Mathematical modeling of rheostat-reactor start of wound-rotor induction motors
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 curre...
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| Дата: | 2022 |
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National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine”
2022
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Electrical Engineering & Electromechanics| id |
eiekhpieduua-article-257781 |
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ojs |
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Electrical Engineering & Electromechanics |
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OJS |
| language |
English Ukrainian |
| topic |
induction motor wound rotor reactor start mathematical model static characteristics transients magnetic core saturation асинхронний двигун фазний ротор реакторний пуск математична модель статичні характеристики перехідні процеси насичення магнітопроводу |
| spellingShingle |
induction motor wound rotor reactor start mathematical model static characteristics transients magnetic core saturation асинхронний двигун фазний ротор реакторний пуск математична модель статичні характеристики перехідні процеси насичення магнітопроводу Malyar, V. S. Hamola, O. Ye. Maday, V. S. Vasylchyshyn, I. I. Mathematical modeling of rheostat-reactor start of wound-rotor induction motors |
| topic_facet |
induction motor wound rotor reactor start mathematical model static characteristics transients magnetic core saturation асинхронний двигун фазний ротор реакторний пуск математична модель статичні характеристики перехідні процеси насичення магнітопроводу |
| format |
Article |
| author |
Malyar, V. S. Hamola, O. Ye. Maday, V. S. Vasylchyshyn, I. I. |
| author_facet |
Malyar, V. S. Hamola, O. Ye. Maday, V. S. Vasylchyshyn, I. I. |
| author_sort |
Malyar, V. S. |
| title |
Mathematical modeling of rheostat-reactor start of wound-rotor induction motors |
| title_short |
Mathematical modeling of rheostat-reactor start of wound-rotor induction motors |
| title_full |
Mathematical modeling of rheostat-reactor start of wound-rotor induction motors |
| title_fullStr |
Mathematical modeling of rheostat-reactor start of wound-rotor induction motors |
| title_full_unstemmed |
Mathematical modeling of rheostat-reactor start of wound-rotor induction motors |
| title_sort |
mathematical modeling of rheostat-reactor start of wound-rotor induction motors |
| title_alt |
Математичне моделювання реостатно-реакторного пуску асинхронних двигунів з фазним ротором |
| description |
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. |
| publisher |
National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” |
| publishDate |
2022 |
| url |
http://eie.khpi.edu.ua/article/view/257781 |
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eiekhpieduua-article-2577812022-05-30T16:52:46Z Mathematical modeling of rheostat-reactor start of wound-rotor induction motors Математичне моделювання реостатно-реакторного пуску асинхронних двигунів з фазним ротором Malyar, V. S. Hamola, O. Ye. Maday, V. S. Vasylchyshyn, I. I. induction motor wound rotor reactor start mathematical model static characteristics transients magnetic core saturation асинхронний двигун фазний ротор реакторний пуск математична модель статичні характеристики перехідні процеси насичення магнітопроводу 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. Розроблено математичні моделі, методи і алгоритми аналізу пускових режимів і статичних характеристик асинхронних двигунів з фазним ротором. В розроблених алгоритмах математична модель двигуна подана диференціальними рівняннями, складеними для електричних контурів в системі ортогональних координат. Математичною основою розроблених алгоритмів розрахунку статичних характеристик є розв’язування нелінійних систем скінченних рівнянь електричної рівноваги методом Ньютона в поєднанні з методом продовження по параметру, а пускових режимів – числове інтегрування нелінійних систем диференціальних рівнянь електромеханічної рівноваги. Елементами матриці Якобі в розроблених алгоритмах є власні і взаємні диференціальні індуктивності електричних контурів, які визначаються на основі характеристик намагнічування основним магнітним потоком, а також потоками розсіювання контурів ротора і статора, що дає змогу здійснювати розрахунок з урахуванням насичення магнітопроводу двигуна. Розроблені програми і алгоритми мають високу швидкодію і дають змогу здійснювати проектний синтез пускових активних і реактивних опорів в колі ротора з метою забезпечення закону зміни електромагнітного моменту під час пуску, який відповідає роботі системи електроприводу в заданих технологічних умовах, а також здійснювати мікропроцесорне керування в динамічних режимах. National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” 2022-05-30 Article Article application/pdf application/pdf http://eie.khpi.edu.ua/article/view/257781 10.20998/2074-272X.2022.3.02 Electrical Engineering & Electromechanics; No. 3 (2022); 8-14 Электротехника и Электромеханика; № 3 (2022); 8-14 Електротехніка і Електромеханіка; № 3 (2022); 8-14 2309-3404 2074-272X en uk http://eie.khpi.edu.ua/article/view/257781/254617 http://eie.khpi.edu.ua/article/view/257781/254618 Copyright (c) 2022 V. S. Malyar, O. Ye. Hamola, V. S. Maday, I. I. Vasylchyshyn http://creativecommons.org/licenses/by-nc/4.0 |