基于PID参数的时滞电力系统稳定性研究*

doi:10.11985/2023.04.029

电气工程学报 ›› 2023, Vol. 18 ›› Issue (4): 268-277.doi: 10.11985/2023.04.029

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基于PID参数的时滞电力系统稳定性研究^*

刘晓桂(), 周湘杰¹(), 蒋逢灵¹(), 刘小勇²()

1.湖南铁路科技职业技术学院铁道供电与电气学院株洲 412006
2.湖南铁道职业技术学院轨道交通电务技术学院株洲 412001

收稿日期:2022-10-12 修回日期:2023-08-17 出版日期:2023-12-25 发布日期:2024-01-12
通讯作者: 周湘杰，男，1986年生，硕士，教授。主要研究方向为电力电子技术、轨道交通电气安全。E-mail：253493095@qq.com
作者简介:刘晓桂，男，1987年生，硕士，讲师。主要研究方向为电力系统、鲁棒控制和网络控制。E-mail：Lxg_htk@163.com
蒋逢灵，男，1982年生，硕士，副教授。主要研究方向为鲁棒控制、智能控制和混沌控制。E-mail：158364038@qq.com
刘小勇，男，1980年生，硕士，讲师。主要研究方向为智能控制和轨道牵引。E-mail：834735244@qq.com
基金资助:
*湖南省科技创新计划(2022RC1097);湖南省教育厅科研(21C1322);湖南铁路科技职业技术学院院级科研(HNTKY-KT-2022-10);湖南省自然科学基金(2022JJ60009);湖南省教育厅科学研究(21C1302)

Research on Stanility of Power System with Time Delay Based on PID Parameters

LIU Xiaogui(), ZHOU Xiangjie¹(), JIANG Fengling¹(), LIU Xiaoyong²()

1. College of Railway Power Supply and Electrical Engineering,Hunan Vocational College of Railway Technology, Zhuzhou 412006
2. College of Rail Transit Electric Technology, Hunan Railway Professional Technology College, Zhuzhou 412001

Received:2022-10-12 Revised:2023-08-17 Online:2023-12-25 Published:2024-01-12

摘要/Abstract

摘要：

基于Lyapunov-Krasovskii泛函稳定理论分析方法，探讨了系统矩阵中含PID参数的时滞电力系统稳定性问题。首先，针对含PID参数的时滞电力系统数学模型进行了分析与构建。其次，通过构造时滞乘积型Lyapunov-Krasovskii泛函，并应用扩展的逆凸二次不等式方法对泛函导数中的逆凸项进行界定，从而推导出一个新的稳定性判据。最后，采用数值算例进行试验仿真，分析了在定常时滞、时变时滞情况下，PI控制增益与系统时滞稳定裕度之间的关系。试验仿真结果表明，所提出的稳定性判据较其他类似工作具备明显的优越性。

关键词: 负荷频率控制, 时滞, Lyapunov-Krasovskii泛函, 稳定性

Abstract:

Based on the Lyapunov-Krasovskii functional stability theory analysis method, the stability problem of delayed power systems with PID parameters in the system matrix is discussed. Firstly, the mathematical model of delayed power system with PID parameters is analyzed and constructed. Secondly, a new stability criterion is derived by constructing a delay-product-type Lyapunov-Krasovskii functional and an extended inverse convex quadratic inequality method is applied to define the inverse convex terms in the derivatives of the functional. Finally, experimental simulations are conducted using numerical example to analyze the relationship between the PI control gain and the system time delay stability margin under constant and time-varying delays. The experimental simulation results show that the stability criterion proposed has obvious advantages over other similar works.

Key words: Load frequency control, time-delay, Lyapunov-Krasovskii functional, stability

中图分类号:

TM73

刘晓桂, 周湘杰, 蒋逢灵, 刘小勇. 基于PID参数的时滞电力系统稳定性研究^*[J]. 电气工程学报, 2023, 18(4): 268-277.

LIU Xiaogui, ZHOU Xiangjie, JIANG Fengling, LIU Xiaoyong. Research on Stanility of Power System with Time Delay Based on PID Parameters[J]. Journal of Electrical Engineering, 2023, 18(4): 268-277.

图/表 9

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图2

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表2

表3

表4

图4

图5

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u	0.1	0.2	0.5	0.8
文献[15]	4.724	3.87	2.67	2.56
文献[20]	4.841	4.163	3.284	2.835
文献[21]	4.939	—	3.298	2.869
文献[22]	4.945	—	3.314	2.882
文献[23]推论1情形(I)	4.946	4.279	3.337	2.918
文献[23]推论1情形(II)	4.966	4.319	3.395	2.983
本文定理2(N=1)	4.961	4.310	3.387	2.977
本文定理2(N=2)	4.984	4.354	3.444	3.015

u	0.1	0.2	0.5	0.8
文献[21]	7.401	4.765	2.709	2.091
文献[23]推论1 情形(I)	7.428	4.825	2.749	2.114
文献[23]推论1情形(II)	7.572	4.947	2.801	2.137
本文定理2(N=1)	7.538	4.923	2.797	2.136
本文定理2(N=2)	7.600	4.959	2.813	2.146

K_P	K_I
	0.05			0.40			1.00
	定理2 (N=1)	文献[17]	文献[14]	定理2 (N=1)	文献[17]	文献[14]	定理2 (N=1)	文献[17]	文献[14]
0	30.914	30.853	27.927	3.381	3.377	3.124	0.923	0.922	0.886
0.05	31.874	31.263	27.881	3.501	3.496	3.215	0.970	0.969	0.927
0.20	34.224	27.763	25.114	3.792	3.784	3.320	1.078	1.077	1.016
0.40	35.830	22.194	20.364	3.980	3.472	2.832	1.118	1.116	1.017
0.60	16.126	15.727	14.618	3.825	2.734	2.130	0.947	0.933	0.827
1.00	0.595	0.594	0.546	0.515	0.515	0.482	0.361	0.360	0.348

K_P	K_I
	0.05			0.40			1.00
	定理2(N=1)	文献[17]	文献[14]	定理2 (N=1)	文献[17]	文献[14]	定理2 (N=1)	文献[17]	文献[14]
0	29.689	27.324	26.374	3.236	2.962	2.854	0.852	0.743	0.674
0.05	30.647	27.240	26.054	3.353	3.068	2.960	0.899	0.785	0.715
0.20	32.844	22.524	21.384	3.625	3.212	2.956	0.997	0.853	0.783
0.40	33.700	14.868	14.108	3.726	2.578	2.176	0.990	0.768	0.696
0.60	3.249	5.574	4.693	3.203	1.090	1.029	0.726	0.554	0.502
1.00	0.508	0.435	0.408	0.448	0.390	0.365	0.329	0.300	0.280

基于PID参数的时滞电力系统稳定性研究^*

Research on Stanility of Power System with Time Delay Based on PID Parameters

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