MATHEMATICAL MODEL AND DYNAMIC ANALYSIS OF THE PMSM
Keywords:
Permanent Magnet Synchronous Motor (PMSM), dynamic model, dq0 transformation, synchronous reference frame, electromagnetic torque, iron losses, eddy current, power efficiency, mathematical model.Abstract
In this paper, a mathematical model of the Permanent Magnet Synchronous Motor (PMSM) drive is developed and analyzed.
The proposed model is designed to accurately describe the dynamic behavior of the PMSM, evaluate power losses, and facilitate control system modeling.
Based on the dynamic equations of the PMSM in the synchronous reference frame (dq0), the state-space equations are derived, where iron losses—particularly eddy current (Foucault) losses—are modeled by means of a resistance connected in parallel with the magnetizing branch.
In addition, analytical expressions for copper (Cu) losses and iron losses under steady-state conditions are presented. The developed model can be effectively used for analyzing the efficiency of PMSM drives, performing numerical simulations, and optimizing control systems.
References
Krishnan, R. Permanent Magnet Synchronous and Brushless DC Motor Drives. CRC Press, 2010.
Morimoto, S., Sanada, M., & Takeda, Y. “Wide-speed operation of interior permanent magnet synchronous motors with high-performance current regulator.” IEEE Transactions on Industry Applications, 1994.
Vas, P. Sensorless Vector and Direct Torque Control. Oxford University Press, 1998.
To'ychiyev, F. N., & Abduxalilov, A. G. (2025). Doimiy magnitli sinxron mashinalarni modellashtirishda klark va park transformatsiyalarining qo'llanilishi. в academic research in modern science (Т. 4, Выпуск 55, сс. 174–178). Zenodo. https://doi.org/10.5281/zenodo.17249313
Abduxalilov, A., & Abdurasulov, M. (2025). Doimiy magnitli sinxron mashinalarning tahlili. Академические исследования в современной науке, 4(36), 90–92. извлечено от https://inlibrary.uz/index.php/arims/article/view/109343
Kichik quvvatli doimiy magnitli sinxron generatorni loyihalash va tahlil qilish. Abduxalilov A.G'., Mahmutxonov S.K. 2025/6/9 Energiya va resurs tejash muammolari. №88(775-780) ISSN (print) 2091-5985 ISSN (online) 2181-1946
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