电力变压器的宽频带建模及阻抗分析

Modeling of power transformer in wide frequency range and analysis of the impedance characteristic

为了能够在设计阶段正确地预测变压器线圈中快速暂态过电压的分布,需要对变压器线圈进行宽频范围的建模。将多传输线模型应用于变压器线圈宽频率范围的建模并计算等值电路的入端阻抗,可以比较全面地了解线圈中自然频率分布及暂态响应的频率特性,并比较容易地通过测量模型变压器的入端阻抗,验证电路模型的频率有效范围。本文首先分析了基于柱坐标的环形多传输线模型与基于直角坐标的直线多传输线模型的等效性,推导了相模转换的计算公式,从而获得传输线π型等值电路参数,然后采用节点法求得入端阻抗和电压传递函数。模型线圈入端阻抗测试结果验证了电路模型在约20MHz频率以内可以满足工程计算的需要。

In order to precisely predict VFTO distributions in the windings during transformer design stage, the modeling of the power transformer winding in the wide frequency range is necessary. Applying multi-transmission line （MTL） theory to establish equivalent circuit of the transformer winding and calculating its driving point impedance and voltage transfer functions, the natural frequencies and transient response can be obtained. The validity of the equivalent circuit can be verified by comparison of the calculated and measured impedance of a model winding. In this paper, the consistence of two MTL models developed on the systems of the circular cylindrical coordinates and the rectangular coordinates respectively for the core type transformer winding is firstly analyzed. Then the phase-modal transformation for MTL equations and the parameters of the π type equivalent circuit for MTL are developed. Finally, the impedance and the voltage transfer functions of the circuit are solved using node analysis. The measured driving-point impedance of a model winding verified that the equivalent circuit is valid for modeling of the transformer windings in the frequency range below 20 MHz.