传输线方程高精度直接积分的数值求解方法*

doi:10.11985/2023.04.039

电气工程学报 ›› 2023, Vol. 18 ›› Issue (4): 370-377.doi: 10.11985/2023.04.039

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传输线方程高精度直接积分的数值求解方法^*

张萍¹^,²(), 刘宁²(), 聂鑫鹏³, 吉增强⁴

1.省部共建电工装备可靠性与智能化国家重点实验室(河北工业大学) 天津 300130
2.河北工业大学人工智能与数据科学学院天津 300130
3.中电建(海口)新能源有限公司海口 570100
4.河北燃气有限公司石家庄 050000

收稿日期:2022-10-06 修回日期:2023-04-12 出版日期:2023-12-25 发布日期:2024-01-12
通讯作者: 刘宁，男，1995年生，硕士研究生。主要研究方向为大型电力变压器绕组的暂态研究。E-mail：1145614134@qq.com
作者简介:张萍，女，1979年生，博士，副教授。主要研究方向为大型电力变压器绕组的暂态研究。E-mail：xiaopipigirl@163.com
基金资助:
*国家自然科学基金青年科学基金资助项目(61803143)

High Precision Numerical Method for Direct Integration of Transmission Line Equation

ZHANG Ping¹^,²(), LIU Ning²(), NIE Xinpeng³, JI Zengqiang⁴

1. State Key Laboratory of Electrical Equipment Reliability and Intelligentization (Hebei University of Technology), Tianjin 300130
2. School of Artificial Intelligence and Data Science, Hebei University of Technology, Tianjin 300130
3. China Power Construction (Haikou) New Energy Co., Ltd., Haikou 570100
4. Hebei Gas Co., Ltd., Shijiazhuang 050000

Received:2022-10-06 Revised:2023-04-12 Online:2023-12-25 Published:2024-01-12

摘要/Abstract

摘要：

提出一种基于精细积分法与时域微分求积法相结合的传输线方程的数值求解方法。首先将传输线方程采用基于紧致有限差分法的四阶差分格式进行空间离散，得到关于时间的一阶线性常微分方程组，四阶差分格式对于空间微分有很好的近似精度。然后利用精细积分法与微分求积法对一阶线性常微分方程组进行数值求解。通过理论分析可知，与传统的传输线方程数值求解方法——时域有限差分法(Finite difference time domain, FDTD)相比，所提方法不涉及到状态矩阵求逆运算，保证了数值求解精度，并且其数值稳定性与计算时间、空间步长无关，可采用大步长进行数值计算，能够有效提高计算效率。最后利用仿真实例进行算法验证，结果显示，相比于时域有限差分法，所提方法能够抑制数值振荡，提高了计算精度。

关键词: 精细积分法, 时域微分求积法, 传输线方程, 紧致有限差分法, 时域有限差分法

Abstract:

A numerical solution method for the transmission line equation based on the combination of the precise integration method and the time-domain differential quadrature method is proposed. First, the transmission line equation is spatially discretized by a fourth-order difference scheme based on the compact finite difference method, and the first-order linear ordinary differential equations about time are obtained. The fourth-order difference scheme has good approximate accuracy for spatial differentiation. Then, the precise integration method and differential quadrature method are used to numerically solve the first-order linear ordinary differential equations. Through theoretical analysis, compared with the traditional numerical solution method for transmission line equations, finite difference time domain(FDTD), this proposed method does not involve state matrix inverse operations, guarantees the accuracy of the numerical solution, and its numerical stability has nothing to do with the calculation time and space step. It can be used numerical calculations with large steps can effectively improve calculation efficiency. Finally, a simulation example is used to verify the algorithm. The results show that compared with the finite difference time domain method, this proposed method can suppress numerical oscillations and improve the calculation accuracy.

Key words: Precise time step integration method, differential quadrature method in time domain, transmission line equation, compact finite difference method, finite difference time domain

中图分类号:

TM743

张萍, 刘宁, 聂鑫鹏, 吉增强. 传输线方程高精度直接积分的数值求解方法^*[J]. 电气工程学报, 2023, 18(4): 370-377.

ZHANG Ping, LIU Ning, NIE Xinpeng, JI Zengqiang. High Precision Numerical Method for Direct Integration of Transmission Line Equation[J]. Journal of Electrical Engineering, 2023, 18(4): 370-377.

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参考文献 20

[1]	CLAYTON R P. Analysis of multiconductor transmission lines[M]. Sebastopol: Wiley-IEEE Press, 2008:89-109.
[2]	闫涛. 特快速暂态过电压下大型电力变压器绕组的时域算法研究[D]. 天津: 河北工业大学, 2016.
	YAN Tao. Time domain algorithm research on windings of large power transformers under ultra-fast transient overvoltage[D]. Tianjin: Hebei University of Technology, 2016.
[3]	孙韬, 刘宗行. 传输线方程解析解求解方法的探讨[J]. 华北电力大学学报, 2005(S1):25-28.
	SUN Tao, LIU Zongxing. Analytical solution method for transmission line equation[J]. Journal of North China Electric Power University, 2005(S1):25-28.
[4]	NURICUMBO-GUILLEN R, GOMEZ P, ESPINO-CORTES F P, et al. Accurate computation of transient profiles along multiconductor transmission systems by means of the numerical Laplace transform[J]. IEEE Transactions on Power Delivery, 2014, 29(5):2385-2393. doi: 10.1109/TPWRD.2014.2313526
[5]	张希, 刘宗行, 孙韬. 传输线方程的一种数值解法[J]. 重庆大学学报, 2004(2):116-119,131.
	ZHANG Xi, LIU Zongxing, SUN Tao. A numerical solution of transmission line equation[J]. Journal of Chongqing University, 2004(2):116-119,131.
[6]	张萍, 汪友华, 聂鑫鹏, 等. 基于Lax-Wendroff算法的变压器绕组高频模型的时域分析[J]. 高压电器, 2012, 48(6):23-27.
	ZHANG Ping, WANG Youhua, NIE Xinpeng, et al. Time domain analysis of transformer winding high frequency model based on Lax-Wendroff algorithm[J]. High Voltage Apparatus, 2012, 48(6):23-27.
[7]	高方平, 姚缨英, 季苏蕾. 用FDTD法求解传输线方程[J]. 华北电力大学学报, 2012, 39(2):12-16.
	GAO Fangping, YAO Yingying, JI Sulei. Solving transmission line equation by FDTD method[J]. Journal of North China Electric Power University, 2012, 39(2):12-16.
[8]	王旭桐, 周辉, 马良, 等. 传输线方程的高精度龙格-库塔数值求解方法[J]. 强激光与粒子束, 2020, 32(3):97-103.
	WANG Xutong, ZHOU Hui, MA Liang, et al. High precision Runge-Kutta numerical method for transmission line equation[J]. High Intensity Laser and Particle Beam, 2020, 32(3):97-103.
[9]	CANGELLARIS A C, PASHA S, PRINCE J L, et al. A new discrete transmission line model for passive model order reduction and macro modeling of high-speed interconnections[J]. IEEE Transactions on Advanced Packaging, 1999, 22(3):356-364. doi: 10.1109/6040.784485
[10]	钟万勰. 暂态历程的精细计算方法[J]. 计算结构力学及其应用, 1995(1):1-6.
	ZHONG Wanxie. A detailed calculation method of transient course[J]. Computational Structural Mechanics and Its Application, 1995(1):1-6.
[11]	汪芳宗, 廖小兵, 谢雄. 微分求积法的特性及其改进[J]. 计算力学学报, 2015, 32(6):765-771.
	WANG Fangzong, LIAO Xiaobing, XIE Xiong. Characteristics and improvement of differential quadrature method[J]. Chinese Journal of Computational Mechanics, 2015, 32(6):765-771.
[12]	郭瑞, 李慧, 赵琰, 等. 基于高精度直接积分法的输电线路过电压电磁暂态快速计算[J]. 智慧电力, 2020, 48(4):91-96.
	GUO Rui, LI Hui, ZHAO Yan, et al. Rapid calculation of transmission line overvoltage electromagnetic transient based on high precision direct integral method[J]. Smart Power, 2020, 48(4):91-96.
[13]	刘磊, 律方成, 刘云鹏, 等. 基于递归卷积法在变压器单绕组多导体传输线模型时域求解的初步研究[C]// 全国电工理论与新技术学术年会论文集, 2005:375-378.
	LIU Lei, LÜ Fangcheng, LIU Yunpeng, et al. A preliminary study on time domain solution of transformer single-winding multi-conductor transmission line model based on recursive convolution[C]// 2005 Annual Conference of National Electrical Theory and New Technology, 2005:375-378.
[14]	王永, 汪芳宗. 拟谱-微分求积混合方法求解一类双曲电报方程[J]. 计算力学学报, 2018, 35(1):69-75.
	WANG Yong, WANG Fangzong. Hybrid method of quasi-spectral differential quadrature to solve a class of hyperbolic telegraph equations[J]. Journal of Computational Mechanics, 2015, 35(1):69-75.
[15]	王永, 马骏, 李靖翔, 等. 非齐次动力学方程的一种精细积分单步方法[J]. 计算力学学报, 2020, 37(2):212-217.
	WANG Yong, MA Jun, LI Jingxiang, et al. A precise integration single-step method for inhomogeneous kinetic equations[J]. Chinese Journal of Computational Mechanics, 2020, 37(2):212-217.
[16]	MA X, ZHAO X, ZHAO Y. A 3-D precise integration time-domain method without the restraints of the Courant-Friedrich-Levy stability condition for the numerical solution of Maxwell’s equations[J]. IEEE Transactions on Microwave Theory and Techniques, 2006, 54(7):3026-3037. doi: 10.1109/TMTT.2006.877427
[17]	贾磊, 张亚婷, 赵训君, 等. 非均匀传输线中电磁暂态过程的新型时域算法[J]. 高电压技术, 2009, 35(2):430-434.
	JIA Lei, ZHANG Yating, ZHAO Xunjun, et al. A new time domain algorithm for electromagnetic transient processes in non-uniform transmission lines[J]. High Voltage Engineering, 2009, 35(2):430-434.
[18]	付倩倩, 陈胜泉, 汪赳羚. 一种基于经典帕德逼近的传输线瞬态响应数值计算方法[J]. 电力科学与技术学报, 2019, 34(4):184-188.
	FU Qianqian, CHEN Shengquan, WANG Jiuling. A numerical method for transient response of transmission line based on classical Parder approximation[J]. Journal of Electric Power Science and Technology, 2019, 34(4):184-188.
[19]	王赞基, 杨钰. 大型电力变压器线圈中特快速暂态电压分布的计算[J]. 高电压技术, 2010, 36(4):918-925.
	WANG Zanji, YANG Yu. Calculation of extra-fast transient voltage distribution in coils of large power transformers[J]. High Voltage Engineering, 2010, 36(4):918-925.
[20]	梁利辉, 董华英, 梁贵书, 等. VFTO下变压器绕组电位分布的计算[J]. 华北电力大学学报, 2009, 36(2):13-17,22.
	LIANG Lihui, DONG Huaying, LIANG Guishu, et al. Calculation of transformer winding potential distribution under VFTO[J]. Journal of North China Electric Power University, 2009, 36(2):13-17,22.

序号	主要参数	数值
1	电导率/(Ω/mm²/m)	0.021 35
2	绝缘材料的相对介电常数	4.5
3	匝间电容/pF	10.619
4	饼间电容/pF	25.682
5	对地电容/pF	2.06

传输线方程高精度直接积分的数值求解方法^*

High Precision Numerical Method for Direct Integration of Transmission Line Equation

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