本文为新西兰坎特伯雷大学（作者：Maria Luiza Viana Lisboa）的博士论文，共168页。

本文介绍了一种新的谐波域三相电磁变压器模型，它是一个复合模型，用短路阻抗表示线性电路，用诺顿等效量表示非线性磁路。所提出的诺顿等效量准确地表示了磁路，因为它们是由磁分支的单个磁化特性的线性化（谐波域）和磁路定律推导而来。

本文还建立了牛顿-拉夫森迭代法，精确地确定了磁通量的非线性分布。研究了磁化特性近似对谐波解的影响，评估了包括三次样条曲线在内的多种近似翻翻的充分性，并探索了奇异值分解法来确定方程参数。此外，还研究了一次和二次端子之间均匀分布磁化电流的公认假设。对于单相变压器模型，这种假设在谐波频率下是不准确的，对于星型连接的三相变压器模型来说是不充分的，并提出了改进的谐波分布系数。推导了最常用绕组电气结构的三相三柱电磁变压器模型，并通过灵敏度分析和与有关文献报道的实际及理论知识的比较，对仿真结果进行了分析。

This thesis describes a new three-limbthree-phase electromagnetic transformer model in the Harmonic Domain. It is acomposite model, with the linear circuit represented by the short-circuitimpedances, and the non-linear magnetic circuit represented in a linearisedform by means of Norton equivalents. The proposed Norton equivalents accuratelyrepresent the magnetic circuit, as they are derived from the linearisation (inthe Harmonic Domain) of individual magnetising characteristics for the magneticbranches and the magnetic circuit laws. A NewtonRaphson iterative procedure is alsodeveloped to accurately determine the non-linear distribution of the magneticfluxes. The influence of the magnetising characteristic approximation upon theharmonic solution is investigated. The adequacy of several approximations,including cubic splines, are assessed and Singular Value Decomposition havebeen explored to determine the equation parameters. The widely acceptedassumption of equally distributing the magnetising currents between the primaryand secondary terminals is also investigated. For single-phase transformermodels this assumption is shown to be inaccurate, at harmonic frequencies, andinadequate, for star-connected three-phase transformer models and improvedharmonic distribution factors for the magnetising currents are proposed. Three-phasethree-limb electromagnetic transformer models for the most commonly usedwinding electrical configurations are derived, and the simulations resultsanalysed by means of sensitivity analysis and comparisons with the practicaland theoretical knowledge reported in the literature.

1. 引言

2. 基础概念

3. 谐波域的功率系统分析

4. 磁化特性

5. 三柱变压器的谐波模型

6. 诺顿谐波等效量的划分

7. 变压器连接模型

8. 结论与未来工作展望

附录A 南岛系统设计数据

附录B 测试系统参数

附录C EMTP变压器诺顿等效量

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