Аппроксимация переходных резонансных напряжений и токов в обмотках силовых трансформаторов для определения собственных частот колебаний и коэффициентов затухани

Abstract

Transient interaction between power transformers and power cable lines may give rise to resonance overvoltages in the transformer primary windings. To develop protection measures against resonance overvoltages and to design transformers resistant to resonance overvoltages, it is necessary to know the natural frequencies of the transformer windings. Recent years have seen very rapid development of transformer windings high-frequency models. However, the mathematical models used in practice, which came from calculations of impulse overvoltages in transformer windings, reproduce the frequency dependences of losses and damping at natural frequencies with insufficient accuracy. To verify and improve the mathematical models used for analyzing high-frequency processes in transformer windings, it is necessary to have sufficient experimental data on the values of natural frequencies and damping factors. Methods for experimentally determining the natural frequencies and damping factors of power transformer windings are considered. Theoretical principles and analytical expressions for transient voltages and currents obtained for simplified equivalent circuits of windings with lumped parameters are given. An approach is proposed, according to which the transient voltages and currents in the winding are represented as the sum of steady-state and free components. The free component is then approximated using the theoretical expressions obtained for the equivalent circuits of the windings. The results of applying the approach to approximating the transient voltage at the midpoint and the current in the neutral of a dry-type transformer’s high-voltage winding are presented.