Mathematical Model of the Initial Overvoltage Pulse Distribution in Two-Winding Transformers

Abstract

A mathematical model for the research of the initial voltage distribution along the windings of a two-winding transformer during the action of a rectangular pulsed overvoltage, is developed. The mathematical model for the research of pulse processes in the windings of two-winding transformers based on a substitution scheme of infinitesimal length element of the two-winding transformer, taking into account electromagnetic connections between windings, longitudinal and transverse mutual inductive connection between windings, the main magnetic flux in the form of differential equations with partial derivatives, is formed. When solving such equations must be found initial and boundary conditions. There is a need to determine the initial voltage distribution along the windings of the transformer during the action of impulse overvoltage. A system of partial differential equations, according to the principles of current continuity for the substitution circuit of an infinitesimal transformer element, taking into account only capacitive elements, and the current in the inductors does not change by a leap, are obtained. The mathematical model for research the initial voltage distribution along windings by solving the system of partial differential equations describing the initial voltage distribution along the windings of a two-winding transformer, based on a modified substitution scheme of an infinitesimal element of a two-winding transformer, is developed. For the first time, the initial voltage distribution along the turns of a two-winding transformer during the action of a rectangular overvoltage pulse, which solves the problem of determining the initial conditions for the boundary value problem of transient wave processes, is obtained. Solving the boundary value problem by the methods of classical mathematical physics allows giving clear mathematical meaning to formal calculations. An approach to the definition of stable integrations of a system of differential equations, with partial derivatives of the second order, is presented.