Transformer Modelling for the Frequency and Transient Analyses, with Non-Uniform Inductance Emulating the Inter-Turn Magnetic Coupling

A new procedure for analyzing power transformer windings with location-dependent circuit parameters, such as the series inductance, is presented. This dependence is introduced in order to take the inter-turn mutual inductive coupling into consideration. It can be expressed either by analytical expressions or even in a tabulated form. The paper addresses both the frequency and time domain analyses. They are based on replacing the winding by an adequate number of equivalent cascade connected two-ports. In contrast to the usual practice of applying the simple medium line representation, each of these two-ports is treated as a long transmission line. Their A, B, C, D generalized circuit constants will be therefore generally location-and frequency-dependent. The analyses will be conducted in the complex s-domain. The corresponding time-domain results can then be obtained by applying a numerical inverse Laplace transform. Expressions for the winding’s input impedance with different treatments of the transformer’s neutral point will be derived for any assumed number of the equivalent two-ports. Results pertinent to the frequency characteristics including the resonance frequencies are presented. The paper also describes the winding’s transient response to the application of two standard voltage stimuli. The suggested approach is validated by its application to a case study for which an analytical closed-form solution is available. The analysis of windings exhibiting nonuniformities in more than one equivalent.