高速永磁无刷电机电磁损耗的研究概况_英文_沈建新.pdf

第 33 卷 第 3 期 中 国 电 机 工 程 学 报 Vol.33 No.3 Jan.25, 2013 62 2013 年 1 月 25 日 Proceedings of the CSEE 2013 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 Art SHEN 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 0 INTRODUCTION High-speed electric machines have found extensive applications 1-8 due to their superior merits such as i) 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 63 lifetime. 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. 250 150 50 10 102 103 104 106105 Power/W Speed range/(kr/min) 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 power Basically, 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 discussed together in this paper, with a unified name as PM brushless machine. There are many issues needing further studies for the 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 BLDC motors) 43 are similar to the rotating field in the induction machines, hence, the stator losses in these two 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 LOSS The 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: 2/ () (1) where and are the wire permeability and 64 中 国 电 机 工 程 学 报 第 33 卷 conductivity, respectively, and is the electric angular frequency of each harmonic of winding current. Usually, that of the fundamental current is used as . 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 is effective for the current flow. Hence, the actual winding resistance Rac becomes larger. For simplicity of calculation, Rac can be solved as 38: acdcR RK R (2) where KR is the skin-effect coefficient, which is related to the frequency and the wire radius r, as shown in Fig. 2 41. 0.1 110 r/ KR 6 4 2 0 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 41 Another practical method is to directly estimate the skin-effect extra copper loss with 38: Cu_skinskin PKf (3) in which f is the fundamental frequency, and the factors Kskin and 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: 224 w Cu_pr 128 Bd l P (4) where Bw is the flux density at the position of winding wires, d and l are the wire diameter and length, respectively, and 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 highest 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, this optimal number is usually very high, and in practice 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. nw PCu_ex/W 600 500 400 300 08 16412 图 3 绕组附加铜耗与导体并联根数的关系38 Fig. 3 Relationship between extra copper loss and the number of parallel wires 38 2 STATOR IRON LOSS Due 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, a simple analytical model, using the factor of specific iron loss, is given below1: 21.3 FeFe000Fe (/) (/)PC KB BffG (5) where 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 65 and 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: 23/2 Fe ()() hcehce PPPPK B fKBfKBf (6) where Kh, Kc and Ke are the coefficients of hysteresis loss (Ph), classical eddy current loss (Pc) and excessive loss (Pe), respectively, whilst is the power exponent of the hysteresis loss. Details of determining Kh, Kc, Ke and 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 the coefficients 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: Fe 12 1 2222 12 1 2 2 3/4 0 () () d( ) d( )1 ()d dd hce N hhkk k N cckk k T y x ee PPPP PKkf BB PKk fBB B t B t PKt Ttt (7) where 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. The 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, which usually requires commercial software. FEA can give detailed 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 to i) 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 the magnetic load, the machine electric load should be increased 16, resulting in a higher stator copper loss. Clearly, the iron loss is usually much higher than the copper loss in the high-speed machines, thus, appropriately adjusting the ratio of iron loss and copper loss is beneficial to decrease the overall loss. iv) 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 the commonly-used silicon steel laminations. 3 ROTOR EDDY CURRENT LOSS 3.1 Mechanism and Effects Rotor 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 to 150 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. PFe(53%) PCu(7%) Pair(40%) Pr(1%) 图 4 损耗比例16 Fig. 4 Percentage of power losses 16 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: 21 1 1 d k eeert i e PJl t T (8) where Je is the eddy current density in each element, e is the element area, lt is the axial length, and r is the conductivity. However, both Je and e need to be solved individually for each element, whilst the integration is not easy to implement, either. More accurate analytical models have been given in35, agreeing well wit