作者:孙方霞1, 刘强2, 王磊3
作者单位:1. 江苏海事职业技术学院轮机电气与智能工程学院,江苏 南京 211170;
2. 南京晓庄学院电子工程学院,江苏 南京 211171;
3. 东南大学电气工程学院,江苏 南京 210096
关键词:图论;矩阵范数;小信号稳定;状态空间;不确定系统
摘要:
该文结合形成网络方程的系统化思想,提出一种基于图论和状态空间的不确定系统小信号稳定判据。该小信号稳定判据不仅减小高维系统的计算负担,而且能判断包含运行状态和结构不确定的参数不确定系统的小信号稳定性。首先,参数不确定系统表示为有向图的形式,其中每个节点是用状态矩阵、输入矩阵和输出矩阵表示的多输入多输出子系统,系统的不确定性用矩阵范数界限约束。利用节点支路关联矩阵以及支路连接矩阵,节点子系统通过支路相连。然后提出基于确定的系统动态、支路连接矩阵、不确定参数的范数界限和最大连通度的小信号稳定判据,此判据与系统结构、节点数和支路数均无关。最后将该稳定判据应用在基于电压源换流器的柔性直流电网中,通过与传统稳定判据伯德图和状态矩阵根轨迹的对比分析,验证所提小信号稳定判据有效。
Small signal stability analysis and test of DC power system with voltage source converters
SUN Fangxia1, LIU Qiang2, WANG Lei3
1. College of Marine Engineering, Electrization and Intelligence, Jiangsu Maritime Institute, Nanjing 211170, China;
2. College of Electronic Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China;
3. School of Electrical Engineering, Southeast University, Nanjing 210096, China
Abstract: This paper presents a new method to evaluate the small signal stability based on graph theory and matrix norm, utilizing the knowledge of the systematic thought of forming network equations. It not only reduces the computational burden of high-dimensional system, but also has the ability to cope with the parameters uncertainty including operation state and system structure uncertainty. The system is first represented by a directed graph. Each vertex in the directed graph denotes a multi-input multi-output subsystem represented by state, input, and output matrices, and constrained by norm bounded uncertainties. The subsystems are connected by edges through vertex-edge incidence matrix and edges connection matrices. Then we propose the small signal stability criteria associated with the certain vertices dynamics and edges connection matrices, the norm bounds of uncertainty, and the maximum degree of the system, independent of the system structure and the vertices and edges number. We apply our methods to the VSC based DC systems with uncertain parameters under master slave control. The comparative analysis of simulations results of Bode diagrams, state matrix eigenvalues, and the new method validate the effectiveness of the proposed small signal stability criteria.
Keywords: graph theory;matrix norm;small signal stability;state space;uncertain system
2023, 49(3):172-180 收稿日期: 2021-04-22;收到修改稿日期: 2021-06-13
基金项目: 江苏省产学研合作项目(2020-166)
作者简介: 孙方霞(1977-),女,山东济南市人,副教授,硕士,研究方向为电子技术及电路仿真与设计、北斗通信等
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