<p>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.</p><p>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.</p><p>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.</p><p>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.</p>

Frequency response analysis (FRA) is a frequency-domain method which is used to detect mechanical faults in transformers. The frequency 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. A problem with FRA is the fact that there is no general agreement about how to interpret the measurement results for detection of winding damages. For instance, the interpretation of measurement results has still not been standardized.The overall goal of this thesis is to try to enhance the understanding of the information contained in FRA measurements. This has been done in two ways: (1) by examining the FRA method for (much) higher frequencies than what is usual, and (2) by developing a new method in which FRA is combined with the ideas of Time Domain Reflectometry (TDR). As tools for carrying out the above mentioned steps, models for the magnetic core and the winding have been developed and verified by comparison to measurements.The usual upper frequency limit for FRA is around 2 MHz, which in this thesis has been extended by an order of magnitude in order to detect and interpret new phenomena that emerge at high frequencies and to investigate the potential of this high-frequency region for detection of winding deteriorations.Further, in the above-mentioned new method developed in this thesis, FRA and TDR are combined as a step towards an easier and more intuitive detection and localization of faults in transformer windings, where frequency response measurements are visualized in the time domain in order to facilitate their interpretation. / QC 20111122

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.