Cogging Torque Reduction Based on a New Pre-Slot Technique for a Small Wind Generator

Cogging torque is a pulsating, parasitic, and undesired torque ripple intrinsic of the design of a permanent magnet synchronous generator (PMSG), which should be minimized due to its adverse effects: vibration and noise. In addition, as aerodynamic power is low during start-up at low wind speeds in small wind energy systems, the cogging torque must be as low as possible to achieve a low cut-in speed. A novel mitigation technique using compound pre-slotting, based on a combination of magnetic and non-magnetic materials, is investigated. The finite element technique is used to calculate the cogging torque of a real PMSG design for a small wind turbine, with and without using compound pre-slotting. The results show that cogging torque can be reduced by a factor of 48% with this technique, while avoiding the main drawback of the conventional closed slot technique: the reduction of induced voltage due to leakage flux between stator teeth. Furthermore, through a combination of pre-slotting and other cogging torque optimization techniques, cogging torque can be reduced by 84% for a given design.


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Increasing interest in the efficiency of electric machinery and reducing maintenance costs is 27 making the use of permanent magnet synchronous generators (PMSGs) more common. PMSGs

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The machine involved in this study is a 6.3 kW PMSG with an interior rotor and 86 surface-mounted magnets comprising 36 slots and 20 poles. Figure 1 Table 1.

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The analysis of the PMSG and the cogging torque reduction methods proposed in this study has The total energy stored in the magnetic field or coenergy Wc in a PMSG is given by [7] 109 where L is the inductance of the windings, i the excitation current, R and Rm are, respectively, the 110 reluctances viewed by the magnetomotive force and by the magnetic field, Фm the flux due to the 111 magnets crossing the air gap, and N the number of winding turns.

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Therefore, substituting in (2) results in The second term of (3) corresponds to magnet reluctance torque and it is known as cogging   where L is the rotor depth, g is the air gap length, Bn the normal flux density, Bt the tangential flux 127 density and r the radius from the center of the rotor to the center of the air gap [7].

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The simulation in FEMM of the PMSG in Figure 1  The main objective is to reduce the cogging torque without affecting the machine's construction 150 characteristics and, therefore, without making any changes in the generator's geometry.

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A closed-slot stator topology reduces reluctance variation in the air gap and, therefore, the       207 208 Figure 9. Harmonic spectrum for the proposed reduction method. Any change in the magnetic circuit alters its reluctance and, therefore, in accordance with (4), it 213 affects the cogging torque and must be considered to reduce it. Consequently, it was found that the 214 holes for correctly aligning the rotor sheet metal with screws in the original design significantly 1(b).

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The impact of these holes on the cogging torque was analyzed for their different positions with 218 respect to the PMs. The conclusion is that the optimal position, which minimizes cogging torque, is a 219 centered position with respect to the magnets. Figure 10 (b) shows the case in which the rotor hole is 220 centered with respect to the PMs. In this situation, the holes have virtually no influence on magnetic 221 field lines linking one magnet with another. In contrast, when the hole is decentered, Figure 10

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Four divisions have been considered in this analysis, as observed in Figure 14. Therefore,

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considering that the cogging torque period is mechanical 2, the shift of one division with respect to 261 another is half of this period, which equals 1. As observed in Table 4 266 Figure 15 shows the cogging torque waveform obtained for the PMSG with centered holes.

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Because of the reluctance periodicity, the cogging torque is a periodic waveform with a frequency 268 given by: where  is the mechanical speed (1392°/s), LCM the least common multiple of the number of slots 270 (Nslots=36) and the number of poles (Npoles=20). The results in Figure 15 show the decrease in the 271 cogging torque with the pre-slot triangular method and that this improvement is even better when   the machine's main geometry. It proposes placing pre-slots in the initial part of the stator slots. These machine winding and, therefore, without altering the PMSG's fill factor.

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Introducing a central part of non-magnetic material prevents leakage flux between the 291 machine's teeth and also stops its induced voltage from reducing significantly with respect to the 292 configuration without pre-slots.

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The proposed method manages to reduce cogging torque in PMSGs with surface-mounted 294 magnets by up to 47.8%. Additionally, the article analyzes how changing the magnetic circuits for 295 construction reasons can affect the cogging torque, which can easily be optimized. The pre-slot 296 technique is also compatible with other cogging torque reduction techniques, such as skewing.

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When the above-mentioned methods are combined, cogging torque is reduced by 84.6% considering 298 manufacturing errors.

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Author Contributions: Miguel García-Gracia and Ángel Jiménez Romero performed the simulations and wrote 301 the paper. 4fores contributed with the prototype and valuable comments and corrections. All authors discussed 302 the results and commented on the manuscript at all stages.

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Acknowledgments: The authors wish to thank 4fores for granting their permission to publish some data 308 presented in this article. Furthermore, the technical support from the Research Group on Renewable Energy

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Integration of the University of Zaragoza (funded by the Gobierno de Aragón) is also gratefully acknowledged.

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Conflicts of Interest: The authors declare no conflict of interest.