作者：张萍^1,2, 田丰源², 赵新贺², 王秋富²

作者单位：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

关键词：VFTO;多导体传输线模型;精细龙格库塔法;过电压计算

摘要：

为计算VFTO下大型电力变压器绕组的过电压分布，提出基于精细龙格库塔法的计算方法。首先建立大型电力变压器绕组的多导体传输线模型，采用欧拉公式对传输线方程进行空间离散，使用精细积分法求解线性常态状态方程组，得到VFTO作用下计算变压器绕组末端过电压的公式。为减少计算误差，且避免大量的矩阵运算，提高计算速率，使用龙格库塔法求解过电压公式中的积分项，并采用矢量匹配法和递归卷积处理频变参数。结果表明：精细龙格库塔法相比较于传统的精细积分法，误差低至1.2%，计算时间减少50.2%，在生产设计变压器结构时，应着重考虑变压器首端的绝缘措施。

Precise Runge-Kutta method to calculate overvoltage distribution of transformer windings
ZHANG Ping^1,2, TIAN Fengyuan², ZHAO Xinhe², WANG Qiufu²
1. State Key Laboratory of Electrical Equipment Reliability and Intelligentization (Hebei University of Technology), Tianjin 300130, China;
2. School of Artificial Intelligence and Data Science, Hebei University of Technology, Tianjin 300130, China
Abstract: In order to calculate the overvoltage distribution of large power transformer windings under VFTO, a calculation method based on the precise Runge-Kutta method is proposed. Firstly, a multi-conductor transmission line model of a large-scale power transformer winding is established. The Euler formula is used to spatially discretize the transmission line equation, and the linear normal state equations are solved by the fine integration method, and the formula for calculating the overvoltage at the end of the transformer winding under the action of VFTO is obtained. In order to reduce the calculation error, avoid a large number of matrix operations, and increase the calculation rate, the Runge-Kutta method is used to solve the integral term in the overvoltage formula, and the vector matching method and recursive convolution are used to process the frequency-varying parameters. The results show that, compared with the traditional precision integration method, the precise Runge-Kutta method has an error as low as 1.2% and a calculation time reduction of 50.2%. In the production and design of the transformer structure, the insulation measures at the first end of the transformer should be considered.
Keywords: VFTO;multi-conductor transmission line model;precise Runge-Kutta method;overvoltage calculation
2022, 48(9):133-139  收稿日期: 2021-05-13;收到修改稿日期: 2021-07-01
基金项目: 国家自然科学基金(51207042)；河北省自然科学基金(E2013202133)
作者简介: 张萍（1979-），女，辽宁大连市人，副教授，博士，主要从事特高压变压器绕组的暂态分析
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