Transients in Transformers with Non-Uniform Inductance and Capacitance Distributions

The electromagnetic transients in transformer windings exhibiting location–dependent inductances and capacitances are investigated in the time domain. Analytical functions describing this dependence are assumed and incorporated in the two integro–differential equations governing the transient voltage and current distributions. The boundary conditions are available from the source initiating the transients and the winding’s end termination. A numerical procedure is applied in order to get frequency domain solutions for the voltage and current in the form of Interpolating and Parametric Functions. The numerical Laplace inversion is then applied to these s–domain expressions. Results pertinent to transients initiated by step- and double-exponential impulse sources are presented and discussed. All possible transformers’ neutral connections are considered. The possible error introduced by neglecting either or both of the inductance and capacitance non-uniformities is addressed. Results indicate that the main error is attributed to neglecting the inductance non-uniformity, whereas the impact of the capacitance non-uniformity is relatively small. In most cases, the winding’s copper and insulation losses have a small effect on the transient response.