王君亮，陈梦茹，刘文君.电力系统小干扰稳定最短路径法研究［J］.河南理工大学学报（自然科学版），2024，43（2）：121-127.

WANG J L，CHEN M R，LIU W J.Investigation of the shortest path method for small disturbance stability in power systems［J］.Journal of Henan Polytechnic University（Natural Science），2024，43（2）：121-127.

电力系统小干扰稳定最短路径法研究

王君亮1，陈梦茹2，3，刘文君2

1.国网河南省电力公司 电力科学研究院，河南 郑州 450001；2.郑州大学 电气工程学院，河南 郑州 450001；3.郑州热力集团有限公司，河南 郑州 450001

摘要: 目的 电网负荷的随机变化会影响系统的小干扰稳定性。不同负荷功率增长方向下的小干扰稳定功率裕度也不同，因此需要确定最危险功率增长方向及其对应的最小功率裕度。方法 基于几何建模分析的最短路径法已成功应用于电力系统静态电压稳定分析中，方便求解最小稳定裕度，但最短路径法尚未用于电力系统的功角小干扰稳定分析。按照预定阻尼比阈值形成小干扰稳定的动态性能边界，分析非零临界特征值下的边界条件；通过虚拟观测向量，推导出适合于小干扰稳定分析的最危险功率增长方向解析表达；形成小干扰稳定最短路径法计算模型，并通过交替迭代方便求解最小稳定裕度。结果 将最短路径法引入小干扰稳定分析，在IEEE 68节点算例系统上，分析所述算法的收敛特性，得到标准化后的最危险功率增长方向，该方向提供了每个节点的功率变化参与度，参与程度高的节点在该功率增长方向上起主要作用，因此在进行系统运行方案安排时，需要着重关注这些节点的功率变化情况。将试算结果与随机生成的30组功率增长方向下的稳定裕度进行对比，结果验证了该算法的有效性。结论 本文按照预定阻尼比阈值形成小干扰稳定的动态性能边界，推导出最危险功率增长方向的解析表达，形成了小干扰稳定最短路径法计算模型。

关键词:小干扰稳定；阻尼比；最小功率裕度；动态性能边界

doi:10.16186/j.cnki.1673-9787.2021110108

基金项目:国家自然科学基金资助项目（52007171）

收稿日期: 2022/11/25

修回日期: 2023/06/03

出版日期:2024/03/25

Investigation of the shortest path method for small disturbance stability in power systems

WANG Junliang1，CHEN Mengru2，3，LIU Wenjun2

1.State Grid Henan Electric Power Company Electric Power Research Institute，Zhengzhou 450001，Henan，China；2.College of Electrical Engineering，Zhengzhou University，Zhengzhou 450001，Henan，China；3.Zhengzhou Heating Group Co.，Ltd.，Zhengzhou 450001，Henan，China

Abstract: Objectives The small disturbance stability of power systems is affected due to the random variations of grid loads.The power margins of small disturbance stability under different load power growth directions are also different.So it is necessary to determine the most dangerous power increasing direction and its corresponding minimum power margin. Methods The shortest path method based on the geometric modeling analysis had been successfully applied to the static voltage stability analysis of power systems to quickly solve the minimum stability margin.However，the shortest path method had not been used in power angle small disturbance stability analysis of power systems.The dynamic performance boundary of small disturbance stable was formed according to a predetermined damping ratio threshold，and the boundary condition under a non-zero critical eigenvalue was analyzed.By using a virtual observation vector，the analytical expression of the most dangerous power growth direction suitable for small disturbance stability analysis was derived.The calculation model of the short path method for small disturbance stable was established，and the minimum stability margin can be quickly solved by an alternating iteration process. Results the shortest path method was introduced into the small disturbance stability analysis.The convergence properties of the proposed approach were analyzed on the IEEE 68 nodes testing system，and the most dangerous power growth direction after standardization was obtained.This direction provided the participation level of power changes for each node， and the nodes with high participation level played a major role in this power growth direction.Therefore，when arranging system operation plans，it is necessary to pay special attention to the power changes of these nodes.The effectiveness of the algorithm was verified by comparing the trial results with the stability margin of 30 randomly generated power growth directions. Conclusions According to the predetermined damping ratio threshold，a small disturbance stable dynamic performance boundary was formed，an analytical expression for the most dangerous power growth direction was derived，and a small disturbance stable shortest path method calculation model was formed.

Key words:small disturbance stability；damping ratio；minimum power margin；dynamic performance boundary