An analytical and optimization method for circulating current loss in Leeds windings

Abstract

The embodiment of the present invention discloses an analysis and optimization method for the circulating current loss of a Leeds winding, which relates to the field of winding copper loss analysis and winding design, and can analyze the circulating current loss of a Leeds winding under a high-frequency alternating magnetic field, thereby reducing the complexity of the analysis of the circulating current loss of the Leeds winding. The present invention includes: obtaining a set of structural parameters of the Leeds winding to be analyzed, and establishing a coordinate function model of the structural parameters of the Leeds winding to be analyzed varying with the axial length; establishing a two-dimensional finite element model of a motor, and sampling to obtain voltage and inductance parameters at different positions in a motor slot; using the coordinate function model and sampling to obtain voltage parameters and inductance parameters, determining the voltage and inductance corresponding to each twisted wire bundle of the Leeds winding; substituting the obtained voltage and inductance corresponding to each twisted wire bundle into the impedance matrix of the Leeds winding, obtaining the circulating current in each twisted wire bundle, and then determining the circulating current loss according to the circulating current in each twisted wire bundle.

Description

Technical Field

[0001] The invention relates to the field of winding copper loss analysis and winding design, and in particular to an analysis and optimization method for circulating current loss of a Leeds winding. Background Art

[0002] The high speed of the motor can reduce the size and weight of the motor, improve its power density, and has the characteristics of being directly connected to high-speed loads, eliminating the traditional mechanical speed increaser, reducing system noise and improving system transmission efficiency. It has broad application prospects in many fields. As the speed increases, the price paid is a higher loss density of the motor, including copper loss, iron loss, and windage loss. Among them, the copper loss of the winding accounts for a large proportion of the motor loss. Excessive copper loss will cause serious heating, leading to damage to the winding insulation, reduced motor performance, and even serious damage to the motor. Therefore, the study of copper loss in the winding is an important part that cannot be ignored.

[0003] In high-speed motors, the current frequency in the winding is high, which brings obvious skin effect and proximity effect, causing more serious AC copper loss, causing the local temperature of the winding to rise, destroying the winding insulation, and endangering the safe operation of the motor. In order to reduce the influence of skin effect or proximity effect, high-speed motors usually use wires with smaller cross-sections to form a turn of winding in the form of multiple strands in parallel, or use Litz windings, which can eliminate the influence of skin effect and proximity effect to a certain extent, reduce eddy current loss, but will reduce the slot fill rate and bring circulating current between the wire harnesses. The circulating current loss refers to the difference in magnetic flux of the turns of multiple wires under the influence of proximity effect and slot leakage when the motor winding is wound in parallel with multiple strands, resulting in unequal induced potentials of different wires. This voltage difference will form a circulating current between the multiple wires. For the calculation of copper loss of Litz windings under high-speed conditions, the analysis and calculation of circulating current loss is of utmost importance.

[0004] Therefore, how to design a circulating current loss analysis method for Leeds windings under high-frequency alternating magnetic fields and reduce the complexity of circulating current loss analysis of Leeds windings has become a problem that needs to be studied. Summary of the invention

[0005] The embodiment of the present invention provides a method for analyzing and optimizing the circulating current loss of a Leeds winding, which can analyze the circulating current loss of a Leeds winding under a high-frequency alternating magnetic field and reduce the complexity of the analysis of the circulating current loss of the Leeds winding.

[0006] To achieve the above object, the embodiments of the present invention adopt the following technical solutions:

[0007] S1. Obtain a set of structural parameters of a Litz winding to be analyzed, and establish a coordinate function model of the structural parameters of the Litz winding to be analyzed varying with axial length;

[0008] S2. Establish a two-dimensional finite element model of the motor, and sample and obtain the voltage and inductance parameters at different positions in the motor slot;

[0009] S3, using the coordinate function model established in S1 and the voltage parameters and inductance parameters obtained by sampling in S2, determining the voltage and inductance corresponding to each strand of the Lidz winding;

[0010] S4. Substitute the voltage and inductance corresponding to each twisted wire bundle obtained in S3 into the impedance matrix of the Litz winding to obtain the circulating current in each twisted wire bundle, and then determine the circulating current loss according to the circulating current in each twisted wire bundle.

[0011] The analysis and optimization method for the circulating current loss of the Litz winding provided in the embodiment of the present invention derives the coordinate position of each strand of the twisted wire bundle of the Litz wire based on the structural parameters of the Litz wire; obtains the voltage and inductance at each location in the non-uniform nonlinear alternating magnetic field through interpolation sampling; combines the coordinate position of each strand of the twisted wire bundle of the Litz wire, and obtains its voltage and inductance through interpolation integration; and accurately calculates its circulating current loss based on the impedance matrix. The calculation method described in the present invention is aimed at the problem that the current AC loss calculation method of general round wires is not applicable in non-uniform nonlinear magnetic fields, and proposes a new AC loss calculation method for twisted wires in the form of winding / twisting. For Litz wire, due to its twisted structure, the eddy current loss is almost zero and can be ignored. Based on its structural parameters and twisting rules, the voltage and inductance at each location can be interpolated, and then substituted into the impedance matrix to calculate its circulating current loss. The traditional analytical formula for copper loss of conductors is difficult to accurately and conveniently calculate the circulating current loss of each strand of the twisted Litz wire bundle with a twisted structure. At the same time, the complexity of the circulating current loss analysis of the Litz winding is reduced by solving the problems of modeling difficulties and time-consuming through three-dimensional finite element simulation analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0013] Figure 1 A flowchart of a method for calculating circulating current loss of a Litz winding provided in an embodiment of the present invention;

[0014] Figure 2 The structure and parameters of the 12 / 8-pole high-speed electrically excited double-salient-pole motor provided in the embodiment of the present invention;

[0015] Figure 3 A structural diagram of a rectangular Litz winding provided for application in an embodiment of the present invention;

[0016] Figure 4 A cross-sectional view of a rectangular Litz winding for use in an embodiment of the present invention;

[0017] Figure 5 A schematic diagram of a Litz winding under a stator pole provided in an embodiment of the present invention;

[0018] Figure 6 A winding connection diagram provided for an embodiment of the present invention;

[0019] Figure 7 A curve showing the change of circulating current loss with the length of the Litz winding slot provided in an embodiment of the present invention;

[0020] Figure 8 A curve showing the change of circulating current loss with the length of the end of the Litz winding provided in an embodiment of the present invention;

[0021] Fig. 9 A curve showing a change in circulating current loss versus litz wire lay length provided in an embodiment of the present invention;

[0022] Fig.10 A curve showing the change of circulating current loss with the length of the Litz winding jumper provided in an embodiment of the present invention;

[0023] Fig.11 The structure and parameters of a 12 / 10-pole high-speed electrically excited double-salient-pole motor provided in an embodiment of the present invention;

[0024] Fig.12 A physical picture of a circular Litz winding used in an embodiment of the present invention;

[0025] Fig.13 A cross-sectional view of a circular Litz winding for use in an embodiment of the present invention;

[0026] Fig.14 A curve showing the change of circulating current loss with the length of the end of the Litz winding provided in an embodiment of the present invention;

[0027] Fig.15 A curve showing the change of circulating current loss with the length of the Litz winding jumper provided in an embodiment of the present invention;

[0028] Fig.16 Schematic diagram of cross-section of Litz wires with different multiple twisted structures provided by embodiments of the present invention;

[0029] Fig.17 A curve showing the change of circulating current loss of Litz windings with strand-level lay lengths of different multi-twisted structures provided in an embodiment of the present invention;

[0030] Fig.18 A schematic diagram of a method flow chart provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0031] In the current research, it is found that when the transposition method adopted is inappropriate, huge circulating current losses will still be generated in the winding wire. Many scholars have also conducted corresponding analysis on the AC loss of the Litz winding. Among them, the AC resistance or AC loss of the wire is analytically derived based on the traditional loss calculation principle, but the structure of the multi-strand parallel-wound wire or Litz wire is complex, and the traditional analytical model calculation is difficult; at the same time, the circulating current between the twisted wire bundles is not considered. In addition, there is also direct simulation analysis through finite element modeling, but because the three-dimensional modeling of the twisted structure is difficult, the loss calculation is relatively time-consuming. Therefore, for the circulating current loss of the Litz wire, how to establish a fast and accurate mathematical model is a key problem to be solved urgently. It is the basis for optimizing the design of the winding structure and reducing the loss, and it has important practical significance for further improving the efficiency and reliability of the motor. Based on the above analysis, this embodiment aims to propose a method for calculating the circulating current loss of the Litz winding under a high-frequency alternating magnetic field, thereby solving the problem of the complexity and difficulty of calculating the circulating current loss of the Litz winding, quickly and accurately obtaining its circulating current loss, and providing a guiding basis for optimizing the design of the winding structure and reducing the loss. Specifically, the embodiment of the present invention provides an analysis and optimization method for the circulating current loss of the Leeds winding, which is applicable to the calculation method of the circulating current loss of the Leeds winding, and aims to solve the problem of the complexity and difficulty of calculating the circulating current loss of the Leeds winding, and quickly and accurately obtain its circulating current loss, such as Fig.18 As shown, including:

[0032] S1. Obtain a set of structural parameters of a Litz winding to be analyzed, and establish a coordinate function model of the structural parameters of the Litz winding to be analyzed varying with axial length;

[0033] S2. Establish a two-dimensional finite element model of the motor, and sample and obtain the voltage and inductance parameters at different positions in the motor slot;

[0034] S3, using the coordinate function model established in S1 and the voltage parameters and inductance parameters obtained by sampling in S2, determining the voltage and inductance corresponding to each strand of the Lidz winding;

[0035] S4. Substitute the voltage and inductance corresponding to each twisted wire bundle obtained in S3 into the impedance matrix of the Litz winding to obtain the circulating current in each twisted wire bundle, and then determine the circulating current loss according to the circulating current in each twisted wire bundle.

[0036] Specifically, since the Litz wire is made of multiple strands of fine wires twisted together, the influence of the skin effect can be largely eliminated, so its eddy current loss can be ignored, and the main source of the wire AC loss is the circulating current loss. And its twisting method has a certain regularity, and the position of each cross section can be obtained by combining its structural parameters. The method includes the following steps, such as Figure 1As shown in the figure: the corresponding parameters are extracted from the actual Litz wire structure and winding structure, including the length and width of the Litz wire cross-section, the number of Litz wire strands, the Litz wire lay pitch, the length in the Litz winding slot (axial length of the motor), the length of the Litz winding end, the distance between strands, the number of winding turns, the distance between winding turns, etc. The coordinate function of each strand of the Litz winding strand bundle that changes with the axial length is derived based on the structural parameters; a two-dimensional finite element model of the motor is established, and simulation is performed according to the actual working conditions. Sampling points are evenly set in the slot to obtain the voltage and inductance values ​​at different positions in the motor slot; then, the coordinate position of each strand of the strand bundle at different axial lengths, and the voltage and inductance amplitude of the sampling points are combined, and the voltage and inductance corresponding to each strand of the strand bundle are obtained through the two-dimensional linear interpolation method; according to the actual circuit principle of the Litz winding, the corresponding impedance matrix equation is listed, and the voltage and inductance of each strand of the strand bundle obtained by interpolation are substituted into the above matrix equation to calculate the circulating current in each strand of the strand bundle, and then the circulating current loss is obtained according to Ohm's law.

[0037] This embodiment avoids the problem that the traditional analytical formula for copper loss of conductors is difficult to accurately and conveniently calculate the circulating current loss of each strand of the twisted Litz wire bundle with a twisted structure. At the same time, through the three-dimensional finite element simulation analysis, modeling difficulties and time-consuming problems can be solved, a fast and accurate mathematical model for the circulating current loss of the Litz winding can be established, providing a guiding basis for the optimization design of the winding structure.

[0038] In this embodiment, in S1, the set of structural parameters of the Litz winding to be analyzed includes:

[0039] Litz wire outer ring cross-sectional length a, Litz wire outer ring cross-sectional width b, Litz wire inner ring cross-sectional length c, Litz wire inner ring cross-sectional width d, Litz wire twisted outer ring strand number n o , the number of strands in the inner coil of the Litz wire i 、Total number of twisted strands of Litz wire n total , Litz wire lay length L t , Litz winding slot length (motor axial length) L s , Litz winding end length L e , distance between strands D, number of winding turns N t , winding turn distance y gap And the number of motor poles p.

[0040] The coordinate function model of the structural parameters of the Litz winding to be analyzed changing with the axial length includes: the horizontal and vertical coordinates x of each stranded wire bundle j ,y j Variation of axial length l with x j (l),y j(l), due to the regularity of the position change of the stranded wire, the bundle coordinate function of the stranded wire is periodic. The horizontal and vertical coordinates of the bundle and strand level of the Litz winding with different multi-twisted structures vary with the axial length l.

[0041] Among them, in the coordinate function model established by S1, for the rectangular cross-section Litz winding, the coordinate x of the j-th strand is j (l),y j (l) is expressed as:

[0042]

[0043] Where, when k=0, it indicates the winding in the left slot, when k=1, it indicates the winding in the right slot, N indicates the Nth turn of the winding, f x1 , f y1 is the coordinate function of the first strand of twisted wire, specifically expressed as:

[0044]

[0045]

[0046] The center position of the Litz wire is)x 1_o ,y 1_o ), the initial position of the first strand of the Litz wire is

[0047] (x 1_ini ,y 1_ini ), n represents a natural number, and θ represents the twisting angle of the Litz wire.

[0048] Optionally, in the coordinate function model established in S1, for a circular cross-section Litz wire, the coordinate x of the jth strand is j (l),y j (l) is expressed as:

[0049]

[0050] where r s Indicates the radius from the center of the Litz wire to the center of each strand. When k = 0, it indicates the winding in the left slot. When k = 1, it indicates the winding in the right slot. j indicates the jth strand. n total It represents the total number of twisted strands of Litz wire, and N represents the Nth turn of the winding.

[0051] For a rectangular cross-section Litz winding, the coordinate x of the jth strand is j (l),y j (l) is expressed as:

[0052]

[0053] Where, when k=0, it indicates the winding in the left slot, when k=1, it indicates the winding in the right slot, N indicates the Nth turn of the winding, f x1 , f y1 is the coordinate function of the first strand of twisted wire, specifically expressed as:

[0054]

[0055]

[0056] Specifically, the center position of the Litz wire is (x 1_o ,y 1_o ), the initial position of the first strand of the Litz wire is (x 1_ini ,y 1_ini ). The relationship between the two is

[0057]

[0058] Therefore, the center position (x1, y1) of the first twisted wire in the Litz wire can be calculated as:

[0059]

[0060] In the formula, f x1 (l), f y1 (l) is a function of x1, y1, l is the axial length of the Litz wire, n is a natural number representing a multiple of the Litz wire lay length, and θ represents the Litz wire twisting angle.

[0061] The distance between the jth strand and the first strand of the Litz wire is

[0062]

[0063] Therefore, the twisting coordinates of the jth strand can be calculated

[0064]

[0065] If the Litz wire is placed in the motor and wound around the stator teeth, it is not a straight line, and there will be a difference between the left and right. Each turn needs to consider the length of the Litz winding end, and there is a certain interval between the turns. The length of the jumper wire between each pole also needs to be considered. The total length of the winding of one phase of the motor can be expressed as L total , for magnetic flux density at L total The voltage of each strand can be obtained by integrating the length, averaging it, and calculating the voltage difference between each strand and the average voltage to calculate the circulating current loss of each strand. The sum of the sum is the total circulating current loss. Specifically:

[0066] The actual length of the Nth turn of Litz wire is L N , N is a positive integer

[0067] L N =[2(N-1)-k]·(L s +L e ) (5)

[0068] Wherein k=0 represents the Litz wire on the right, and k=1 represents the Litz wire on the left.

[0069] The actual length of the Nth turn of the pth pole is expressed as

[0070] L p =L N +N t ·(p-1)(L s +L e )+(p-1)L c (6)

[0071] The actual coordinates of the first strand in the motor can be calculated as

[0072]

[0073] Therefore, the actual coordinates of the jth strand in the motor can be calculated as

[0074]

[0075] Similarly, the horizontal and vertical coordinates x of the circular cross-section Litz winding can be calculated j ,y j The function x of the axial length l j (l),y j (l), specifically:

[0076] Let the center coordinates of the Nth turn be (x j ,y j ) (j=1,2,…), which can be expressed as

[0077]

[0078] Taking this point as the origin, a polar coordinate system is established, and the coordinates of the i-th strand of the twisted wire harness can be expressed as:

[0079]

[0080] In the formula, ρ i represents the polar angle of the i-th strand of the twisted wire bundle, r strand represents the polar diameter of the i-th strand of the twisted wire bundle, l litz Indicates the total length of the specific number of turns at a specific axial length l in the nth pole slot, Δθ i represents the rotation angle relative to the initial position of the i-th strand, θ gap_i represents the angle between the first and the i-th strands, which can be expressed as:

[0081] l litz = l + (j-1) · (L s +L e )+(N-1)·L c (11)

[0082]

[0083]

[0084] Similarly, the variation functions of the horizontal and vertical coordinates and the axial length of the bundle and strand level of the Lidz winding with different multi-twisted structures of circular cross-section can be calculated, specifically:

[0085] The bundle twist angle is (where L tb Indicates the bundle level lay length):

[0086]

[0087] The strand twist angle is (where L ts Indicates strand lay length)

[0088]

[0089] Assume that the initial position of the first turn of Litz wire is (x ini ,y ini ), the position of the jth beam is (x j1 ,y j1 ),but

[0090]

[0091] Where mb is the number of beam levels, r mb is the radius of the mb-th layer, and the mb-th layer has a total of j ms bundle.

[0092] Similarly, the coordinates of the i-th strand of the j-th bundle are

[0093]

[0094] Among them, ms is the number of stock levels, r ms is the radius of the msth layer, and the msth layer has i ms bundle.

[0095] When the multi-twisted structure is 19*19, the number of bundle-level layers and their distribution are:

[0096]

[0097] The number of stock levels and their distribution are

[0098]

[0099] When the multi-twisted structure is 7*51, the number of bundle levels and their distribution are:

[0100]

[0101] The number of stock levels and their distribution are

[0102]

[0103] When the multi-twisted structure is 5*72, the number of bundle-level layers and their distribution are:

[0104] mb=1 r mb =r 1b j mb =5 (22)

[0105] The number of stock levels and their distribution are

[0106]

[0107] The starting length L of the Nth turn of Litz wire N for

[0108] L N =[2(N-1)-k]·(L s +L e ) (twenty four)

[0109] Wherein k=0 represents the Litz wire on the right, and k=1 represents the Litz wire on the left.

[0110] Then the actual length at L of the Nth turn (N=1,2,3...) is

[0111] L N =[2(N-1)-k]·(L s +L e )+L (25)

[0112] Then the starting length of the Litz wire of the p-th pole Nth turn is expressed as

[0113] L p =L N +6(p-1)(L s +L e )+(p-1)L c (26)

[0114] Then the actual length at the pth pole L is

[0115] L p =L N +6(p-1)(L s +L e )+(p-1)L c(27)

[0116] Therefore, the actual coordinates of the i-th strand of the j-th bundle are

[0117]

[0118] Furthermore, in S2, it includes: evenly setting sampling points in the slots of the motor, wherein each sampling point is set as a winding under the condition of ensuring that the ampere-turns remain unchanged, and the sampling points are connected in series in the external circuit, and the output voltage of the sampling points increases in proportion to the number of turns.

[0119] In S3, it includes: for the coordinates of the minimum unit of the impedance matrix of the Leeds winding, sampling the voltage and inductance corresponding to each point in the minimum unit, wherein the voltage corresponding to each point is associated with the voltages of four interpolation points, and the inductance corresponding to each point is associated with the inductances of four interpolation points.

[0120] In S4, the circulating current loss determined based on the circulating current in each strand is: n is a natural number, j represents the Litz wire number, i jcir represents the circulating current of the jth Litz wire, R litz Indicates the resistance of each strand of twisted wire.

[0121] Specifically, the voltage and inductance corresponding to each strand of the twisted wire harness can be obtained by a two-dimensional linear interpolation method, which is:

[0122] According to the specific coordinates of the smallest rectangular unit: s1(-a,-b), s2(a,-b), s3(-a,b), s4(a,b), the voltage at any point (x,y) in the sampling unit can be expressed as

[0123] U(x,y)=N s1 U s1 +N s2 U s2 +N s3 U s3 +N s4 U s4 (29)

[0124] Where U s1 ,U s2 ,U s3 ,U s4 Indicates the voltage of the 4 interpolation points. Interpolation coefficient N s1 ,N s2 ,N s3 ,N s4 It can be expressed as

[0125]

[0126] The self-inductance of the jth strand at (x, y) can be obtained using the same method as above:

[0127] L j,j (x,y)=N s1 L s1 +N s2 L s2 +N s3 L s3 +N s4 L s4 (31)

[0128] Where L s1 ,L s2 ,L s3 ,L s4 Represents the self-inductance of the four interpolation points.

[0129] Calculate the mutual inductance L between the i-th and j-th strands i,j (x i ,y i ,x j ,y j ), where the positions of the i-th and j-th strands are (x i ,y i ) and (x j ,y j ). The point closest to the i-th stock is s1, and the point closest to the j-th stock is s5.

[0130] L 1j represents the interpolation mutual inductance between point s1 and the jth branch, and its coefficient can be obtained by equation (10). i5 is the interpolation mutual inductance between the s5th point and the i-th strand. 15 represents the mutual inductance between point s1 and point s5. The mutual inductance L between the i-th and j-th strands i,j (x i ,y i ,x j ,y j ) can be obtained by adding and subtracting the three. Specifically expressed as:

[0131] L 1,j (x,y)=N s5 L s5 +N s6 L s6 +N s7 L s7 +N s8 (32)

[0132] L i,5 (x,y)=N s1 L s1 +N s2 L s2 +Ns3 L s3 +N s4 (33)

[0133] L i,j (x i ,y i ,x j ,y j )=L 1,j +L i,5 -L 1,5 (34)

[0134] The obtained voltage and inductance corresponding to each twisted wire bundle are substituted into the impedance matrix of the Litz winding to obtain the circulating current in each twisted wire bundle, and then the circulating current loss is determined according to the circulating current in each twisted wire bundle.

[0135] Furthermore, in S4, the corresponding matrix equations are listed, and the voltage and inductance of each twisted wire bundle obtained by interpolation are substituted into the above impedance matrix equation to calculate the circulating current in each twisted wire bundle, where: In S4, the circulating current of each wire is expressed as:

[0136]

[0137] Among them, i c is the circulating current matrix, s is the Laplace operator, L is the inductance matrix, R is the resistance matrix, E1 is the column vector, E2 is the row vector, and u is the induced voltage matrix;

[0138] Without considering the circulating current, that is, when the currents of each strand of the twisted wire bundle are equal, the voltage equation can be written as

[0139]

[0140] Can be abbreviated as

[0141] [u]=[sL+R][i]+[sL bcf ][i bcf ]

[0142] in

[0143]

[0144] Where R is the resistance matrix, which is a diagonal matrix. The resistance of each strand of twisted wire can be calculated as

[0145]

[0146] L bcf is the inductance matrix of phase B, C and excitation winding, i bcf is the current of phase B, C and excitation winding.

[0147] At this time, since the circulating current is not considered, the current of each strand is equal, that is,

[0148] i1=i2=…=i n

[0149] make

[0150]

[0151]

[0152] Where L 1,bcf is the inductance matrix of phase B, phase C and excitation. In order to eliminate the influence of phase B, phase C and excitation on the circulating current, we can get

[0153] [sL+R][i]=[u]-x

[0154] In the actual circuit, each strand of the twisted wire harness is connected in parallel, and their induced voltages are equal, that is,

[0155] [u]=[u x ]=[sL+R][i x ]+[sL bcf ][i bcf ]

[0156] [i x ]=[sL+R] -1 ([u x ]-x)

[0157] i x The current of each strand of the twisted wire harness.

[0158] [i x ]=[sL+R] -1 ([u x ]-([u]-[sL+R][i]))

[0159] =[sL+R] -1 [u x ]-[sL+R] -1 ([u]-[sL+R][i])

[0160] Multiply the unit row vector E1 on both sides

[0161] E1[i x ]=E1[sL+R] -1 [u x ]-E1[sL+R] -1 [u]+E1[sL+R] -1 [sL+R][i]

[0162] I A=E1[sL+R] -1 [u x ]-E1[sL+R] -1 [u]+I A

[0163] Since the total current of phase A is theoretically equal in both cases, we can get

[0164] E1[sL+R] -1 [u x ]=E1[sL+R] -1 [u]

[0165]

[0166] Where E2 is a unit column vector. Therefore, the current of each strand can be expressed as

[0167]

[0168] Since [i] in the above formula is the current of each strand when the circulating current is not considered, the circulating current is

[0169]

[0170]

[0171] The circulation i c Transform to time domain c (t), the circulation loss can be expressed as

[0172]

[0173] Furthermore, in this embodiment, it also includes: obtaining a design index requirement for circulating current loss, and modifying the structural parameters according to the design index requirement, wherein: the design index requirement points to the minimum circulating current loss of the Litz winding, and then the length of the Litz winding slot is set to be equal to an integer multiple of the Litz wire lay pitch;

[0174] When the sum of the length of the Litz winding slot and the length of the Litz winding end is equal to an integer multiple of the Litz wire lay pitch, the Litz winding circulating current loss is maximum;

[0175] The design indicator requirement indicates that the circulating current loss is minimized, so the jumper wire length is set to be equal to 1 / 4 times the Litz wire lay length or 3 / 4 times the Litz wire lay length;

[0176] The design indicator requirement indicates that the circulating current loss is partially suppressed, so the jumper wire length is set equal to 1 / 2 times the Litz wire lay length.

[0177] In order to verify the effectiveness of the calculation method of the circulating current loss of the Litz winding described in this case, a rectangular Litz winding used in a 12 / 8-pole electrically excited double-salient-pole motor is taken as Case 1. Figure 2 is the motor structure and parameters, Figure 3 The actual picture of the Litz winding used is shown below. Figure 4 The cross-section of the applied Litz winding is shown below. The outer coil has 9 strands, length a = 5 mm, width b = 4 mm, and the inner coil has 3 strands, length c = 2 mm, width d = 1 mm. Figure 5 Schematic diagram of Litz winding under a stator pole. Figure 6 The winding connection diagram is shown in Figure 2.

[0178] The Litz wire lay length is fixed at 70mm, and the length of the Litz winding slot is changed. The change law of the Litz winding circulating current loss with the length of the Litz winding slot is as follows Figure 7 As shown in the figure, the minimum value of the circulating current loss appears at:

[0179] L s = k·L t k=(1,2,…)

[0180] The maximum value of circulating current loss occurs at:

[0181] L s +L e = k·L t k=(1,2,…)

[0182] When the circulating current loss is the smallest, the length of the Litz winding slot is equal to an integer multiple of the Litz wire lay length. This is because at this time, each strand of the winding wire is completely transposed, balancing the unequal induced potentials. Complete transposition means that after a strand of winding wire passes a certain winding length, its cross-sectional position returns to the initial coordinate. When the circulating current loss is the largest, the sum of the length of the Litz winding slot and the length of the Litz winding end is equal to an integer multiple of the Litz wire lay length. This is because at this time, the degree of transposition of each strand of winding wire is the most unreasonable, and the induced potential is the most unbalanced.

[0183] Figure 8 This is the variation law of the circulating current loss of the Litz winding with the length of the Litz winding end. Figure 7 and Figure 8 It can be seen that the highest and lowest points of the circulating current loss are consistent with the above analysis. When the length of the Litz winding slot is set to 70mm, no matter how the length of the Litz winding end changes, the circulating current loss remains very small but always exists, because at this time, although each strand of the twisted wire itself is completely transposed, due to the rectangular Litz wire structure, there is still circulating current between the inner and outer layers. This is a problem caused by the manufacturing structure of the rectangular Litz wire itself.

[0184] Fig. 9In order to study the influence of the change of Litz wire lay pitch on the circulating current loss, the ratio relationship between the length of the Litz winding slot and the length of the Litz winding end was compared and analyzed. The law of the highest and lowest points of the circulating current loss is consistent with that described above.

[0185] Fig.10 The influence of the jumper length on the circulating loss is shown in Figure 2. Under the condition of fixed length of the Litz winding slot and the length of the Litz winding end, the circulating loss without considering the jumper is assumed to be P max , normalize the circulating current loss, adjust the jumper length, and the circulating current loss will show the following pattern: Figure 8 As shown. It can be seen that when L c =L t / 4,L c =L t / 2,L c =3L t / 4 can suppress the loss, L c =L t / 4,L c =3L t / 4 when the loss is minimum; L c =L t / 2, the loss can be partially suppressed.

[0186] In order to verify the effectiveness of the calculation method of the circulating current loss of the Litz winding described in this case, a circular Litz winding used in a 12 / 10-pole electrically excited double-salient-pole motor is taken as Case 2. Fig.11 is the motor structure and parameters, Fig.12 The actual picture of the applied Litz winding is 5 strands and the Litz wire lay length is 100mm. Fig.13 This is a cross-sectional view of the applied Litz winding. The radius of the Litz wire is 2.2mm and the radius of the stranded wire bundle is 1.2mm.

[0187] Fig.14 is the curve of circulating current loss changing with the length of Litz winding end, Fig.15 Figure 2 is the curve of circulating current loss changing with jumper length. The changing pattern of circulating current loss is consistent with the analysis in Case 1.

[0188] In order to verify the validity of the calculation method of the circulating current loss of the Litz winding described in this case, a circular double-twisted Litz winding used in a 12 / 8-pole electrically excited double-pole motor is used as Case 3. The motor structure and parameters are the same as those in Case 1. There are three types of circular Litz winding double-twisted structures, namely 5*72, 7*51, and 19*19. The cross-sections are as follows: Fig.16 As shown, the bundle level lay length is 60mm.

[0189] Fig.17The curve of circulating current loss changing with strand-level lay length is shown in Figure 2. By comparing the minimum value, we can see that the 5*72 structure is the best, and its minimum value is smaller than the other two multi-twisted structures. When the bundle level is completely transposed, the circulating current between the inner and outer layers cannot be eliminated, and the 5*72 multi-twisted structure has the lowest loss because it has no distinction between inner and outer layers.

[0190] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The above is only a specific implementation method of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for analyzing and optimizing the circulating current loss of a Litz winding, characterized in that: include: S1. Obtain a set of structural parameters of a Litz winding to be analyzed, and establish a coordinate function model of the structural parameters of the Litz winding to be analyzed varying with axial length; S2. Establish a two-dimensional finite element model of the motor, and sample the voltage and inductance parameters at different positions in the motor slot; S3, using the coordinate function model established in S1 and the voltage parameters and inductance parameters obtained by sampling in S2, determining the voltage and inductance corresponding to each strand of the Lidz winding; S4, substituting the voltage and inductance corresponding to each twisted wire bundle obtained in S3 into the impedance matrix of the Litz winding to obtain the circulating current in each twisted wire bundle, and then determining the circulating current loss according to the circulating current in each twisted wire bundle; In S1, the set of structural parameters of the Litz winding to be analyzed includes: Litz wire outer ring cross-sectional length a, Litz wire outer ring cross-sectional width b, Litz wire inner ring cross-sectional length c, Litz wire inner ring cross-sectional width d, Litz wire twisted outer ring strand number n o , the number of strands in the inner coil of the Litz wire i 、Total number of twisted strands of Litz wire n total , Litz wire lay length L t , Litz winding slot length L s , Litz winding end length L e , Leeds winding jumper length L c , distance between strands D, number of winding turns N t , winding turn distance y gap and the number of motor poles p; The coordinate function model of the structural parameters of the Litz winding to be analyzed varying with the axial length includes: The horizontal and vertical coordinates of each strand of twisted wire harness are x j ,y j Variation of axial length l with x j (l),y j (l); The horizontal and vertical coordinates of the bundle and strand levels of Litz windings with different multi-twist structures, as a function of the axial length l; In S4, the circulation of each line is expressed as: Among them, i c is the circulating current matrix, s is the Laplace operator, L is the inductance matrix, R is the resistance matrix, E1 is the column vector, E2 is the row vector, and u is the induced voltage matrix; The circulating current loss determined by the circulating current in each strand of the twisted wire bundle is: j represents the Litz wire number, i jcir represents the circulating current of the jth Litz wire, R litz Indicates the resistance of each strand of twisted wire.

2. The method according to claim 1, characterized in that: In the coordinate function model established by S1, for a rectangular cross-section Litz winding, the coordinate x of the jth strand is j (l),y j (l) is expressed as: Where, when k=0, it indicates the winding in the left slot, when k=1, it indicates the winding in the right slot, N indicates the Nth turn of the winding, f x1 , f y1 is the coordinate function of the first strand of twisted wire, specifically expressed as: The center position of the Litz wire is (x 1_o ,y 1_o ), the initial position of the first strand of the Litz wire is (x 1_ini ,y 1_ini ), n represents a natural number, and θ represents the twisting angle of the Litz wire.

3. The method according to claim 1, characterized in that In the coordinate function model established by S1, for a circular cross-section Litz wire, the coordinate x of the jth strand is j (l),y j (l) is expressed as: where r s Indicates the radius from the center of the Litz wire to the center of each strand. When k = 0, it indicates the winding in the left slot. When k = 1, it indicates the winding in the right slot. j indicates the jth strand. n total It represents the total number of twisted strands of Litz wire, and N represents the winding number.

4. The method according to claim 1, characterized in that In S2, it includes: Sampling points are evenly arranged in the slots of the motor, wherein each sampling point is arranged as a winding while maintaining the ampere-turns unchanged, and the sampling points are connected in series in an external circuit, and the output voltage of the sampling points increases in proportion to the number of turns.

5. The method according to claim 1, characterized in that In S3, this includes: For the coordinates of the minimum unit of the impedance matrix of the Leeds winding, the voltage and inductance corresponding to each point in the minimum unit are sampled, wherein the voltage corresponding to each point is associated with the voltages of four interpolation points, and the inductance corresponding to each point is associated with the inductances of four interpolation points.

6. The method according to claim 1, characterized in that Also includes: Obtain the design index requirement of the circulating current loss, and modify the structural parameters according to the design index requirement, wherein: The design index requirement points to the minimum circulating current loss of the Litz winding, so the length of the Litz winding slot is set equal to the Litz wire lay length L t Integer multiples; The design indicator requirement points to the minimum suppression of circulating current loss, so the Leeds winding jumper length L is set; c Equal to 1 / 4 times the lay length of Litz wire or 3 / 4 times the lay length of Litz wire; The design indicator requirement indicates that the circulating current loss is partially suppressed, so the jumper wire length is set equal to 1 / 2 times the Litz wire lay length.

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