WO2022083014A1 - 基于分数槽集中绕组永磁电机的双绕组低谐波设计方法 - Google Patents

基于分数槽集中绕组永磁电机的双绕组低谐波设计方法 Download PDF

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WO2022083014A1
WO2022083014A1 PCT/CN2021/072473 CN2021072473W WO2022083014A1 WO 2022083014 A1 WO2022083014 A1 WO 2022083014A1 CN 2021072473 W CN2021072473 W CN 2021072473W WO 2022083014 A1 WO2022083014 A1 WO 2022083014A1
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winding
armature
slot
harmonic
secondary winding
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PCT/CN2021/072473
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English (en)
French (fr)
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杜怿
徐晨
朱孝勇
全力
肖凤
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江苏大学
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Priority to GB2113756.7A priority Critical patent/GB2611295A/en
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K21/00—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets
    • H02K21/12—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets
    • H02K21/22—Synchronous motors having permanent magnets; Synchronous generators having permanent magnets with stationary armatures and rotating magnets with magnets rotating around the armatures, e.g. flywheel magnetos
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K1/00—Details of the magnetic circuit
    • H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
    • H02K1/12—Stationary parts of the magnetic circuit
    • H02K1/16—Stator cores with slots for windings
    • H02K1/165—Shape, form or location of the slots
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K15/00—Methods or apparatus specially adapted for manufacturing, assembling, maintaining or repairing of dynamo-electric machines
    • H02K15/0006—Disassembling, repairing or modifying dynamo-electric machines
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K2213/00—Specific aspects, not otherwise provided for and not covered by codes H02K2201/00 - H02K2211/00
    • H02K2213/03—Machines characterised by numerical values, ranges, mathematical expressions or similar information

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  • the invention relates to the field of motors and transmissions, in particular to a design method of a fractional slot concentrated winding permanent magnet motor, and designs a low harmonic double-winding permanent magnet motor capable of reducing non-working harmonics of an armature reaction magnetic field.
  • Fractional slot concentrated winding motors are widely used in electric vehicles, aerospace and other fields due to their advantages of high copper filling factor, low cogging torque, and short winding ends.
  • the armature reaction magnetic field of this type of motor often contains a large number of harmonic magnetic fields with different pole pairs.
  • Some harmonics can effectively participate in the electromechanical energy conversion of the motor and belong to working harmonics, while some harmonics can only generate torque ripple. , loss and other adverse consequences belong to non-working harmonics.
  • the existence of a large number of non-working harmonics not only reduces the current utilization rate, but also greatly increases the loss of permanent magnets and stator and rotor cores because the non-working harmonics of different pole pairs rotate at different speeds relative to the rotor.
  • the Chinese patent publication number CN110401273A proposes a low-harmonic fractional slot concentrated winding design method, so that each phase winding has conductors distributed in all stator slots, and the number of conductors is different, thereby reducing the armature.
  • the harmonic content of the magnetomotive force But this approach makes the winding configuration more complicated.
  • Chinese invention patent publication numbers CN102579753 A and CN108336837 A propose that on the basis of split-tooth vernier permanent magnet motor, by adding a set of armature windings, the power density of the motor can be improved and the operation mode can be diversified. However, more complex harmonics of the armature reaction magnetic field are introduced, which aggravates the motor loss and reduces the current utilization rate.
  • the purpose of the invention is to solve the problem of large non-working harmonic content of the armature reaction magnetic field in the current fractional slot concentrated winding permanent magnet motor, and to provide a dual-winding low harmonic design method based on the fractional slot concentrated winding permanent magnet motor.
  • a set of three-phase auxiliary windings is added to the iron core of the stator yoke of the motor, and a low-harmonic design method of inner and outer double-phase windings is formed to cancel the non-working harmonics in the reaction magnetic field of the original winding armature.
  • the fractional slot concentrated winding permanent magnet motor adopts an inner stator structure, including N s1 stator teeth and a stator core yoke, an outer stator slot is formed between two adjacent stator teeth, and the inner stator slot is Winding the original armature winding, including the following steps:
  • Step 1) Passing three-phase current into the original armature winding to obtain the air-gap flux density of the armature reaction magnetic field of the original armature winding, the number of pole pairs p 1 of the fundamental wave of the single-phase armature reaction magnetic field, and the pair of poles of p 1
  • the amplitude of the working harmonic A 1 ⁇ 0 n 1 i 1 F am1 /1+ ⁇ k1 n 1 i 1 F am1' /m 1
  • ⁇ 0 is the Fourier coefficient of the fundamental wave
  • n 1 is the number of turns of each coil of the primary armature winding
  • i 1 is the RMS current of the primary armature winding
  • F am1 is the armature reaction magnetism of the primary armature winding
  • ⁇ k1 is the higher harmonic Fourier coefficient
  • Step 2) open N s2 inner slots on the inner side of the outer slots of the stator on the yoke of the stator core, the ratio of the number of inner slots N s2 to the number of pole pairs p 1 is an integer, The secondary winding is wound in the slot, and the number of pole pairs of the secondary winding is p 1 ;
  • the value of i 2 is C; n 2 is the number of turns of each coil of the secondary winding, i 2 is the rms current value of the secondary winding, F am2 is the decomposition coefficient of the armature reaction magnetomotive force of the secondary winding, and F am2' is the Coefficient of Fourier decomposition of secondary winding armature reaction magnetomotive force after air-gap permeability, ⁇ k2
  • Step 5 According to the formula Determine the half-groove radial cross-sectional area S 2 of the inner groove, and ⁇ is the groove full rate, which is taken as 0.5-0.8. J is the cell current density.
  • the present invention cancels the non-working harmonic content in the air gap flux density of the armature reaction magnetic field in the original fractional slot concentrated winding permanent magnet motor by adding a set of secondary windings, compared with the existing low harmonic design method, such as doubling the stator
  • the number of slots, unequal number of turns of adjacent phase coils or unequal number of conductors on the side of the element, etc. have the characteristics of not needing to change the number of stator teeth and winding structure of the original armature winding part, and it is easy to retain the copper filling factor of the original fractional slot concentrated winding High, short winding ends and other advantages.
  • the present invention proposes to add a set of windings on the yoke of the stator core to realize low harmonic design, which effectively improves the utilization of the internal space of the motor, especially for motors with larger volume and more pole pairs, this advantage is particularly obvious.
  • the low harmonic design method based on fractional slot concentrated winding permanent magnet motor double windings proposed by the present invention can increase torque, reduce torque ripple, reduce rotor loss, improve motor efficiency, and improve motor vibration and noise.
  • Fig. 1 is the structure diagram of the original fractional slot concentrated winding permanent magnet motor
  • Figure 2 is a structural diagram of a dual-winding low-harmonic permanent magnet motor
  • Figure 3 is a star diagram of the inner tank potential
  • the reference signs in the figure are: 1- rotor yoke core; 2- rotor permanent magnet; 3- stator core; 4- primary armature winding; 5- stator teeth; 6- stator outer slot; 7- stator core yoke ; 8-inner slot; 9-secondary winding.
  • an existing three-phase fractional slot concentrated winding permanent magnet motor namely the original fractional slot concentrated winding permanent magnet motor (referred to as the original motor), includes an outer rotor and an inner stator, and the outer rotor includes a rotor yoke core 1.
  • the outer rotor includes a rotor yoke core 1.
  • On the inner surface of the iron core 1 of the rotor yoke there are 2 ⁇ ppm rotor permanent magnets 2 alternately magnetized radially, so as to form a ppm pair of permanent magnet magnetic fields in the original motor.
  • the inner stator includes a stator core 3 and an original armature winding 4.
  • the stator core 3 adopts a slot structure, including N s1 stator teeth 5 and a stator core yoke 7, and a stator outer slot 6 is formed between two adjacent stator teeth 5.
  • the original armature winding 4 is wound in the outer stator slot 6, and each phase of the original armature winding 4 includes n w1 coils, and the number of turns of each coil is n 1 .
  • ⁇ e is the electrical velocity
  • i 1 is the effective value of the current
  • t is the current cycle.
  • ⁇ e is the electrical velocity
  • i 1 is the effective value of the current
  • a vABC , b vABC are the Fourier coefficients
  • ⁇ is the rotor position angle
  • v is the odd harmonic in the total armature reaction magnetomotive force of the original armature winding 4
  • Equation (1) the total armature reaction magnetomotive force F ABC1 ( ⁇ , t) of the original armature winding 4 can be expressed as:
  • F am1 is the coefficient of Fourier decomposition.
  • F am1 is the coefficient of Fourier decomposition of the original armature winding 4 armature reaction magnetomotive force.
  • F am1' is the Fourier decomposition coefficient of the armature reaction magnetomotive force of the original armature winding 4 after passing through the air gap flux.
  • N s1 is the stator tooth 5 number
  • p s is the number of pole pairs of the original armature winding 4
  • p 1 is the number of pole pairs of the fundamental wave of the original armature winding 4 single-phase armature reaction magnetic field.
  • the ps pole and N s1 -ps pole harmonics belong to the working harmonics. Except for the working harmonics, the rest of the harmonics belong to the non-working harmonics.
  • a low harmonic design method is proposed based on the existing three-phase fractional slot concentrated winding permanent magnet motor by opening inner slots on the yoke 7 of the stator core.
  • the inner slots 8 are located inside the stator outer slots 6, and each inner slot 6 has the same structure, and is called the original stator outer slot 8.
  • the groove 6 is an outer groove, which further forms an inner and an outer groove structure.
  • the secondary winding 9 is wound in the inner slot 8 .
  • n 2 is the number of turns of each coil of the secondary winding 9
  • i 2 is the RMS current of the secondary winding 9
  • ⁇ 0 and ⁇ k are the Fourier coefficients of the fundamental wave and higher harmonics
  • F am2 The secondary winding 9 electric current
  • the coefficient of the armature reaction magnetomotive force decomposition, F am2' is the Fourier decomposition coefficient of the armature reaction magnetomotive force of the secondary winding 9 after passing through the air gap flux.
  • ⁇ 0 is the Fourier coefficient of the fundamental wave
  • n 2 is the number of turns of each coil of the secondary winding 9
  • i 2 is the RMS current of the secondary winding 9
  • F am2 is the armature reaction magnetomotive force decomposition of the secondary winding 9
  • F am2' is the Fourier decomposition coefficient of the armature reaction magnetomotive force of the secondary winding 9 after passing through the air-gap flux
  • ⁇ k2 is the Fourier coefficient of the higher harmonic wave of the secondary winding 9
  • ⁇ k2 ⁇ ⁇ k is a special case of ⁇ k .
  • n 2 i 2 is unknown in the above formula, that is, the product of n 2 and i 2 is unknown.
  • the left side of the above equation can be substituted into the known quantity of the original motor to obtain a specific value by calculation.
  • the right side of the equation is an expression of the product of the number of turns n 2 of each coil of the secondary winding 9 and the rms value i 2 of the current passing through the secondary winding 9 . From the calculation, the value of n 2 ⁇ i 2 can be obtained as C.
  • the half-slot area S 2 of the inner slot 8 can be obtained from the slot current density formula (11) and the value C of n 2 ⁇ i 2 of the secondary winding obtained in step (5);
  • ⁇ is the full rate of the slot, which is determined by the processing technology of the motor and the heat dissipation conditions, generally taking 0.5 to 0.8
  • S 2 is the radial cross-sectional area of the half-slot of the inner slot
  • J is the slot current density, which is determined by factors such as the heat dissipation conditions of the motor. Under natural cooling conditions, it is generally about 5.
  • the inner slot 8 is set at the stator core yoke 7 by the N s2 selected in the step (1) and the half-slot area S 2 determined in the step (6), and the inner slot 8 is required to be evenly distributed on the circumference; in order to The wire embedding of the secondary winding 9 is convenient, and the best solution is to set the inner slot 8 and the stator outer slot 6 to be aligned in the diameter direction.
  • d is the maximum outer diameter of the selected copper wire enameled wire.
  • the spatial position angle difference between the original armature winding 4 and the secondary winding 9 can be obtained at this time as ⁇ , see Fig. 2 It is determined by the difference ⁇ between the inner and outer slots and the winding position.
  • the A-phase current through the original armature winding 4 is The A-phase current through the secondary winding 9 is The phase angle difference between the two sets of windings of the primary armature winding 4 and the secondary winding 9 is ⁇ .
  • the current phase angle of the secondary winding 9 is equal to ⁇ , that is:

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  • Power Engineering (AREA)
  • Manufacturing & Machinery (AREA)
  • Windings For Motors And Generators (AREA)

Abstract

本发明公开电机领域中的一种基于分数槽集中绕组永磁电机的双绕组低谐波设计方法，先给原电枢绕组中通入三相电流，得到单相电枢反应磁场基波极对数p 1以及p 1对极非工作谐波的幅值A 1，在定子铁心轭部上开设位于N s2个内槽，内槽数N s2与p 1之比为整数，在内槽内绕制极对数为p 1的副绕组，确定槽距角α＝360×p 1/N s2和副绕组绕制方式，再在副绕组中通入三相电流，得到p 1对极幅值B 1，且A 1＝B 1，最后确定内槽的半槽径向截面积；本发明通过增加一套副绕组抵消原分数槽集中绕组永磁电机中电枢反应磁场气隙磁密中非工作谐波含量，具有不需要改变原电枢绕组部分的定子齿数和绕组结构的特点，有效提高电机内部空间利用，可增加转矩，提高电机效率。

Description

基于分数槽集中绕组永磁电机的双绕组低谐波设计方法 技术领域
本发明涉及电机与传动领域，特别涉及一种分数槽集中绕组永磁电机的设计方法，设计一种能降低电枢反应磁磁场的非工作谐波的低谐波双绕组永磁电机。
背景技术
分数槽集中绕组电机由于具有铜填充系数高、齿槽转矩低、绕组端部短等优势，在电动汽车、航空航天等领域被广泛利用。但是，该类电机的电枢反应磁场往往含有大量不同极对数的谐波磁场，有些谐波能有效参与电机的机电能量转换，属于工作谐波，而有些谐波则仅能产生转矩脉动、损耗等不良后果，属于非工作谐波。大量非工作谐波的存在，不仅降低了电流利用率，而且由于不同极对数的非工作谐波相对于转子以不同速度旋转，大幅增加了永磁体和定、转子铁心的损耗。此外，还会导致声学噪声和振动、局部铁心饱和、减少磁阻转矩、增加电机的杂散损耗和降低电机效率等不良影响。因此，降低电机的电枢反应磁磁场的非工作谐波已经成为永磁电机领域的研究热点之一。
为了解决上述问题，有学者提出了分数槽集中绕组电机不等匝数得设计方法，即在每个定子槽内放置至多四层线圈，同时每相绕组由两种或两种以上不同匝数得线圈串联构成，通过调整线圈的匝数比来降低电枢谐波磁动势。但这种方法通常将一相绕组的各个线圈匝数设置成固定比例，只对某些特定极槽数的电机有较好的效果。
中国发明专利公开号为CN110401273A的文献中提出了一种低谐波的分数槽集中绕组设计方法，使每相绕组在所有定子槽内均有导线分布，且导体数不相同，从而降低了电枢磁动势的谐波含量。但是这种方法使得绕组配置更为复杂。中国发明专利公开号为CN102579753 A和CN108336837 A的文献中提出在裂齿式游标永磁电机基础上，通过增加一套电枢绕组的方式，实现电机功率密度的提升和运行模式的多样化，但却由此引入了更为复杂的电枢反应磁场谐波，加剧电机损耗、降低电流利用率。
发明内容
本发明目的是为了解决目前分数槽集中绕组永磁电机中电枢反应磁场非工作谐波含量大的问题，提供了一种基于分数槽集中绕组永磁电机的双绕组低谐波设计方法，在原电机定子轭部铁心增加一套三相副绕组，并形成内、外双三相绕组的低谐波设计方法，来抵消原绕组电枢反应磁场中的非工作谐波。
本发明采用的技术方案是：分数槽集中绕组永磁电机采用内定子结构，包括N s1个定子 齿和一个定子铁心轭部，相邻两个定子齿之间形成定子外槽，定子外槽内绕制原电枢绕组，包括以下步骤：
步骤1)：给原电枢绕组中通入三相电流，得到原电枢绕组的电枢反应磁场气隙磁密、单相电枢反应磁场基波极对数p 1以及p 1对极非工作谐波的幅值A 1＝Λ 0n 1i 1F am1/1+Λ k1n 1i 1F am1’/m 1，且k 1和m 1符合k 1N s1±m 1p 1＝p 1；Λ 0为基波傅里叶系数，n 1为原电枢绕组每个线圈的匝数，i 1为原电枢绕组电流有效值，F am1为原电枢绕组电枢反应磁动势傅里叶分解的系数，Λ k1为原电枢绕组高次谐波傅里叶系数，Λ k1∈Λ k，Λ k为高次谐波傅里叶系数，F am1’为经气隙磁导后原电枢绕组电枢反应磁动势傅里叶分解的系数，m 1∈m，m为经气隙磁导后原电枢绕组电枢反应磁动势中奇数次谐波的次数，m＝1,3,5…，k 1∈k，k为谐波次数，k＝1,2,3…；
步骤2)：在所述定子铁心轭部上开设位于所述定子外槽的内侧的N s2个内槽，内槽数N s2与所述极对数p 1之比为整数，在所述内槽内绕制副绕组，副绕组极对数为p 1；
步骤3)：根据内槽数N s2和副绕组的极对数p 1确定槽距角α＝360×p 1/N s2和副绕组的绕制方式；
步骤4)：在副绕组中通入三相电流，得到副绕组的电枢反应磁场气隙磁密以及p 1对极幅值B 1＝Λ 0n 2i 2F am2/1+Λ k2n 2i 2F am2’/m 2，A 1＝B 1，且k 2和m 2符合k 2N s1±m 2p 1＝p 1，由幅值A 1＝B 1得到其中的n 2×i 2的值为C；n 2为副绕组的每个线圈的匝数，i 2为副绕组的电流有效值，F am2为副绕组电枢反应磁动势分解的系数，F am2’为经气隙磁导后副绕组电枢反应磁动势傅里叶分解的系数，Λ k2∈Λ k，m 2∈m；；
步骤5)：根据公式
Figure PCTCN2021072473-appb-000001
确定所述内槽的半槽径向截面积S 2，δ为槽满率，取0.5～0.8，。J为槽电流密度。
本发明采用上述技术方案后的有益效果是：
1)本发明通过增加一套副绕组抵消原分数槽集中绕组永磁电机中电枢反应磁场气隙磁密中非工作谐波含量，相比于现有的低谐波设计方法，如加倍定子槽数、设置相邻相线圈不等匝数或不等元件边导体根数等，具有不需要改变原电枢绕组部分的定子齿数和绕组结构的特点，易于保留原分数槽集中绕组铜填充系数高、绕组端部短等优势。
2)本发明提出在定子铁心轭部增设一套绕组实现低谐波设计，有效提高了电机内部空间利用，特别对于体积较大、极对数较多的电机该优势尤为明显。
3)本发明提出的基于分数槽集中绕组永磁电机双绕组低谐波设计方法，可增加转矩，减小转矩脉动，降低转子损耗，提高电机效率，改善电机振动和噪声。
附图说明
为了使本发明内容更容易被清楚地理解，下面根据本发明的具体实施方式并结合附图，对本发明作进一步详细的说明，其中：
图1为原分数槽集中绕组永磁电机的结构图；
图2为双绕组低谐波永磁电机的结构图；
图3为内槽电势星型图；
图4为本发明实施效果示意图；
图中附图标记表示为：1-转子轭部铁心；2-转子永磁体；3-定子铁心；4-原电枢绕组；5-定子齿；6-定子外槽；7-定子铁心轭部；8-内槽；9-副绕组。
具体实施方式
如图1所示为已有的一台三相分数槽集中绕组永磁电机，即原分数槽集中绕组永磁电机(简称原电机)，包括外转子和内定子，外转子包括转子轭部铁心1，在转子轭部铁心1的内表面贴有2×p pm块径向交替充磁的转子永磁体2，以此在原电机中形成p pm对永磁磁场。内定子包括定子铁心3和原电枢绕组4，定子铁心3采用齿槽结构，包括N s1个定子齿5和一个定子铁心轭部7，相邻两个定子齿5之间形成定子外槽6，定子外槽6内绕制原电枢绕组4，原电枢绕组4每相包括n w1个线圈，每个线圈的匝数为n 1。原电枢绕组4的绕组极对数为p s，p s＝p pm。当原电机正常运行时，给原电枢绕组4中通入三相电流，原电枢绕组4中的三相电流i A、i B、i C可表示为：
Figure PCTCN2021072473-appb-000002
ω e为电速度；i 1为电流有效值，t为电流周期。
此时，按本领域的基本原理可得到原电枢绕组4单相电枢反应磁场基波极对数为p 1，原电枢绕组4总电枢反应磁动势F ABC1(θ,t)可由傅里叶级数表示为：
Figure PCTCN2021072473-appb-000003
Figure PCTCN2021072473-appb-000004
其中，ω e为电速度；i 1为电流有效值，a vABC，b vABC为傅里叶系数，θ为转子位置角，v为原电枢绕组4总电枢反应磁动势中奇数次谐波的次数，v＝1,3,5…，n 1为原电枢绕组4每个线圈的匝数，下标A、B、C表示A、B、C三相绕组。
将式(1)代入式(2)得到原电枢绕组4总电枢反应磁动势F ABC1(θ,t)可表示为：
Figure PCTCN2021072473-appb-000005
其中，F am1为傅里叶分解的系数。
由于电机定子齿5会使气隙磁导发生变化，对原电枢绕组4电枢反应气隙磁密产生影响，根据定子齿5的形状以及在气隙圆周上的位置，可得气隙磁导Λ 1(θ)为：
Figure PCTCN2021072473-appb-000006
Figure PCTCN2021072473-appb-000007
其中，k为谐波次数，k＝1,2,3…；N s1是定子齿5的数量；Λ 0和Λ k为基波和高次谐波傅里叶系数；μ 0为空气磁导率；g为实际气隙长度；b 0为定子开槽宽度；σ为开槽宽度b 0与定子极距t d之比；β是关于b 0的函数：
Figure PCTCN2021072473-appb-000008
FC k是关于σ的函数，代表第k次谐波的幅值，k＝1,2,3…。
Figure PCTCN2021072473-appb-000009
由上式(4)和(5)可得原电枢绕组4电枢反应磁场气隙磁密B ABC1(θ,t)为：
Figure PCTCN2021072473-appb-000010
式中，F am1为原电枢绕组4电枢反应磁动势傅里叶分解的系数。F am1’为经气隙磁导后原电枢绕组4电枢反应磁动势傅里叶分解的系数。m为经气隙磁导后原电枢绕组4电枢反应磁动势中奇数次谐波的次数，m＝1,3,5…。
原电枢绕组4电枢反应磁场气隙磁密B ABC1(θ,t)中包含的谐波的极对数为式(9)中转子位置角θ前面的系数，分为两部分，即vp 1和kN s1±mp 1对极，k＝1,2,3…，v＝1,3,5…，m＝1,3,5…。其中，当v＝p s/p 1，且k＝1，m＝p s/p 1时，那么：vp 1＝p s，kN s1±mp 1＝N s1-p s，N s1是定子齿5数，p s是原电枢绕组4绕组极对数，p 1是原电枢绕组4单相电枢反应磁场基波极对数。此时，p s对极和N s1-p s对极谐波属于工作谐波。除去工作谐波，其余谐波均属于非工作谐波。
由式(9)可得，原电枢绕组4的电枢反应磁场气隙磁密B ABC1(θ,t)中各次谐波的幅值为A (k,v,m)＝Λ 0n 1i 1F am1/v+Λ kn 1i 1F am1/m(k＝1,2,3…v＝1,3,5…m＝1,3,5…)。由于当谐波次数v增大时，所有原电枢绕组4产生的电枢反应磁场谐波的幅值A (k,v,m)均将减小，所以极对数为p 1的非工作谐波中的幅值最大。此时，可以找到k 1和m 1的值使得k 1N s1±m 1p 1＝p 1，其中，k 1∈k，为k的特例，m 1∈m，为m的特例，故由幅值A (k,v,m)＝Λ 0n 1i 1F am1/v+Λ k n 1i 1F am1’/m(k＝1,2,3…v＝1,3,5…m＝1,3,5…)公式可以得到：p 1对极非工作谐波的幅值可表示为A 1＝Λ 0n 1i 1F am1/1+Λ k1n 1i 1F am1’/m 1，其中，Λ 0为基波傅里叶系数，n 1为原电枢绕组4每个线圈的匝数，i 1为原电枢绕组4电流有效值，F am1为原电枢绕组4电枢反应磁动势傅里叶分解的系数，Λ k1为原电枢绕组4高次谐波傅里叶系数，Λ k1∈Λ k，为Λ k的特例，F am1’为经气隙磁导后原电枢绕组4电枢反应磁动势傅里叶分解的系数。
为抵消非工作谐波，提出一种在已有的三相分数槽集中绕组永磁电机基础上，通过在定子铁心轭部7上开设内槽的低谐波设计方法。如图2所示，在原电机的定子铁心轭部7上，开设N s2个内槽8，内槽8位于定子外槽6的内侧，每个内槽6结构完全相同，并称原来的定子外槽6为外槽，进而形成内、外槽结构。在内槽8内绕制副绕组9。具体步骤如下：
(1)首先确定所开设内槽8的槽数N s2。为增加副绕组9的谐波抵消效果，取内槽8 的槽数N s2与原电枢绕组4单相电枢反应磁场基波极对数p 1之比为整数。
(2)再确定内槽6内的副绕组9的极对数。取原电枢绕组4电枢反应磁场气隙磁密B ABC1(θ,t)中，由于非工作谐波极对数是vp 1，当v最小的时候，幅值最大，而v最小值是等于1，所以幅值最大的非作谐波的极对数为p 1。幅值最大的非工作谐波极对数p 1也是内层副绕组9的极对数，即副绕组9的极对数为p 1。
(3)再根据内槽8的槽数N s2和副绕组9的极对数p 1，确定槽距角α＝360×p 1/N s2，并绘制槽电势星型图，如图3所示，按照副绕组A2，B2，C2三相对称,确定副绕组9的绕制方式。
(4)由副绕组9的绕制方式，在副绕组9中通入三相电流，同理可得公式(1)～(9)，最终得到副绕组9电枢反应磁场气隙磁密B ABC2(θ,t)可表示为：
Figure PCTCN2021072473-appb-000011
式中，n 2为副绕组9每个线圈的匝数，i 2为副绕组9电流有效值，Λ 0和Λ k为基波和高次谐波傅里叶系数，F am2副绕组9电枢反应磁动势分解的系数，F am2’为经气隙磁导后副绕组9电枢反应磁动势傅里叶分解的系数。
副绕组9电枢反应磁场气隙磁密B ABC2(θ,t)中包含的谐波的极对数为式(10)中转子位置角θ前面的系数，分为两部分，即vp 1和kN s1±mp 1对极(k＝1,2,3…v＝1,3,5…m＝1,3,5…)。副绕组9电枢反应磁场气隙磁密B ABC2(θ,t)中各次谐波的幅值由式(10)可得为：B (k,v,m)＝Λ 0n 2i 2F am2/v+Λ kn 2i 2F am2’/m(k＝1,2,3…v＝1,3,5…m＝1,3,5…)。当v＝1时，此时，可以找到k 2和m 2使得其符合k 2N s1±m 2p 1＝p 1，其中，k 2∈k，为k的特例，m 2∈m，为m的特例，故p 1对极的幅值可表示为：B 1＝Λ 0n 2i 2F am2/1+Λ k2n 2i 2F am2’/m 2。其中，Λ 0为基波傅里叶系数，n 2为副绕组9的每个线圈的匝数，i 2为副绕组9的电流有效值，F am2为副绕组9电枢反应磁动势分解的系数，F am2’为经气隙磁导后副绕组9电枢反应磁动势傅里叶分解的系数，Λ k2为副绕组9高次谐波傅里叶系数，Λ k2∈Λ k，为Λ k的特例。
(5)为了尽可能多的抵消p 1对极非工作谐波，使得原电枢绕组4电枢反应磁场气隙磁 密B ABC1(θ,t)中幅值最大的p 1对极非工作谐波的幅值A 1与副绕组9电枢反应磁场气隙磁密B ABC2(θ,t)中p 1对极谐波的幅值B 1相等，即A 1＝B 1，即
Λ 0n 1i 1F am1/1+Λ k1n 1i 1F am1’/m 1＝Λ 0n 2i 2F am2/1+Λ k2n 2i 2F am2’/m 2
由于原电机已知，上式中仅有n 2i 2未知，即n 2与i 2的乘积未知，上述等式左边可代入原电机的已知量由计算得到一具体数值。等式的右边是副绕组9每个线圈的匝数n 2与副绕组9所通电流有效值i 2乘积的一个表达式。由计算可得n 2×i 2的值为C。
(6)确定所开内槽8的径向截面积。由槽电流密度公式(11)和步骤(5)中已求得的副绕组的n 2×i 2的值C可得内槽8的半槽面积S 2；
Figure PCTCN2021072473-appb-000012
式中，δ为槽满率，由电机的加工工艺和散热条件决定，一般取0.5～0.8，S 2为内槽半槽的径向截面积。J为槽电流密度，由电机的散热条件等因素决定，自然冷却条件下，一般取5左右。
(7)由步骤(1)中选定的N s2和步骤(6)中确定的半槽面积S 2在定子铁心轭部7处开设内槽8，要求内槽8在圆周上均匀分布；为了副绕组9的嵌线方便，最佳方案为设置内槽8和定子外槽6在直径方向上对齐。
(8)根据电机系统功率需求、电源电压和本领域常规知识选取合适的副线圈匝数n 2，由步骤(5)中所得n 2×i 2的值为C，进而可计算出电流i 2＝C/n 2，并由此选择铜导线的线径，并对槽满率δ进行校核，槽满率δ在0.5～0.8范围：
Figure PCTCN2021072473-appb-000013
式中，d为所选铜导线漆包线最大外径。
(9)确定副绕组9的电流相位。为实现副绕组电枢反应磁场气隙磁密中p 1对极谐波对原电枢绕组电枢反应磁场气隙磁密中幅值最大的p 1对极非工作谐波有效抵消，两绕组产生的相互抵消的谐波磁场相位应相差180°，即原电枢绕组产生的幅值最大的非工作谐波磁场和副绕组产生的幅值最大的谐波磁场相位应相差180°。相位差由两套绕组的空间位置差和电流相位差共同决定。故需要合理设置两套三相绕组之间的空间位置和各自电流的相位差。
由于外槽定子槽6是已知的，而内槽8已按照上述步骤开设，因此，此时可以得到原电枢绕组4与副绕组9之间的空间位置角差为Δβ，参见图2所示，由内外槽位置Δβ差Δβ与绕组绕制的位置共同决定。由式(1)，原电枢绕组4所通A相电流为
Figure PCTCN2021072473-appb-000014
副绕组9所通A相电流为
Figure PCTCN2021072473-appb-000015
原电枢绕组4与副绕组9这两套绕组通入的电流相位角相差为Δθ。为使内、外槽两套绕组各自的p 1对极谐波可以相互抵消，副绕组9的电流相位角等于Δθ，即：
△θ＝±(±180°+z360°-p 1△β)       (13)
其中，z为正整数。
当已有的一台三相分数槽集中绕组永磁电机，包含36个定子齿，永磁体和原电枢绕组4极对数均为21，利用本发明所述的双绕组低谐波设计方法，所开设内槽个数为18，副绕组9的极对数为3的时候，本发明的具体实施效果如图5所示，可见在原电枢绕组4和副绕组9中按要求通入电流后，原电枢绕组4电枢反应气隙磁密中最大幅值的3对极谐波被抵消，实现了分数槽集中绕组的低谐波设计。

Claims (6)

  1. 一种基于分数槽集中绕组永磁电机的双绕组低谐波设计方法，分数槽集中绕组永磁电机采用内定子结构，包括N s1个定子齿和一个定子铁心轭部，相邻两个定子齿之间形成定子外槽，定子外槽内绕制原电枢绕组，其特征是包括以下步骤：
    步骤1)：给原电枢绕组中通入三相电流，得到原电枢绕组的电枢反应磁场气隙磁密、单相电枢反应磁场基波极对数p 1以及p 1对极非工作谐波的幅值A 1＝Λ 0n 1i 1F am1/1+Λ k1n 1i 1F am1’/m 1，且k 1和m 1符合k 1N s1±m 1p 1＝p 1；Λ 0为基波傅里叶系数，n 1为原电枢绕组每个线圈的匝数，i 1为原电枢绕组电流有效值，F am1为原电枢绕组电枢反应磁动势傅里叶分解的系数，Λ k1为原电枢绕组高次谐波傅里叶系数，Λ k1∈Λ k，Λ k为高次谐波傅里叶系数，F am1’为经气隙磁导后原电枢绕组电枢反应磁动势傅里叶分解的系数，m 1∈m，m为经气隙磁导后原电枢绕组电枢反应磁动势中奇数次谐波的次数，m＝1,3,5…，k 1∈k，k为谐波次数，k＝1,2,3…；
    步骤2)：在所述定子铁心轭部上开设位于所述定子外槽的内侧的N s2个内槽，内槽数N s2与所述极对数p 1之比为整数，在所述内槽内绕制副绕组，副绕组极对数为p 1；
    步骤3)：根据内槽数N s2和副绕组的极对数p 1确定槽距角α＝360×p 1/N s2和副绕组的绕制方式；
    步骤4)：在副绕组中通入三相电流，得到副绕组的电枢反应磁场气隙磁密以及p 1对极幅值B 1＝Λ 0n 2i 2F am2/1+Λ k2n 2i 2F am2’/m 2，A 1＝B 1，且k 2和m 2符合k 2N s1±m 2p 1＝p 1，由幅值A 1＝B 1得到其中的n 2×i 2的值为C；n 2为副绕组的每个线圈的匝数，i 2为副绕组的电流有效值，F am2为副绕组电枢反应磁动势分解的系数，F am2’为经气隙磁导后副绕组电枢反应磁动势傅里叶分解的系数，Λ k2∈Λ k，m 2∈m；
    步骤5)：根据公式
    Figure PCTCN2021072473-appb-100001
    确定所述内槽的半槽径向截面积S 2，δ为槽满率，取0.5～0.8，。J为槽电流密度。
  2. 根据权利要求1所述的基于分数槽集中绕组永磁电机的双绕组低谐波设计方法，其特征是：步骤1)中，原电枢绕组电枢反应磁场气隙磁密中包含的谐波的极对数为vp 1和kN s1±mp 1对极，当v＝p s/p 1，且k＝1，m＝p s/p 1时，有：vp 1＝p s，kN s1±mp 1＝N s1-p s；p s对极和N s1-p s对极谐波属于工作谐波，其余谐波均属于非工作谐波，极对数为p 1的非工作谐波中的幅值最大；v为原电枢绕组总电枢反应磁动势中奇数次谐波的次数，v＝1,3,5…，p s是原电枢绕组极对数。
  3. 根据权利要求1所述的基于分数槽集中绕组永磁电机的双绕组低谐波设计方法，其特征是：步骤2)中，N s2个内槽结构相同且在所述定子铁心轭部上沿圆周上均匀分布。
  4. 根据权利要求1所述的基于分数槽集中绕组永磁电机的双绕组低谐波设计方法，其 特征是：步骤2)中，内槽和定子外槽在直径方向上对齐。
  5. 根据权利要求1所述的基于分数槽集中绕组永磁电机的双绕组低谐波设计方法，其特征是：步骤5)后，原电枢绕组产生的幅值最大的非工作谐波磁场和副绕组产生的幅值最大的谐波磁场相位相差180°，原电枢绕组所通A相电流
    Figure PCTCN2021072473-appb-100002
    副绕组所通A相电流
    Figure PCTCN2021072473-appb-100003
    Δθ是原电枢绕组和副绕组通入的电流相位角差值，ω e为电速度，t为电流周期。
  6. 根据权利要求5所述的基于分数槽集中绕组永磁电机的双绕组低谐波设计方法，其特征是：副绕组的电流相位角等于△θ＝±(±180°+z360°-p 1△β)，z为正整数，Δβ是原电枢绕组与副绕组之间的空间位置角差。
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