High Frequency Transformer Model based on duality principle and finite element method analysis

Abstract

This paper deals with a new High Frequency Transformer Model HFTM, taking into account magnetic core and fractionated winding. For electromagnetic transient phenomena, capacitive effects are considered by a series of capacitors among different transformer elements. This model has been tested using excitation by ramp or surge overvoltage applied to the windings terminal. Leakage impedances, magnetizing branches, zero-sequences (homopolar) fluxes and losses in windings have been developed using duality principle. In this model, electrical parameters are depending on frequency due to skin and proximity effects. Parallel Foster circuits have been fitted to represent in the time domain the damping produced by eddy currents in the windings and the iron core. The lumped parameters of these equivalents circuits have been established from inductive and resistive parameters deduced from Finite Element Method (FEM) simulation results of magnetic field distribution in winding and magnetic core for multiples frequencies up to 1MHz. The analytics HF formulas for one lamination or turn have been exploited. The Foster network elements chosen with five terms should be connected in parallel with the nonlinear magnetizing branch representing iron saturation in rated frequency. The obtained results show a satisfactory agreement with FEM analysis results. Complete model of 10kVA three-phase three-legged transformer has been achieved based on duality principle and taking into account winding resistance and core frequency dependence as well as capacitive effects. The model has been tested to simulate voltage propagation in windings and neutral current response subject to surge overvoltage.