阅读说明：本技术 一种低谐波模块化绕组的设计方法 (Design method of low-harmonic modular winding ) 是由 郭玉敬 王帅 徐瑞海 金平 于 2020-12-16 设计创作，主要内容包括：本发明公开了一种低谐波模块化绕组的设计方法,包括步骤1、确定每极每相槽型；步骤2、计算槽极比q；步骤3、确定整数槽和假分数槽中的绕组类型；步骤4、计算整数槽和假分数槽中的绕组层数m；步骤5、确定真分数槽中的绕组类型及绕组层数m；步骤6、计算每层绕组的线圈匝数：根据磁链变化和正弦曲线的拟合过程,分别计算整数槽和假分数槽绕组中每层线圈的匝数、以及真分数槽绕组中每层线圈的匝数。本发明包括磁链计算和正弦拟合两部分,将不同极槽配合下的模块化多层绕组设计进行统一,并保证绕组磁动势具有最低的谐波含量,并能通过调节绕组排布方式和绕组匝数,在不增加成本的情况下将磁动势谐波降到最低,提高模块化电机性能指标。(The invention discloses a design method of a low-harmonic modular winding, which comprises the following steps of 1, determining a groove type of each phase of each pole; step 2, calculating the slot pole ratio q (ii) a Step 3, determining winding types in the integer slots and the false fractional slots; step 4, calculating the winding layer number in the integer slots and the false fractional slots m (ii) a Step 5, determining the winding type and the winding layer number in the genuine fraction groove m (ii) a Step 6, calculating the number of turns of the coil of each layer of winding: respectively calculating the number of turns of each layer of coil in the integer slot winding and the false fractional slot winding and the number of turns of each layer of coil in the true fractional slot winding according to the flux linkage change and the fitting process of the sine curveThe number of turns. The modular motor stator winding design method comprises two parts of flux linkage calculation and sine fitting, unifies modular multilayer winding design under the matching of different pole slots, ensures that the magnetomotive force of the winding has the lowest harmonic content, and can reduce the magnetomotive force harmonic to the lowest under the condition of not increasing cost by adjusting the winding arrangement mode and the number of turns of the winding, thereby improving the performance index of the modular motor.)

1. A design method of a low-harmonic modular winding is characterized by comprising the following steps: the method comprises the following steps:

step 1, determining groove types of each phase of each pole: calculating the number v of slots of each pole and each phase of the motor winding, and dividing the slot type of each pole and each phase of the motor winding into an integer slot, a false fractional slot and a true fractional slot according to a v value result;

step 2, calculating the slot pole ratio q: the slot pole ratio Q is Q/P, wherein Q is the number of stator slots, and P is the number of motor poles;

step 3, determining winding types in the integer slots and the false fractional slots: determining winding types in the integer slots and the pseudo fractional slots according to the slot type v of each phase of each pole determined in the step 1 and the slot pole ratio q calculated in the step 2, wherein the winding types comprise triangular windings and trapezoidal windings;

and 4, calculating the number m of winding layers in the integer slots and the false fractional slots, wherein the specific calculation method comprises the following steps:

step 4A, when the slot type of each phase of each pole is an integer slot or a pseudo fractional slot and a triangular winding is adopted, the number m of winding layers simultaneously satisfies the following formulas (1) to (3):

wherein k is a positive integer, i.e., m is a divisor of Q/3;

step 4B, when the slot type of each phase of each pole is an integer slot or a pseudo fractional slot and a trapezoidal winding is adopted, the number m of winding layers simultaneously satisfies the following formulas (4) to (6):

step 5, determining the winding type and the winding layer number m in the true fraction slot: when each phase slot type of each pole is a true fraction slot, the number m of the winding layers needs to satisfy a formula (1) in the step 4A or a formula (4) in the step 4B, and m belongs to [2,4 ]; the winding type preferably takes into account the winding type in the formula (1) or (4) corresponding to m ═ 3;

step 6, calculating the number of turns of the coil of each layer of winding: and respectively calculating the number of turns of each layer of coil in the integer slot winding and the false fractional slot winding and the number of turns of each layer of coil in the true fractional slot winding according to the flux linkage change and the fitting process of the sine curve.

2. The method of designing a low harmonic modular winding of claim 1, wherein: in step 6, the method for calculating the number of turns of each layer of coils in the integer slot winding and the pseudo fractional slot winding comprises the following steps:

step 6A1, numbering the turns of the m layers of coils: the number of turns of the m layers of coils is N from small to large₁、N₂、……、N_i、……、N_m-1、N_m；

Step 6A2, number N of turns of i-th layer coil_iThe calculation method comprises the following steps:

wherein the content of the first and second substances,

in the formula, alpha is the electrical angle occupied by a single stator slot;

step 6A3, arranging the turns of the m layers of coils, wherein the specific arrangement method is as follows:

when m is an odd number, the number of turns of the m layers of coils is set as: n is a radical of_m＝N₀，N₁+N_m-1＝N₀、N₂+N_m-2＝N₀、…、N_i+N_m-i＝N₀(ii) a Wherein N is₀An upper limit of turns that can be accommodated by a single stator slot; wherein, i is more than or equal to 1 and less than or equal to (m-1)/2;

when m is an even number, the number of turns of the m layers of coils is set as: n is a radical of_m＝N₀，N_m/2＝N₀/2，N₁+N_m-1＝N₀，N₂+N_m-2＝N₀、…、N_i+N_m-i＝N₀(ii) a Wherein, i is more than or equal to 1 and less than or equal to (m-2)/2.

3. The method of designing a low harmonic modular winding of claim 1, wherein: in step 6, the method for calculating the number of turns of each layer of coils in the true fraction slot winding comprises the following steps:

and 6B1, calculating e, wherein the specific calculation method formula is as follows:

(1) calculating the pole-slot ratio q by the following formula:

in the formula, Q₁And n₁The numerator and denominator are in the form of the simplest fraction of the polar trough ratio q;

(2) e is calculated, and the calculation formula is as follows:

e＝(2k-1)-(2k-2)q (9)

in the formula (9), k is a natural number, and the value of k is such that e is more than or equal to-1;

step 6B2, calculating f (k): calculating f (k) for e corresponding to each value k in the step 6B1 according to the following formula (10):

wherein sign () is a sign function, and fix () is a rounding function that rounds to zero; all values k meeting the requirements are calculated to obtain f (k), and the f (k) is respectively ordered into f (1), f (2), f (3) and f (k) from small to large according to the k value;

step 6B3, calculating a row vector A: the row vector a is a row vector related to f (k), and the specific expression is as follows:

A＝[A₁ A₂ A₁ A₂...] (11)

wherein the content of the first and second substances,

A₁is the sequence: f (1) f (2) f (3).. f (k)

A₂Is the sequence: f (k) f (k-1).. f (2) f (1)

In the formula (11), A₁And A₂The sequence elements are identical but arranged in the opposite order; vector A is A₁And A₂The total number of elements in A is not less than 2m-2+ Q after combination₁Or 2m-1+ Q₁A plurality of;

step 6B4, solving coefficient matrix B_triOr B_traThe concrete solving formula is as follows:

in the formula, B_triCoefficient matrix corresponding to the triangular winding, B_traA coefficient matrix corresponding to the trapezoidal winding; a (1), A (2), A (3), A (Q)₁)、A(Q₁+1)、A(Q₁+2m-2) and A (Q)₁+2m-1) respectively represent the 1 st, 2, 3, Q in the vector A₁、Q₁+1、Q₁+2m-2 and Q₁+2m-1 elements;

step 6B5, calculating a flux linkage coefficient F: let N_a＝x，N_m-aY, and x + y N₀，x,y∈[0,N₀]Then, the calculation method of the flux linkage coefficient F is:

(1) when the winding type is a triangular winding, the calculation formula of the flux linkage coefficient F is as follows:

F＝B_triX_a·x+B_triY_a·y

wherein, the vector X_aAnd Y_aThe method is determined according to the parity of the winding layer number m, and the specific determination method comprises the following steps:

when m is an odd number, a is an interval [1, (m-1)/2]Internal integer, in m ∈ [2, 4]]When a is 1, vector X_aAnd Y_aComprises the following steps:

X_a＝[0_1×(a-1) 1 0_1×(m-a-1) 1 0_1×(m-a-1) 1 0_1×(a-1)]^T

Y_a＝[0_1×(m-a-1) 1 0_1×(a-1) 1 0_1×(a-1) 1 0_1×(m-a-1)]^T.

when m is an even number, a is an interval of [1, (m-2)/2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

(2) when the winding type is a trapezoidal winding, the calculation formula of the flux linkage coefficient F is as follows:

F＝B_traX_a·x+B_traY_a·y

wherein, the vector X_aAnd Y_aThe method is determined according to the parity of the winding layer number m, and the specific determination method comprises the following steps:

when m is an odd number, a is an interval [1, (m-1)/2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

X_a＝[0_1×(a-1) 1 0_1×(m-a-1) 1 1 0_1×(m-a-1) 1 0_1×(a-1)]^T

Y_a＝[0_1×(m-a-1) 1 0_1×(a-1) 1 1 0_1×(a-1) 1 0_1×(m-a-1)]^T.

when m is an even number, a is an interval of [1, (m-2)/2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

(3) q should be included in the calculated flux linkage coefficient F₁Taking absolute value of each element, extracting the element backwards from the element with the minimum absolute value until repeated elements appear, and respectively recording the elements as f₁、f₂、…、f_g；

Step 6B6, calculating the electrical angle alpha, wherein the specific calculation formula is as follows:

in the formula, Q₁Molecules in the form of the fraction of the polar trough ratio q;

step 6B7, determining an objective fitting function: f determined in step 6B6₁、f₂、…、f_gFitting by adopting a least square method principle to obtain a target fitting function;

step 6B8, determine x and y: x + y is equal to N₀And substituting the electrical angle alpha obtained by calculation in the step 6B6 into the target fitting function determined in the step 6B7, wherein when the target fitting function is minimum, the corresponding x and y values are the solved N_aAnd N_m-a。

4. The method of designing a low harmonic modular winding of claim 1, wherein: in step 3, the specific determination method of the winding types in the integer slots and the pseudo fractional slots comprises the following steps:

step 3A, when the groove type of each phase of each pole is an integer groove, if the groove pole ratio q is an even number, adopting a trapezoidal winding; if the slot pole ratio q is an odd number, adopting a triangular winding;

step 3B, when the groove type of each phase of each pole is a false fractional groove, if the nearest integer of the groove pole ratio q is an even number, adopting a trapezoidal winding; if the nearest integer of the slot pole ratio q is an odd number, a triangular winding is adopted.

Technical Field

The invention relates to the field of synchronous motors, in particular to a design method of a low-harmonic modular winding.

Background

With the increasing requirements of industrial production on the production efficiency and reliability of motors, modular winding structures are increasingly applied to synchronous motors.

Permanent magnet synchronous motors have been widely used in recent years because of their advantages of high torque density, high efficiency, compact structure, etc. In order to improve industrial production efficiency and fault-tolerant capability, concentrated windings are widely adopted in the permanent magnet synchronous motor, and have the advantages of no overlapping, short end turns, high slot filling coefficient, easiness in manufacturing and the like. However, it has very high space harmonics in the air gap magnetomotive force, resulting in higher torque ripple, increased core loss, and reduced power factor. The efficiency of the multilayer winding is significantly improved because it reduces the winding factor/amplitude of the MMF subharmonic components of the stator. Redesigning the winding layout is therefore an effective way to solve the above mentioned problems.

Disclosure of Invention

The invention aims to solve the technical problem of the prior art and provides a design method of a low-harmonic modular winding, which can enable the flux linkage change of a coil to be closer to sine, lower the content of magnetomotive force harmonic and improve the efficiency and power factor of a motor. In addition, the winding is easy to modularly design and assemble, has good redundant design, and can reduce the production and maintenance cost.

In order to solve the technical problems, the invention adopts the technical scheme that:

a design method of a low-harmonic modular winding comprises the following steps.

Step 1, determining groove types of each phase of each pole: and calculating the number v of slots of each pole and each phase of the motor winding, and dividing the slot type of each pole and each phase of the motor winding into an integer slot, a false fractional slot and a true fractional slot according to a v value result.

Step 2, calculating the slot pole ratio q: and the slot pole ratio Q is Q/P, wherein Q is the number of stator slots, and P is the number of motor poles.

Step 3, determining winding types in the integer slots and the false fractional slots: and determining winding types in the integer slots and the pseudo fractional slots according to the slot type v of each pole and each phase determined in the step 1 and the slot pole ratio q calculated in the step 2, wherein the winding types comprise triangular windings and trapezoidal windings.

And 4, calculating the number m of winding layers in the integer slots and the false fractional slots, wherein the specific calculation method comprises the following steps:

step 4A, when the slot type of each phase of each pole is an integer slot or a pseudo fractional slot and a triangular winding is adopted, the number m of winding layers simultaneously satisfies the following formulas (1) to (3):

wherein k is a positive integer, i.e., m is a divisor of Q/3;

step 4B, when the slot type of each phase of each pole is an integer slot or a pseudo fractional slot and a trapezoidal winding is adopted, the number m of winding layers simultaneously satisfies the following formulas (4) to (6):

step 5, determining the winding type and the winding layer number m in the true fraction slot: when the slot type of each phase of each pole is a real fraction slot, the number m of the winding layers needs to satisfy the formula (1) in the step 4A or the formula (4) in the step 4B, and m is equal to m ∈ [2,4 ]. The winding type preferably takes into account the winding type in the formula (1) or (4) to which m-3 corresponds.

Step 6, calculating the number of turns of the coil of each layer of winding: and respectively calculating the number of turns of each layer of coil in the integer slot winding and the false fractional slot winding and the number of turns of each layer of coil in the true fractional slot winding according to the flux linkage change and the fitting process of the sine curve.

In step 6, the method for calculating the number of turns of each layer of coils in the integer slot winding and the pseudo fractional slot winding comprises the following steps:

step 6A1, numbering the turns of the m layers of coils: the number of turns of the m layers of coils is N from small to large₁、N₂、……、N_i、……、 N_m-1、N_m。

Step 6A2, number N of turns of i-th layer coil_iThe calculation method comprises the following steps:

wherein the content of the first and second substances,

where α is the electrical angle occupied by a single stator slot.

Step 6A3, arranging the turns of the m layers of coils, wherein the specific arrangement method is as follows:

when m is an odd number, the number of turns of the m layers of coils is set as: n is a radical of_m＝N₀，N₁+N_m-1＝N₀、N₂+N_m-2＝N₀、…、N_i+N_m-i＝N₀(ii) a Wherein N is₀An upper limit of turns that can be accommodated by a single stator slot; wherein, i is more than or equal to 1 and less than or equal to (m-1)/2;

when m is an even number, the number of turns of the m layers of coils is set as: n is a radical of_m＝N₀，N_m/2＝N₀/2，N₁+N_m-1＝N₀，N₂+N_m-2＝N₀、…、 N_i+N_m-i＝N₀(ii) a Wherein, i is more than or equal to 1 and less than or equal to (m-2)/2.

In step 6, the method for calculating the number of turns of each layer of coils in the true fraction slot winding comprises the following steps:

and 6B1, calculating e, wherein the specific calculation method formula is as follows:

(1) calculating the pole-slot ratio q by the following formula:

in the formula, Q₁And n₁The numerator and denominator under the form of the simplest fraction of the polar trough ratio q.

(2) E is calculated, and the calculation formula is as follows:

e＝(2k-1)-(2k-2)q (9)

in the formula (9), k is a natural number, and the value of k is such that e is not less than-1.

Step 6B2, calculating f (k): calculating f (k) for e corresponding to each value k in the step 6B1 according to the following formula (10):

where sign () is a sign function and fix () is a rounding function that rounds to zero. All values k meeting the requirements are calculated to obtain f (k), and the f (k) is respectively ordered into f (1), f (2), f (3) and.

Step 6B3, calculating a row vector A: the row vector a is a row vector related to f (k), and the specific expression is as follows:

A＝[A₁ A₂ A₁ A₂...] (11)

wherein the content of the first and second substances,

A₁is the sequence: f (1) f (2) f (3).. f (k)

A₂Is the sequence: f (k) f (k-1).. f (2) f (1)

In the formula (11), A₁And A₂The sequence elements are identical but arranged in the opposite order. Vector A is A₁And A₂The total number of elements in A is not less than 2m-2+ Q after combination₁Or 2m-1+ Q₁And (4) respectively.

Step 6B4, solving coefficient matrix B_triOr B_traThe concrete solving formula is as follows:

in the formula, B_triCoefficient matrix corresponding to the triangular winding, B_traA coefficient matrix corresponding to the trapezoidal winding. A (1), A (2), A (3), A (Q)₁)、A(Q₁+1)、A(Q₁+2m-2) and A (Q)₁+2m-1) respectively represent the 1 st, 2, 3, Q in the vector A₁、Q₁+1、Q₁+2m-2 and Q₁+2m-1 elements.

Step 6B5, calculating a flux linkage coefficient F: let N_a＝x，N_m-aY, and x + y N₀，x,y∈[0,N₀]Then, the calculation method of the flux linkage coefficient F is:

(1) when the winding type is a triangular winding, the calculation formula of the flux linkage coefficient F is as follows:

F＝B_triX_a·x+B_triY_a·y

wherein, the vector X_aAnd Y_aThe method is determined according to the parity of the winding layer number m, and the specific determination method comprises the following steps:

when m is an odd number, a is an interval [1, (m-1)/2]Internal integer, in m ∈ [2, 4]]When a is 1. Vector X_aAnd Y_aComprises the following steps:

X_a＝[0_1×(a-1) 1 0_1×(m-a-1) 1 0_1×(m-a-1) 1 0_1×(a-1)]^T

Y_a＝[0_1×(m-a-1) 1 0_1×(a-1) 1 0_1×(a-1) 1 0_1×(m-a-1)]^T.

when m is an even number, a is an interval of [1, (m-2)/2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

(2) when the winding type is a trapezoidal winding, the calculation formula of the flux linkage coefficient F is as follows:

F＝B_traX_a·x+B_tra Y_a·y

wherein, the vector X_aAnd Y_aThe method is determined according to the parity of the winding layer number m, and the specific determination method comprises the following steps:

when m is an odd number, a is an interval [1, (m-1)/2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

X_a＝[0_1×(a-1) 1 0_1×(m-a-1) 1 1 0_1×(m-a-1) 1 0_1×(a-1)]^T

Y_a＝[0_1×(m-a-1) 1 0_1×(a-1) 1 1 0_1×(a-1) 1 0_1×(m-a-1)]^T.

when m is an even number, a is an interval of [1, (m-2)/2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

(3) q should be included in the calculated flux linkage coefficient F₁Taking absolute value of each element, extracting the element backwards from the element with the minimum absolute value until repeated elements appear, and respectively recording the elements as f₁、f₂、…、f_g。

Step 6B6, calculating the electrical angle alpha, wherein the specific calculation formula is as follows:

in the formula, Q₁The polar channels are less than q molecules in the fraction of the simplest form.

Step 6B7, determining an objective fitting function: f determined in step 6B6₁、f₂、…、f_gAnd fitting by adopting a least square method principle to obtain a target fitting function.

Step 6B8, determine x and y: x + y is equal to N₀And substituting the electrical angle alpha obtained by calculation in the step 6B6 into the target fitting function determined in the step 6B7, wherein when the target fitting function is minimum, the corresponding x and y values are the solved N_aAnd N_m-a。

In step 3, the specific determination method of the winding types in the integer slots and the pseudo fractional slots comprises the following steps:

and 3A, when the groove type of each phase of each pole is an integer groove, if the groove pole ratio q is an even number, adopting a trapezoidal winding. If the slot pole ratio q is odd, a triangular winding is adopted.

And 3B, when the slot type of each phase of each pole is a pseudo fractional slot, if the nearest integer of the slot pole ratio q is an even number, adopting a trapezoidal winding. If the nearest integer of the slot pole ratio q is an odd number, a triangular winding is adopted.

The invention has the following beneficial effects:

1. the invention aims at the modularized winding structure, gives the appropriate winding coil distribution and ensures that the winding coil has the lowest magnetomotive force harmonic content. The method has wide application range, and is suitable for integer slot windings, true fraction slots and false fraction slot windings. The winding design method provided by the invention greatly improves the design efficiency of the modular winding, and through optimizing the number of turns of the coils of each part, the change of the magnetic linkage of each phase is sinusoidal, so that the problem of high content of magnetomotive force harmonic of the modular winding is solved.

2. The method comprises two parts of flux linkage calculation and sine fitting, can unify the design method of the modular multilayer winding under the matching of different pole slots, and ensures that the magnetomotive force of the winding has the lowest harmonic content. The winding design method provided by the invention is convenient for improving the modularization and redundancy design efficiency of the synchronous motor winding. And the magnetomotive force (MMF) harmonic can be reduced to the lowest by adjusting the winding arrangement mode and the winding turns without increasing the cost, and the performance index of the modular motor is improved.

Drawings

Fig. 1 shows a schematic diagram of a winding according to the invention, in which: (a) is a triangular winding; (b) is a trapezoidal winding.

Fig. 2 shows a schematic view of the winding layering when m is 3.

Fig. 3 shows a schematic of an 18 slot 16 pole, m-3 adjustable winding.

Fig. 4 shows an analytical representation of the winding under 18 poles and 16 slots, (a) a general winding layout; (b) and (4) optimized winding arrangement.

Fig. 5 shows a comparison graph of the spectral analysis of the winding under 18 poles and 16 slots.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and specific preferred embodiments.

In the description of the present invention, it is to be understood that the terms "left side", "right side", "upper part", "lower part", etc., indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and that "first", "second", etc., do not represent an important degree of the component parts, and thus are not to be construed as limiting the present invention. The specific dimensions used in the present example are only for illustrating the technical solution and do not limit the scope of protection of the present invention.

A design method of a low-harmonic modular winding comprises the following steps.

Step 1, determining the groove type of each phase of each pole.

Step 11, calculating the number v of slots of each pole and each phase of the motor winding, wherein the calculation formula is as follows:

in the formula, Q is the number of stator slots, P is the number of poles of the motor, and M is the number of winding phases.

In the present embodiment, an 18-slot 16-pole three-phase motor will be described in detail as an example. An 18-slot 16-pole three-phase motor, namely, Q is 18, P is 16, M is 3, and v is 3/8.

And 12, dividing the slot type of each pole and phase of the motor winding into an integer slot, a false fractional slot and a true fractional slot according to the v value result. The 18-slot 16-pole three-phase motor in the present embodiment is a true-fraction slot because v is 3/8.

Step 2, calculating the slot pole ratio q: and the slot pole ratio Q is Q/P, wherein Q is the number of stator slots, and P is the number of motor poles.

In the 18-slot 16-pole three-phase motor in the embodiment, the slot pole ratio Q is Q/P18/16 is 9/8.

And 3, determining the winding types in the integer slots and the false fractional slots.

And (2) determining the winding types in the integer slots and the pseudo fractional slots according to the slot type of each pole and each phase determined in the step (1) and the slot pole ratio Q/P calculated in the step (1), wherein the specific determination method comprises the following steps:

step 3A, when the groove type of each phase of each pole is an integer groove, if the groove pole ratio Q/P is an even number, adopting a trapezoidal winding; if the slot pole ratio Q/P is odd, a triangular winding is adopted.

Step 3B, when the groove type of each phase of each pole is a false fractional groove, if the nearest integer of the groove pole ratio Q/P is an even number, adopting a trapezoidal winding; if the nearest integer of the slot pole ratio Q/P is an odd number, a triangular winding is adopted.

The above-described delta winding is defined as a delta winding because the coil having the largest number of turns in the winding is wound around only a single tooth in each phase zone, as shown in fig. 1 (a).

The trapezoidal winding is defined as a trapezoidal winding in which a coil having the largest number of turns is wound around two different teeth in each phase zone, as shown in fig. 1 (b).

Compared with a trapezoidal winding, the triangular winding has the following differences: the number of coils with the largest number of turns per phase strip is different, which makes the phase strip of the delta winding always occupy an odd number of slots, while the phase strip of the trapezoidal winding always occupies an even number of slots. That is, the two types of windings can be applied to the case where the slot pole ratio Q/P is odd or even under the integer slot, respectively, and the delta or trapezoidal winding is selected according to the parity of the integer closest to the slot pole ratio Q/P under the pseudo-fractional slot.

And 4, calculating the number m of winding layers in the integer slots and the false fractional slots, wherein the specific calculation method is as follows.

Step 4A, when the slot type of each phase of each pole is an integer slot or a pseudo fractional slot and a triangular winding is adopted, the number m of winding layers simultaneously satisfies the following formulas (1) to (3):

wherein k is a stator slot space utilization coefficient and is a natural number; as described aboveFunction can returnAnd the greatest common divisor of P; the round () above is a rounding function.

Step 4B, when the slot type of each phase of each pole is an integer slot or a pseudo fractional slot and a trapezoidal winding is adopted, the number m of winding layers simultaneously satisfies the following formulas (4) to (6):

the above equations (1) and (4) can ensure that all stator slots are used efficiently.

The above equations (2) and (5) can make the three-phase flux linkage mutually different by 120 degrees.

The above equations (3) and (6) are not strict equations, and m only needs to be as close as possible to the right of the equation, and in practical applications, m should satisfy m e [2,4 ].

And 5, determining the winding type and the winding layer number m in the true fraction slot.

When the slot type of each phase of each pole is a real fraction slot, the number m of the winding layers needs to satisfy the formula (1) in the step 4A or the formula (4) in the step 4B, and m belongs to [2,4 ]. The winding type preferably takes into account the winding type in the formula (1) or (4) to which m-3 corresponds.

In the 18-slot 16-pole three-phase motor in the embodiment, since the motor is a true fractional slot type, the design process of the winding type and the number m of winding layers is as follows:

the calculation process using equation (1) is:

when k is equal to 1, the first step is carried out,does not satisfy m epsilon [2,4 ∈]Therefore, the process is left off;

when k is equal to 2, the number of the bits is increased,satisfy m is in the range of [2, 4]]；

When k is 3, the number of the groups is 3,satisfy m is in the range of [2, 4]]；

When k is equal to 4, the number of the first symbols is 4,does not satisfy m epsilon [2,4 ∈]So is discarded and the calculation is terminated.

The calculation process using equation (4) is:

when k is equal to 1, the first step is carried out,does not satisfy m epsilon [2,4 ∈]Therefore, the process is left off;

when k is equal to 2, the number of the bits is increased,satisfy m is in the range of [2, 4]]；

When k is 3, the number of the groups is 3,does not satisfy m epsilon [2,4 ∈]So is discarded and the calculation is terminated.

As can be seen from the above analysis, m may be 2 or 3, preferably m is 3, and m is 3 corresponds to formula (1), and the winding type corresponding to formula (1) is a delta winding, so that the 18-slot 16-pole three-phase motor in the present embodiment is preferably a delta winding, and m is 3.

If the equations (1) and (4) can both satisfy that m is equal to 3, the winding type may be a delta winding or a trapezoidal winding, and is specifically selected as required.

Step 6, calculating the number of turns of the coil of each layer of winding: and respectively calculating the number of turns of each layer of winding in the integer slots and the false fractional slots and the number of turns of each layer of winding in the true fractional slots according to the flux linkage change and the fitting process of the sine curve.

In step 6, the method for calculating the number of turns of each layer of coils in the integer slot winding and the pseudo fractional slot winding comprises the following steps.

Step 6A1, numbering the turns of the m layers of coils: the number of turns of the m layers of coils is N from small to large₁、N₂、……、N_i、……、 N_m-1、N_m。

Step 6A2, number N of turns of i-th layer coil_iThe calculation method comprises the following steps:

wherein the content of the first and second substances,

where α is the electrical angle occupied by a single stator slot.

Step 6A3, arranging the turns of the m layers of coils, wherein the specific arrangement method is as follows:

when m is an odd number, the number of turns of the m layers of coils is set as: n is a radical of₁+N_m-1＝N₀、N₂+N_m-2＝N₀、…、N_i+N_m-i＝N₀、…、 N_(m-1)/2+N_(m+1)/2＝N₀、N_m＝N₀. Wherein N is₀An upper limit of the number of turns that can be accommodated by a single stator slot. Wherein, i is more than or equal to 1 and less than or equal to (m-1)/2.

When m is an even number, the number of turns of the m layers of coils is set as: n is a radical of_m＝N₀＝2N_m/2，N₁+N_m-1＝N₀。N₂+N_m-2＝N₀。…、 N_i+N_m-i＝N₀、…、N_m/2-1+N_m/2+1＝N₀. Wherein, i is more than or equal to 1 and less than or equal to (m-2)/2.

In step 6, the method for calculating the number of turns of each layer of coils in the true fraction slot winding comprises the following steps.

And 6B1, calculating e, wherein the specific calculation method formula is as follows:

e＝(2k-1)-(2k-2)q (9)

in the formula: q ═ Q/P (8)

In the formula, k is a natural number, and the value of k is such that e is not less than-1.

In the 18-slot 16-pole three-phase motor in the embodiment, the calculation process of e is as follows:

when k is 1, e ═ q ═ 2k-1) - (2k-2) (2 × 1-1) - (2 × 1-2) × 9/8 ═ 1;

when k is 2, e ═ q ═ 2 x 2-1) - (2k-2) q ═ 3/4 (2 x 2-1) - (2 x 2-2) x 9/8 ═ 3/4;

when k is 3, e ═ q ═ 2k-1) - (2k-2) (2 × 3-1) - (2 × 3-2) × 9/8 ═ 1/2;

when k is 4, e ═ q ═ 2k-1) - (2k-2) (2 × 4-1) - (2 × 4-2) × 9/8 ═ 1/4;

when k is 5, e ═ q ═ 2k-1) - (2k-2) (2 × 5-1) - (2 × 5-2) × 9/8 ═ 0;

when k is 6, e ═ q ═ 2k-1) - (2k-2) (2 × 6-1) - (2 × 6-2) × 9/8 ═ 1/4;

when k is 7, e ═ q ═ 2k-1) - (2k-2) (2 × 7-1) - (2 × 7-2) × 9/8 ═ 1/2;

when k is 8, e ═ q ═ 2k-1) - (2k-2) (2 × 8-1) - (2 × 8-2) × 9/8 ═ 3/4;

when k is 9, e ═ q ═ 2k-1) - (2k-2) (2 × 9-1) - (2 × 9-2) × 9/8 ═ 1;

when k is 10, e ═ q ═ 2k-1) - (2k-2) (2 × 10-1) - (2 × 10-2) × 9/8 ═ 4/5.

And when k is 10, e is less than-1, the calculation is terminated, and k takes a value of 1-9.

Step 6B2, calculating f (k): calculating f (k) for each value k and corresponding e in the step 6B1 according to the following formula (10):

where sign () is a sign function and fix () is a rounding function that rounds to zero. All values k meeting the requirements are calculated to obtain f (k), and the f (k) is respectively ordered into f (1), f (2), f (3) and.

In the present embodiment, the calculation process of the 18-slot 16-pole three-phase motor f (k) is as follows:

when k is 1, fix (1) 1, and e (fix) (e), so f (1) sign (e) sign (1) 1;

when k is equal to 2, the number of the bits is increased,e ≠ fix (e), thus,

when k is 3, the number of the groups is 3,e ≠ fix (e), thus,

when k is equal to 4, the number of the first symbols is 4,e ≠ fix (e), thus,

when k is 5, e is 0, fix (0) is 0, and e is fix (e), so f (5) sign (e) sign (0) is 0;

when k is equal to 6, the number of the first symbols is 6,e ≠ fix (e), thus,

when k is equal to 7, the process is repeated,e ≠ fix (e) thus，

When k is equal to 8, the number of the first symbols is 8,e ≠ fix (e), thus,

when k is 9, e is-1, fix (e) fix (-1) is-1, and e is fix (e), so f (9) sign (e) sign (-1) is-1.

Therefore, in the embodiment, f (k) corresponds to f (1), f (2), f (3) and f (9) in the order of k values from small to large, and the corresponding values are respectively: 1. 3/4, 1/2, 1/4, 0, -1/4, -1/2, -3/4, -1.

Step 6B3, calculating a row vector A: the row vector a is a row vector related to f (k), and the specific expression is as follows:

A＝[A₁ A₂ A₁ A₂...] (11)

wherein the content of the first and second substances,

A₁is the sequence: f (1) f (2) f (3).. f (k)

A₂Is the sequence: f (k) f (k-1).. f (2) f (1)

In the formula (11), A₁And A₂The sequence elements are identical but arranged in the opposite order. Vector A is A₁And A₂The total number of elements in A is not less than Q after combination₁+2m-2 or Q₁+2 m-1.

In the 18-slot 16-pole three-phase motor in the embodiment, m is 3, and the total number of vectors in A is not less than Q₁+2m-2, i.e. 13, so that A₁And A₂The number of cycles is preferably 1, and the number of specific cycles is not particularly limited in order to prevent calculation errors caused by an insufficient number of A elements, and normally the number of cycles does not exceed 2 to 3.

In the present embodiment, the 18-slot 16-pole three-phase motor has the row vectors a and a₁And A₂Respectively represent asThe following:

A₁＝[f(1)f(2).....f(9)]＝[1,3/4,1/2,1/4,0,-1/4,-1/2,-3/4,-1]；

A₂＝[f(9)f(8).....f(1)]＝[-1,-3/4,-1/2,-1/4,0,1/4,1/2,3/4,1]；

A＝[1,3/4,1/2,1/4,0,-1/4,-1/2,-3/4,-1,-1,-3/4,-1/2,-1/4,0,1/4,1/2,3/4,1,]。

step 6B4, solving coefficient matrix B_triOr B_traThe concrete solving formula is as follows:

in the formula, B_triCoefficient matrix corresponding to the triangular winding, B_traA coefficient matrix corresponding to the trapezoidal winding; a (1), A (2), A (3), A (Q)₁)、 A(Q₁+1)、A(Q₁+2m-2) and A (Q)₁+2m-1) respectively represent the 1 st, 2, 3, Q in the vector A₁、Q₁+1、Q₁+2m-2 and Q₁+2m-1 elements;

in the present embodiment, the 18-slot 16-pole three-phase motor adopts a triangular winding, Q₁＝9，Q₁+2m-2 + 9+2 x 3-2-13, so its coefficient matrix B_triExpressed as:

step 6B5, calculating a flux linkage coefficient F: let N_a＝x，N_m-aY, and x + y N₀，x,y∈[0,N₀]Then, the calculation method of the flux linkage coefficient F is:

(1) when the winding type is a triangular winding, the calculation formula of the flux linkage coefficient F is as follows:

F＝B_triX_a·x+B_triY_a·y

wherein, the vector X_aAnd Y_aThe method is determined according to the parity of the winding layer number m, and the specific determination method comprises the following steps:

when m is an odd number, a is an interval [1, (m-1)/2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

X_a＝[0_1×(a-1) 1 0_1×(m-a-1) 1 0_1×(m-a-1) 1 0_1×(a-1)]^T

Y_a＝[0_1×(m-a-1) 1 0_1×(a-1) 1 0_1×(a-1) 1 0_1×(m-a-1)]^T.

when m is an even number, a is an interval of [1, (m-2)/2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

(2) when the winding type is a trapezoidal winding, the calculation formula of the flux linkage coefficient F is as follows:

F＝B_traX_a·x+B_tra Y_a·y

wherein, the vector X_aAnd Y_aThe method is determined according to the parity of the winding layer number m, and the specific determination method comprises the following steps:

when m is an odd number, a is an interval [1, (m-1)/2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

X_a＝[0_1×(a-1) 1 0_1×(m-a-1) 1 1 0_1×(m-a-1) 1 0_1×(a-1)]^T

Y_a＝[0_1×(m-a-1) 10_1×(a-1) 1 1 0_1×(a-1) 1 0_1×(m-a-1)]^T.

when m is an even number, a is the interval [1, (m-2) & gt2]Integer within, vector X_aAnd Y_aThe values of (A) are as follows:

in the 18-slot 16-pole three-phase motor and the delta winding in the present embodiment, the flux linkage coefficient F is calculated by the above method (1), m is an odd number because m is 3, and the vector X is an odd number_aAnd Y_aThe specific determination method comprises the following steps:

a is an integer in the interval [1, (m-1)/2], that is, a is 1.

Then vector X_aAnd Y_aThe values of (A) are as follows:

X_a＝[0_1×(a-1) 1 0_1×(m-a-1)1 0_1×(m-a-1) 1 0_1×(a-1)]^T＝[1 0 1 0 1]^T

Y_a＝[0_1×(m-a-1) 1 0_1×(a-1) 1 0_1×(a-1) 1 0_1×(m-a-1)]^T.＝[0 1 1 1 0]^T

(3) q should be included in the calculated flux linkage coefficient F₁Taking absolute value of each element, extracting the element backwards from the element with the minimum absolute value until repeated elements appear, and respectively recording the elements as f₁、f₂、…、f_g。

In the 18-slot 16-pole three-phase motor in the embodiment, after taking absolute values, the extracted elements are respectively recorded as:

f₁＝0；f₂＝0.75x+0.75y；f₃＝1.5x+1.5y；f₄＝2x+2.25y；f₅＝2.25x+2.75y

step 6B6, calculating the electrical angle alpha, wherein the specific calculation formula is as follows:

in the formula, Q₁The molecules are in the form of the fraction of the polar trough ratio q.

In this embodiment, the three-phase motor, Q, has 18 slots and 16 poles₁＝9。

Step 6B7, determining an objective fitting function: f determined in step 6B6₁、f₂、…、f_gFitting by adopting a least square method principle to obtain a target fitting function as follows:

in this embodiment, an 18-slot 16-pole three-phase motor, f₁The target fitting function obtained is 0, g 5:

step 6B8, determine x and y: x + y is equal to N₀And substituting the electrical angle alpha obtained by calculation in the step 6B6 into the target fitting function determined in the step 6B7, wherein when the target fitting function is minimum, the corresponding x and y values are the solved N_aAnd N_m-a。

If N is present₀90, i.e. x + y 90

Substituting y into S when being 90-x

In m is equal to [2, 4]]Under the limitation ofA can only take 1, essentially requiring only the number of turns of one set of coils, i.e. N₁And N_m-1。

In the case of the 18-slot 16-pole three-phase motor in the present embodiment, if N is provided₀When the value is 90, then N₁＝90，N₂＝0，N₃＝90。

The actual winding layout is shown in fig. 4(b), the total harmonic distortion when the common concentrated winding is adopted as shown in fig. 4(a) is 8.72%, and the total harmonic distortion of the optimized winding is 2.58%, which is reduced by about 70%. The harmonic spectrum is shown in fig. 5, and the 3 rd harmonic, the major component of the harmonic, is almost completely eliminated.

Table two shows the calculation results of the number of turns of the winding under different pole slot combinations in practical application:

although the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the details of the embodiments, and various equivalent modifications can be made within the technical spirit of the present invention, and the scope of the present invention is also within the scope of the present invention.