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

doi:10.11985/2023.04.029

Abstract

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

CLC Number:

TM73

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.

Figures/Tables 9

References 23

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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