### MATRIX-TOPOLOGICAL MODEL OF ELECTROMAGNETIC CIRCUITS

#### 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.

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Anisimov, Y. F. (1979). Marine power semiconductor technics [Sudovaya silovaya poluprovodnikovaya tehnika], Shipping industry, Leningrad, 192. [in Russian]

Boyko, V. I., Zory A.A., Kornev V.D. (2009). Theoretic bases for the analysis of electronic circuits [Osnovi analIzu elektronnih shem], DonNTU, Donetsk, 306. [in Russian]

Collatz, L. (1966). Functional analysis and computational mathematics, Academic Press, 494. [in English]

Curtiss, C. F., Hirschfelder, J. O. (1952). Integration of stiff equations, Proc. Nat. Acad. Sci. USA, 38. [in English]

Deskur Jan (1999). Models of magnetic circuits and their equivalent electrical diagrams, COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 18 4, 600 – 610. [in English]

Kabyshev, A. V., Obuhov S.G. (2005). Calculation and designing of power supply systems: Reference materials for electrical equipment [Raschet i proektirovanie sistem elektrosnabzheniya: Spravochnyie materialyi po elektrooborudovaniyu], TPU, Tomsk, 168. [in Russian]

Khepp, Kh. (1974). Diakoptika and electrical circuits [Diakoptika i elektricheskie tsepi],World, Мoskow, 343. [in Russian]

Knysh, V. A. (1981). Semiconductor converters in systems capacitor charging [Poluprovodnikovyie preobrazovateli v sistemah zaryada nakopitelnyih

kondensatorov], Energoizdat, Leningrad, 160. [in Russian]

Kogan, V.L. (1982). The algorithm for calculating schemes in the basis of nodal potentials using the explicit methods of integrating [Algoritm rascheta shem

v bazise uzlovyih potentsialov s primeneniem yavnyih metodov integrirovaniya], News of high schools: Electronics, 6, 9-12. [in Russian]

Kostikov, V. G., Nikitin I. Y. (1986 ). Power supply high voltage REA [Istochniki elektropitaniya vyisokogo napryazheniya REA], Radio and communication, Мoskow, 200. [in Russian]

Krasnov, V. V. (1972). Methods of mathematical modeling of ship electric power systems: Study guide” [Metodyi matematicheskogo modelirovaniya sudovyih elektroenergeticheskih sistem], NSI, Nikolaev, 90. [in Russian]

Krasnov, V. V. and Siddelev, N. I. (2013). Matrixtopological description of electromagnetic circuits [Matrychno-topologichnyj opys elektromagnitnyhkil], Electrical and Computer Systems, 87, 66-73. [in Russian]

Kron, G. (1972). The study of complex systems in parts - diakoptika [Issledovanie slozhnyih sistem po chastyam – diakoptika],Science, Мoskow, 544. [in Russian]

Mustafa G.M., Fedotov Y.B. (1983). The program for the calculation of circuits with ideal transformers [Programma dlya rascheta tsepey s idealnyimi transformatorami], Electrical industry, Conversion equipment, 5, 3-5. [in Russian]

Ortega J., Reynolds V. (2000). Iterative solution of nonlinear equations in several variables, Society for Industrial and Applied Mathematics Philadelphia, 560. [in English]

Ortner M. G., Christian Magele, and Klaus Krischan(2010). Solver for a Magnetic Equivalent Circuit and Modeling the Inrush Current of a 3-Phase Transformer, World Academy of Science, Engineering and Technology, 40. [in English]

Parmantier J. P. (2007). EM topology: From theory to application”, Ultra-wideband, Short-pulse Electromagnetics, 7, 3-12. [in English]

Rakitskij, J. V., Ustinov, S. M., Chernoruckij, I. G. (1979). Numerical methods for solving rigid systems” [Chislennye metody reshenija zhestkih sistem], Science, USSR, Moskow, 208. [in Russian]

Riabenkey, V. M., Dragan S. V., Solobuto L. V. (2008). Fundamentals of modeling of systems and processes in electrical engineering (Use the package of applied programs of MATLAB/Simulink) [Osnovimodelyuvannya sistem I protsesIv v elektrotehnItsI (Vikoristannya paketa prikladnih program MATLAB/Simulink)], New World, Lvov, 385. [in Ukrainian]

Siddelev, N. I. (2015). Matrix-topological description of electromagnetic circuits in the form Cauchy [Matrichno-topologicheskoe opisanie jelektromagnitnyh

cepej v forme Koshi], Electrical and Computer Systems, 96, 63-73. [in Russian]

Siddelev, N. I. (2017). Manage digital model based on matrix-topological description electromagnetic circuits [Upravlyaemaya tsifrovaya model na osnove matrichno-topologicheskogo opisaniya elektromagnitnyih tsepey], Electrical and Computer Systems, 26, 102, 32-40. [in Russian]

Siddelev, N.I. (1982). On the control of iterative calculations for modeling physical processes [Ob upravlenii iteratsionnyimi vyichisleniyami pri modelirovanii fizicheskih protsessov], NSI, Nikolaev, 190, 36-39. [in Russian]

Tesche, F. M., M. V. Ianoz, and T. Karlsson. (1997). EMC Analysis Methods and Computational Models, John Wiley & Sons Inc, New York, 656. [in English]

Volkov, K. V., Gubarevich V.N., Isakov V.N., Kaban V.P. (1981). Principles of construction and optimization of schemes for inductive-capacitive transducers [Printsipyi postroeniya i optimizatsii shem indukivno-emkostnyih preobrazovateley], Scientific Thought , 176. [in Russian]

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

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