| In this work, new models are developed for single-phase and three-phase shell-type transformers for the simulation of low-frequency transients, with the use of the coupled leakage model. This approach has the advantage that it avoids the use of fictitious windings to connect the leakage model to a topological core model, while giving the same response in short-circuit as the indefinite admittance matrix (BCTRAN) model.;The outcome of this method is used to calculate the self and mutual inductances between the coils of the coupled leakage model and the results are showing good correspondence with terminal short-circuit measurements.;Typically, leakage inductances in transformers are calculated from short-circuit measurements and the magnetizing branch is calculated from no-load measurements, assuming that leakages are unimportant for the unloaded transformer and that magnetizing current is negligible during a short-circuit. While the core is assumed to have an infinite permeability to calculate short-circuit inductances, and it is a reasonable assumption since the core's magnetomotive force is negligible during a short-circuit, the same reasoning does not necessarily hold true for leakage fluxes in no-load conditions. This is because the core starts to saturate when the transformer is unloaded. To take this into account, a new analytical method is developed in this dissertation, which removes the contributions of leakage fluxes to properly calculate the magnetizing branches of the new models.;However, in the new analytical method for calculating short-circuit inductances (as with other analytical methods), eddy-current losses are neglected. Similarly, winding losses are omitted in the coupled leakage model and in the new analytical method to remove leakage fluxes to calculate core parameters from no-load tests. These losses will be taken into account in future work.;To further increase the model sophistication, it is proposed to divide windings into coils in the new models. However, short-circuit measurements between coils are never available. Therefore, a novel analytical method is elaborated for this purpose, which allows the calculation in 2-D of short-circuit inductances between coils of rectangular cross-section. The results of this new method are in agreement with the results obtained from the finite element method in 2-D. Furthermore, the assumption that the leakage field is approximately 2-D in shell-type transformers is validated with a 3-D simulation.;Both transformer models presented in this dissertation are based on the classical hypothesis that flux can be discretized into flux tubes, which is also the assumption used in a category of models called topological models. Even though these models are physically-based, there exist many topological models for a given transformer geometry. It is shown in this work that these differences can be explained in part through the concepts of divided and integral fluxes, and it is explained that divided approach is the result of mathematical manipulations, while the integral approach is more "physically-accurate". Furthermore, it is demonstrated, for the special case of a two-winding single-phase transformer, that the divided leakage inductances have to be nonlinear for both approaches to be equivalent.;Even between models of the divided or integral approach models, there are differences, which arise from the particular choice of so-called flux paths" (tubes). This arbitrariness comes from the fact that with the classical hypothesis that magnetic flux can be confined into predefined flux tubes (leading to classical magnetic circuit theory), it is assumed that flux cannot leak from the sides of flux tubes. Therefore, depending on the transformer's operation conditions (degree of saturation, short-circuit, etc.), this can lead to different choices of flux tubes and different models. In this work, a new theoretical framework is developed to allow flux to leak from the sides of the tube, and generalized to include resistances and capacitances in what is called electromagnetic circuit theory. Also, it is explained that this theory is actually equivalent to what is called finite formulations (such as the finite element method), which bridges the gap between circuit theory and discrete electromagnetism. Therefore, this enables not only to develop topologically-correct transformer models, where electric and magnetic circuits are defined on dual meshes, but also rotating machine and transmission lines models (wave propagation can be taken into account). |
