电力变压器仿真模型的设计摘要随着电力系统的飞速发展，对变压器的保护要求也越来越高。

研究三相变压器地暂态过程，建立一个完善的变压器仿真模型，对变压器保护方案的设计具有非常重要地意义。

本文在Matlab的编程环境下，分析了当前的变压器仿真的方法。

在单相情况下，分析了在饱和和不饱和的励磁涌流现象，和单相励磁涌流的特征。

在三相情况下，在用分段拟和加曲线压缩法的基础上，分别用两条修正的反正切函数，和两条修正的反正切函数加上两段模拟饱和情况的直线两种方法建立了Yd11、Ynd11、Yny0和Yy0四种最常用接线方式下三相变压器的数学仿真模型，并在Matlab下仿真实现。

通过对三相励磁涌流和磁滞回环波形分析，三相励磁涌流的特征分析，总结出影响三相变压器励磁涌流地主要因素。

最后，分析了两种方法的优劣，建立比较完善的变压器仿真模型。

关键词：三相变压器、励磁涌流、仿真、数学模型AbstractAlong with the electric power system’ development, the request of the protection of the transformer is more and more high. It has count for much meaning to the transformer protecting project to study the transient of a three-phase transformer, and found a perfect three-phase transformer’s digital model.This paper is worked with Matlab, analyzes the current methods of transformer’s digital model. In single-phase transformer, it is analyzed that the inrush current in saturate and unsaturated states, and the characters of the single-phase transformer’s inrush current. In three-phase transformer, with the foundation of the method of compressing curves, we use respectively two modified functions, and two modified functions and two straight line to establish four kinds of transformer’s digital model, such as Yd11, Ynd11, Yny0, Yy0, and realize these with Matlab. After analyzing the wave form of the three-phase transformer’s inrush current and hysteresis, and the characters of three-phase transformer’s inrush current, it is concluded that the primary factors which affect three-phase transformer’s inrush current. Finally, after analyzing the advantages and disadvantages of two methods, a good digital model of three-phase transformer is established.Keywords:three-phase transformer, inrush current, simulation, digital model目录绪论............................................................ - 7 -一．本课题意义...................................................................... - 7 -二．本论文的主要工作.......................................................... - 8 -三．使用工具介绍.................................................................. - 8 -第一章变压器的基本原理.................... - 10 -§1.1变压器的工作原理........................................................ - 10 -§1.2 单相变压器的等效电路............................................... - 11 -§1.3 三相变压器的等效电路及连接组问题 ...................... - 12 -第二章变压器仿真的方法简介............ - 14 -§2.1 基于基本励磁曲线的静态模型................................... - 14 -§2.2基于暂态磁化特性曲线的动态模型 ........................... - 15 -§2.3非线性时域等效电路模型............................................ - 16 -§2.4基于ANN的变斜率BP算法...................................... - 17 -第三章单相变压器的仿真.................... - 19 -§3. 1 单相变压器仿真的数学模型...................................... - 19 -§3.1.1单相变压器的等效电路分析.................................... - 19 -§3.1.2龙格－库塔法则的介绍 ............................................ - 20 -§3.2 单相变压器仿真的程序流程及功能介绍 .................. - 22 -§3.3 单相变压器仿真的实例计算及结果分析 .................. - 23 -§3.3.1单相变压器仿真的波形分析..................................... - 23 -§3.3.2单相变压器的励磁涌流的分析................................. - 24 -§3.3.3单相变压器励磁涌流的特征..................................... - 27 -第四章三相变压器的仿真.................... - 28 -§4. 1 三相变压器仿真的数学模型...................................... - 28 -§4.1.1仿真的数学依据 ......................................................... - 28 -§4.1.1.1三相变压器Yd11连接组模式 ................................. - 28 -§4.1.1.2三相变压器Ynd11连接组模式 ............................... - 30 -§4.1.1.3三相变压器Yny0连接组模式 ................................. - 31 -§4.1.1.4三相变压器Yy0连接组模式 ................................... - 31 -§4.1.2电源电压的描述 ......................................................... - 32 -§4.1.3铁心动态磁化过程简述 ............................................. - 32 -§4.1.3.1极限磁滞回环的数学描述........................................ - 33 -§4.1.3.2暂态局部磁滞回环的描述........................................ - 34 -§4.1.3.3剩磁的处理................................................................ - 35 -§4.2 三相变压器仿真的程序流程及功能介绍 .................. - 35 -§4.2.1分段拟和加曲线压缩法方法一（两段修正的反正切函数） ........................................................................................ - 35 -§4.2.2分段拟和加曲线压缩法方法二（两段修正的反正切函数加两段直线） ........................................................................ - 37 -§4.3 三相变压器仿真的计算实例及结果分析 .................. - 38 -§4.3.1励磁涌流的仿真 ......................................................... - 38 -§4.3.1.1方法一：用两段修正的反正切函数拟和压缩 ....... - 38 -§4.3.1.2方法二：用两段修正的反正切函数加两段直线拟和压缩.............................................................................................. - 40 -§4.3.1.3两种方法的比较分析................................................ - 41 -§4.3.2影响变压器励磁涌流的主要因素及结果分析......... - 41 -§4.3.2.1剩磁对变压器励磁涌流的影响 ............................... - 41 -§4.3.2.2合闸初相角对变压器励磁涌流的影响 ................... - 42 -§4.3.3三相变压器励磁涌流的特征..................................... - 43 -第五章结论与展望................................ - 45 -参考文献...................................................... - 46 -附录Matlab程序 .................................... - 47 -§1.在Yd11接线方式下两段反正切函数拟和极限磁滞回环的程序 ........................................................................................ - 47 -§2.在Ynd11接线方式下两段反正切函数拟和极限磁滞回环的程序.................................................................................... - 51 -§3.在Yny0接线方式下两段反正切函数拟和极限磁滞回环的程序 ........................................................................................ - 53 -§4.在Yy0接线方式下两段反正切函数拟和极限磁滞回环的程序 ........................................................................................ - 54 -§5.在Yd11接线方式下两段反正切函数加两段直线拟和极限磁滞回环的程序.................................................................... - 55 -§6.在Ynd11接线方式下两段反正切函数加两段直线拟和极限磁滞回环............................................................................ - 58 -§7.在Yny0接线方式下两段反正切函数加两段直线拟和极限磁滞回环的程序.................................................................... - 59 -§8.在Yy0接线方式下两段反正切函数加两段直线拟和极限磁滞回环的程序.................................................................... - 60 -致谢............................... 错误！未定义书签。