A method, system or device for calculating copper loss of motor windings

Abstract

The invention belongs to the field of motors, and discloses a method, system or device for calculating the copper loss of motor windings, comprising the following steps: converting any stator slot type of the motor into rectangular slots of equal area; redistributing the windings so that, except for the stator slots of the top layer, the number of windings placed in the stator slots of the remaining layers is equal, and the remaining windings are placed in the stator slots of the top layer; obtaining the active power of each layer of stator slots after the windings are redistributed; substituting skin effect factors and proximity effect factors into the active power to form an analytical model for the copper loss of the stator slot windings of each layer, superimposing the analytical models of the copper loss of the stator slot windings of each layer to obtain a total loss model of the motor windings, thereby obtaining the copper loss of the entire motor windings; without the need for precise modeling, quickly and accurately predicting the winding copper loss, thereby improving the accuracy of predicting motor efficiency.

Description

Technical Field

[0001] The invention relates to a method, system or device for calculating copper loss of motor windings, and belongs to the field of motors. Background Art

[0002] In the initial design of the motor, it is necessary to calculate the impact of copper loss on motor efficiency. However, the calculation of copper loss is relatively complicated and the mutual influence between conductors is difficult to explain clearly. For distributed windings, the span is large, and the impact of the ends on the conductors is aggravated. The copper loss of the motor winding will increase, which will further lead to increased temperature rise, reduced motor efficiency, and may cause irreversible demagnetization of permanent magnets. Therefore, it is necessary to establish a set of fast and accurate methods to predict copper loss.

[0003] Among the existing methods for calculating copper loss, the finite element method and the analytical method are usually used. Although the results of copper loss calculation by the finite element method are relatively accurate, the modeling requires high precision and is time-consuming, making it difficult to obtain results quickly. In contrast, the analytical method is more flexible, but its accuracy does not meet the requirements because its calculation conditions are too ideal. Summary of the invention

[0004] In a first aspect, the technical problem to be solved by the present invention is to provide a method for calculating motor winding copper loss, which can quickly and accurately predict winding copper loss without the need for precise modeling, thereby improving the accuracy of predicting motor efficiency.

[0005] The present invention adopts the following technical solutions to solve the above technical problems

[0006] A method for calculating motor winding copper loss comprises the following steps:

[0007] Convert any stator slot of the motor into rectangular slots of equal area;

[0008] The windings are redistributed so that the number of windings placed in the stator slots of each layer except the stator slots of the top layer is equal, and the remaining windings are placed in the stator slots of the top layer;

[0009] Obtaining the active power of each layer of stator slots after the winding is redistributed;

[0010] The skin effect factor and the proximity effect factor are substituted into the active power to form an analytical model of the copper loss of the stator slot winding of each layer. The analytical models of the copper loss of the stator slot winding of each layer are superimposed to obtain the total loss model of the motor winding, thereby obtaining the copper loss of the entire motor winding.

[0011] In some disclosures, the conversion of any stator slot shape of a motor into rectangular slots of equal area is achieved by a conformal mapping method.

[0012] In some disclosures, the active power of each layer of stator slots after the windings are redistributed is obtained, including: according to Ampere's circuit law, the electromagnetic field strength of each layer of stator slots is obtained, using Poynting's theorem, the complex power flowing into the closed volume is obtained, and the complex power is decomposed into the active power of each layer of stator slots.

[0013] In some disclosures, each layer of stator slot winding is regarded as an electromagnetic loop, and according to Ampere's loop law, the magnetic field strength of the k+1th layer winding is obtained as:

[0014]

[0015] In the formula, is the magnetic field strength; is the total magnetic field strength in the k layer and below; is the magnetic field strength of the k+1th layer; J z is the current density; k k+1 is the slot filling rate of the k+1th winding layer; is the total current of the kth layer and below;

[0016] Using the modified complex eddy current equation, the magnetic field intensity can be transformed into a second-order differential equation, which can be expressed as follows:

[0017] H x =c1e -ty +c2e ty

[0018] In the formula, c1 and c2 are ordinary differential coefficients, which can be substituted into the boundary conditions of the winding to solve; the expression of the t function is as follows:

[0019]

[0020] Where ω is the angular frequency; μ0 is the vacuum magnetic permeability; σ is the electrical conductivity; k k+1 is the slot occupancy rate of the k+1 layer;

[0021] According to Ampere's circuit law, the boundary condition of the magnetic field intensity in the k+1th layer of winding can be expressed by the following formula.

[0022]

[0023] In the formula, i k+1 is the current of the k+1th winding; It represents the sum of the total current of the lower winding and the current of the upper kth layer and below. In order to facilitate subsequent calculations, Available k To express:

[0024] According to the above boundary conditions, the expression of magnetic field intensity is as follows:

[0025]

[0026] The electric field strength can be obtained by the same method The expression is

[0027]

[0028] Then, the complex power flowing into the closed volume is calculated according to Poynting's theorem That is, the sum of the motor's active power P and reactive power Q, as shown below:

[0029]

[0030] In the formula, the complex power It can be expressed by the following formula;

[0031]

[0032] because and are all in conjugate complex form, so for the discrete model, its complex power can be expressed as

[0033]

[0034] Where L1 is the height of each layer; l is the axial length of the winding.

[0035] In some publications, the adhesion effect factor is added and the proximity effect factor ψ(ξ), the following expression is obtained:

[0036]

[0037] In the formula, i k+1 is the current value of the K+1th layer; χ is a set of functional relationships about the current phase angle, as shown below:

[0038] χ=i low 2 +2i low i k0 cosθ+i low i k+1 cosθ+i k0 (i k0 +i k+1 )

[0039] In the formula, i low is the total current of the lower winding; i k0is the current of layer k and below in the upper winding; θ is the current phase difference between the upper and lower windings. The copper loss analysis model of the centralized winding is:

[0040]

[0041] In some disclosures, the copper loss of the entire motor winding is obtained through an analytical model of the copper loss of each layer of the stator slot winding, which can be replaced by superimposing the copper loss of each layer of the stator slot winding to obtain the copper loss of the entire motor winding.

[0042] In some disclosures, for motors with distributed windings, the end compensation length is supplemented according to the relationship between the short-distance coefficient β and the winding loss, and the active power of each layer of stator slots after the new winding is redistributed is obtained. The skin effect factor and the proximity effect factor are substituted into the active power to form an analytical model of the copper loss of the stator slot windings of each layer, thereby obtaining the copper loss of the entire motor winding.

[0043] In some publications, the finite element method is used to fit the copper loss curve under different short-distance coefficients, and an approximate parabolic equation is obtained. Therefore, it is assumed that the relationship between the short-distance coefficient β and the winding loss is as follows:

[0044] P l =Q((a1β 2 +b1β+e1)P a1 +(a2β 2 +b2β+e2)P a2 )

[0045] Where Q is the number of slots; P a1 is the upper winding loss in the same slot; P a2 is the lower winding loss in the same slot; a 1,2 、b 1,2 、e 1,2 They are all constant coefficients and can be solved according to the winding boundary conditions;

[0046] Add the end compensation length l' to the model and update it. The calculation formula of l' is as follows:

[0047]

[0048] In the formula, m is the number of phases of the motor; p is the number of poles of the winding; r is the radius from the rotor axis to the center of the stator slot;

[0049] Then the active power model of the distributed winding can be rewritten as:

[0050]

[0051] The skin effect factor and proximity effect factor are substituted into the active power to form an analytical model of the copper loss of the stator slot winding of each layer, thereby obtaining the copper loss of the entire motor winding.

[0052] In a second aspect, the technical problem to be solved by the present invention is to provide a system for calculating motor winding copper loss, which can quickly and accurately predict winding copper loss without the need for precise modeling, thereby improving the accuracy of predicting motor efficiency.

[0053] A system for calculating copper loss of motor windings, the copper loss calculation system comprising a storage medium, the storage medium containing a program, and when the program is executed, the method for calculating copper loss of motor windings of the first aspect is implemented.

[0054] In a third aspect, the technical problem to be solved by the present invention is to provide a device for calculating motor winding copper loss, which can quickly and accurately predict winding copper loss without the need for precise modeling, thereby improving the accuracy of predicting motor efficiency.

[0055] A device for calculating the copper loss of motor windings, the device comprising the copper loss calculation system of the second aspect.

[0056] The present invention has one or more of the following beneficial effects:

[0057] 1. By adopting the stator slot equivalent transformation method, slots of any shape can be transformed into specified rectangular slots according to the area equivalence principle, and irregularly arranged windings are arranged in layers, which can calculate the conductors in the slots more clearly and reduce the calculation time;

[0058] 2. It is proposed to add the influence of slot fill rate on loss in the calculation, and use rectangular slots for equivalent replacement, so that the slot area of ​​each layer after stratification is the same, and after placing the same number of windings, the slot fill rate of each layer is equal, except for the top layer, so as to reduce the change of complexity of the analytical model after adding the slot fill rate, shorten the calculation time, and increase the calculation accuracy;

[0059] 3. The proximity effect factor and skin effect factor are added, and the influence of actual current frequency change on the winding can be considered in the calculation process. And because most existing drive motors are distributed windings with a large span, the compensation length l' of the winding end is added when calculating the axial length, thereby improving the calculation accuracy of the winding loss;

[0060] 4. Substitute some finite element methods, simulate and analyze the losses of different spans, and perform curve fitting. It is found that as the short-distance coefficient increases, the loss rises parabolically. Therefore, based on this characteristic, the equation is fitted with assumptions and substituted into the loss equation to obtain the hybrid calculation model proposed in the end. The calculation time and accuracy are optimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a topological diagram of a distributed double-layer winding motor.

[0062] Figure 2 It is a flow chart of copper loss calculation of the present invention;

[0063] Figure 3 is the equivalent stator slot transformation diagram of any stator tooth;

[0064] Figure 4 is a relationship diagram between proximity effect, skin effect factor and structural parameters in the present invention;

[0065] Figure 5 This is a winding loss diagram corresponding to different frequencies and different currents of the present invention.

[0066] Figure 6 It is a comparison chart of the calculation results of the model of the present invention and the calculation results obtained by finite element and experimental methods under the same conditions. DETAILED DESCRIPTION

[0067] The following will be combined with the drawings in the embodiments of the present disclosure to clearly and completely describe the technical solutions in the embodiments of the present disclosure. Obviously, the described embodiments are only part of the embodiments of the present disclosure, not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present disclosure.

[0068] The present invention proposes a hybrid copper loss calculation method for multi-layer windings, including the following steps, the flow chart of which is as follows: Figure 2 shown.

[0069] The essence of the present invention is that it can be applied to calculate the copper loss of motors of all winding forms, which can be directly reflected in concentrated winding permanent magnet synchronous motors, distributed winding permanent magnet synchronous motors, concentrated winding vernier motors, distributed winding vernier motors, etc., and single-layer windings or multi-layer windings can be analytically calculated according to this method;

[0070] The steps for solving the copper loss of concentrated windings are as follows.

[0071] Step 1: Using the area equivalence principle, convert any stator slot type into a rectangular slot with equal area. For example, use the conformal mapping method to convert any stator slot type into a rectangular slot with equal area. Preliminarily set the length L and width D3 of the rectangular slot, such as Figure 3 shown.

[0072] Step 2: Take the double-layer winding as an example, S slot =Ses =L*D32. For a motor with double-layer distributed windings, take double-layer windings as an example. The windings on the upper and lower sides of the stator slots are initially divided into m / 2 layers, and the windings are placed in the stator slots planned on each layer. Except for the top layer, the number of windings placed on the other layers is equal, and the remaining windings are placed on the top layer. If there are three windings in total, the number of layers needs to be divided into m / 3, and so on.

[0073] 2.1: The slots are layered and the area of ​​each layer is equal. The following conditions should be met:

[0074] S es1 =S es2 =…=S esn =L1*D3

[0075] 2.2: Rearrange the windings. Except for the top layer, the number of windings placed on each layer is the same. This arrangement will reduce the calculation time, and the slot fill rate of each layer satisfies the following formula.

[0076] k1=k2=…=k m / 2-1

[0077] In the formula, k1, k2…k m / 2-1 The slot area of ​​the top layer is the same as that of the lower layer, but the top layer winding is only the remainder due to the equal division of the lower layer winding, so the slot area needs to be recalculated.

[0078] The existing motor copper consumption is calculated based only on the thickness, length and other considerations of the wire, without considering the connection between copper wires or the influence between slots. However, this application regards the slots and windings as a whole, and uses the whole to solve the problem, taking into account the influence between the whole. Since the windings are regarded as a whole, the slot fill rate needs to be considered. However, in order to facilitate calculation, the windings are rearranged to form a model with a consistent slot fill rate.

[0079] For example, if there are 23 conductors, then they can be arranged in 5 layers as 5-5-5-5-3. If there are 6 layers, then they can be arranged in 4-4-4-4-4-3. Then the slot filling rates of the first few layers must be the same, and you only need to recalculate the last layer.

[0080] Step 3. In this step, the copper loss calculation model needs to be derived and the complex power is rewritten into the conjugate complex form of the magnetic field intensity and the electric field intensity.

[0081] 3.1: First, consider each layer of winding in 2 as an electromagnetic loop, and according to Ampere's loop law, the magnetic field strength of the k+1th layer of winding can be obtained, which can be written as:

[0082]

[0083] The modified complex eddy current equation is used to obtain an analytical expression for the magnetic field intensity, as follows:

[0084]

[0085] The magnetic field strength can be formulated as a second-order differential equation, which can be expressed as follows:

[0086] H x =c1e -ty +c2e ty

[0087] For the convenience of subsequent expression, the parameter p can be written as:

[0088]

[0089] 3.2: According to Ampere's circuit law, the boundary condition of the magnetic field intensity in the k+1th layer of winding can be expressed as follows.

[0090]

[0091] In the formula, i k+1 is the current of the k+1th winding; It represents the sum of the total current of the lower winding and the current of the upper kth layer and below. In order to facilitate subsequent calculations, Available k To express.

[0092] Based on the above boundary conditions, the expression for the magnetic field strength is as follows.

[0093]

[0094] The electric field strength can be obtained by the same method The expression is

[0095]

[0096] 3.3: Calculation of the complex power flowing into a closed volume using Poynting's theorem The complex power can be expressed by the cross product of the magnetic field strength and the electric field strength, which is also the sum of the motor's active power P and reactive power Q, as shown below:

[0097]

[0098] because and are all in conjugate complex form, so for the discrete model, its complex power can be expressed as

[0099]

[0100] 3.4: Decompose the above equation according to Euler's formula and obtain the expression of active power as shown below.

[0101]

[0102] In the formula, ξ=L1*λ; Since the upper and lower windings may have non-same-phase currents, χ is expressed as

[0103] χ=i low 2 +2i low i k0 cosθ+i low i k+1 cosθ+i k0 (i k0 +i k+1 )

[0104] When there is no phase difference between the upper and lower currents, that is, the upper and lower currents are in phase, then θ = 0, and χ = i k (i k +i k+1 ).

[0105] Step 4: In order to consider the influence of skin effect factor and proximity effect factor on winding loss, the expression of active power is transformed as shown below. Substitute the skin effect factor and proximity effect factor to form an analytical model for the copper loss of each layer of winding, and obtain the variation range of the two factors according to the parameter changes, such as Figure 4 (a) shown.

[0106]

[0107] In the formula, is the skin effect factor; ψ(ξ) is the proximity effect factor. In order to verify the influence of these two parameters on the armature winding loss, the influence of different frequencies and different slot fill rates on the two effect factors are studied respectively, such as Figure 4 (b) as shown.

[0108] Therefore, the total loss model for the concentrated winding can be obtained as shown below.

[0109]

[0110] Where Q is the number of stator slots in the motor.

[0111] Furthermore, in order to study the loss model of the distributed winding, based on the analysis of steps 1 to 4, the distributed winding is analyzed again, step 5 is added, and steps 1 to 4 are no longer explained, as shown below.

[0112] Step 5: Since the span of distributed windings is large and most of them are short-distance windings, the result of the analytical method has too large an error and the calculation is inaccurate. Therefore, the finite element method is used to analyze the copper loss model under the short-distance coefficient β of 1 / 2 to 1 and fit the curve to obtain an approximate parabolic equation. Therefore, it is assumed that there is a nonlinear relationship between the short-distance coefficient and the loss, and the quadratic equation is substituted into the above formula to obtain a new analytical equation.

[0113] P l =Q((a1β 2 +b1β+c1)P a1 +(a2β 2 +b2β+c2)P a2 )

[0114] According to the boundary conditions of the analytical model, the final constant coefficients are obtained, and the distributed winding hybrid calculation model is obtained.

[0115] P l =Q(4β(1-β)P a1 +β(2β-1)P a2 )

[0116] In order to further improve the calculation accuracy of the distributed copper loss calculation model, on the basis of steps 1 to 5, the end compensation length is added to the solution of the axial length, and steps 1 to 5 are no longer elaborated, as shown below.

[0117] In some disclosures, when calculating copper loss, the end winding length is directly ignored, and only the axial length in the winding slot is calculated, resulting in a large error between the final calculation result and the actual result, especially for the copper loss calculation of distributed windings with a large span. Therefore, the compensation length l′ of the end should be added to the calculation to improve the calculation accuracy of the winding loss. The calculation formula is shown below.

[0118]

[0119] In the formula, m is the number of phases of the motor; p is the number of poles of the winding; and r is the radius from the rotor axis to the center of the stator slot. The active power formula in 4 is updated to the following.

[0120]

[0121] Then the loss model after considering the compensation length is

[0122]

[0123] In order to verify the proposed hybrid calculation copper loss model, the losses under different conditions were analyzed, such as Figure 5 , 6In order to verify the accuracy of the model, the results obtained by this method were verified by using finite element method and experimental method. Figure 6 shown.

[0124] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims

1. A method for calculating motor winding copper loss, characterized in that: The following steps are involved: Convert any stator slot of the motor into rectangular slots of equal area; The windings are redistributed so that the number of windings placed in the stator slots of each layer except the stator slots of the top layer is equal, and the remaining windings are placed in the stator slots of the top layer; Obtaining the active power of each layer of stator slots after the winding is redistributed; The skin effect factor and the proximity effect factor are substituted into the active power to form an analytical model of the copper loss of the stator slot winding of each layer. The analytical models of the copper loss of the stator slot winding of each layer are superimposed to obtain the total loss model of the motor winding, thereby obtaining the copper loss of the entire motor winding; Obtaining the active power of each layer of stator slots after the windings are redistributed, including: obtaining the electromagnetic field strength of each layer of stator slots according to Ampere's loop law, obtaining the complex power flowing into the closed volume by using Poynting's theorem, and decomposing the complex power into the active power of each layer of stator slots; The stator slot winding of each layer is regarded as an electromagnetic loop, and according to Ampere's loop law, the magnetic field strength of the k+1th layer winding is obtained as: In the formula, is the magnetic field strength; is the total magnetic field strength in the k layer and below; is the magnetic field strength of the k+1th layer; J z is the current density; k k+1 is the slot filling rate of the k+1th winding layer; is the total current of the kth layer and below; Using the modified complex eddy current equation, the magnetic field intensity is transformed into a second-order differential equation, which is expressed as follows: H x =c1e -ty +c2e ty In the formula, c1 and c2 are ordinary differential coefficients. Substitute them into the boundary conditions of the winding and solve them. The expression of the t function is as follows: Where ω is the angular frequency; μ0 is the vacuum magnetic permeability; σ is the electrical conductivity; k k+1 is the slot occupancy rate of the k+1 layer; According to Ampere's circuit law, the boundary condition of the magnetic field intensity in the k+1th layer of winding is expressed as follows: In the formula, i k+1 is the current of the k+1th winding; It represents the sum of the total current of the lower winding and the current of the upper kth layer and below. In order to facilitate subsequent calculations, Use i k To express: According to the above boundary conditions, the expression of magnetic field intensity is as follows: The electric field strength was obtained by the same method. The expression is: Then, the complex power flowing into the closed volume is calculated according to Poynting's theorem That is, the sum of the motor's active power P and reactive power Q, as shown below: In the formula, the complex power It is expressed as follows: because and are all in conjugate complex form, so for the discrete model, its complex power is expressed as Where L1 is the height of each layer; l is the axial length of the winding.

2. The method for calculating motor winding copper loss according to claim 1, characterized in that: The conversion of any stator slot type of the motor into rectangular slots of equal area is achieved through conformal mapping method.

3. The method for calculating motor winding copper loss according to claim 1, characterized in that: Adding the factors affecting the adhesion effect and the proximity effect factor ψ(ξ), the following expression is obtained: In the formula, i k+1 is the current value of the K+1th layer; χ is a set of functional relationships about the current phase angle, as shown below: χ=i low 2 +2i low i k0 cosθ+i low i k+1 cosθ+i k0 (i k0 +i k+1 ) In the formula, i low is the total current of the lower winding; i k0 is the current of layer k and below in the upper winding; θ is the current phase difference between the upper and lower windings. The copper loss analysis model of the centralized winding is:

4. The method for calculating motor winding copper loss according to claim 1, characterized in that: The copper loss of the entire motor winding is obtained through the analytical model of the copper loss of the stator slot winding of each layer, which is replaced by: the copper loss of the stator slot winding of each layer is superimposed to obtain the copper loss of the entire motor winding.

5. The method for calculating motor winding copper loss according to claim 1, characterized in that: For the distributed winding of the motor, the end compensation length is supplemented according to the relationship between the short-distance coefficient β and the winding loss to obtain the active power of each layer of the stator slot after the new winding is redistributed. The skin effect factor and proximity effect factor are substituted into the active power to form an analytical model of the copper loss of the stator slot winding of each layer, thereby obtaining the copper loss of the entire motor winding.

6. The method for calculating motor winding copper loss according to claim 5, characterized in that: The finite element method is used to fit the copper loss curve under different short-distance coefficients, and an approximate parabolic equation is obtained. Therefore, it is assumed that the relationship between the short-distance coefficient β and the winding loss is as follows: P l =Q((a1β 2 +b1β+e1)P a1 +(a2β 2 +b2β+e2)P a2 ) Where Q is the number of slots; P a1 is the upper winding loss in the same slot; P a2 is the lower winding loss in the same slot; a 1,2 , b 1,2 、e 1,2 They are all constant coefficients and are solved according to the winding boundary conditions; Add the end compensation length l' to the model and update it. The calculation formula of l' is as follows: In the formula, m is the number of phases of the motor; p is the number of poles of the winding; r is the radius from the rotor axis to the center of the stator slot; Then the active power model of the distributed winding is rewritten as: The skin effect factor and proximity effect factor are substituted into the active power to form an analytical model of the copper loss of the stator slot winding of each layer, thereby obtaining the copper loss of the entire motor winding.

7. A system for calculating copper loss of motor windings, characterized in that: The copper loss calculation system comprises a storage medium, wherein the storage medium contains a program, and when the program is executed, the method for calculating the copper loss of the motor winding of any one of claims 1-6 is implemented.

8. A device for calculating copper loss of motor windings, characterized in that: The device comprises the copper loss calculation system of claim 7.

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