Partial Solution Operator Discretization-Based Methods for Efficiently Computing Least-Damped Eigenvalues of Large Time Delayed Power Systems  

作　　者：Hua Ye Xiaofan Jia Muyang Liu Yutian Liu Sicong Zhang 

机构地区：[1]Key Laboratory of Power System Intelligent Dispatch,and Control of Ministry of Education,Shandong University,Jinan 250061,China [2]School of Electrical Engineering,Xinjiang University,Urumqi 830046,China [3]State Grid Jiangsu Electric Power Research Institute,Nanjing 211103,China

出　　处：《CSEE Journal of Power and Energy Systems》2025年第2期671-682,共12页中国电机工程学会电力与能源系统学报(英文)

基　　金：supported in part by the National Natural Science Foundation of China(No.51677107,52077126)。

摘　　要：To investigate impact of time delays on the small signal stability of power systems, the least-damped eigenvalues with the smallest damping ratios have been calculated by eigen-analysis methods based on Solution Operator Discretization (SOD) with Pseudo-Spectral collocation (PS) and Implicit Runge-Kutta (IRK) methods. This paper evolves SOD-PSIIRK into their partial counterparts, i.e., PSOD-PSIIRK, with greatly enhanced efficiency and reliability in analyzing large-scale time delayed power systems. Compared with SOD-PSIIRK, PSOD-PSIIRK are characterized in constructing low order discretization matrices of solution operator as well as efficiently and directly solving the embedded Matrix-Inverse-Vector Products (MIVPs). The dimensions of the discretization matrices of solution operator are largely reduced as only the retarded state variables are discretized, rather than all state variables as in SOD-PSIIRK. Meanwhile, the proposed PSOD-PSIIRK optimize the most computationally expensive operations in SOD-PSIIRK by avoiding the iterative solutions to the two embedded MIVPs. PSOD-PS/IRK directly and efficiently compute the MIVPs via factorizing the Kronecker product-like discretization matrices of the solution operator into Schur complements. The Central China-North China ultra-high-voltage power grid with 80577 state variables serves to validate the proposed PSOD-PSIIRK and shows that compared with SOD-PSIIRK, the computational time consumed by PSOD-PSIIRK is cut down by 49.96 times without loss of any accuracy.

关 键 词：Eigenvalue analysis low frequency oscillation Schur complement decomposition small signal stability solution operator discretization spectral discretization time delay wide-area measurement system 

分 类 号：TM712[电气工程—电力系统及自动化]