# Mathematical modeling of rheostat-reactor start of wound-rotor induction motors

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

## Keywords:

induction motor, wound rotor, reactor start, mathematical model, static characteristics, transients, magnetic core saturation

## Abstract

Introduction. Wound-rotor induction motors are less common compared squirrel-cage induction motors. However, they occupy a significant share among electric drives with difficult starting conditions. Their advantage is obtaining a high starting electromagnetic torque at lower values of starting currents. Problem. Due to the possibility of including different devices in the rotor circuit, it is possible to shape the starting characteristics according to the needs of the technological process. Due to a narrower range of applications of electric drives based on wound-rotor induction motors, they are less investigated. Selection of parameters of starting and regulating devices, included in the rotor circuit, is carried out by simplified methods, which do not satisfy modern requirements to regulated electric drives. Goal. The paper aims to develop mathematical models and methods for calculating the dynamic modes and static characteristics of the wound-rotor induction motor with a reactor in the rotor circuit. Methodology. In the developed algorithms, the mathematical model of the motor is presented by the differential equations made for electric circuits in a system of orthogonal coordinates that allows excluding angular coordinate from equations of electric equilibrium. The elements of the Jacobi matrix of equilibrium equations of motor circuits are eigenvalues, and mutual is the differential inductances of electrical circuits, which are determined based on the magnetization characteristics of the main magnetic flux and leakage fluxes of the rotor and stator circuits. Results. Mathematical models for the study of starting modes of wound rotor induction motor allow to calculate transients and static characteristics and, on their basis, to carry out design synthesis of starting reactors, which provide the law of change of electromagnetic torque during start-up operating conditions. Originality. The mathematical basis of the developed algorithms is the method of solving nonlinear systems of equations by Newton method in combination with the method of continuation by parameter. The developed mathematical models and software made on their basis have high speed that allows to carry out high-reliability calculation of starting modes taking into account saturation of a magnetic circuit of the motor. Practical value. The developed algorithms do not require significant computing resources, have high speed, and can be used both for the design synthesis of start-control devices and control of the electric drive in real time and to predict its course.

## Author Biographies

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

Doctor of Technical Science, Professor

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

PhD, Associate Professor

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

PhD, Associate Professor

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

PhD, Associate Professor

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## How to Cite

Malyar, V. S., Hamola, O. Y., Maday, V. S., & Vasylchyshyn, I. I. (2022). Mathematical modeling of rheostat-reactor start of wound-rotor induction motors. Electrical Engineering & Electromechanics, (3), 8–14. https://doi.org/10.20998/2074-272X.2022.3.02

## Section

Electrical Machines and Apparatus