变压器直流偏磁瞬态场路耦合计算的稳定性分析

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摘要变压器瞬态场路耦合计算存在稳定性、计算效率及精确度的问题。利用瞬态场路耦合方法, 结合能量扰动原理计算磁场变化对应的动态电感。根据四阶龙格库塔法求解的高阶收敛性, 推导绝对稳定域以判断计算是否收敛, 分析时间步长与状态矩阵特征值的关系, 定义电感变化函数评价磁场计算精确度。对单相变压器建模和仿真, 计算正常运行和直流偏磁时的瞬态磁场和等效电路参数, 研究耦合参数在不同励磁饱和程度时的变化规律, 结果说明利用动态电感参数可以反映时变的励磁饱和情况。与传统欧拉法和改进欧拉法对比, 四阶龙格库塔法具有更高的稳定性和精确性, 同时验证了绝对稳定域的正确性。以稳定性为前提, 合理选取磁场求解频率可以有效提高计算效率和精确度。通过实验验证了瞬态场路耦合计算的可行性和稳定性分析的可靠性, 为实际变压器瞬态场路计算提供新的思路。

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关键词 ：变压器直流偏磁, 瞬态场路耦合, 稳定性, 动态电感

Abstract：Problems about stability, efficiency and accuracy in the computation of transformer, which are based on the transient magnetic-electric coupled method, have been concerned. Dynamic inductance is calculated according to the energy perturbation. Combining with the high-order convergence of the fourth Runge-Kutta, the absolutely stable region is determined to judge the convergence of computation. And the variation function of dynamic inductances is established to evaluate the magnetic changing. Then an actual single-phase transformer is modeled and simulated. Computation and case study about normal operation and DC-biasing are given to work out the transient magnetic and equivalent circuit parameters. The varying regularity of coupling parameters in different saturated excitations is learned, and the relation between state matrix and time step is studied. Result shows that the dynamic inductances are feasible to reflect the time-varying magnetic saturation. Compared with the traditional and improved Euler method, the fourth Runge-Kutta takes advantages in stability and accuracy. Meanwhile, the absolutely stable region is valid. On the basis of stability analysis, proper solving frequency of magnetic field can optimize the computational accuracy and efficiency. Tests are carried out to prove the transient magnetic-circuit method and stability analysis, which will be a new way for practical DC-biased transformers.

Key words： DC-biased transformer transient magnetic-circuit coupling stability dynamic inductance

收稿日期: 2011-12-09 出版日期: 2014-03-20

PACS:	TM74
	TM41

作者简介: 潘超男, 1981年生, 博士研究生, 主要研究方向为电磁场数值计算、电力系统电磁兼容。王泽忠男, 1960年生, 教授, 博士生导师, 主要从事电磁场分析计算、电力系统电磁兼容和电磁测量等科学研究和教学工作。

引用本文:

潘超, 王泽忠, 杨敬瑀, 刘连光. 变压器直流偏磁瞬态场路耦合计算的稳定性分析[J]. 电工技术学报, 2012, 27(12): 226-232. Pan Chao, Wang Zezhong, Yang Jingyu, Liu Lianguang. Stability Analysis Based on Transient Magnetic-Circuit Coupled Method for DC-Biased Transformer. Transactions of China Electrotechnical Society, 2012, 27(12): 226-232.

链接本文:

http://dgjsxb.ces-transaction.com/CN/Y2012/V27/I12/226

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