Effect of pole number and slot number on performance of dual rotor permanent magnet wind power generator using ferrite magnets Effect of pole number and slot number on performance of dual rotor perman[.]
Effect of pole number and slot number on performance of dual rotor permanent magnet wind power generator using ferrite magnets Peifeng Xu, Kai Shi, Yuxin Sun, and Huangqiu Zhua Citation: AIP Advances 7, 056631 (2017); doi: 10.1063/1.4974497 View online: http://dx.doi.org/10.1063/1.4974497 View Table of Contents: http://aip.scitation.org/toc/adv/7/5 Published by the American Institute of Physics Articles you may be interested in Design and analysis of tubular permanent magnet linear generator for small-scale wave energy converter AIP Advances 7, 056630056630 (2017); 10.1063/1.4974496 Design and analysis of a 3D-flux flux-switching permanent magnet machine with SMC cores and ferrite magnets AIP Advances 7, 056632056632 (2017); 10.1063/1.4974524 AIP ADVANCES 7, 056631 (2017) Effect of pole number and slot number on performance of dual rotor permanent magnet wind power generator using ferrite magnets Peifeng Xu,a Kai Shi, Yuxin Sun, and Huangqiu Zhua School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China (Presented November 2016; received 21 September 2016; accepted 28 October 2016; published online 17 January 2017) Dual rotor permanent magnet (DRPM) wind power generator using ferrite magnets has the advantages of low cost, high efficiency, and high torque density How to further improve the performance and reduce the cost of the machine by proper choice of pole number and slot number is an important problem to be solved when performing preliminarily design a DRPM wind generator This paper presents a comprehensive performance comparison of a DRPM wind generator using ferrite magnets with different slot and pole number combinations The main winding factors are calculated by means of the star of slots Under the same machine volume and ferrite consumption, the flux linkage, back-electromotive force (EMF), cogging torque, output torque, torque pulsation, and losses are investigated and compared using finite element analysis (FEA) The results show that the slot and pole number combinations have an important impact on the generator properties © 2017 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4974497] I INTRODUCTION For the past few years, the applications of permanent magnet generators (PMGs) in wind energy conversion system have been increasing for their significant advantages of high efficiency, simple structure, reliable operation and no additional power supply.1 NdFeB magnets are usually used in PMGs for the sake of their high remanence and coercivity values However, the price volatility and unstable supply of the raw material for NdFeB have been compelling designers of wind power generator to test alternative solutions with less or without NdFeB magnets Ferrite magnets possess the merits of low cost, low weight density, stainless and having a stable supply PMGs that use ferrite magnets have been studied.2 It is obvious that the performance is dramatically decreased when using ferrite magnets on account of its relatively low residual flux density In order to solve this problem, dual rotor permanent magnet (DRPM) machine using ferrite magnets was proposed and compared with a traditional induction machine (IM) and interior PM machine (IPM).3 The torque density of a DRPM using ferrite magnets is almost times the density of an IM and 2.2 times the density of an IPM, with efficiency only slightly lower than the IPM but higher than the IM Thus we may transplant the DRPM machine using ferrite magnets to wind power generation without sacrificing too much performance For a DRPM wind generator using ferrite magnets, how to improve the performance and reduce the cost of the machine by proper choice of slot and pole number is an important problem to be solved The reported results mainly focused on the slot and pole number combination of PM machines,4 but rarely studied on DRPM machines The main contribution of this paper is the calculation of the winding factor using star of slots, as well as the comparison and analysis of the DRPM wind generators with different slot and pole a Corresponding author: Peifeng Xu (Electronic mail: xupeifeng2003@126.com) 2158-3226/2017/7(5)/056631/6 7, 056631-1 © Author(s) 2017 056631-2 Xu et al AIP Advances 7, 056631 (2017) FIG Configuration and pole arrangement of the DRPM wind generator number combinations To investigate the influence of slot and pole number combinations, six combinations are compared using finite element analysis (FEA) The results show that slot and pole number combinations have an important impact on generator properties, and some reference merits can be obtained in the DRPM wind generators II TOPOLOGIES AND PARAMETERS OF INVESTIGATED DRPM WIND GENERATORS The configuration and magnet pole arrangement of a DRPM wind generator analyzed in this paper is illustrated in FIG A cup stator is sandwiched between two concentric rotors, and the surface mounted ferrite magnets are radially polarized in different directions Accordingly, the magnetic circuits in the inner and outer parts of the DRPM wind generator are in parallel, and they share one common stator yoke The back-to-back toroidally wound winding is adopted, and there is no need of layer insulation inside the slot, which brings advantages such as short end winding, less copper loss, and simple maintenance The fluxes passing through the inner and outer parts are in parallel, so the DRPM wind generator can be seen as an inner rotor generator nested inside an outer rotor one with single-layer winding Consequently, some applications of slot and pole number combinations in PM machine can be reference for the DRPM wind generators It has been proved that when the coil pitch is as close to the pole pitch as possible, the maximum of the winding flux linkage and torque density can be obtained.5 The closet slot and pole number combinations are Ns = 2p ± 1, Ns = 2p ± (1) where N s is the slot number, and p is the pole pair number However, machines with N s =2p±1 combinations exhibit a significant unbalanced magnetic force due to the asymmetric disposition of the stator slots and coils, which will compromise the bearing life and result in unavoidable noise and vibration.6 Thus, the more appropriate slot and pole number combinations are governed by N s =2p±2 In this paper, N s =2p±2 are chosen, the winding of the inner and outer parts can respectively be seen as fractional slot concentrated winding (FSCW) wound on alternate teeth The primary design specifications of the DRPM wind generators are listed in Table I As the rotating speed of the DRPM wind generators is relatively low, and the frequency which is proportional to the product of the pole pair number and the rotor speed can’t be too low, a relatively large number of poles will be needed However, too large number of slots will bring manufacturing difficulty for stator In this paper, the slot and pole combinations of the DRPM wind generators are chosen as 12-slot/10-pole, 12-slot/14-pole, 18-slot/16-pole, 18-slot/20-pole, 24-slot/22-pole, and 24-slot/26- pole The inner and outer windings are wound in the same layouts with opposite current TABLE I Specifications of the DRPM wind generators Specifications Outer diameter of stator (mm) Inner diameter of stator (mm) Stack length (mm) Values Specifications Values 200 100 200 Air gap length (mm) Inner ferrite magnet length (mm) Outer ferrite magnet length (mm) 0.5 10 056631-3 Xu et al AIP Advances 7, 056631 (2017) TABLE II Winding placements of the DRPM wind generators with different slot and pole number (N s /2p) combinations Items Type A: 12/10 Type C: 18/16 Type E: 24/22 Wound teeth Items Wound teeth A-Y-C-X-B-Z A-Y-Y-C-X-X-B-Z-Z A-A-Y-Y-C-C-X-X-B-B-Z-Z Type B: 12/14 Type D: 18/20 Type F: 24/26 A-Z-B-X-C-Y A-Z-Z-B-X-X-C-Y-Y A-A-Z-Z-B-B-X-X-C-C-Y-Y directions, and only alternate teeth carry a coil The inner winding placements for different types of the DRPM wind generators are shown in Table II III MAIN WINDING FACTORS The main winding factors of the DRPM wind generators can be calculated by means of the star of slots The star of slots of type A, B, C, D, E and F are shown in FIG (a), (c), (e), (g), (i) and (k), and the phasors of phase A are connected together in FIG (b), (d), (f), (h), (j) and (l), receiving the resultant phasor E phase-A which can be expressed as ◦ 2E1 + 2E1 ej(-30 ) , for type A and B ◦ ◦ ◦ Ephase-A = 2E1 + 2E1 ej(-20 ) + E1 ej20 + E1 ej(-40 ) , for type C and D ◦ ◦ ◦ j(-15 ) j(-30 ) 2E1 + 2E1 e + 2E1 e + 2E1 ej(-45 ) , for type E and F (2) where E is the EMF phasor of one slot at zero angle The main winding factor can be calculated by Kw1 = + 2e-j30◦ , for type A and B + 2e-j20◦ + ej20◦ + e-j40◦ , for type C and D + 2e-j15◦ + 2ej30◦ + 2e-j45◦ , for type E and F (3) FIG Star of slots and resultant phasors for different slot and pole number combinations (a) Star of slots of type A (b) E phase-A of type A (c) Star of slots of type B (d) E phase-A of type B (e) Star of slots of type C (f) E phase-A of type C (g) Star of slots of type D (h) E phase-A of type D (i) Star of slots of type E (j) E phase-A of type E (k) Star of slots of type F (l) E phase-A of type F 056631-4 Xu et al AIP Advances 7, 056631 (2017) For generator with m-phase and the slot-pitch angle αs =360◦ /(2p), define t=N s /2m, and the main winding factor can be induced to X t e - j(t−i)αs i=1 , t is even t Kw1 = t−1 X - j(t−1−i)αs jαs - j(t - 1)αs 2e + e + e i=1 , t is odd 2t (4) IV EFFECT OF SLOT AND POLE NUMBER COMBINATIONS In order to compare the different combinations of the DRPM wind generators, the performances are quantitatively analyzed by FEA All of the analyzed generators are compared under the same ferrite consumption and machine size, that is, the length of ferrite magnets in magnetization direction, the pole-arc coefficients of the inner and outer poles, the inner and outer diameters of stator, diameters of the inner and outer rotors, the length of the inner and outer air-gaps, and the length of axial length Meanwhile, for fair comparison, the widths of the inner and outer stator teeth are adjusted to have the same flux densities, and the number of turns per slot is adjusted to maintain the same copper filling factor The flux linkage, back-EMF, cogging torque and output torque waveforms at 375 rpm are shown in FIG as well as the values listed in Table III It can be seen that when the pole number increases, the flux linkage decreases due to the leakage flux increment and flux decrement per pole For the same slot number N s , the larger pole number, the smaller the widths of the inner and outer stator teeth, and the larger slot area as well as the larger turns per slot Thus, the fundamental EMF amplitude of type A, C and E (p=N s /2-1) are less than those of type B, D and F (p=N s /2+1) and the difference will become smaller and smaller as slot number increases For wind generator, large cogging torque will make it difficult to start at no load Therefore, in order to increase the utilization of the wind energy, it is desirable to make the cogging torque as small as possible The feature of the slot and pole number combinations q can be depicted by the slot FIG Effect of slot and pole number combinations (a) Flux linkage (b) Back-EMF (c) Cogging torque (d) Output torque 056631-5 Xu et al AIP Advances 7, 056631 (2017) TABLE III Basic differential parameters of the DRPM wind generators Machine type Fundamental EMF (V) Cogging torque (Nm) d in (5) Torque (Nm) Torque ripple (%) Output power (W) Copper loss (W) Iron loss (W) A B C D E F 156.6 0.783 -42.6 17.8 1586 59.7 23.2 200.6 0.732 -29 22.8 1103 23.8 22 176.8 0.094 -47.6 4.8 1770 81.6 19.6 202.7 0.082 10 -34.6 6.9 1307 39.4 16.8 198.1 0.065 11 -51.2 2.8 1910 83.2 14.4 205.1 0.033 13 -38.8 5.2 1462 49.7 11 number N s per pole and per phase m q= Ns c =b + pm d (5) where b is an integer and d is the denominator of the irreducible fraction c/d According to FIG (c) and Table III, it can be seen that the cogging torque decreases along with the increment of d and the difference for different combinations is quite large Consequently, during the generator design process the choice of slot and pole number combinations should be careful In the output torque, two kinds of pulsating torques exist One is cogging torque, the other is the ripple torque produced by the harmonic content of the current and voltage waveforms in the generator Based on FIG (d) and Table III, it can be seen that the average output torque is larger and torque ripple is smaller for type A, C and E (p=N s /2-1) than for type B, D and F (p=N s /2+1) In the DRPM wind generators, due to low frequency, losses in ferrite magnets can be neglected in comparison to the copper and iron losses Table III summarizes the copper losses and iron losses It can be seen that the higher pole number, the higher slot number, and the smaller turns per slot, but the larger turns per phase, thus the higher copper losses However, as pole number increases, the larger flux densities in the rotor cores bring larger iron losses From the comparison it can be seen that 18-slot/16-pole combination is a good choice for its high output torque, low torque ripple and low leakage flux V CONCLUSION This paper has deduced the main winding factor and compared the effect of N s =2p±2 combinations on performance of the DRPM wind generator The conclusions of this paper have been drawn based on the design conditions set in this paper During design process, the choice of slot and pole number combination should take into account the EMF, cogging torque, output toque and its pulsation as well as the losses ACKNOWLEDGMENTS This work was supported in part by the National Natural Science Foundation of China under grant 51407085, the Postdoctoral Science Foundation of China under Award No 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(2017) Effect of pole number and slot number on performance of dual rotor permanent magnet wind power generator using ferrite magnets Peifeng Xu,a Kai Shi, Yuxin Sun, and Huangqiu Zhua School of. .. comprehensive performance comparison of a DRPM wind generator using ferrite magnets with different slot and pole number combinations The main winding factors are calculated by means of the star of slots... contribution of this paper is the calculation of the winding factor using star of slots, as well as the comparison and analysis of the DRPM wind generators with different slot and pole a Corresponding