A mathematical model has been developed to study the wave processes of two-winding transformers, taking into account the electromagnetic connections between the turns of the winding and between the windings. To solve differential-integral equations in partial derivatives, a method of separation of variables is proposed. References 12, figures 2.

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Purpose. To create a method for mathematical modeling of wave processes in power two-winding transformers based on a substitute scheme, which takes into account the design features of power transformers. Methodology. Formation of mathematical models for the research on wave processes in power two-winding transformers and further development of the analytical method for solving the system of partial differential equations. Findings. A mathematical model for the research on wave processes in power two-winding transformers based on a substitution scheme, witch adequately takes into account both electrical and magnetic connections, is created and an improved analytical method is proposed for solving a system of partial differential equations which allows taking into account the interval time of propagation of electromagnetic waves along the entire length of the windings and the time interval, during which the voltage changes significantly from its complete change during the wave processes,. Originality. The paper proposes a mathematical model for the research on wave processes in the windings of power two-winding transformers based on its alternative scheme, which takes into account electrical and magnetic connections, and improves the Fourier method for solving a system of differential equations with partial derivatives. Practical value. A mathematical model is created for calculating wave processes in transformers, which allows analyzing the voltage distribution in the transformer windings during the action of pulse voltage on them and adjusting their insulating abilities, given that the operation of power transformers is subject to high requirements for the reliability of their work.

Purpose. Mathematical modeling of high-frequency periodic processes in winding power transformers to improve the technology of their design and operation. Methodology. The methods of the formation of mathematical models for the research of high-frequency periodic processes in transformers and methods of solving systems of partial differential equations are applied. Findings. The mathematical model for the research of high-frequency periodic processes in two-winding transformers, with adequate considering of electromagnetic connections of windings and structural parameters of transformers, is created. Originality. To form a mathematical model for the research of high-frequency periodic processes, a substitute scheme of a two-windings transformer, taking into account the parameters of the electric and magnetic circuits of windings and electromagnetic connections between them, is proposed. Practical value. The mathematical model, which allows analyzing the voltage distribution in the transformer windings for high-frequency periodic processes in windings, and adjusting their insulating abilities, is created.

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