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ЕLECTROMAGNETIC FIELD EQUATIONS IN NONLINEAR ENVIRONMENT
(2024) Lyshuk, Viktor; Tkachuk, Anatolii; Zablotskyi, Valentyn; Selepyna, Yosyp
The paper proposes electromagnetic field equations from the point of view of their adaptation to numerical methods. Maxwell'sequations with partial derivatives are used, written concerning field vectors, which most fully reproduce the picture of physical processes in electrical engineeringdevices. The values of these vectors provide comprehensive information about the field at any spatio-temporal point. The concept of creating mathematical models of electrical devices adequate to physical processes has been developed. Mathematical transformations are carried out according to the rulesof differential calculus. Dynamic processes in the elements of electrotechnical devices were analyzed using the apparatus of mathematical modeling.An algorithm for implementing differential equations with partial derivative numerical methods using computer simulation was implemented. The obtained results made it possible to understand the nature of electromagnetic phenomena in nonlinear media. The paper provides calculations of the field parameters in a flat ferromagnetic plate and the groove of the rotor of an electric machine
MODELLING OF DYNAMIC MODES IN A DC MOTOR FOR ELECTRIC VEHICLE
(Polytechnika Lubelska, 2026) Lyshuk, Viktor; Tkachuk, Anatolii; Moroz, Serhiy; Yevsiuk, Mykola; Khvyshchun, Mykola; Prystupa, Stanislav; Zablotskyi, Valentyn
The paper investigates mathematical models of a DC electric motor with independent excitation for electric vehicles and PWM as a speed control method. Differential equations of electromechanical state are written in normal Cauchy form. This representation simplifies the computational process, since integration is carried out by the explicit numerical method of Runge-Kutta of the fourth order, which is simpler than implicit and more accurate than single-step explicit methods. The symbolic programming language Force 2.0, which is a variant of the Fortran language, is used for modelling. Compared to mathematical packages of simulation modelling, it is convenient in terms of low time costs for compiling the program itself, since the program includes model equations together with initial conditions, a numerical method, and an integration procedure. The developed models take into account electromagnetic couplings of the motor's electrical circuits and make it possible to simulate dynamic operating modes. Such models can be used to analyse the operation of motors both autonomously and as an element of an electromechanical system, including valve converters. The operation and transient modes of a DC motor are simulated, the simulation results are given, and their analysis is presented. The results confirmed the correctness of the chosen approach to modelling and numerical methods, as well as compliance with the classical theory of electric machines.
Modeling dynamic and static operating modes of a low-power asynchronous electric drive
(2025-06-27) Lyshuk, Viktor; Moroz, Sergiy; Selepyna, Yosyp; Zablotskyi, Valentyn; Yevsiuk, Mykola; Satsyk, Viktor; Tkachuk, Anatolii
The article presents a mathematical model of the asynchronous motor in oblique coordinates, based on differential equations expressedin the standard Cauchy form. The differential equations of traditional models are implicitly formulated; therefore, during numerical implementationfor prolonged processes, matrix coefficient rotation leads to significant time expenditure and the accumulation of errors during integration. This complex task is proposed to be addressed by ensuring that the differential equations of the electromechanical state are non-stiff and, importantly, writtenin standard Cauchy form. The standard Cauchy form is essential for analyzing asynchronous motors, as changes in the number of unknowns significantlyrestructure the coefficient matrix. This formulation of the equations is convenient for numerical integration, as explicit methods, which are considerably simpler than implicit methods, can be implemented. To create a mathematical model, coordinate transformations were performed based on the classical theory of electric machines. The advantage of the proposed method of using different coordinate axes is the possibility of analyzing new variablesand obtaining constant coefficients in the equations of state of the electric motor.The model accounts for the electromagnetic interactions of the motor’s electrical circuits and their nonlinearity, enabling the simulation of electromagnetic and electromechanical processes. Transitional operating modes of the asynchronous motor have been modeled and analyzed. The proposed model can be utilized for analyzing the operation of motors both as standalone elements and as components of an electromechanical system. It is demonstrated that this model aligns with classical electrical machine theory.Simulation results are provided, along with their analysis.

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