# MODELLING OF DYNAMIC MODES OF AN INDUCTION ELECTRIC DRIVE AT PERIODIC LOAD

## Authors

• V. S. Malyar Lviv Polytechnic National University, Ukraine
• O. Ye. Hamola Lviv Polytechnic National University, Ukraine
• V. S. Maday Lviv Polytechnic National University, Ukraine

## Keywords:

induction motor, periodic load, mathematical model, steady-state dynamic mode, transient, static characteristics, saturation of the magnetic core, displacement of current

## Abstract

Goal. Development of methods and mathematical models, based on them, for the calculation of transients and steady-state modes of induction electric drives operating in periodic load mode. Methodology. The developed algorithms are based on a mathematical model of an induction motor, which takes into account the saturation of the magnetic core and the displacement of current in the rotor bars. The processes are described by a system of nonlinear differential equations in the orthogonal axes x, y, which enables the results to be obtained with the smallest amount of calculations. The magnetization characteristics by the main magnetic flux and the leakage fluxes are used to calculate the electromagnetic parameters of the motor. To account for the current displacement in the rotor bars, the short-circuited winding is considered as a multilayer structure formed by dividing the bars in height by several elements. Results. Due to the variable load on the motor shaft, electromagnetic processes in both transient and steady state modes of the electric drive in any coordinate system are described by a system of nonlinear differential equations. The result of the calculation of the transients is obtained as a result of their integration time dependencies of coordinates (currents, electromagnetic torque, etc.) at a given law of change of the moment of loading. The proposed method of calculating steady-state mode is based on algebraization of differential equations on the mesh of nodes of the process cyclicity period and allows to obtain periodic dependencies in the time domain. Originality. The problem of calculating a steady-state periodic mode is solved as a boundary problem for a system of first-order differential equations with periodic boundary conditions, which allows to obtain instantaneous dependences during the period of currents, electromagnetic torque, capacities and other coordinates. Practical significance. Using the developed algorithm, it is possible to calculate the static characteristics of periodic processes as dependencies on different parameters of the cycle of periodic load or other coordinates, which is the basis for the choice of the motor for overload, power, heating, etc., as well as to detect the possibility of resonance.

## References

Voldek А.I., Popov V.V. Elektricheskiye mashiny. Mashiny peremennogo toka [Electric machines. AC machines].Saint Petersburg, Piter Publ., 2010. 350 p. (Rus).

Safaryan V.S., Gevorgyan S.G. Ascertainment of the equivalent circuit parameters of the asynchronous machine. Energetika. Proceedings of CIS higher education institutions and power engineering associations, 2015, no. 6, pp. 20-34. (Rus).

Rogal V.V., Kapshtik V.S. Reactive power compensation in intermittent duties. Electronics and Communication. Thematic issue «Electronics and Nanotechnology», 2011, no. 3, pp. 101-108. (Ukr).

Petrushin V.S., Plotkin J.R., Yenoktaiev R.N., Bendahmane Boukhalfa. Development of energy–efficient asynchronous electric drive for intermittent operation. Bulletin of the National Technical University «KhPI». Series: Problems of automated electrodrive. Theory and practice, 2019, no. 16 (1341), pp. 70-79. doi: 10.20998/2079-8024.2019.16.13.

Petuhov S.V., Krishyanis M.V. Elektroprivod promyishlennyih ustanovok [Electric driver industrial-scale plants]. Arkhangelsk, S(A)FU Publ., 2015. 303 p. (Rus).

Hrisanov V.I. Transient process analysis at various methods of starting asynchronous machines. Technical electrodynamics. Thematic issue «Electric drive», 2000, pp. 24-27. (Rus).

Fil'ts R.V. Matematicheskie osnovy teorii elektromekhanicheskikh preobrazovatelei [Mathematical foundations of the theory of electromechanical transducers]. Kyiv, Naukova dumka Publ., 1979. 208 p. (Rus).

Malyar V.S., Malyar A.V. Mathematical modeling of periodic modes of operation of electrical devices. Electronic Modeling, 2005, vol.27, no.3, pp. 39-53. (Rus).

Zhulin S.S. The method of continuation by parameter and its application to the tasks of optimal control. Numerical methods and programming, 2007, vol. 8, no. 2, pp. 205-217. (Rus).

2020-06-24

## How to Cite

Malyar, V. S., Hamola, O. Y., & Maday, V. S. (2020). MODELLING OF DYNAMIC MODES OF AN INDUCTION ELECTRIC DRIVE AT PERIODIC LOAD. Electrical Engineering & Electromechanics, (3), 9–14. https://doi.org/10.20998/2074-272X.2020.3.02

## Section

Electrical Machines and Apparatus