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第 33 卷 第 3 期中 国 电 机 工 程 学 报Vol.33 No.3 Jan.25, 2013622013 年 1 月 25 日Proceedings of the CSEE2013 Chin.Soc.for Elec.Eng.文章编号：0258-8013 (2013) 03-0062-13中图分类号：TM 85文献标志码：A学科分类号：47040高速永磁无刷电机电磁损耗的研究概况沈建新，李鹏，郝鹤，杨光(浙江大学电气工程学院，浙江省 杭州市 310027)Study on Electromagnetic Losses in High-speed Permanent Magnet Brushless Machines-the State of the ArtSHEN Jianxin, LI Peng, HAO He, YANG Guang(College of Electrical Engineering, Zhejiang University, Hangzhou 310027, Zhejiang Province, China)ABSTRACT: High-speed permanent magnet (PM) brushless machines have attracted extensive attentions, while their electromagnetic power losses and relevant reduction methods are critical research issues. Firstly, since the fundamental frequency is high (1 kHz), extra copper loss occurs due to the skin effect and the proximity effect of the stator windings. It can be suppressed by winding with thin wires in parallel. Moreover, due to the high alternating frequency of stator core field, iron loss increases significantly. It can be reduced by choosing a small number of poles, designing the stator cores with uncommonly low field, and using core materials with low specific iron loss. Further, as the frequencies of stator MMF harmonics and that of airgap permeance variation are some times higher than the fundamental frequency, rotor eddy current loss which is usually negligible in low or moderate-speed machines becomes remarkable in the high speed machines. It can be suppressed by reducing the stator MMF harmonics, decreasing the stator slot openings, enlarging the airgap length, axially segmenting the magnets, employing the rotor conductive shield, or circumferentially grooving the rotor retaining sleeve. Finally, appropriate control strategies, such as the phase-advancing control for PM brushless dc motors and the field-weakening control for PM synchronous machines, are beneficial to reduce the electromagnetic losses.KEY WORDS: high-speed electric machines; permanent magnet brushless machines; electromagnetic losses; stator extra copper loss; stator iron losses; rotor eddy current losses摘要：高速永磁无刷电机得到越来越多的关注，其电磁损耗 及抑制措施就是一个研究热点。首先，由于基波频率高(可基金项目：国家自然科学基金项目(51077116)；国家重点基础研究 发展计划项目(973 项目)(2011CB 707204)。Project Supported by the Natural Science Foundation of China (51077116); The National Basic Research Program of China (973 Program)(2011CB707204).达到 1 kHz 以上)，定子绕组的集肤效应和临近效应产生附 加铜耗。附加铜耗可以通过采用细导线并绕的方法来抑制。 其次，定子铁心中的磁场交变频率高，导致铁耗明显增加。 为降低定子铁耗，需要设计较少的电机极数、远低于常规电 机的定子铁心磁密，并采用低损耗的铁心材料。再次，由于 定子磁动势的谐波频率及气隙磁场的变化频率都数倍于基 波频率，在转子中产生涡流损耗，而这种涡流损耗在中、低 速永磁无刷电机中往往是忽略不计的。为抑制转子涡流损 耗，应减小定子磁动势的谐波分量，也可采取减小定子槽开 口、加大气隙长度、对永磁体进行轴向分块、采用转子导电 屏蔽层、对转子保护套周向开槽等措施。此外，适当的控制 策略(如永磁无刷直流电机超前触发、永磁同步电机弱磁控 制)也有助于减小电磁损耗。关键词：高速电机；永磁无刷电机；电磁损耗；定子附加铜 耗；定子铁耗；转子涡流损耗0INTRODUCTIONHigh-speed electric machines have found extensive applications 1-8 due to their superior merits such asi) high power density, which makes them particularly suitable for applications with strict volume limitation.ii) ability of directly driving high-speed loads, which eliminates the necessity of mechanical boost-up gearing system. For many loads (e.g., compressors), high-speed operation is desirable to enhance the system performance and to reduce the volume. While for many other loads (e.g., fly-wheel energy storage systems), high-speed operation is a basic requirement. Conventionally, such loads are driven with general-speed machines and gear boxes, causing large size, high cost, low efficiency, loud noise, and short第 3 期沈建新等：高速永磁无刷电机电磁损耗的研究概况63lifetime. However, these drawbacks can all be overcome by replacing the motor/gear system with a high-speed machine.Therefore, utility of high-speed machines can not only improve the power density of the electric machines themselves, but also enhance the power density, efficiency and reliability of the whole systems. Due to these advantages, high-speed electric machines have been extensively studied 9-13.However, it is difficult to make a strict definition for the high-speed electric machines. While defining the “high speed”, people should always take the machine power into account 8. Usually, the larger the power is, the lower the achievable “high speed”. Nowadays the said “high speed” versus the machine power can be roughly illustrated by Fig. 1. Obviously, higher speed is expectable in the future.Speed range/(kr/min)25015050the high-speed PM brushless machines 10, such as the rotor strength 12 and dynamics 18, thermal performance 3,23-25, bearing applications or bearingless design 13,15-16, and power losses 26-42. Like the power density, the loss density is also very high in high-speed machines 23-28 and may cause high temperature rise and even local over-heating, and consequent possible damage to the machine insulation, magnets and bearing lubrication, etc. Moreover, some losses which are negligible in the low or moderate-speed machines become rather significant. Therefore, it is always essential to investigate the power losses in the high-speed PM brushless machines. Of course, there are many types of power losses 29-34, 40, such as the electromagnetic losses, bearing loss, windage loss and some other stray losses. In this paper, only the electromagnetic losses and their reduction methods will be reviewed, from the points of view of machine design and control. It should be noted that the field variation in the PM brushless machines (i.e., rotating field for BLAC motors and stepping field for BLDC10102103104Power/W105106motors) 43 are similar to the rotating field in the induction machines, hence, the stator losses in these图 1 现阶段所能实现的高速电机转速范围与功率的关系Fig. 1 Range of currently achievable high speed versus machine powerBasically, high-speed machines should employ brushless configurations 14, such as the induction machine 6-7, the switched reluctance (SR) machine 15 and the permanent magnet (PM) brushless machine. Each of these configurations has its own merits and demerits 7-8, whilst the PM brushless machine is, in general, the most attractive 1,9. Moreover, there are two drive modes for the PM brushless machines, viz., the sine-wave drive (so-called the brushless ac (BLAC) machine, or PM synchronous machine (PMSM)4,8,16-18 and the square-wave drive (the so-called brushless dc (BLDC) machine) 5,19-22. Both drives have similar machine and inverter topologies, hence, they will be discussedtogether in this paper, with a unified name as PMtwo categories of electric machines are similar. Thus, the stator losses analysis and reduction methods for the PM brushless machines are valuable for the induction machines. Nevertheless, the field variation in the SR machines is quite different, hence, their stator losses are also unique, and will not be included hereafter.1 STATOR COPPER LOSSThe stator copper loss can be calculated with the current RMS value and the winding resistance. However, during high-speed operation, the actual operational resistance (i.e., the ac resistance, Rac) can be larger than what is measured with a conventional ohm meter (i.e., the dc resistance, Rdc). This is because the skin effect is significant 1,34,38,41, reducing the effective cross area of wires.The skin depth of the wire can be calculated as:brushless machine.d = 2/ (wms )(1)There are many issues needing further studies forwhere m and s are the wire permeability and64中 国 电 机 工 程 学 报第 33 卷conductivity, respectively, and w is the electric angular frequency of each harmonic of winding current. Usually, that of the fundamental current is used as w. Thus, if the wire radius r is larger than the skin depth, it can be roughly regarded that instead of the full cross section area of the wire, only the outer-ring area with a depth of d is effective for the current flow. Hence, the actual winding resistance Rac becomes larger. For simplicity of calculation, Rac can be solved as 38:operation frequency. Another solution is to use litz wires, which actually have many thin wires in parallel. However, it should be pointed out that there is an optimal number of parallel wires for a certain frequency, beyond which the skin effect will hardly be further cured 34,38,41. This can be seen from Fig. 338, which gives the relationship between the extra copper loss (PCu_ex) due to the skin effect and the proximity effect and the number of parallel wires (nw) in a 75kW and 60 kr/min PM machine. Nevertheless,Rac = KR Rdc(2)this optimal number is usually very high, and inwhere KR is the skin-effect coefficient, which is related to the frequency w and the wire radius r, as shown in Fig. 2 41.6KR4200.1110r/dpractice the number of parallel wires hardly reaches it. Other methods to reduce the skin effect and/or the proximity effect include 34,41: smoothening the current waveform to reduce the harmonics, reducing the field leakage in the slots, designing the appropriate slot-openings, and fixing the winding wires at proper position in the slots.600PCu_ex/W500图 2 绕组交、直流电阻比与导线半径、透入深度比的关系Fig. 2 Relationship between winding ac/dc resistances ratio and wire radius/skin-depth ratio 41Another practical method is to directly estimate4003000481216nwthe skin-effect extra copper loss with 38:P= KfbCu_skinskin(3)图 3 绕组附加铜耗与导体并联根数的关系38Fig. 3 Relationship between extra copper loss and the number of parallel wires 38in which f is the fundamental frequency, and thefactors Kskin and b can be experimentally determined.Moreover, during high-speed operation, the proximity effect may also be remarkable 5,34,44-45, causing another extra loss in the windings, which can be approximately calculated as5,34,41:pB2 w2 d 4l2 STATOR IRON LOSSDue to the high operation speed, the alternating frequency of magnetic field in the stator iron core is high, resulting in significant iron loss. There are many methods to predict the stator iron loss. For example, asimple analytical model, using the factor of specificP=w (4)Cu_pr128riron loss, is given below1:21.3where Bw is the flux density at the position of windingPFe = CFe K0 (B / B0 ) ( f / f0 )GFe(5)wires, d and l are the wire diameter and length, respectively, and r is the wire resistivity.To reduce the influence of both the skin effect and the proximity effect, the windings can be wound with some thin wires in parallel16, rather than with one thick wire. Make sure that the wire radius is similar to or smaller than the skin depth at the highestwhere K0 is the specific iron loss at the nominal flux density B0 and frequency f0 in the iron core with a per unit weight, B and f are the actual flux density and frequency, GFe is the iron core weight, and CFe is a calibration factor for the material characteristic of being anisotropic. Since the field distribution in the iron core is not even, whilst the actual flux density第 3 期沈建新等：高速永磁无刷电机电磁损耗的研究概况6523/2and especially the actual frequency may be far away from the nominal values, the above analytical model is not accurate enough. Thus, the more complicated Bertotti model, considering the three components of the iron loss, can be used 26,38:lumped-parameter magnetic circuit method is more accurate than the analytical models, but is rather time-consuming.The most effective and accurate method is the time-step finite element analysis (FEA)29-32, whichaPFe =Ph + Pc + Pe = Kh B f + Kc (Bf )+ Ke (Bf )(6)usually requires commercial software. FEA can givewhere Kh, Kc and Ke are the coefficients of hysteresis loss (Ph), classical eddy current loss (Pc) and excessive loss (Pe), respectively, whilst a is the power exponent of the hysteresis loss. Details of determining Kh, Kc, Ke and a are given in 26,29,38, by measuring the overall iron loss at different frequencies and then separate its three components. Since the coefficients are determined with experiments, the iron loss due to both alternating and circular rotational magnetizations can be included 29,41-42. Nevertheless, these coefficients are actually variables with f and B, hence, polynomials are sometimes preferable to express thecoefficients with higher accuracy 27. Moreover, since a high-speed PM brushless motor is driven with an inverter, its armature current contains harmonics which cause extra iron loss. Thus, (6) can be further improved as30:PFe = Ph + Pc + Pedetailed field distribution in each part 26 or even each element30 of the iron core, and also the iron loss distribution, such that the total iron loss can be obtained with accumulation.According to the mechanism of the stator iron loss, in order to reduce this loss in the high-speed PM brushless or induction machines, it is desirable toi) Design with a small number of poles. Usually 2 poles or 4 poles are preferred 1,10.ii) Avoid local saturation in the iron core 7. FEA can be used to investigate the field distribution over the full load range.iii) Employ a low field in the iron core 10,16. The core flux density of a general-speed machine can be around 1.8 T, however, it should be decreased to around 1.0 T in the high-speed machines, or even down to 0.5 T if the machine volume is not strictly limited. Of course, to compensate the decrease of theNmagnetic load, the machine electric load should beaaPh = Kh kf (Bk1 + Bk 2 )k =1Nincreased 16, resulting in a higher stator copper loss.Clearly, the iron loss is usually much higher than theP = Kk 2 f 2 (B2+ B2 )(7)cc k =11 Tk1dB (t) 2k 2ydB (t) 2copper loss in the high-speed machines, thus, appropriately adjusting the ratio of iron loss andP = K (x+)3/ 4 dtcopper loss is beneficial to decrease the overall loss. ee T 0dtdtwhere k is the order of harmonics, Bx and By are the flux density in the radial and tangential directions, respectively, whilst the subscripts “1” and “2” stand for the maximum and minimum values of the flux density.To consider the influence of unequal field distribution inside the iron core, the lumped-parameter magnetic circuit method can be used. By dividing the core to some parts (such as the tooth tips, tooth bodies, back iron, etc.) and assuming that the field in each part is equal, this method can be used to solve the flux density and calculate the iron loss with (5) or (6) for each part, and finally obtain the total iron loss. Theiv) Use high grade core materials. High-silicon steel laminations with proper heat treatment usually give a solution for low iron loss with low cost 7,16. Furthermore, thin (0.10.2 mm) silicon steel laminations are often preferred. Other material laminations, such as those of permalloy and amorphous alloy 10, can provide lower iron loss than the silicon steel laminations, hence they are also attractive options. However, the thinner the laminations are, the higher price and the more difficult processing. For example, the punching dies must be very precise (meaning high cost and critical requirement on manufacture facilities) if they are used to punch the laminations thinner than 0.2 mm.66中 国 电 机 工 程 学 报第 33 卷Another optional material is the soft magnetic composite (SMC)24-25. Its made of coated iron powders, and can be manufactured to a net shape of the iron core. SMC has a very low eddy current loss, but a relatively high hysteresis loss. Only when the field alternating frequency is over 1 kHz, the eddy current loss plays a dominant role in the overall iron loss, then the SMC can perform better than thecommonly-used silicon steel laminations.ii) Spatial harmonics of the stator magnetic motive force (MMF).iii) Variation of airgap permeance due to the stator slots, which always exists even if there is no current in the armature windings.Therefore, the rotor eddy current loss should be reduced from the related factors. In general, it can be calculated as47:e e r tk3 ROTOR EDDY CURRENT LOSSP = 1Teei =1J 2 D s -1l dt(8)3.1 Mechanism and EffectsRotor eddy current loss is usually negligible in moderate or low-speed PM brushless machines. However, this is not the case in high-speed machines 1,19.In general, the rotor eddy current loss is just a small portion in the overall power loss. However, it may cause over-heating on the rotor due to the weak cooling condition, especially if an inner rotor is protected with a fiber retaining sleeve which has a low thermal conductivity. As an example, Fig. 4 shows that the rotor eddy current loss (Pr) is less than 1% of the total power losses in a 40 kW and 40 kr/min PM BLAC motor, but the rotor temperature can be up to150 although the winding temperature is 110 only 16. Over-heating on the rotor may permanently demagnetize the magnets, shorten the lifespan of bearing lubrication, and damage the retaining sleeve if its thermal expansion is smaller than that of the inside parts. Therefore, it is very important to analyze and reduce the rotor eddy current loss. The purpose is not just to enhance the machine efficiency, but more importantly, it is to avoid over-heating of the rotor.The rotor eddy current loss is mainly caused by the following factors 3,16,28,39,46:i) Time harmonics in the armature currents.PCu(7%)where Je is the eddy current density in each element,De is the element area, lt is the axial length, and sr is the conductivity. However, both Je and De need to be solved individually for each element, whilst the integration is not easy to implement, either. Moreaccurate analytical models have been given in35, agreeing well with the FEA for a 75 kW and 60 kr/min PM motor prototype, but are more complicated to solved. Therefore, the rotor eddy current loss is usually investigated with FEA software directly 39,48.To reduce the rotor eddy current loss, issues in the following sub-sections should be considered. Although most data given below were obtained with small power (23 kW) high-speed PM BLDC motors, the methods of analysis and the consideration issues are of reference for larger power machines.3.2 Influence of Stator Current Time HarmonicsFor PM BLDC machines, the armature currents are ideally of square-wave, and practically with some distortion, both containing time harmonics. However, such harmonics are mainly at relatively low frequencies, hence, the caused eddy current loss in the rotor is not severe.On the other hand, the PWM chopping on theinverter brings high frequency current harmonicsPair(40%)Pr(1%)PFe(53%)35-37,41. Especially, the high-speed PM brushlessmachines usually have small winding inductances, whilst the inverter PWM frequency is limited, hence, the PWM chopping will result in significant current ripples and harmonics, and consequently sever eddy图 4 损耗比例16Fig. 4 Percentage of power losses 16current loss in the rotor. Therefore, generally speaking, it is not recommended to apply PWM chopping on the第 3 期沈建新等：高速永磁无刷电机电磁损耗的研究概况67inverter for high- speed operation. If variable speed is required, a PWM chopper and a dc filter can be used in front of a non- PWM inverter. Another solution is to apply external line inductors 3, which can smoothen the motor currents, but are usually bulky and may decrease the machine time response.The rotor eddy current loss due to the time harmonics can be calculated with FEA software, but is difficult to measure directly. On the other hand, the significance of the rotor eddy current loss can be investigated with the rotor temperature rise, sincethese two issues are closely related. Fig. 5 shows theeddy current loss and temperature rise in the rotor. Again, the aforementioned 3 kW and 120 kr/min prototype motor was driven with the BLAC mode, and the measured rotor temperature rise validated the extra rotor eddy current loss (Fig. 6). Therefore, it should be very careful to run the machine at high speed in the BLAC mode.BLDC PWM inverter BLAC PWM inverter200160Tr/K12080400measured rotor temperature rise (Tr) of a prototype high-speed PM BLDC motor, its ratings being 3 kW507090nw/(kr/min)110130and 120 kr/min, and its load being an air compressor. The prototype motor was driven with a “PWM inverter” and a “PWM chopper + non-PWM inverter”, respectively. The speed (n) and load conditions for these two drive modes were the same. Clearly, the PWM chopping on the inverter causes more current harmonics and consequently more rotor eddy current loss. At the maximum speed (120 kr/min), there was almost no PWM chopping on the inverter, hence, the temperature rise with the “PWM inverter” was almost the same as that with the “PWM chopper”.On the other hand, for PM BLAC machines, the currents are ideally sinusoidal, having no time harmonics. However, they are actually modulated by the inverter PWM chopping. Such a modulation is usually satisfactory over the low to moderate speed range. However, over the high speed range, since the current fundamental frequency is not far away from the PWM frequency, the modulation can hardly2p-3s non 2p-6s over 2p-6s nonpresent good sine-waves of the currents, causing extra图 6 变速永磁无刷直流和交流电机的转子温升比较Fig. 6 Comparison of rotor temperature rise of variable speed PM BLDC and BLAC motors3.3 Influence of Stator MMF Spatial HarmonicsThe spatial harmonics of stator MMF are mainly determined by the stator winding structure. Fig. 7(a) shows three common structures for high-speed PM BLDC machines: 2-pole 3-slot non-overlapping windings (denoted as “2p-3s non”), 2-pole 6-slot overlapping windings (denoted as “2p-6s over”), and 2-pole 6-slot non-overlapping windings (denoted as “2p-6s non”), respectively. For these different stators, the rotor eddy current loss (Pr) can be calculated with, for example, the equivalent current sheet-based(a) Common machine structuresBLDC PWM inverter BLDC PWM chopper200160Tr/K1208040050709011013020Pr/W100306090nw/(kr/min)120150nw/(kr/min)图 5 变速永磁无刷直流电机不同PWM 斩波方式与转子温升Fig. 5 Rotor temperature rise at various PWM chopping modes for variable speed PM BLDC motor(b) Rotor eddy current loss with different stator structures图 7 负载条件下永磁无刷直流 电机转子涡流损耗受定子结构的影响28Fig. 7 Influence of stator structures on rotor eddy current loss in loaded PM BLDC motors 2868中 国 电 机 工 程 学 报第 33 卷analytical model or FEA software. Fig. 7(b) compares the FEA results for three prototype PM BLDC motors 28, which have the same airgap length (3 mm) and slot opening width (3 mm), the same rotor and the same ratings (2.3 kW and 150 kr/min), and are all loaded with the same air compressor. Clearly, among these machines, the “2p-6s over” and “2p-6s non” have the similar performance, whilst the most common “2p-3s non” structure is the worst, thus, should be carefully considered for utility in high- speed motors.3.4 Influence of Stator Slot OpeningsThe stator slot openings also have influence on the stator MMF spatial harmonics, since the MMF can be expressed with equivalent current sheets located at the slot openings. Therefore, the slot openings have the same width as the current sheets 41. However, such influence on the MMF spatial harmonics is much less than that of the stator structure, hence it is usually neglected.The major influence of the stator slot openings is the variation of airgap permeance. Basically, the larger the slot opening is, the severer the permeance variation, and the more significant the rotor eddy current loss 36. Therefore, it is essential to reduce the slot openings. However, if the slot opening is too small, winding assembling will be quiet difficult. On the other hand, large (14 mm) physical airgap is usually applied in the high-speed PM brushless machines, therefore, the influence of slot openings is actually minor. This can be validated by Fig. 8, which gives the calculated rotor eddy current loss (Pr) of the aforementioned 2.3 kW and 150 kr/min prototypes with different slot openings (ws), all under the no-load2p-3s non 2p-6s over 2p-6s non4Pr/W2condition 28. Similar conclusion has been drawn in 36,39,41. It should be pointed out that, under the no-load condition, the rotor eddy current loss is solely caused by the slot openings, hence, it can straightly reflect the slot opening influence.Sometimes slotless stator structure is used in high-speed machines, in which the armature windings are located in the airgap. This can help to reduce the eddy current in the rotor, and also suppress the cogging torque. However, since the windings are directly located in the strong alternating magnetic field in the airgap (note, the field in the stator slots is usually much weaker), the skin effect in the copper wires will be more significant than in the slotted windings. Moreover, in general, the slotless windings are mechanically weaker than the slotted windings, so they are less suitable for large machines.3.5 Influence of Airgap LengthObviously, the larger the airgap is, the lower influence of the aforementioned three factors which cause the rotor eddy current loss, since the rotor is farther away from the stator. Fig. 9 shows the variation of the rotor eddy current loss with the physical (not the magnetic) airgap length (la) for the aforementioned PM BLDC motors running under the rated condition (2.3 kW and 150 kr/min)28. As can be concluded, a large airgap is usually preferred for the high-speed PM brushless machine, and this has also been verified in 36,41.It should also be considered that the airgap field decreases if the airgap is enlarged, thus, more magnets should be used, or else the electric load of the armature windings should be increased. On the other hand, the rotor air-friction loss is also related to the2p-3s non 2p-6s over 2p-6s non50Pr/W30023456ws/min图 8 空载条件下永磁无刷直流 电机转子涡流损耗受定子槽开口的影响28Fig. 8 Influence of stator slot openings on rotor eddy current loss in no-load PM BLDC motors 2810123la/mm图 9 负载条件下永磁无刷直流 电机转子涡流损耗受气隙大小的影响28Fig. 9 Influence of airgap length on rotor eddy current loss in loaded PM BLDC motors 28第 3 期沈建新等：高速永磁无刷电机电磁损耗的研究概况69airgap. Usually, the loss reaches the maximum when the airgap length is between 1 and 1.5 mm 11. Therefore, in actual design of the moderate or small-power high-speed PM brushless machines, the physical airgap length is often designed within the range of 1.52.5 mm.3.6 Influence of Magnet SegmentingMagnet segmenting is a common technique to reduce the eddy current in the conductive magnets, such as sintered NdFeB or SmCo magnets. However, in the high-speed PM brushless machines, magnet segmenting does not certainly reduce the eddy current. Regarding the aforementioned 2.3 kW and 150 kr/min motor prototypes, Fig. 10 shows that a small number of circumferential segmenting even increases the eddy current loss in the magnets (Pm)28. The reason of such a phenomenon is that the eddy current not only causes loss, but also excites a magnetic field which suppresses the variation of the airgap field. Therefore, when the magnet is segmented to a small number of pieces, the variation of airgap field is less suppressed. Only when the magnet is segmented to sufficient pieces, the overall rotor eddy current loss decreases. However, for actual products, it is not practical to circumferentially segment themagnet to so many pieces.On the other hand, axial segmenting of magnets can more effectively obscure the eddy current flow path and reduce the loss. This can be seen from Fig. 11, the results were obtained with a 3 kW and 15 kr/min fly-wheel PM machine 39. In general, the axial segmenting of the magnets is more effective than the circumferential segmenting for eddy current loss reduction, and is somewhat easier for manufacture.30Pm/W2010054Pm/W32101248Number of magnet segments图 11 负载条件下永磁无刷电机的 永磁体涡流损耗受其轴向分块数的影响39Fig. 11 Influence of magnet axial segmenting on magnet eddy current loss in loaded PM brushless machine 393.7 Influence of Retaining Sleeve, Conductive Shield and Squirrel CageThe high-speed PM brushless machine usually uses a nonmagnetic retaining sleeve to protect the rotor against centrifugal force. The sleeve can be made of metal such as stainless steel, Titanium or Inconel, or made of fiber such as glass fiber or carbon fiber. Clearly, eddy current exists in the conductive metal sleeve, resulting in strong loss. This can be validated by Fig. 12(a)28. The results were obtained with two 2.3 kW and 150 kr/min PM BLDC motors which were almost the same, except that the retaining sleeves were of carbon fiber (note, carbon fiber is slightly conductive) and Titanium, respectively. Basically, the eddy current loss in the retaining sleeve increases with the sleeve conductivity, and reaches a maximum value if the conductivity is around the values of aluminum or copper 41. Hence, from this point of view, a metal sleeve is worse than a nonmetal sleeve.However, it can also be noticed from Fig. 12(a) that the eddy current loss in the magnet is reduced by using the metal sleeve. This is because the eddy current in the sleeve helps to smoothen the varying field in the magnets. Due to this mechanism, if a shield with high conductivity (e.g., copper shield) is applied on the rotor, its eddy current can help to reduce the losses in the other parts of the rotor.1248121836Although the eddy current leads to an extra loss in theNumber of magnet segments图 10 负载条件下永磁无刷电机的 转子涡流损耗受永磁体周向分块数的影响28Fig. 10 Influence of magnet circumferential segmenting on rotor eddy current lossin loaded PM brushless machine 28shield itself, the loss is not high because the resistance of the shield is small. Therefore, the overall rotor eddy current loss can be reduced by employing the conductive shield, as validated in Fig. 12(b)28. Obviously, the conductive shield should be similar to70中 国 电 机 工 程 学 报第 33 卷R: in retaining sleeve; M: in magnets;Y: in rotor yoke; O: overallOOMRMRYY30Pr/W20100with carbonfiber sleevewith titanium fiber sleevedemagnetization but is more complicated.3.8 Influence of Grooves on Metal Retaining SleeveUsually the metal retaining sleeve has a smooth outer profile. However, if shallow circumferential grooves are made, Fig. 13(a), they can obscure the flowing path of the eddy currents, and reduce the(a) Rotor eddy current losses with different retaining sleevesR: in retaining sleeve; S: in conductive shield;M: in magnets; Y: in rotor yoke; O: overall.OMSORYSRMY30power loss. Fig. 13(b) illustrates the influence of thegrooves depth (d ) on the rotor eddy current losses (P )srPr/W20100with carbon fiber sleevewithout copper shieldwith carbon fiber sleeve with copper shieldin a 10 kW and 70 kr/min machine 50. Clearly, grooves with an appropriate depth are beneficial for loss reduction. Moreover, such grooves hardly deteriorate the strength of the retaining sleeve. And, they can enhance the cooling condition of the rotor, since a larger surface area is achieved. They can even(b) Reduction of rotor eddy current losses by conductive shield图 12 负载条件下永磁无刷直流 电机转子涡流损耗受不同材料保护套及导电环的影响28Fig. 12 Influence of retaining sleeve with different materials and conductive shield on rotor eddy current losses for loaded PM BLDC motor 28or slightly thicker than its skin depth at the maximum operating frequency 19, 41.Moreover, it should be pointed out that although the amount of loss reduction is small, the rotor temperature decrease is really significant.The conductive shield is usually made of copper, and is placed inside the retaining sleeve due to its weak strength.If interior permanent magnets are used for high-speed motors, they can be wrapped with a copper shield or coated with a copper layer 49. This canslightly reduce the air-friction loss 11. On the other hand, axial shallow slots on the retaining sleeve surface can also help to reduce the rotor eddy current loss 51, and bring little extra air-friction loss 11. However, the axial slots will reduce the mechanical strength of the retaining sleeve, possibly worsen the rotor dynamic balance, and are relatively more difficult to manufacture than the circumferential grooves. Therefore, the axial slots are less suitable for practical high-speed machines.(a) Rotor with circumferentially grooved sleeve 8060Pr/W40Loss in sleeveLoss in magnetalso reduce the eddy current in the magnets, and20protect the magnets from the demagnetizing force of0Loss in rotor yoke0.00.10.20.30.40.5the armature currents. Also, the conductive shield can be replaced with a squirrel cage 49, which is commonly used in line-start permanent magnet synchronous machines. The cage can not only reduce the rotor eddy current losses, but also help the magnets to withstand demagnetization from the armature currents. And, it can also increase the machine torque density. In practice, both single-cage and dual-cage structures can be considered, whilst the latter has a better ability to protect the magnets fromds/mm(b) Variation of eddy current losses with different groove depth图 13 转子涡流损耗受保护套表面周向开槽的影响50 Fig. 13 Influence of retaining sleeve circumferential grooves on rotor eddy current losses 504 Effect of Control StrategiesThe performance (including the electromagnetic losses) of a high-speed PM brushless machine is closely related to the control strategies 27. Thus, it is essential to utilize the proper control strategies so as第 3 期沈建新等：高速永磁无刷电机电磁损耗的研究概况71to minimize the power losses.In PM BLDC machines, usually the applied terminal voltage is in phase with the back electromotive force (EMF), in other words, each phase starts to be energized at the moment of 30 electric degrees after its back EMF zero-crossings. However, during high-speed operation, the influence of winding inductances is significant, which causes retarding of the phase currents 22. This will further increase both peak and RMS values of the currents, and also increase the electromagnetic losses. An example with a 5 kW and 120 kr/min PM BLDC motor was given in 22, showing that the current retarding caused 13% extra currents and 0.1 kW extra electromagnetic losses in the machine. Therefore, to overcome the problem of current retarding, phase-advancing is usually required, by firing the inverter in advance with an appropriate phase angle. Now that the phase-advancing control is applied, large winding inductances become acceptable. Moreover, large inductances help to smoothen the winding currents, and further suppress the rotor eddy current loss and stator iron loss.The advancing angle should vary dynamically,according to the machine speed and load, as well as the parameters such as the winding inductances and resistance. Therefore, to realize the phase-advancing control, a continuous signal of the rotor position, the same as what is obtained with an encoder or a resolver, is required 20. The conventional Hall-effect sensors for PM BLDC machines provide discrete position signals only, hence they are not directly applicable for the phase-advancing control 22,52. Moreover, encoders or resolvers are not suitable, either, due to the difficulty of coupling them on the high-speed machine shaft.For PM BLAC machines, the phase-advancing control is also desirable, in order to achieve, for example, field-weakening over the high-speed range or utility of the reluctance torque. The field- weakening control is beneficial to reduce the iron loss during high-speed operation. The PM BLAC machines inherently require a continuous signal of the rotor position.To obtain the continuous rotor position signal, various methods can be used. For example, discrete position signals are obtained with the Hall-effect sensors or the back EMF-based sensorless method, and then the machine speed is calculated, whilst the continuous position signal is estimated with integration of the speed 22,52-53. Otherwise, the continuous position signal can be directly estimated with a sensorless control method, such as the rotor flux observer-based method 20,54, which has been successfully applied for the high-speed machines of up to 120 kr/min 54.5 CONCLUSIONSWhen a PM brushless machine operates at high speed, its electromagnetic power losses can be much severer than those at low or moderate speed. Moreover, the high-speed machine has a relatively small volume. Therefore, its loss density can be very high, resulting in many undesirable disadvantages.This paper gives a survey of the research on the major electromagnetic losses, including the extra copper loss of stator winding due to the skin effect and the proximity effect, the significant stator iron loss due to the high operating frequency, and the specific rotor eddy current losses which are influenced by the stator current time harmonics and MMF spatial harmonics, the stator slot openings, the airgap length, and the rotor retaining sleeve and conductive shield. All these electromagnetic losses are also related to the control strategies. 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