# Mathematical modelling of starting modes of induction motors with squirrel-cage rotor

## Authors

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

## Keywords:

induction motor, mathematical models, starting static characteristics, transients, saturation of the magnetic core, current displacement, compensation of reactive power

## Abstract

Purpose. Development of methods and algorithms for calculation of starting modes of the induction motors with the squirrel-cage rotor. Methodology. Mathematical modelling of starting modes of asynchronous electric drives in various coordinate systems with the use of numerical methods for solving boundary problems for systems of differential equations and nonlinear systems of final equations and calculation with their use of static characteristics. Results. Methods and algorithms for numerical analysis of the starting modes of asynchronous electric drive have been developed, which make it possible to calculate the static characteristics and transients in fixed three-phase and orthogonal two-phase coordinate systems. Academic novelty. Known in the literature methods of calculation of starting modes have in their basis classical equivalent circuits with different approximate methods of calculating the parameters taking into account the saturation of a magnetic core and current displacement in a rotor winding. This approach requires a special solution of the adequacy problem for each problem. The methods described in the article for the saturation accounting use real magnetization characteristics of the main magnetic flux and leakage fluxes separately, and the skin effect phenomenon is taken into account by representing the squirrel-cage rotor winding as multilayer. Such mathematical model of the motor is universal and makes it possible to take into account the saturation and current displacement in any dynamic mode, including the start-up process. Mathematical models developed on the basis of the proposed methods provide the adequacy of results with a minimum amount of calculations and make it possible to perform optimization calculations. Practical value. Created on the basis of developed algorithms calculation programs allow to carry out with high reliability calculation of starting modes both in three-phase and two-phase axes of coordinates that gives the chance to analyze not only symmetric, but also asymmetric modes and to predict special features of functioning of system of the electric drive in the set technological conditions of operation and to form requirements to development and adjustment of starting systems with the purpose of maintenance of power effective and reliable operation of system of asynchronous electric drives.

## Author Biographies

### V. S. Malyar, Lviv Polytechnic National University, Ukraine

Doctor of Technical Science, Professor,

### O. Ye. Hamola, Lviv Polytechnic National University, Ukraine

PhD, Associate Professor

### V. S. Maday, Lviv Polytechnic National University, Ukraine

PhD, Associate Professor

### I. I. Vasylchyshyn, Lviv Polytechnic National University, Ukraine

PhD, Associate Professor

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2021-04-10

## How to Cite

Malyar, V. S. ., Hamola, O. Y. ., Maday, V. S. ., & Vasylchyshyn, I. I. . (2021). Mathematical modelling of starting modes of induction motors with squirrel-cage rotor. Electrical Engineering & Electromechanics, (2), 9–15. https://doi.org/10.20998/2074-272X.2021.2.02

## Section

Electrical Machines and Apparatus