# Науковий вісник НГУ

## The mathematical model of asynchronous traction motor taking into account the saturation of magnetic circuits

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Authors:

D.O. Kulagin, Cand. Sci. (Tech.), Associate Professor, Zaporizhzhia National Technical University, Senior Lecturerof the Department of Electrosupply of Industrial Enterprises, Zaporizhzhya, Ukraine

Abstract:

Purpose. Development of mathematical model of asynchronous traction machines in (d, q) frame of axis with taking into account the saturation of magnetic circuits.

Methodology. In the paper, we used the method of dynamic inductances, which is connected with the use of a systematic study of properties of the traction motor.

Findings. We have designed the analytical model of magnetic circuit asynchronous traction motor which takes into account action of the tangential and radial dynamic inductances. Based on this we have built tensor dynamic inductances rich machine, which was recorded in (d, q) frame of axis of equations of rotor and stator circles asynchronous traction motor taking into account the saturation. We suggest the method of dynamic inductances for construction of mathematical models of traction asynchronous engine. This allows to take into account the saturation of the main magnetic path for the modes with a wide range of changes in the flow of mutual induction between the stator and the rotor; saturation flow path scattering modes that are characterized by large current circuits of the machine; induction caused by processes of saturation between mutually perpendicular to the contours of the machine; as well as the joint saturation worker thread and threads scattering modes that are characterized by the significant size of the workflow and large values of currents contours of the machine. These modes are specific to asynchronous traction machines with consideration of the operation mode of traction electric rolling stock of Railways.

Originality. We have considered variations in the magnetic state of traction induction motor, which is a topical issue in view of such a change in a wide range of operating modes of traction electric rolling stock of Railways.

Practical value. The mathematical model allows taking into account the change of the magnetic state of asynchronous traction motor. It is required for creation of adequate drives control systems and systems for driving traction electric rolling stock of Railways.

References:

1Boldea, I. And Nasar, S.A. (2002), Induction Machines Handbook, CRC Press Boca Raton, London, New York, Washington, D.C.

2. Виноградов А.Б. Векторное управление электроприводами переменного тока / Виноградов А.Б. –ГОУВПО „Ивановский государственный энергетический университет им. В.И. Ленина“. – Иваново, 2008. – 320с.

Vinogradov, A.B. (2008), Vektornoye upravleniye elektroprivodami peremennogo toka [Vector Control of AC Electric Drives], GOUVPO “Ivanovskiy Gosudarstvennyy Energeticheskiy Universitet im. V.I. Lenina”, Ivanovo, Russia.

3Мищенко В.А. Теория, способы и системы векторного и оптимального векторного управления электроприводами переменного тока: монография / Мищенко В.А. – М.: Издательство „Информэлектро“,2002. – 168с.

Mishchenko, V.A. (2002), Teoriya, sposoby i sistemy vektornogo i optimalnogo vektornogo upravleniya elektroprivodami peremennogo toka [Theory, Methods and Systems of the Vector and the Optimal Vector Control Electric Drives of an Alternating Current], Monograph, Informelektro, Moscow, Russia.

4. Пивняк Г.Г. Современные частотно-регулируемые асинхронные электроприводы с широтно-импульсной модуляцией / Г.Г. Пивняк, А.В. Волков – Днепропетровск, 2006. – 421с.

Pivnyak, G.G. and Volkov, A.V. (2006), Sovremennye chastotnoreguliruemye asinkhronnye elektroprivody s shyrotno-impulsnoy modulyatsyey [Modern Frequency-Controlled Asynchronous Electric Drives with Pulse-Width Modulation], Dnepropetrovsk, Ukraine.

5. Потапенко Е.М. Робастные алгоритмы векторного управления асинхронным приводом / Е.М. Потапенко, Е.Е. Потапенко. – Запорожье: ЗНТУ, 2009. –353 с.

Potapenko, Ye.M. and Potapenko Ye.Ye. (2009), Robastnye algoritmy vektornogo upravleniya asinkhronnym privodom [Robust Algorithms for Vector Control Asynchronous Drive], ZNTU, Zaporozhe, Ukraine.

6. Беспалов Б.Я. Математическая модель асинхронного двигателя в обобщенной ортогональной системе координат /Б.Я. Беспалов, Ю.А. Мощинский, А.П. Петров// Электричество. –2002. –№8. –С. 33–39.

Bespalov, B.Ya., Moshchinskiy, Yu.A. and Petrov, A.P. (2002), “Mathematical model of the induction motor in a generalized orthogonal coordinate system”, Elektrichestvo, no. 8, pp. 33–39.

7. Снегирев Д.А. Дифференциальные уравнения для исследования электромагнитных переходных процессов частотно-регулируемого асинхронного двигателя с учетом насыщения / Д.А. Снегирёв, А.В. Тикунов // Электротехнические комплексы и системы управления. – 2006. –№2. –С. 69–73.

Snegirev, D.A. and Tikunov, A.V. (2006), “Differential equations for research of electromagnetic transients of frequency-controlled asynchronous motor with taking into account the saturation”, Elektrotekhnicheskie Kompleksy i Sistemy Upravleniya, no. 2, pp. 69–73.

8Копылов И.П. Математическое моделирование электрических машин / Копылов И.П. – М.: Высшая школа,2001. – 327с.

Kopylov, I.P. (2001), Matemeticheskoye modelirovaniye elektricheskikh mashyn [Mathematical Modelling of Electrical Machines], Vysshaya Shkola, Moscow, Russia..

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