DOI: https://doi.org/10.15588/1607-6761-2018-1-1

### MATRIX-TOPOLOGICAL MODEL OF ELECTROMAGNETIC CIRCUITS

N. І. SIDDELEV

#### Abstract

Purpose. To develop a digital model of electromagnetic devices for research and optimization of powerful secondary electric power sources and electromagnetic converters.

Methodology. Nodal potential method, Contour current method, Topologically isomorphic transformations.

Findings. The purpose of this work is to create a mathematical apparatus that allows solving problems of modeling and researching electromagnetic devices in parts (by types of accumulated energy). This will simplify the research and optimization of technical characteristics such as efficiency, weight and size indicators, etc. The proposed mathematical model of electromagnetic circuits has the greatest degree of detail of the electric and magnetic circuit. The magnetic circuit is represented in the same detail as the electric circuit, and is described by a contour matrix. A mathematical description of electromagnetic devices is obtained in which inductive parameters are determined by the geometric dimensions and characteristics of magnetic circuits. The topology of the electrical circuit is represented by matrix blocks, which allowed obtaining a mathematical description, which simultaneously takes into account the distribution of currents and charges in the elements of the circuit. The system of equations reduces to the Cauchy form and is composed with respect to increments of magnetic fluxes and potentials on capacitors, which simplifies its solution by numerical methods on a computer. Thus, it is convenient to monitor the energy processes in the reactive powerconsuming elements of the circuit. A stable and adaptive digital model of electromagnetic circuits has been developed that makes it possible to combine several methods of integrating a system of differential equations. Feedback is provided through a special parameter. This makes it possible to maximize the correctness of the computations for the energy components in the simulation of the electromagnetic circuit. The originality of the mathematical description lies in the fact that the topology of the electromagnetic circuit is represented in the form of separate matrices that are connected by a matrix of coil connections. The practical value of the digital model of the electromagnetic circuit is that the parameters of the magnetic circuits are introduced in the form of geometric dimensions of the magnetic circuits. This eliminates the need for equivalent transformations to produce data for a specific model. This simplifies the study of secondary power supplies and other powerful electric power consumers by efficiency criteria, weight and size parameters.

Originality. The topology of the electromagnetic circuit is represented in the form of separate matrices that are connected by a matrix of coil connections.

Practical value. The parameters of the magnetic circuits are introduced in the form of geometric dimensions of the magnetic circuits.

#### Keywords

electric circuit; magnetic circuit; static electromagnetic devices; topological isomorphic modeling; matrix topological description; topological matrices; incidence matrices; block structure of the topological matrix; matrix of helical links; secondary power supplies; pulse current generators; topol

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