DCPPS)的特征分析。首先，整个延迟间隔被系统中的时间延迟划分为几个子间隔。分段划分允许在评估延迟点的系统状态时避免插值。其次，利用两种时间积分方法，即LMS 和IRK，在每个子区间上离散化无穷小生成器，从而产生高度结构化和稀疏的离散化矩阵。第三，有效地实施 IGD-LMS/IRK 来计算系统的机电振荡模式。使用移位反转预处理技术，并利用增强系统状态矩阵的稀疏性来保证 IGD-LMS/IRK 在处理大型 DCPPS 时的效率和可扩展性。在两区域四机测试系统和现实生活中的大型输电网上的数值结果验证了所提出的方法在分析具有大时延的 DCPPS 时的效率和准确性的提高。