A High Frequency Transformer Winding Model for FRA Applications

Frequency response analysis (FRA) is a method which is used to detect mechanical faults in transformers. The FRA response of a transformer is determined by its geometry and material properties, and it can be considered as the transformer’s fingerprint. If there are any mechanical changes in the transformer, for example if the windings are moved or distorted, its fingerprint will also be changed so, theoretically, mechanical changes in the transformer can be detected with FRA. The purpose of this thesis is to partly create a simple model for the ferromagnetic material in the transformer core, and partly to investigate the high frequency part of the FRA response of the transformer winding. To be able to realize these goals, two different models are developed separately from each other. The first one is a time- and frequency domain complex permeability model for the ferromagnetic core material, and the second one is a time- and frequency domain winding model based on lumped circuits, in which the discretization is made finer and finer in three steps. Capacitances and inductances in the circuit are calculated with use of analytical expressions derived from approximated geometrical parameters. The developed core material model and winding model are then implemented in MATLAB separately, using state space analysis for the winding model, to simulate the time- and frequency response. The simulations are then compared to measurements to verify the correctness of the models. Measurements were performed on a magnetic material and on a winding, and were compared with obtained results from the models. It was found that the model developed for the core material predicts the behavior of the magnetic field for frequencies higher than 100 Hz, and that the model for the winding predicts the FRA response of the winding for frequencies up to 20 MHz