Abstract
This paper presents an analytical, circuit model of three-phase electrical machine with permanent magnets submerged in ferromagnetic rotor, modified in relation to the model presented in the first part of the study. This modification involves taking account of armature reaction, what required changes in the structure of the model. The model takes into account a strong, local saturation of the magnetic circuit of the rotor that depends also on the armature currents. Of course, the model also includes a voltage–current equations of the armature on the stator. The paper presents the results of the measurement verification of this model. The range of the control tests contains electrical waveforms in steady states only, since he had to check the overall usefulness of mathematical formalism, which was not used yet. The verification of the model was performed for the machine operating as a generator, with a single-phase resistive load. The verification results are positive.
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Notes
- 1.
\( \begin{aligned} \sin (\nu \tfrac{\pi }{2})\sin p_{b} \nu \tfrac{1}{2}(\alpha_{4} - \alpha_{1} ) & = \sin (\nu \tfrac{\pi }{2})\sin (\tfrac{\pi }{2}\nu - p_{b} \nu (\gamma - \kappa )) \\ & = \,\sin (\nu \tfrac{\pi }{2})\left\{ {\,\sin (\nu \tfrac{\pi }{2})\,\cos p_{b} \nu (\gamma - \kappa ) - \,\cos (\nu \tfrac{\pi }{2})\,\sin p_{b} \nu (\gamma - \kappa )} \right\} \\ & = \,\cos p_{b} \nu (\gamma - \kappa ) = \,\cos p_{b} \nu \alpha_{1} \left\{ {\left[ {\,\sin p_{b} \nu \alpha_{1} } \right]\,\cos p_{b} \nu \varphi } \right. \\ & \quad \left. { \pm \left[ {\,\sin \nu \tfrac{\pi }{2}\,\sin p_{b} \nu \tfrac{1}{2}(\alpha_{4} - \alpha_{1} )} \right]{\kern 1pt} \,\sin p_{b} \nu \varphi } \right\} \\ & = \pm \,\sin p_{b} \nu (\varphi - \alpha_{1} ) \\ \end{aligned} \).
- 2.
When the rotor of the generator has a constant rotational speed, the magnetic flux coupled with the windings and the magnetic flux coupled with the coil are a periodic functions of time, capable of being represented by Fourier series. Coefficients d cρ express the relationship between the harmonics of both waveforms. At unladen generator, the coefficients d cρ allow to separate components of individual teeth in the magnetic flux coupled to the phase winding.
References
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Drabek, T., Skwarczyński, J. (2018). An Analytical Model of an Electrical Machine with Internal Permanent Magnets. In: Mazur, D., Gołębiowski, M., Korkosz, M. (eds) Analysis and Simulation of Electrical and Computer Systems. Lecture Notes in Electrical Engineering, vol 452. Springer, Cham. https://doi.org/10.1007/978-3-319-63949-9_6
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DOI: https://doi.org/10.1007/978-3-319-63949-9_6
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