Mathematical optimization of the MMF-function and -spectrum in concentrated winding machines

Mayer, Johann; Dajaku, Gurakuq; Gerling, Dieter

doi:10.1109/icems.2011.6073823

“…Further, the loss densities reported in Tables 1 and 2 are predictions using Model C. However, using Figure 3 or its approximation (26), it can be determined that Model A provides sufficient accuracy (i.e., within a 20% deviation from Model B and Model C) for all cases considered in Tables 1 and 2. (compiling results from [8,10,29,30]) is, for completeness, described in this appendix.…”

Section: Losses For P and Q S Common In Automotive Applicationsmentioning

confidence: 99%

“…Now, ψ m (θ r ) (a function of the rotor position θ r ) is introduced to denote the flux in a PM pole due to F δ . From the geometries depicted in Figure A1, it follows that ψ m (θ r ) can be approximated as: If (37) is not fulfilled, the winding factor can then be computed by numerically computing the 261 harmonic content of F δ as in [10,30]. …”

Section: Losses For P and Q S Common In Automotive Applicationsmentioning

confidence: 99%

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Limitations and Constraints of Eddy-Current Loss Models for Interior Permanent-Magnet Motors with Fractional-Slot Concentrated Windings

Zhang

¹

,

Wallmark

²

2017

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This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

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“…Furthermore, the increase of PM length from l m = 10 mm to l m = 30 mm rules out all but two combinations of p and Q s . Further, the loss densities reported in Tables 1 and 2 are predictions using Model C. However, using Figure 3 or its approximation (26), it can be determined that Model A provides sufficient accuracy (i.e., within a 20% deviation from Model B and Model C) for all cases considered in Tables 1 and 2. (compiling results from [8,10,29,30]) is, for completeness, described in this appendix. A sufficient condition for (34) to be valid is [29]: If (37) is not fulfilled, the winding factor can then be computed by numerically computing the 261 harmonic content of F δ as in [10,30].…”

Section: Losses For P and Q S Common In Automotive Applicationsmentioning

confidence: 99%

“…How to predict the magnitudes B ν m and corresponding harmonic orders ν m in FSCW-IPMs (compiling results from [8,10,29,30]) is, for completeness, described in this Appendix.…”

Section: Appendix A1 Preliminariesmentioning

confidence: 99%

Limitations and Constraints of Eddy-Current Loss Models for IPM Motors with Fractional-Slot Concentrated Windings

Zhang¹,

Wallmark²

2017

Preprint

3

0

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This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

show abstract