三次谐波法无传感器控制的高速永磁无刷直流电机的研究
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摘要
高速永磁无刷直流电机具有效率高、功率密度大等优点,因此在涡轮增压器、高速加工中心、飞轮储能、电动工具、空气压缩机、分子泵等许多领域有着广阔的应用前景,成为各国学者的研究热点。高速永磁无刷直流电机设计牵涉到转子损耗、轴承技术、转子动力学、等电磁技术与机械技术,必须重点考虑。
高速永磁无刷直流电机正因为功率密度大、体积小,其损耗密度也很大,因此电机的温升往往比较高,所以当霍尔元件这一类的位置传感器安装在电机内部时往往无法正常工作。另外,位置传感器的使用也会受到体积上的限制。在功率较大的电机中,位置传感器信号也容易受到干扰。此外,永磁无刷直流电机高速运行时通常需要不同程度的超前触发控制,但直接使用转子位置信号进行换相时无法实现可变的超前触发控制。
为了解决位置传感器带来的各种缺陷,许多学者开展了无传感器控制技术的研究,其主要思想是利用电机绕组中的有关电信号,通过适当的方法估算出转子的位置和转速,以此来取代转子位置传感器。在各种转子位置和速度的检测方法中,最常用的是通过检测每相反电势或三次谐波反电势来获得转子的位置信息。每相反电势法容易实现,但续流二极管导通引起的电压脉冲将干扰该信号。尤其是在高速、重载、或者绕组电气时间常数大等情况下,续流二极管导通角很大,此时通过检测每相反电势过零点的方法并不适合无位置传感器运行。相对于每相反电势法,三次谐波反电势法不受二极管导通角和逆变器PWM斩波的影响,对滤波器要求低,有更宽的调速范围。
本文针对一台80,000r/min,15kW的高速永磁无刷直流电机及其基于三次谐波反电势的无位置传感器控制策略,研究了电机设计和控制的若干重要问题。
1、研究了不同定子结构对三次谐波反电势的影响。对3齿2极和6齿2极集中绕组结构进行了对比研究,前者由于三次谐波的绕组系数为0,其相绕组中并不包含三次谐波反电势,因此其磁链和相反电势接近正弦分布,故不适合应用三次谐波反电势控制。后者的三次谐波绕组系数为1,其磁链和每相反电势包含大量的三次谐波,其波形远远偏离了正弦分布,因此适合三次谐波反电势控制,但基波绕组系数为0.5,绕组得不到充分利用。结合以上两种结构的优缺点,对不同齿宽(注：小齿为辅助齿)的6齿2极结构进行了研究,发现该结构既能利用三次谐波反电势控制,又能提高绕组的利用率。同时,也对各种结构电机的电感与单边磁拉力进行了对比分析。分析表明,由于3齿2极和不等齿宽6齿2极结构均具有空间不对称性,在电机运行时,具有较大的单边磁拉力,电机的噪声较大,影响轴承的寿命。因此最终采用等齿宽6齿2极集中绕组的对称结构。
2、研究了转子结构对电机气隙磁场三次谐波和三次谐波反电势的影响。对电机中的气隙磁场进行有限元分析与解析计算。在采用表面粘贴磁瓦时,随着极弧系数的减小,气隙磁场的分布越来越偏离正弦,气隙磁场中的三次谐波也会相应地增加。这有利于增大每相反电势中的三次谐波。但同时,气隙磁场中的基波随永磁体极弧系数的减小而减小。由于气隙磁场的畸变增加了气隙磁场中的谐波,使电机定子铁耗增大,将影响电机的性能。因此,为了提高气隙磁场中的三次谐波同时又不减小气隙磁场中的基波,采用“平行充磁且每极分两块”的结构。对不同的转子磁瓦分块数的气隙磁场进行分析,可知随着分块数的增加,气隙磁场分布趋于径向充磁结构的分布,接近方波。随着分块数的增加,气隙磁场中基波分量也随之增加,但当每极转子分块数为2块时,气隙磁场中的三次谐波最大。因此为了提高利用三次谐波反电势控制时的抗干扰能力,采用转子每极磁瓦分块数为2的结构。对“平行充磁且极弧系数小于1”、“平行充磁且每极磁瓦分两块”、“径向充磁且极弧系数为1”共三种转子结构进行了研究。研究发现“平行充磁且极弧系数小于1”、“平行充磁且每极磁瓦分两块”这两种结构均能在电机相绕组中产生足够大的三次谐波反电势。其次,由于转子损耗在中、低速无刷直流电机中往往是可忽略的,但是在高速无刷电机中比较严重,能引起转子永磁体过热和不可恢复性退磁。因此,对三种不同的转子结构引起的额定负载转矩下的转子涡流损耗进行了对比研究,结果表明：“平行充磁且极弧系数小于1”结构引起的转子涡流损耗小于“平行充磁且每极分两块”的结构,“径向充磁且极弧系数为1”结构的转子涡流损耗小于“平行充磁且极弧系数小于1”和“平行充磁且每极分两块”的结构。但“径向充磁且极弧系数为1”的结构应用较少,永磁体充磁时需要专门的工装夹具,加工困难。“平行充磁且极弧系数小于1”结构和“平行充磁且每极分两块”的结构容易实现。
3、研究了基于三次谐波反电势的无位置传感器超前触发控制。利用三次谐波反电势控制时,用比较器产生的过零点信号与电机触发信号密切相关。在实际系统中并不能确保比较器产生的过零点信号并不包含噪音信号。如果信号中噪音信号被控制系统误认为有效信号,将导致错误的换向信息,并且一旦产生一次错误的换向状态,将导致整个控制系统的崩溃。因此为了滤除噪音信号,有必要从软件上进行数字滤波,判断是否真正的发生信号跳变。采用数字滤波,必然导致信号滞后,进而引起电机的滞后换相。滞后的时间与数字滤波的深度有关。对于高速电机,将产生较严重的滞后。由于数字滤波引起滞后触发,电机电流变大,同时整个系统的功率因数、效率、功率输出能力降低、电机的温升更严重,对电机的冷却系统也提出了更高的要求,因此有必要采取超前触发控制。电机运行时,由于转子转动惯量的作用,其电周期不会发生突变,可以认为前一个换向周期的时间基本等于后一个换向周期,因此,如果知道前一个换向周期的时间,同时知道由于数字滤波产生的滞后时间,然后用延时导通来实现下一拍换相的正常触发控制甚至超前触发控制,研究表明超前触发可以明显的提高系统地功率因数、效率、输出功率,同时减小了损耗。
在论文的科研工作中,解决了以上电机设计与控制方面的重要问题,并制作了样机。相关实验也证明了理论分析、设计措施与控制方法的正确性。
Due to the advantage of high efficiency and power density, high-speed permanent magnet brushless DC (BLDC) machines are emerging as a key technology for applications such as turbocharger, spindle drives, flywheel energy storage system, machine tools, compressors, molecule pumps. Researchers all around the world are getting more and more attention on high-speed machines. However, their high rotation speed demands that careful consideration should be given to both electromagnetic and mechanical design issues, such as e.g. rotor loss, bearing technology, rotor dynamics, and aerodynamic loss.
Since high-speed machines have high power density and small volume, their loss density is also high. In result, the temperature rise inside the motor is usually high which can cause Hall-effect position sensors unworkable if they are installed inside the motor. Meanwhile, the small volume may also limit the use of the position sensors. And more importantly, in high power rating motors, the position sensor signals are easy to be disturbed by the noise. Moreover, BLDC machines require variable advanced-firing control during high-speed operation. However, if the firing sequence is directly determined by the position sensor signals, advance-firing commutation cannot be implemented.
In order to solve the drawbacks of using position sensors, lots of researchers have been working on sensorless controls. The main idea of sensorless control is to use electrical signals derived from the motor windings, with suitable methods, to calculate the rotor position and speed. The most common sensorless control is based on the detection of zero crossings of the phase back-EMF or the third harmonic back-EMF. In high-speed motors, however, the phase currents can flow more or less continuously due to the effect of winding inductances, thus preventing the detection of zero-crossings of the phase back-EMF. On the other hand, the method of detecting the third harmonic back-EMF zero-crossings is not affected by the diode conduction angle or the inverter PWM on-off noise. And, this method has a lower requirement on the filters, and is suitable for a wide speed range.
This thesis focuses on the third harmonic back-EMF-based sensorless control of a 15kW, 80,000rpm high-speed PM BLDC motor, with consideration of major problems in the motor design and sensorless control.
Firstly, the influence of different stator structures on third harmonic back-EMF is studied. The 3-slot/2-pole and 6-slot/2-pole non-overlapping-winding structures have been comparatively studied, showing that the 3-slot/2-pole structure is not suitable for the 3rd harmonic EMF-based sensorless operation, because the 3rd harmonic winding factor is 0. The 6-slot/2-pole structure in which the fundamental winding factor is 0.5 and the third harmonic winding factor is 1, is suitable for the 3rd harmonic EMF-based sensorless operation. However, its fundamental winding factor is low, the winding is thus not fully utilized. In order to combine the advantage of both structures, another topology is proposed by employing unequal teeth, where the small teeth have no winding wound around. The proposed 6-slot/2-pole unequal-teeth structure improves the utility of the winding and is also suitable for the3rd harmonic EMF-based sensorless operation. Meanwhile, the inductance and the unbalanced magnetic force in these three different stator structures are also comparatively studied with different structure, showing that the 3-slot/2-pole structure and the 6-slot/2-pole unequal-teeth structure exhibit significant unbalanced magnetic force due to diametrically asymmetric, which will reduce the bearing service life and increase the motor vibration and acoustic noise. The 6-slot/2-pole structure with all teeth wound gives highest third harmonic component of back-EMF and lowerest unbalanced magnetic force, hence, is eventually employed in this thesis.
Secondly, influence of the rotor structures with different magnet assemblies on the third harmonic airgap field and third harmonic back-EMF is studied. The airgap field is analyzed with both FEM and analytical model. In surface-mounted permanent magnet motors, when the pole-arc to pole-pitch ratio decreases, the airgap field distribution waveform becomes farther away from sinusoidal waveform, containing more higher 3rd harmonic component. This will produce higher third harmonic back-EMF which can be used for the sensorless control. However, the fundamental component decreases as pole-arc to pole-pitch ratio decreases, which will deteriorate the motor performance. Therefore, in order to enhance the third harmonic airgap field but meanwhile hardly decrease the fundamental component, it is not sufficiently good to reduce the pole-arc to pole-pitch ratio solely. Instead, magnet-segmenting technique can be employed. Influence of the number of magnet segments on the airgap field distribution is also investigated with FEM, showing that the number of segments has a significant effect on the airgap field waveform. It is also shown that the structure with two magnet segments per pole exhibits the highest third harmonic in the airgap field, and even the fundamental component is higher than that with one segment per pole. This is beneficial to improve the motor performance. Therefore, the structure with two magnet segments per pole is employed in the designed high-speed BLDC motor. Three motor configurations, viz., (1) parallel magnetization with pole-arc less than 1, (2) parallel magnetization with magnet segmenting and (3) radial magnetization, are comparatively studied. It is shown that the first and second configurations can give sufficient high third harmonic back-EMF in the motor windings. On the other hand, the rotor loss is negligible in low or moderate-speed PM BLDC motors, but becomes significant in high-speed motors in which case the magnets may be over-heated and permanently demagnetized. Therefore, the influence of the three motor configurations on the rotor eddy-current loss is also comparatively studied, showing that the third configuration is superior to the first and the second. However, the third configuration has difficulty in manufacturing, thus the first and the second configurations are usually employed.
Thirdly, the advanced-firing commutation based on the third-harmonic back-EMF sensorless control is achieved. In this sensorless control, the commutation signal has a relationship with the comparator output of the zero-crossing signal. In a practical system, the zero-crossing signal may contain noise, which could cause an erroneous update of the estimated rotor position. Hence, this will cause the whole system unworkable. It is necessary to filter out the noise signal using software. For high speed motor, the digital filter will make the motor commutation retarded. Consequently, the commutation retarding will cause lower power factor, lower efficiency, lower power output power capability and high temperature rise, and the cooling system must be enhanced. Therefore, it is necessary to use the advanced-firing commutation based on the third-harmonic back-EMF sensorless control. Due to the rotor inertia during the motor operation, the electric cycle will not abruptly change. Hence, the electric cycle in the successive two commutations is almost the same. Hence, if the former commutation cycle and the digital filter time-constant are known, the next-step advanced-firing commutation can be achieved by using the timer delay. It is shown that the advanced-firing commutation can largely improve the motor power factor, efficiency, power output power capability, and at the same time reduce the loss.
The above-mentioned three major problems have been solved during the research, whilst a prototype has been manufactured. Experiments have verified the related theoretical analysis, design method and sensorless control strategy.
高速永磁无刷直流电机正因为功率密度大、体积小,其损耗密度也很大,因此电机的温升往往比较高,所以当霍尔元件这一类的位置传感器安装在电机内部时往往无法正常工作。另外,位置传感器的使用也会受到体积上的限制。在功率较大的电机中,位置传感器信号也容易受到干扰。此外,永磁无刷直流电机高速运行时通常需要不同程度的超前触发控制,但直接使用转子位置信号进行换相时无法实现可变的超前触发控制。
为了解决位置传感器带来的各种缺陷,许多学者开展了无传感器控制技术的研究,其主要思想是利用电机绕组中的有关电信号,通过适当的方法估算出转子的位置和转速,以此来取代转子位置传感器。在各种转子位置和速度的检测方法中,最常用的是通过检测每相反电势或三次谐波反电势来获得转子的位置信息。每相反电势法容易实现,但续流二极管导通引起的电压脉冲将干扰该信号。尤其是在高速、重载、或者绕组电气时间常数大等情况下,续流二极管导通角很大,此时通过检测每相反电势过零点的方法并不适合无位置传感器运行。相对于每相反电势法,三次谐波反电势法不受二极管导通角和逆变器PWM斩波的影响,对滤波器要求低,有更宽的调速范围。
本文针对一台80,000r/min,15kW的高速永磁无刷直流电机及其基于三次谐波反电势的无位置传感器控制策略,研究了电机设计和控制的若干重要问题。
1、研究了不同定子结构对三次谐波反电势的影响。对3齿2极和6齿2极集中绕组结构进行了对比研究,前者由于三次谐波的绕组系数为0,其相绕组中并不包含三次谐波反电势,因此其磁链和相反电势接近正弦分布,故不适合应用三次谐波反电势控制。后者的三次谐波绕组系数为1,其磁链和每相反电势包含大量的三次谐波,其波形远远偏离了正弦分布,因此适合三次谐波反电势控制,但基波绕组系数为0.5,绕组得不到充分利用。结合以上两种结构的优缺点,对不同齿宽(注：小齿为辅助齿)的6齿2极结构进行了研究,发现该结构既能利用三次谐波反电势控制,又能提高绕组的利用率。同时,也对各种结构电机的电感与单边磁拉力进行了对比分析。分析表明,由于3齿2极和不等齿宽6齿2极结构均具有空间不对称性,在电机运行时,具有较大的单边磁拉力,电机的噪声较大,影响轴承的寿命。因此最终采用等齿宽6齿2极集中绕组的对称结构。
2、研究了转子结构对电机气隙磁场三次谐波和三次谐波反电势的影响。对电机中的气隙磁场进行有限元分析与解析计算。在采用表面粘贴磁瓦时,随着极弧系数的减小,气隙磁场的分布越来越偏离正弦,气隙磁场中的三次谐波也会相应地增加。这有利于增大每相反电势中的三次谐波。但同时,气隙磁场中的基波随永磁体极弧系数的减小而减小。由于气隙磁场的畸变增加了气隙磁场中的谐波,使电机定子铁耗增大,将影响电机的性能。因此,为了提高气隙磁场中的三次谐波同时又不减小气隙磁场中的基波,采用“平行充磁且每极分两块”的结构。对不同的转子磁瓦分块数的气隙磁场进行分析,可知随着分块数的增加,气隙磁场分布趋于径向充磁结构的分布,接近方波。随着分块数的增加,气隙磁场中基波分量也随之增加,但当每极转子分块数为2块时,气隙磁场中的三次谐波最大。因此为了提高利用三次谐波反电势控制时的抗干扰能力,采用转子每极磁瓦分块数为2的结构。对“平行充磁且极弧系数小于1”、“平行充磁且每极磁瓦分两块”、“径向充磁且极弧系数为1”共三种转子结构进行了研究。研究发现“平行充磁且极弧系数小于1”、“平行充磁且每极磁瓦分两块”这两种结构均能在电机相绕组中产生足够大的三次谐波反电势。其次,由于转子损耗在中、低速无刷直流电机中往往是可忽略的,但是在高速无刷电机中比较严重,能引起转子永磁体过热和不可恢复性退磁。因此,对三种不同的转子结构引起的额定负载转矩下的转子涡流损耗进行了对比研究,结果表明：“平行充磁且极弧系数小于1”结构引起的转子涡流损耗小于“平行充磁且每极分两块”的结构,“径向充磁且极弧系数为1”结构的转子涡流损耗小于“平行充磁且极弧系数小于1”和“平行充磁且每极分两块”的结构。但“径向充磁且极弧系数为1”的结构应用较少,永磁体充磁时需要专门的工装夹具,加工困难。“平行充磁且极弧系数小于1”结构和“平行充磁且每极分两块”的结构容易实现。
3、研究了基于三次谐波反电势的无位置传感器超前触发控制。利用三次谐波反电势控制时,用比较器产生的过零点信号与电机触发信号密切相关。在实际系统中并不能确保比较器产生的过零点信号并不包含噪音信号。如果信号中噪音信号被控制系统误认为有效信号,将导致错误的换向信息,并且一旦产生一次错误的换向状态,将导致整个控制系统的崩溃。因此为了滤除噪音信号,有必要从软件上进行数字滤波,判断是否真正的发生信号跳变。采用数字滤波,必然导致信号滞后,进而引起电机的滞后换相。滞后的时间与数字滤波的深度有关。对于高速电机,将产生较严重的滞后。由于数字滤波引起滞后触发,电机电流变大,同时整个系统的功率因数、效率、功率输出能力降低、电机的温升更严重,对电机的冷却系统也提出了更高的要求,因此有必要采取超前触发控制。电机运行时,由于转子转动惯量的作用,其电周期不会发生突变,可以认为前一个换向周期的时间基本等于后一个换向周期,因此,如果知道前一个换向周期的时间,同时知道由于数字滤波产生的滞后时间,然后用延时导通来实现下一拍换相的正常触发控制甚至超前触发控制,研究表明超前触发可以明显的提高系统地功率因数、效率、输出功率,同时减小了损耗。
在论文的科研工作中,解决了以上电机设计与控制方面的重要问题,并制作了样机。相关实验也证明了理论分析、设计措施与控制方法的正确性。
Due to the advantage of high efficiency and power density, high-speed permanent magnet brushless DC (BLDC) machines are emerging as a key technology for applications such as turbocharger, spindle drives, flywheel energy storage system, machine tools, compressors, molecule pumps. Researchers all around the world are getting more and more attention on high-speed machines. However, their high rotation speed demands that careful consideration should be given to both electromagnetic and mechanical design issues, such as e.g. rotor loss, bearing technology, rotor dynamics, and aerodynamic loss.
Since high-speed machines have high power density and small volume, their loss density is also high. In result, the temperature rise inside the motor is usually high which can cause Hall-effect position sensors unworkable if they are installed inside the motor. Meanwhile, the small volume may also limit the use of the position sensors. And more importantly, in high power rating motors, the position sensor signals are easy to be disturbed by the noise. Moreover, BLDC machines require variable advanced-firing control during high-speed operation. However, if the firing sequence is directly determined by the position sensor signals, advance-firing commutation cannot be implemented.
In order to solve the drawbacks of using position sensors, lots of researchers have been working on sensorless controls. The main idea of sensorless control is to use electrical signals derived from the motor windings, with suitable methods, to calculate the rotor position and speed. The most common sensorless control is based on the detection of zero crossings of the phase back-EMF or the third harmonic back-EMF. In high-speed motors, however, the phase currents can flow more or less continuously due to the effect of winding inductances, thus preventing the detection of zero-crossings of the phase back-EMF. On the other hand, the method of detecting the third harmonic back-EMF zero-crossings is not affected by the diode conduction angle or the inverter PWM on-off noise. And, this method has a lower requirement on the filters, and is suitable for a wide speed range.
This thesis focuses on the third harmonic back-EMF-based sensorless control of a 15kW, 80,000rpm high-speed PM BLDC motor, with consideration of major problems in the motor design and sensorless control.
Firstly, the influence of different stator structures on third harmonic back-EMF is studied. The 3-slot/2-pole and 6-slot/2-pole non-overlapping-winding structures have been comparatively studied, showing that the 3-slot/2-pole structure is not suitable for the 3rd harmonic EMF-based sensorless operation, because the 3rd harmonic winding factor is 0. The 6-slot/2-pole structure in which the fundamental winding factor is 0.5 and the third harmonic winding factor is 1, is suitable for the 3rd harmonic EMF-based sensorless operation. However, its fundamental winding factor is low, the winding is thus not fully utilized. In order to combine the advantage of both structures, another topology is proposed by employing unequal teeth, where the small teeth have no winding wound around. The proposed 6-slot/2-pole unequal-teeth structure improves the utility of the winding and is also suitable for the3rd harmonic EMF-based sensorless operation. Meanwhile, the inductance and the unbalanced magnetic force in these three different stator structures are also comparatively studied with different structure, showing that the 3-slot/2-pole structure and the 6-slot/2-pole unequal-teeth structure exhibit significant unbalanced magnetic force due to diametrically asymmetric, which will reduce the bearing service life and increase the motor vibration and acoustic noise. The 6-slot/2-pole structure with all teeth wound gives highest third harmonic component of back-EMF and lowerest unbalanced magnetic force, hence, is eventually employed in this thesis.
Secondly, influence of the rotor structures with different magnet assemblies on the third harmonic airgap field and third harmonic back-EMF is studied. The airgap field is analyzed with both FEM and analytical model. In surface-mounted permanent magnet motors, when the pole-arc to pole-pitch ratio decreases, the airgap field distribution waveform becomes farther away from sinusoidal waveform, containing more higher 3rd harmonic component. This will produce higher third harmonic back-EMF which can be used for the sensorless control. However, the fundamental component decreases as pole-arc to pole-pitch ratio decreases, which will deteriorate the motor performance. Therefore, in order to enhance the third harmonic airgap field but meanwhile hardly decrease the fundamental component, it is not sufficiently good to reduce the pole-arc to pole-pitch ratio solely. Instead, magnet-segmenting technique can be employed. Influence of the number of magnet segments on the airgap field distribution is also investigated with FEM, showing that the number of segments has a significant effect on the airgap field waveform. It is also shown that the structure with two magnet segments per pole exhibits the highest third harmonic in the airgap field, and even the fundamental component is higher than that with one segment per pole. This is beneficial to improve the motor performance. Therefore, the structure with two magnet segments per pole is employed in the designed high-speed BLDC motor. Three motor configurations, viz., (1) parallel magnetization with pole-arc less than 1, (2) parallel magnetization with magnet segmenting and (3) radial magnetization, are comparatively studied. It is shown that the first and second configurations can give sufficient high third harmonic back-EMF in the motor windings. On the other hand, the rotor loss is negligible in low or moderate-speed PM BLDC motors, but becomes significant in high-speed motors in which case the magnets may be over-heated and permanently demagnetized. Therefore, the influence of the three motor configurations on the rotor eddy-current loss is also comparatively studied, showing that the third configuration is superior to the first and the second. However, the third configuration has difficulty in manufacturing, thus the first and the second configurations are usually employed.
Thirdly, the advanced-firing commutation based on the third-harmonic back-EMF sensorless control is achieved. In this sensorless control, the commutation signal has a relationship with the comparator output of the zero-crossing signal. In a practical system, the zero-crossing signal may contain noise, which could cause an erroneous update of the estimated rotor position. Hence, this will cause the whole system unworkable. It is necessary to filter out the noise signal using software. For high speed motor, the digital filter will make the motor commutation retarded. Consequently, the commutation retarding will cause lower power factor, lower efficiency, lower power output power capability and high temperature rise, and the cooling system must be enhanced. Therefore, it is necessary to use the advanced-firing commutation based on the third-harmonic back-EMF sensorless control. Due to the rotor inertia during the motor operation, the electric cycle will not abruptly change. Hence, the electric cycle in the successive two commutations is almost the same. Hence, if the former commutation cycle and the digital filter time-constant are known, the next-step advanced-firing commutation can be achieved by using the timer delay. It is shown that the advanced-firing commutation can largely improve the motor power factor, efficiency, power output power capability, and at the same time reduce the loss.
The above-mentioned three major problems have been solved during the research, whilst a prototype has been manufactured. Experiments have verified the related theoretical analysis, design method and sensorless control strategy.
引文
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