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




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


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


Chornyi O.P., Tolochko O.I., Tytiuk V.K., Rodkin D.Y., Chekavskyi H.S. Matematychni modeli ta osoblyvosti chyselnykh rozrakhunkiv dynamiky elektropryvodiv z asynkhronnymy dvyhunamy: monohrafiia [Mathematical models and features of numerical calculations of dynamics of electric drives with induction motors: monograph]. Kremenchuk, PE Shcherbatykh O.V. Publ., 2016. 302 p. (Ukr).

Veshenevskyi S.N. Kharakteristiki dvigatelei v elektroprivode [Characteristics of motors in the electric drive]. Moscow, Energy Publ., 1977. 432 p. (Rus).

Meshcheriakov V.N., Morozov S.V., Telychko L.Ia. Calculation of induction resistance parameters for a wound-rotor induction motor. Izvestiia of the USSR Higher Educational Institutions. Electromechanics, 1989, no. 3, pp. 50-52. (Rus).

Kyrychek H.M. Induction resistances in the rotor circuit of a two-speed induction motor. Technical Electrodynamics, 1979, no. 1, pp. 52-56. (Rus).

Golovan V.I. Mathematical formulation of the problem of induction motor system synthesis with inductive resistance in the rotor circuit. Technical Electrodynamics, special issue, 2002, part 4, pp. 37-42. (Rus).

Golovan V.I. Asinkhronnyi dvigatel' s induktsionnym soprotivleniem v tsepi faznogo rotora: monografiia [Induction motor with induction resistance in the phase rotor circuit]. Chernivtsi, Prut Publ., 2000. 160 p. (Ukr).

Golovan V.I., Golovan I.V. Automated design of induction resistance of an induction motor. Technical Electrodynamics, special issue, 2000, part 5, pp. 100-105. (Rus).

Golovan V.I., Golovan I.V. Resource-saving aspects in the development of technical solutions for induction motors with induction rheostat in the rotor circuit. Electrical Engineering & Electromechanics, 2003, no. 2, pp. 19-23. (Ukr).

Hany M. Jabr, Narayan C. Kar. Leakage flux saturation effects on the transient performance of wound-rotor induction motors. Electric Power Systems Research, 2008, vol. 78, no. 7, pp. 1280-1289. doi:

Hilmi F. Ameen. Computer Simulation and Mathematical Modelling of Static Rotor Resistance Chopper Control of WRIM by Reference Frame Theory. Procedia Computer Science, 2011, vol. 3, pp. 1009-1017. doi:

Joksimovic G. Modelling and analysis of series-connected wound rotor induction motor. 2008 18th International Conference on Electrical Machines, 2008, pp. 1-5. doi:

Omel’chenko E.Y. Mathematical model of the wound-rotor three-phase induction motor. Russian Electrical Engineering, 2007, vol. 78, no. 11, pp. 580-585. doi:

Omelchenko E.Y., Telezhkin O.A., Enin S.S., Tanich V.O. Computer Model of a Synchronized Asynchronous Motor. Procedia Engineering, 2015, vol. 129, pp. 629-634. doi:

Rozov Yu.M., Tyhunov A.P. Metodicheskie rekomendatsii po raschetu asinkhronnogo dvigatelia s induktsionnym rotornym soprotivleniem [Methodical recommendations for the calculation of an induction motor with induction rotor resistance]. AS of the USSR. Institute for Problems of Modeling in Power Engineering. Naukova Dumka Publ., Kyiv, 1981. 52 p. (Rus).

Vlasov V.G. Experimental studies and methods of calculation of induction motors with induction resistance in the rotor circuit. Electrical industrial. Series «Electric Drive», 1967, no. 293, pp. 3-6. (Rus).

Al-Jufout S., Khandakji K. Dynamic simulation of starting and chopper speed control of wound-rotor induction motor. International Journal of Simulation: Systems, Science & Technology, 2007, vol. 8, no. 2, pp. 1-7.

Yahaya A.E., Adamu M.Z., Paul O.A.-A., Isah A.A. Analysis of power flow and torque of asynchronous induction motor equivalent circuits. International Journal of Advanced Scientific and Technical Research, 2013, vol. 3, no. 6, pp. 713-732.

Tytiuk V., Baranovska M., Rozhnenko Z., Chornyi O., Burdilna Е., Kobylianskyi B. Application of the generalized electromechanical converter theory to analysis of the static characteristics of an induction motor. Electromechanical and Energy Saving Systems, 2020, vol. 2, no. 50, pp. 16-24. (Rus).

Kopylov I.P., Goryainov F.A., Klokov B.K. Proektirovanie elektricheskikh mashin [Electrical machines designing]. Moscow, Energy Publ., 1980. 496 p. (Rus).

Milykh I.I., Polyakova N.V. Determination of electromagnetic parameters of electric machines based on numerical calculations of magnetic fields. Electrical Engineering & Electromechanics, 2006, no. 2, pp. 40-46.

Malyar V., Hamola O., Maday V., Vasylchyshyn I. Mathematical modeling start-up and steady state modes of asynchronous motors operation with capacitive compensation of reactive power. Przeglad Elektrotechniczny, 2020, vol. 96, no. 11, pp. 109-114. doi:

Mengoni M., Rizzoli G., Zarri L., Tani A., Amerise A., Serra G. Control of a Three-Phase Wound-Rotor Induction Motor Drive for Automation Applications. 2019 IEEE International Electric Machines & Drives Conference (IEMDC), 2019, pp. 1267-1272. doi:

Meshcheryakov V.N., Muravyev A.A., Boikov A.I., Pikalov V.V. The Soft Starting System for an Induction Motor with an Induction Resistance in the Wound Rotor Circuit. 2019 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), 2019, pp. 1-5. doi:

Telezhkin O.A. Razrabotka avtomatizirovannogo elektroprivoda blochnogo stana grubogo volocheniia na osnove sinkhronizirovannogo asinkhronnogo dvigatelia: avtoref. dis. [Development of automated electric drive for block coarse-drawing mill based on synchronized induction motor. Cand. tech. sci. diss.]. Magnitogorsk, MSTU Publ., 2018. 20 p. (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).



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.



Electrical Machines and Apparatus