An effort to understand what factors affect the transfer function of a two-winding transformer

The transfer function (TF) of a transformer winding (or its natural frequencies) is known to be dependent on many factors, like the type of winding excited, terminal configuration and type of secondary winding, arrangement of windings, clearances, tap and its positions, phase position, etc. Further, it was well established about half a century ago that the natural frequencies are influenced due to the complex interactions that exist between windings. Strangely, all publications dealing with TF until now have, so far, ignored this interaction. However, to date, what is not clearly understood is the extent of contribution from the individual windings, influence of the type of winding (disc/layer, interleaved, etc.), and effect of the terminal condition of the secondary winding in defining the shape of the resultant TF. This paper attempts to provide quantitative answers to many of these questions by considering a two-winding transformer. Further, it is demonstrated how knowledge about the TF of individual windings, when considered in isolation, could be utilized to identify the contributions from each winding to the pole structure of a two-winding TF. This feature is a novelty being reported for the first time, and it is conjectured that this finding could extend the diagnosing capability of TF method from fault detection to fault location. The results presented are based on extensive analytical calculations, circuit simulations, and experiments on model coils for different terminal conditions and winding types. It is believed that the contributions of this paper resolve some issues existing in TF interpretation and impart new impetus for further research.