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Soft starters based on thyristor voltage converters are widely used to reduce the voltage dips during start-up of high-voltage induction motors. In this way, the start of the high inertial electric drives is accompanied by overheating of the rotor winding, which causes severe thermomechanical stress for the rotor elements leading to the motor failure. The aim of this work is to obtain analytical relations for approximate estimation of the rotor winding overheating in the starting modes. In this paper, we used analytical methods based on Fredholm integral equations and numerical simulation based on the method of thermal circuits in Matlab/Simulink. Based on solution of the Fredholm equation, the analytical relations were obtained to calculate the maximum temperature of the rotor winding during starting considering of heat transfer into the environment. The calculation results obtained by these expressions were tested using an integrated model that includes all the elements of the drive from the supply net to the operating mechanism. It is shown that the adiabatic approach to estimating of the rotor winding temperature maximum during start-up at which the heat transfer to the environment is not taken into account can lead to substantial error. The analytical expressions were obtained to perform approximate allowance for the uneven distribution of rotor winding temperatures when evaluating its maximum temperature. The proposed approach allows estimation of the maximum winding temperature at start-up on the basis of the relations between the temperature of motor components and the energy that is released in them and transferred to the environment, without the solution of differential equations, which describe the time variation of temperature. The obtained results make it possible to evaluate the maximum temperature of the rotor winding at start-up modes without the involvement of the numerical modeling, for which the electric drive designer often does not have not enough information.


Induction motor, rotor winding, Fredholm integral equation, thermal model, thermomechanical stress.

Anatoliy M. Ziuzev. D.Sc. (Engineering). Professor, Department of Electric drive and automation of industrial plants, Ural Federal University named after the first President of Russia B.N. Yeltsin, Ekaterinburg, Russia.

Vladimir P. Metelkov. Ph.D. (Engineering), Associate Professor, Department of Electric drive and automation of industrial plants, Ural Federal University named after the first President of Russia B.N. Yeltsin, Ekaterinburg, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

1. Zhang P., Du Y., Habetler T.G., and Lu B. A Survey of Condition Monitoring and Protection Methods for Medium-Voltage Induction Motors. IEEE Trans. Ind. Appl., vol. 47, no. 1, pp. 34-46, 2011.

2. Albers T. and Bonnett A. H. Motor temperature considerations for pulp and paper mill applications. IEEE Trans. Ind. Appl., vol. 38, no. 6, pp. 1701–1713, 2002.

3. Bonnett A.H., Soukup G.C. Cause and analysis of stator and rotor failures in three-phase squirrel-cage induction motors. IEEE Trans. Ind. Appl., vol. 28, no. 4, pp. 921−937, 1992.

4. Tavner P., Ran L., Penman J., Sedding H. Condition Monitoring of Rotating Electrical Machines, London: The Institution of Engineering and Technology, 2008, 304 pp.

5. Fu F.L. Engineering calculation of the starting temperature rise for the asynchronous motor. Electr. Machinery Technol., vol. 2, pp. 9−11, 1993.

6. Klyuchev V.I. Teoriya elektroprivoda [Theory of electric drive]. Moscow, Energoatomizdat Publ., 1985, 560 pp. (In Russian)

7. Sheng Z. W. Calculation of temperature rise of rotor bars and end rings of squirrel cage induction motors during starting. Explosionproof Electr. Mach., vol. 40, pp. 12-14, 2005.

8. IEC 60034-2-1:2007. Rotating electrical machines − Part 2-1: Standard methods for determining losses and efficiency from tests (excluding machines for traction vehicles).

9. Boyko E.P., Gaintsev Yu.V., Kovalev Yu.M., et al. Asinhronnye dvigateli obshchego naznacheniya [Induction motors of general purpose]. Moscow, Energiya Publ., 1980, 488 pp. (In Russian)

10. Polyanin A.D., Manjirov A.V. Spravochnik po integralnym uravneniyam [Handbook of Integral Equations]. Moscow, Fizmatlit Publ., 2003, 608 pp. (In Russian)

11. Staton D., Susnjic L. Induction Motors Thermal Analysis. Strojarstvo, vol. 51 (6), pp. 623−631, 2009.

12. Chan C.C., Wang H.-Q. An effective method of rotor resistance identification for high-performance induction motor vector control. IEEE Trans. Ind. Electron., vol. 37, no. 6, pp.477−482, 1990.

13. Gao Z., Habetler T.G., Harley R.G. A robust rotor temperature estimator for induction machines in the face of changing cooling conditions and unbalanced sypply. Proc. IEEE Int. Elect. Mach. Drives Conf., San Antonio, TX, May 15−18, 2005, pp. 591−596.

14. Gao Z., Habetler T.G., Harley R.G., Colby S. A sensorless rotor temperature estimator for induction machines based on a current harmonic spectral estimation scheme. IEEE Trans. Ind. Electron., vol. 55, no. 1, pp. 407-416, 2008.

15. Ziuzev A.M., Metelkov V.P., Yashin D.A. Analysis of start-up modes of asynchronous electric drive for supercharger RC 4A-3N-95. Avtomatizaciya v ehlektroehnergetike i ehlektrotekhnike. Materialy II mezhdunarodnoj nauchno-tekhnicheskoj konferencii [II International Scientific and Technical Conference on Automation in Power industry and Electrical Engineering]. APEE, 2016 (21−22 April 2016), pp. 136-143. (In Russian)

16. Ziuzev A.M.; Metelkov V.P. Research of the start-up modes of multi-stage blower asynchronous drive. Proc. IEEE IX Int. Conf. on Power Drives Systems (ICPDS), Perm, Oct. 3−7, 2016, pp.1−5.

17. Boglietti A., Cavagnino A., Staton D.A. TEFC Induction Motors Thermal Models: A Parameter Sensitivity Analysis. IEEE Trans. on Ind. Appl., vol. 41, issue 3, pp. 756–763, 2005.

18. Boglietti A., Cavagnino A., Staton D., Shanel M., Mueller M., Mejuto C. Evolution and Modern Approaches for Thermal Analysis of electrical machines. IEEE Trans. Ind. Electron., vol. 56, no. 3, pp. 871 882, 2009.

19. Tang W.H., Wu Q.H., Richardson Z.J. A Simplified Transformer Thermal Model Based on Thermal-Electric Analogy. IEEE Trans. On Power Delivery, vol. 19, no. 3, pp. 1112–1119, 2004.

20. Zyuzev A.M., Metelkov V.P. On the Temperature Dependence of the Electric Motors Thermodynamic Models Parameters. Izvestiya vysshih uchebnyh zavedenij. Ehlektromekhanika [Russian Electromechanics], 2016, no. 2 (544), pp. 12−17. (In Russian)

21. Shreiner R.T. Matematicheskoe modelirovanie ehlektroprivodov peremennogo toka s poluprovodnikovymi preobrazovatelyami chastoty [Mathematical modeling of AC drives with solid-state frequency converters]. Ekaterinburg: URO RAN Publ., 2000, 654 pp. (in Russian)