多时滞风电系统的小信号多连通稳定区域划分  

Small-signal Multiply Connected Stability Region Partition for Multi-time-delay Wind Power System

作　　者：马晓阳 赵阳俊 梁锦文 肖先勇[1] 万雨恒 汪颖[1] MA Xiaoyang;ZHAO Yangjun;LIANG Jinwen;XIAO Xianyong;WAN Yuheng;WANG Ying(College of Electrical Engineering,Sichuan University,Chengdu 610065,China)

机构地区：[1]四川大学电气工程学院,四川省成都市610065

出　　处：《电力系统自动化》2025年第3期71-81,共11页Automation of Electric Power Systems

基　　金：国家自然科学基金资助项目(52107117)。

摘　　要：在含风电的电力系统中,由时滞导致的非线性分岔现象对于系统稳定性有重要影响。时滞的引入会使风电系统转变为无限维动力系统,难以直接用分岔理论刻画系统的稳定区域。因此,提出一种基于Lyapunov-Schmidt约化的时滞风电系统稳定域划分方法,实现时滞风电系统的分岔分析与小信号稳定域的划分。首先,建立系统的非线性微分-代数方程模型,基于延拓法定位各类分岔点,并以此为边界划分参数平面中的小信号稳定域。其次,考虑时滞的影响,建立修改后的风电系统动力学模型。然后,基于Lyapunov-Schmidt约化对无限维多时滞风电系统进行降维。接着,通过求解降维后的有限维分岔映射,得到时滞影响下分岔点的分布情况,进而对时滞空间中的小信号多连通稳定区域进行划分。最后,通过时域仿真验证了时滞空间中稳定域划分的准确性。The nonlinear bifurcation phenomenon caused by time delay in power systems containing wind power has an important influence on the system stability.The introduction of time delay may transform the wind power system into the infinite-dimensional power system,causing difficulty in describing the stability region of the system directly with bifurcation theory.Therefore,a stability region partition method based on Lyapunov-Schmidt reduction for time-delay wind power systems is proposed to realize the bifurcation analysis and small-signal stability region partitioning.Firstly,the nonlinear differential-algebraic equation(DAE)model of the system is established,various types of bifurcation points are located based on the extension method,and the smallsignal stability region on the parameter plane is divided by this boundary.Secondly,considering the effect of time delay,a modified dynamics model of the wind power system is established.Then,the dimensionality of infinite-dimensional multi-time-delay wind power systems is reduced based on Lyapunov-Schmidt reduction.Then,by solving the finite-dimensional bifurcation map after dimensionality reduction,the distribution of the bifurcation points under the influence of time delay is obtained,and then the smallsignal multiply connected stability region in the time-delay space is partitioned.Finally,the accuracy of the stability region partition in the time-delay space is verified by time domain simulation.This work is supported by National Natural Science Foundation of China(No.52107117).

关 键 词：风电系统 小信号稳定性 分岔 稳定域划分 时滞 Lyapunov-Schmidt约化 

分 类 号：O17[理学—数学]