New Solution Technique for the Frequency and Transient Response of Transformer Windings with All Inter-Turn Mutual Inductances and Capacitances Included

Abstract

This paper addresses the frequency response, the identification of the resonance frequencies as well as the transient response of transformer windings taking into account all possible inter-turn mutual inductances and capacitances. The mutual inductances and capacitances between any turn to all other turns, i.e. not only the immediately adjacent ones, are considered. The analysis starts with writing the set of simultaneous differential equations relating the currents and voltages within the sections representing the transformer winding. This is followed by their solution, only once, in the form of analytic expressions for the voltage and current distributions in the Laplace s-domain. The resonance and anti-resonance frequencies can then be directly identified for the different possibilities of the transformer’s neutral treatment (solid-earthing, isolated neutral, resistive- or inductive-earthing). Results show the importance of taking into account the mutual inductances between any turn and all other winding turns. It was found that the error introduced by neglecting the mutual capacitances to turns other than the immediately neighboring ones is practically insignificant. The results of a parameter study on the effect of the transformer’s circuit parameters on the resonance frequencies are presented. The closed-form expressions of the voltages and currents lend themselves to the determination of their time response using the numerical inversion of their Laplace transforms. This was applied to find the winding response to unit-step voltage input and the transient voltage due to current chopping.   

Keywords: power transformers, transformer resonant frequency, transformer           representation, electromagnetic transient analysis