Equivalent magnetic network modeling and eddy current loss calculation method for flux-switching permanent magnet motor

Abstract

The present invention discloses a method for modeling an equivalent magnetic network and calculating eddy current losses of a flux-switching permanent magnet motor. The method comprises the following steps: establishing an equivalent magnetic network model, wherein the equivalent magnetic network model of the flux-switching permanent magnet motor consists of four branches: an iron core magnetic impedance branch, a permanent magnet magnetic reluctance magnetic potential source branch, an armature winding magnetic potential source branch, and an air magnetic reluctance branch; correcting the magnetic resistance value of the iron core magnetic impedance branch using an extrapolation method based on the B-H curve of the iron core material; and correcting the magnetic induction value of the iron core magnetic impedance branch using an iterative method based on the eddy current effect of the iron core material. In the process of solving the equivalent magnetic network model of the flux-switching permanent magnet motor, a real-domain WZ decomposition method and a successive super-relaxation iteration method are used to simplify and accelerate the solution process of the complex equation system established by the nodal magnetic potential method. The present invention can quickly and accurately evaluate the torque performance and eddy current losses of the flux-switching permanent magnet motor, effectively shortening the calculation time in the motor analysis and design stage.

Description

Technical Field

[0001] The present invention belongs to the technical field of motor modeling and loss calculation, and specifically relates to a method for modeling an equivalent magnetic network and calculating eddy current losses of a flux switching permanent magnet motor. Background Art

[0002] As the power source of electric vehicles, electric motor technology is experiencing a new wave of development. Flux-switching permanent magnet motors (PMMs) are gaining widespread attention due to their high torque density, robust structure, high efficiency, and excellent heat dissipation. The magnetic circuit method, magnetic network method, and finite element method (FEM) are widely used and effective tools in motor analysis and design. Compared to the finite element method, which consumes a lot of memory and computation time, and the magnetic circuit method, which has lower computational accuracy and can resolve limited performance, the magnetic network method offers a better balance between accuracy and computation time requirements for electromagnetic performance.

[0003] To achieve higher power density, electric vehicle motors operate at relatively high speeds, and flux-switching permanent magnet motors have more pole pairs than traditional permanent magnet synchronous motors, making eddy current loss one of the most important factors affecting the operating efficiency of flux-switching permanent magnet motors. Existing motor design methods generally evaluate eddy current losses based on the finite element method. The calculation accuracy is highly dependent on the material parameter library built into the finite element software. Furthermore, mainstream finite element software is all developed abroad and is difficult to cover commonly used motor core processing materials in China. Furthermore, the data used by existing finite element software to evaluate eddy current losses is mostly measured under sinusoidal excitation, while the flux waveform in the core of a flux-switching permanent magnet motor is not sinusoidal, further increasing the technical difficulty of accurately evaluating eddy current losses.

[0004] In summary, for flux-switching permanent magnet motors, it is particularly important to develop an equivalent magnetic network model that combines solution accuracy and solution time, and can accurately evaluate eddy current losses, during the motor design stage. Summary of the Invention

[0005] Technical problem solved: The present invention discloses a method for modeling the equivalent magnetic network and calculating eddy current losses of a flux-switching permanent magnet motor, which can quickly and accurately evaluate the torque performance and eddy current losses of the flux-switching permanent magnet motor, effectively shortening the calculation time in the motor analysis and design stage.

[0006] Technical solution:

[0007] A method for modeling an equivalent magnetic network and calculating eddy current losses of a flux-switching permanent magnet motor, comprising the following steps:

[0008] Step 1, giving the size parameters of the flux switching permanent magnet motor;

[0009] Step 2, determining the initial rotor position of the flux switching permanent magnet motor;

[0010] Step 3: Establish an equivalent magnetic network model. The equivalent magnetic network model of the flux switching permanent magnet motor consists of four branches: the iron core magnetic impedance branch, the permanent magnet magnetic resistance magnetic potential source branch, the armature winding magnetic potential source branch, and the air magnetic resistance branch. The eddy current effect in the iron core of the flux switching permanent magnet motor is characterized by the magnetic induction element of the iron core magnetic impedance branch, and the eddy current loss in the iron core of the flux switching permanent magnet motor is calculated by the magnetic induction parameter of the iron core magnetic impedance branch. Confirm the parameters of each branch and give the calculated value of the motor stator and rotor iron core magnetic impedance branch.

[0011] Step 4: Based on the current rotor position and the preset air gap reluctance calculation interval, the air gap reluctance between any pair of stator and rotor teeth is calculated, and all air gap permeance branches are generated;

[0012] Step 5: Based on the nodal magnetic potential method, a nodal magnetic potential equation group is established. The real and imaginary parts of the nodal magnetic potential equation group are separated using the real-domain WZ decomposition method. The separated matrix is ​​numerically solved using successive super-relaxation iterations, and the complex solutions of the nodal magnetic potential equation group are inferred from the calculation results.

[0013] Step 6: Determine whether the calculation results meet the convergence conditions. If not, adjust the parameters of the core magnetic impedance branch, return to step 3, and re-establish the equivalent magnetic network model until the convergence conditions are met.

[0014] Step 7: After the branch convergence conditions are met, the calculation results of the current rotor position are stored to determine whether the preset rotor position has been reached. If not, return to step 3 and update the rotor position to simulate the rotation process of the flux switching permanent magnet motor rotor until the preset solution cycle is completed and the electromagnetic performance is output.

[0015] Furthermore, based on the BH curve of the core material, the extrapolation method is used to correct the magnetic resistance value of the core magnetic impedance branch; based on the eddy current effect of the core material, the initial value of the core magnetic induction of the flux switching permanent magnet motor is given according to the magnetic induction value under sinusoidal excitation, and the iterative method is used to continuously approximate the actual value of the magnetic induction of each branch to correct the magnetic induction value of the core magnetic impedance branch.

[0016] Furthermore, based on the BH curve of the core material, the process of correcting the magnetic resistance value of the core magnetic impedance branch by using the extrapolation method includes the following steps:

[0017] Solve the node magnetic potential equations to obtain the magnetic flux density B(i) of each branch;

[0018] According to the BH curve, find the magnetic field intensity H(i) corresponding to the calculated magnetic flux density B(i) of each branch, and calculate the magnetic permeability μ k+1 (i);

[0019] According to the magnetic permeability μ obtained from the table k+1 (i) The permeability μ set when the equivalent magnetic network model was established last time k (i) Make corrections. The correction formula is:

[0020]

[0021] Where, the subscript k refers to the number of iterations, and the variable i is the branch number;

[0022] Substitute the updated magnetic permeability into the core magnetic resistance calculation formula, recalculate the branch parameters, and establish an equivalent magnetic network;

[0023] Solve the equivalent magnetic network model after updating the parameters, obtain the magnetic flux density of each branch, and find the magnetic permeability according to the BH curve again to determine whether the convergence condition is met. If the condition is met, stop the iteration, otherwise continue to repeat the above process; the convergence judgment condition of the iteration is:

[0024] |μ k+1 (i)-μ k (i)|<ε1

[0025] Where ε1 is the solution accuracy of magnetic permeability.

[0026] Furthermore, the process of correcting the magnetic induction value of the core magnetic impedance branch includes the following steps:

[0027] Step A1, solve the theoretical calculated value of the core magnetic induction under sinusoidal excitation and use it as the iterative initial value of the branch magnetic induction, marked as

[0028] Step A2, establishing an equivalent reluctance network of the flux switching permanent magnet motor, establishing a core branch model with the reluctance branch, and calculating the branch reluctance parameters;

[0029] Step A3, solve the equivalent reluctance network, obtain the calculation results of each core reluctance branch, and calculate the magnetic flux φ and effective value φ of each silicon steel sheet in the core reluctance branch. rms , and the induced voltage dφ / dt caused by eddy current in each silicon steel sheet;

[0030] Step A4, solve the magnetic induction parameters

[0031]

[0032] And determine whether the convergence conditions are met:

[0033]

[0034] Where, Δ Feis the thickness of silicon steel sheet, ε2 is the solution accuracy of branch magnetic induction parameters, magnetic induction parameters The subscript 1 indicates that the magnetic induction parameter is obtained by the first equivalent magnetic network calculation, l and w are the length and height of each silicon steel sheet in the stator tooth area respectively;

[0035] Step A5, based on the theoretical calculation value of the core magnetic induction under sinusoidal excitation Use the damping method to update the magnetic induction parameters of each branch:

[0036]

[0037] in, Indicates the initial value The proportion is 90%, Indicates magnetic induction parameters The proportion is 10%;

[0038] Step A6: Using the updated magnetic induction parameters of each branch Perform equivalent magnetic network modeling. In this case, each core branch in the model is a magnetic impedance branch with magnetic resistance and magnetic induction in series. After solving the model, determine the convergence conditions:

[0039]

[0040] And update the branch magnetic induction parameters:

[0041]

[0042] in, Indicates that the theoretical calculated value of magnetic induction accounts for 90%; Indicates magnetic induction parameters The proportion is 10%;

[0043] If not, return to step A4 until the convergence condition is met, stop the iteration, and save the result.

[0044] Furthermore, the magnetic induction of each silicon steel sheet in the stator tooth area is:

[0045]

[0046] Among them, P e is the eddy current loss;

[0047] The magnetic induction parameters of each silicon steel sheet in the rotor tooth core area are:

[0048]

[0049] The magnetic induction parameters of each silicon steel sheet in the stator and rotor yoke core area are:

[0050]

[0051] Among them, Δ Fe is the thickness of the silicon steel sheet, l and w are the length and height of each silicon steel sheet in the stator tooth area, h, w1 and w2 are the height, upper side length and lower side length of each silicon steel sheet in the rotor tooth area, θ, R1 and R2 are the radian, inner radius and outer radius of each silicon steel sheet in the stator and rotor yoke area, ρ is the electrical conductivity, and its temperature correction formula is:

[0052] ρ(T)=ρ(T0)[1+α c (T-T0)]

[0053] Where T0 is the reference temperature, T is the temperature of the motor at rated operation, α c is the temperature coefficient of the core material;

[0054] The process of calculating branch reluctance parameters includes the following steps:

[0055] The reluctance parameters of the stator tooth area are:

[0056]

[0057] The reluctance parameters of the rotor tooth area are:

[0058]

[0059] The reluctance parameters of the stator and rotor yoke area are:

[0060]

[0061] Where μ is the relative magnetic permeability, l a is the axial length, l and w are the length and height of each silicon steel sheet in the stator tooth area, h, w1 and w2 are the height, upper side length and lower side length of each silicon steel sheet in the rotor tooth area, θ, R1 and R2 are the radian, inner radius and outer radius of each silicon steel sheet in the stator and rotor yoke area;

[0062] Based on the vector magnetic circuit theory, the magnetic induction of the core magnetic impedance branch is regarded as the parallel connection of the corresponding magnetic induction of each silicon steel sheet in the area. The initial value of the magnetic impedance parameter of the core magnetic impedance branch is calculated as follows:

[0063]

[0064] Where n is the number of stacked silicon steel sheets in the region, and ω = 2πf is the alternating angular frequency of the magnetic flux in the core.

[0065] Furthermore, the magnetic admittance value of the core magnetic impedance branch is converted by the following formula:

[0066]

[0067] Wherein, the subscript x refers to different core regions; ω = 2πf, is the alternating angular frequency of the magnetic flux in the core; j is the imaginary unit; They are the magnetic impedance, magnetic resistance and magnetic induction values ​​corresponding to the core area, are the calculated magnetic admittance, permeance and susceptance values ​​of the corresponding core area respectively.

[0068] Furthermore, the established node magnetic potential equations are:

[0069]

[0070] The magnetic admittance matrix is a sparse symmetric complex coefficient matrix, and are the node magnetic potential and magnetic flux respectively; when solving, the real domain WZ decomposition method is used to separate the real part and the imaginary part, and the separated matrix is ​​numerically solved by successive super-relaxation iterations, and then the complex solutions of the original node magnetic potential equations are inferred from the calculation results.

[0071] Furthermore, the electromagnetic performance of the flux switching permanent magnet motor is calculated using the following method:

[0072] The coil flux linkage of the flux switching permanent magnet motor is obtained based on the branch parameters corresponding to the coil enclosed area:

[0073]

[0074] Where N is the number of coil turns, and is the magnetic potential at both ends of the branch, is the magnetic admittance of branch i, F m0 (i) is the initial magnetic potential of the branch;

[0075] Based on the current-flux linkage within one electrical cycle, the electromagnetic torque of the flux-switching permanent magnet motor is calculated by the magnetic common energy method:

[0076]

[0077] Where m is the number of motor phases; P r is the number of rotor teeth, that is, the number of pole pairs of the flux switching permanent magnet motor; S i-Ψ It is the integral value of the flux linkage of each phase to the current.

[0078] Furthermore, based on the vector magnetic circuit theory, the corresponding eddy current loss on each core magnetic admittance branch can be calculated as follows:

[0079]

[0080] Where, ω = 2πf is the alternating angular frequency of the magnetic flux in the iron core; is the magnetic induction corresponding to the i-th core magnetic admittance branch; Φ i is the effective value of the magnetic flux flowing through the i-th iron core magnetic admittance branch.

[0081] Beneficial effects:

[0082] First, the equivalent magnetic network modeling and eddy current loss calculation method of the flux switching permanent magnet motor of the present invention, compared with the finite element method, performs equivalent magnetic network modeling of the flux switching permanent magnet motor based on magnetic induction, which greatly reduces the difficulty of solving the motor performance, especially the eddy current loss, greatly shortens the solution time and memory usage, improves the analysis efficiency of the motor design, and plays a good auxiliary role in the motor analysis and design stage.

[0083] Second, the equivalent magnetic network modeling and eddy current loss calculation method of the flux switching permanent magnet motor of the present invention, compared with other eddy current loss calculation methods, starts from the principle of the eddy current effect and addresses the problem of non-sinusoidal magnetic flux linkage in the iron core of the flux switching permanent magnet motor. When establishing the equivalent magnetic network model, the magnetic induction is introduced to simplify the analysis and calculation process, and better accuracy is achieved in the eddy current loss calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a cross-sectional view of a flux switching permanent magnet motor;

[0085] Figure 2 Schematic diagram and dimension marking of the core structure of each region, where (a) is the schematic diagram and dimension marking of the stator tooth core; (b) is the schematic diagram and dimension marking of the rotor tooth core; (c) is the schematic diagram and dimension marking of the stator and rotor yoke core;

[0086] Figure 3 This is a schematic diagram for calculating the magnetic induction of the stator tooth core branch;

[0087] Figure 4 This is a schematic diagram of the calculation of the magnetic induction of the rotor tooth core branch;

[0088] Figure 5 This is a schematic diagram for calculating the magnetic induction of the core branch of the stator and rotor yoke;

[0089] Figure 6 It is a schematic diagram of the equivalent magnetic network of a flux switching permanent magnet motor;

[0090] Figure 7a This is a flow chart of the equivalent magnetic network modeling and eddy current loss calculation method of the flux switching permanent magnet motor based on magnetic induction;

[0091] Figure 7b It is a schematic diagram of iterative calculation of the core branch magnetic resistance;

[0092] Figure 7cIt is a schematic diagram of iterative calculation of the magnetic induction of the core branch;

[0093] Figure 8 This is a comparison chart of the magnetic flux calculated by the method of the present invention and the results of the finite element method analysis;

[0094] Figure 9 This is a comparison chart of the torque calculated by the method of the present invention and the results of the finite element method and experimental measurement;

[0095] Figure 10 This is a comparison chart of the eddy current loss calculated by the method of the present invention and the results of the finite element method and experimental measurement. DETAILED DESCRIPTION

[0096] The following examples may enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0097] The present invention provides a method for modeling an equivalent magnetic network and calculating eddy current losses of a flux-switching permanent magnet motor based on magnetic induction, which includes two parts: equivalent magnetic network modeling based on the principle of magnetic induction, and calculation of motor eddy current losses based on branch magnetic induction. The equivalent magnetic network model of the flux-switching permanent magnet motor consists of four types of branches: the core magnetic impedance branch, the permanent magnet magnetic reluctance magnetic potential source branch, the armature winding magnetic potential source branch, and the air magnetic reluctance branch. After establishing the equivalent magnetic network model, the real-domain WZ decomposition method and the successive super-relaxation iteration method are used to simplify and accelerate the complex equations established by the node magnetic potential method. In addition, during the solution process, the magnetic resistance value of the core magnetic impedance branch is corrected by the extrapolation method based on the BH curve of the core material, and the magnetic induction value of the core magnetic impedance branch is corrected by the iterative method based on the eddy current effect of the core material, thereby achieving an accurate evaluation of the motor magnetization state and the core eddy current loss. The calculated results are in good agreement with the finite element and experimental measurement results.

[0098] Figure 1 It is a topological structure diagram of the flux switching permanent magnet motor which is the research object of the embodiment of the present invention. Figure 1The flux switching permanent magnet motor shown in the figure includes, from the outside to the inside, a motor stator 1, an air gap 2, and a salient pole rotor 3. The stator 1 of the flux switching permanent magnet motor under study is composed of structures such as stator teeth 11, a stator yoke 12, permanent magnets 13, and an armature winding 14; the rotor 3 is composed of two parts: rotor teeth 31 and a rotor yoke 32. The stator body is composed of 12 U-shaped iron cores and 12 permanent magnets. Every two stator teeth 11 and a permanent magnet 13 sandwiched therebetween form a stator pole, and the armature winding 14 is wound on the stator pole. The embodiment of the present invention has a total of 12 stator poles and 10 rotor teeth, so it is called a 12-10 flux switching permanent magnet motor. This embodiment of the present invention uses a fractional-slot concentrated winding design for the armature winding, with a winding coefficient of 0.87. The stator and rotor cores are made of 50WW270 silicon steel sheets with a thickness of 0.5 mm and an axial stack of 75 mm. The permanent magnets utilize tangentially magnetized rare earth neodymium iron boron (NdFeB) material, with adjacent permanent magnets magnetized in opposite directions. The parameters of the flux-switching permanent magnet motor in this embodiment of the present invention are shown in Table 1.

[0099] Table 1 Parameters of the flux switching permanent magnet motor according to the embodiment of the present invention

[0100] Rated speed 1000r / min Rotor inner diameter 22mm Rated power 1kW Rotor tooth width 10.5° Number of stator poles 12 Rotor tooth bottom width 21° Number of rotor teeth 10 Rotor tooth height 8.71mm Axial length 75mm Armature current density (peak) <![CDATA[5A / mm 2 ]]> Stator outer diameter 128mm Slot fill rate 0.4 Crack Ratio 0.55 Number of turns per phase 280 Air gap length 0.35mm Number of parallel strands 1 Stator yoke width 4.6mm Wire diameter 0.756 Stator tooth width 7.5° Lamination type 50WW470 Permanent magnet width 4.61mm Permanent magnet type N35(Br=1.2T) Permanent magnet length 28.8mm

[0101] exist Figure 1 Based on the topological structure diagram of the embodiment of the present invention shown, the motor structure is divided into three categories according to the topological structure of a 12-10 flux switching permanent magnet motor and the material properties of each component: the core-based magnetic impedance calculation region, the vacuum magnetic permeability region, and the magnetic potential source region. The core magnetic impedance region is divided into seven parts: the stator yoke 1, the stator tooth near yoke 2, the permanent magnet 3, the stator tooth near air gap 4, the rotor yoke 5, the rotor tooth near yoke 6, and the rotor tooth near air gap 7. In addition, there are also leakage magnetic regions and air gap regions. The calculation of the parameters of each of these branches is explained below.

[0102] First, the parameter calculation method of the core region is described. According to the core region division of the embodiment of the present invention, the core magnetic impedance region can be summarized into three typical shapes, such as Figure 2 As shown, the magnetic resistance calculation method of the three regions is as follows:

[0103] Figure 2 (a) is the stator tooth area, and the calculation formula is as follows:

[0104]

[0105] Figure 2 (b) is the rotor tooth area, and the calculation formula is as follows:

[0106]

[0107] Figure 2 (c) is the stator and rotor yoke area, and the calculation formula is as follows:

[0108]

[0109] Among them, μ is the relative magnetic permeability, which needs to be updated iteratively, l a is the axial length, h, w1, w2, l, θ, R1 and R2 are Figure 2 Dimensions and angles in .

[0110] Secondly, based on the principle of eddy current effect, it is explained Figure 2 The calculation method of magnetic induction parameters of the three core areas is shown in the following figure. Figures 3 to 5 . Due to the obvious DC bias phenomenon in the iron core of the flux switching permanent magnet motor, and due to the modulation effect of the stator and rotor salient poles, the magnetic flux density waveform in the iron core is non-sinusoidal. The above phenomena make the calculation of eddy current loss more complicated. In order to reduce the difficulty of calculation and improve the calculation accuracy, the embodiment of the present invention gives the initial value of the magnetic induction of the iron core of the flux switching permanent magnet motor based on the magnetic induction value under sinusoidal excitation, and then uses the iterative method to continuously approximate the actual value of the magnetic induction of each branch, thereby accurately evaluating the eddy current loss of the flux switching permanent magnet motor.

[0111] by Figure 2 Take the stator tooth area shown in a as an example, Figure 3 This is a schematic diagram of the calculation of the magnetic induction of the core lamination in the stator tooth area. In a silicon steel sheet, it is assumed that the magnetic flux density in this section of the core changes sinusoidally with an angular frequency ω, that is, B(t) = B m sinωt, then according to Faraday's law, the induced voltage between the upper and lower ends of the silicon steel sheet causing eddy current is:

[0112]

[0113] Where V m (x) = ωB m wx is the amplitude of the induced voltage.

[0114] The resistance of the silicon steel sheet in the incremental dx region is:

[0115]

[0116] Furthermore, the amplitude of the eddy current density can be calculated:

[0117]

[0118] The corresponding eddy current loss power is:

[0119]

[0120] Furthermore, Figure 3 The magnetic induction of a silicon steel sheet in the stator tooth area is shown as follows:

[0121]

[0122] Accordingly, Figure 4 The figure below is a schematic diagram of calculating the magnetic induction parameters of each silicon steel sheet in the rotor tooth core area. The simplified initial value calculation formula under sinusoidal excitation is as follows:

[0123]

[0124] Figure 5 The figure below is a schematic diagram of calculating the magnetic induction parameters of each silicon steel sheet in the stator and rotor yoke core area. The simplified initial value calculation formula under sinusoidal excitation is as follows:

[0125]

[0126] Among them, Δ Fe is the thickness of silicon steel sheet, h, w1, w2, l, θ, R1 and R2 are Figure 5 The dimensions and angles in the figure are marked, ρ is the conductivity, and its temperature correction formula is:

[0127] ρ(T)=ρ(T0)[1+α c (T-T0)] (11);

[0128] Where T0 is the reference temperature, T is the temperature of the motor at rated operation, α c is the temperature coefficient of the core material.

[0129] Furthermore, based on the vector magnetic circuit theory, for the laminated core of the motor, the magnetic induction of a section of the core magnetic impedance branch can be regarded as the parallel connection of the corresponding magnetic induction of each silicon steel sheet in this area. The initial value of the magnetic reactance parameter of the core magnetic impedance branch is calculated as follows:

[0130]

[0131] Where n is the number of silicon steel sheets stacked in the region, and ω = 2πf is the alternating angular frequency of the magnetic flux in the core.

[0132] At this point, the initial calculation of the core region's magnetic impedance parameters has been completed. To facilitate the establishment of the equation group using the nodal magnetic potential method, the magnetic admittance value of the core magnetic impedance branch can be converted using the following formula:

[0133]

[0134] Wherein, the subscript x refers to different core regions; ω = 2πf, is the alternating angular frequency of the magnetic flux in the core; j is the imaginary unit; the other parameters are and They are the magnetic impedance, magnetic resistance, and magnetic induction values ​​of the corresponding core area, and the magnetic admittance, magnetic permeance, and magnetic susceptance values ​​calculated therefrom.

[0135] In addition to the above-mentioned core branch, the parameters of the other three branches are calculated as follows. The two leakage magnetic permeance calculation methods of the embodiment of the present invention are:

[0136]

[0137]

[0138] Where μ0 is the vacuum permeability, l a is the axial length, X is the width of the permanent magnet, and w is the width of the end leakage magnetic path.

[0139] To simplify the air gap permeance calculation process, the embodiment of the present invention divides the air gap permeance calculation intervals into 11 intervals determined by 12 boundaries based on the relative position between the stator and rotor teeth of the flux switching permanent magnet motor. Based on the flux direction within each interval, the air gap permeance within that interval can be calculated. The air gap permeance calculation model can be summarized into four cases, and the air gap permeance of each interval can be calculated by combining the above four cases. The corresponding calculation method is as follows:

[0140]

[0141]

[0142]

[0143]

[0144] Where μ0 is the vacuum permeability, l a is the axial length, g is the air gap length, X is the width of the stator and rotor teeth overlap region, R1 is the air gap magnetic path radius on the stator tooth side, and R2 is the air gap magnetic path radius on the rotor tooth side. The flux-switching permanent magnet motor of the embodiment of the present invention has a total of 24 stator teeth and 10 rotor teeth. By detecting the relative position between any stator tooth and any rotor tooth and determining the calculation interval to which they belong, the air gap permeance connecting the stator tooth and rotor tooth can be calculated. If the relative position between a stator tooth and a rotor tooth does not fall within any of the above-preset intervals, no air gap permeance branch is provided between the two.

[0145] The magnetomotive force source of a flux-switching permanent magnet motor includes permanent magnets and armature windings, and the corresponding modeling method is as follows. The magnetomotive force and magnetic permeance generated by the permanent magnets are calculated as follows:

[0146] F PM =H c h PM (20);

[0147]

[0148] The armature magnetic potential is calculated as follows:

[0149] F aw =J a S a k pf (twenty two);

[0150]

[0151] When calculating the loading performance of a flux-switching permanent magnet motor, it is sufficient to add an armature magnetic potential source to the stator yoke branch.

[0152] The air gap magnetic permeability branch, the iron core magnetic admittance branch, the permanent magnet branch and the leakage magnetic branch, as well as the permanent magnet and the armature winding magnetic potential source in the embodiment of the present invention are connected in sequence to form an equivalent magnetic network model of a flux switching permanent magnet motor based on magnetic induction. Figure 6 This is a schematic diagram of the equivalent magnetic network model of an embodiment of the present invention. Excluding the air gap permeance branch, the model has a total of 158 nodes and 218 branches. Of these, 168 branches are located on the stator side of the motor, 96 of which are stator core magnetic admittance (reluctance-induction) branches, and the remaining 72 are permanent magnet or leakage magnetic permeance branches. The rotor core has a total of 50 branches, all of which are rotor core magnetic admittance branches.

[0153] After completing the branch parameter calculation, the node magnetic potential equations are established in the form of:

[0154]

[0155] The magnetic admittance matrix Y is a sparse, symmetric complex matrix. The nodal magnetic potential equations are nonlinear complex matrix equations. The real-domain WZ decomposition method is used to separate the real and imaginary parts. Successive super-relaxation iterations are used to numerically solve the separated matrices. The complex solutions of the original nodal magnetic potential equations are then inferred from the calculated results.

[0156] At this point, the equivalent magnetic network modeling method based on magnetic induction has been completed. Next, the equivalent magnetic network model should be solved, and on this basis, the electromagnetic performance of the flux switching permanent magnet motor should be further solved. The process of the equivalent magnetic network modeling and eddy current loss calculation method of the flux switching permanent magnet motor based on magnetic induction is as follows: Figures 7a to 7c As shown, it includes the following steps:

[0157] Step 1: Given motor parameters. The parameters of the embodiment of the present invention are shown in Table 1.

[0158] Step 2: Determine the initial rotor position of the flux switching permanent magnet motor.

[0159] Step 3: Establish an equivalent magnetic network model, confirm the parameters of each branch, and give the calculated value of the magnetic impedance branch of the motor stator and rotor core.

[0160] Step 4: Based on the current rotor position and the preset air gap magnetic resistance calculation interval, the air gap magnetic resistance between any pair of stator and rotor teeth is calculated, and all air gap magnetic permeance branches are generated accordingly.

[0161] Step 5: Based on the nodal magnetic potential method, a complex equation system (Equation (24)) is established and then solved. This system of equations is a complex matrix equation. The real and imaginary parts are separated using the real-domain WZ decomposition method. The separated matrix is ​​numerically solved using successive super-relaxation iterations. The complex solutions of the original nodal magnetic potential equation system are then inferred from the calculated results.

[0162] Step 6: Determine whether the calculation results meet the convergence conditions. If not, adjust the parameters of the core magnetic impedance branch and then return to step 3 to repeatedly build the equivalent magnetic network model until the convergence conditions are met.

[0163] Step 7: After the branch convergence condition is met, the calculation result of the current rotor position is stored, and then the rotor position is updated to simulate the rotation process of the flux switching permanent magnet motor rotor. Return to step 2 and repeat the above process until the preset solution cycle is completed.

[0164] The core of the equivalent magnetic network calculation method proposed in this invention is to adjust the parameters of the magnetic impedance branch of the stator and rotor core of the flux switching permanent magnet motor by using an iterative method. Based on the BH curve of the core material, the magnetic resistance value of the core magnetic impedance branch is corrected by an extrapolation method. The iterative method is as follows: Figure 7b As shown, the steps are as follows:

[0165] Step 1: Solve the node magnetic potential equations to obtain the magnetic flux density B(i) of each branch.

[0166] Step 2: According to the BH curve, find the magnetic permeability μ corresponding to the calculated magnetic flux density B(i) of each branch k+1 (i).

[0167] Step 3: Calculate the magnetic permeability μ from the table k+1 (i) The permeability μ set when the equivalent magnetic network model was established last time k (i) Make corrections. The correction formula is:

[0168]

[0169] Step 4: Substitute the updated magnetic permeability into the core magnetic resistance calculation formula, recalculate the branch parameters, and establish an equivalent magnetic network.

[0170] Step 5: Solve the equivalent magnetic network model after updating the parameters, obtain the magnetic flux density of each branch, and find the magnetic permeability according to the BH curve again to determine whether the convergence condition is met. If the condition is met, stop the iteration, otherwise continue to repeat the above process. The convergence judgment condition of the iteration is:

[0171] |μ k+1 (i)-μ k (i)|<ε1 (26);

[0172] Wherein, ε1 is the solution accuracy of magnetic permeability, and the value in the embodiment of the present invention is 10-7.

[0173] The embodiment of the present invention is based on the eddy current effect of the core material, and introduces a magnetic induction element into the core branch of the flux switching permanent magnet motor to characterize the eddy current effect and calculate the eddy current loss. In order to simplify the derivation process, the embodiment of the present invention derives the initial value of the core magnetic induction based on the sinusoidal magnetic density. However, there is a DC bias phenomenon in the core of the flux switching permanent magnet motor, and the waveform is non-sinusoidal. It is necessary to correct the initial value of the magnetic induction of the core branch to more accurately evaluate the eddy current loss. Therefore, an iterative method is used to correct the magnetic induction value of the core magnetic impedance branch. The iterative method is as follows: Figure 7c As shown, the steps are as follows:

[0174] Step 1: Calculate the theoretical value of the core magnetic induction under sinusoidal excitation The calculation method is shown in equations (8) to (10), and this value is used as the initial value of the iteration of the branch magnetic induction, marked as

[0175] Step 2: Establish an equivalent reluctance network of the flux switching permanent magnet motor, that is, establish a core branch model with a reluctance branch. The calculation method of the branch reluctance parameters is shown in equations (1) to (3).

[0176] Step 3: Solve the equivalent magnetic resistance network obtained in step 2, obtain the calculation results of each core magnetic resistance branch, and calculate the magnetic flux φ and effective value φ in each silicon steel sheet in the branch. rms , and the induced voltage dφ / dt caused by eddy current in each silicon steel sheet.

[0177] Step 4: Based on the calculation results of step 3, solve the magnetic induction parameters

[0178]

[0179] And determine whether the convergence conditions are met:

[0180]

[0181] Where ε2 is the solution accuracy of the branch magnetic induction parameter, which is set to 10 -2 , where the magnetic induction parameter The subscript “1” indicates that the parameter is obtained from the first equivalent magnetic network calculation.

[0182] Step 5: Theoretical calculation value of the core magnetic induction under sinusoidal excitation Update the magnetic induction parameters of each branch as follows:

[0183]

[0184] Step 6: Use the updated magnetic induction parameters of each branch Perform equivalent magnetic network modeling. In this case, each core branch in the model is a magnetic impedance branch with magnetic resistance and magnetic induction in series. After solving the model, repeat steps 4 and 5 above to determine the convergence conditions:

[0185]

[0186] And update the branch magnetic induction parameters:

[0187]

[0188] When the convergence condition is met, the iteration stops and the results are saved.

[0189] According to a method for modeling the equivalent magnetic network and evaluating eddy current losses of a flux-switching permanent magnet motor based on magnetic induction, an embodiment of the present invention establishes an equivalent magnetic network model of the flux-switching permanent magnet motor listed in Table 1 and solves the electromagnetic performance to illustrate that the present invention has high accuracy in solving motor performance and calculating core eddy current losses.

[0190] In the embodiment of the present invention, the armature winding of the flux-switching permanent magnet motor is wound around the stator pole and includes two stator teeth and a permanent magnet. The magnetic network model is used to calculate the coil flux linkage of the flux-switching permanent magnet motor based on the branch parameters corresponding to the coil enclosed area. The calculation method is as follows:

[0191]

[0192] Where, N is the number of turns of the coil; n is the number of branches surrounded by the coil, which is 4 in the embodiment of the present invention; F m1 (i) and F m2 (i) is the magnetic potential at both ends of the i-th branch among the n branches surrounded by the coil, F m0 (i) is the initial magnetic potential of the branch.

[0193] Figure 8The figure is a comparison of the flux calculated by the method of the present invention and the analysis results of the finite element method. The flux waveforms obtained by the two calculation methods are highly consistent, indicating that the equivalent magnetic network modeling and eddy current loss calculation method based on magnetic induction has high calculation accuracy and can be expected to become an effective alternative to the finite element method in the analysis process. In addition, in order to illustrate the complementarity of the armature winding of the flux switching permanent magnet motor, the flux in the two complementary coils in phase A is also Figure 8 This is shown in the figure, with the waveform between 240° and 300° partially magnified. This shows that in addition to accurately calculating the flux linkage of each phase, the equivalent magnetic network method based on magnetic induction can also reflect the complementarity of the armature windings.

[0194] Based on the integral of the flux linkage of each phase to the current within one electrical cycle, the electromagnetic torque of the flux switching permanent magnet motor can be calculated by the magnetic common energy method. The calculation method is as follows:

[0195]

[0196] Wherein, m is the number of motor phases; P is the number of rotor teeth, that is, the number of pole pairs of the flux switching permanent magnet motor in the embodiment of the present invention; S i-Ψ It is the integral result of the flux linkage of each phase to the current in one electrical cycle.

[0197] Figure 9 It is a comparison chart of the torque calculated by the method of the present invention and the results of the finite element method and experimental measurement. As the armature current density changes, there is good consistency between the equivalent magnetic network method, the finite element method and the experimental measurement results, and the errors among the three are very small. The maximum error of the equivalent magnetic network method of the present invention and the finite element method is within 4%, and the maximum error of the experimental measurement data is within 7%. In addition, the average torque value calculated by the equivalent magnetic network is slightly larger. This is because the present invention only considers two types of leakage magnetic conditions, and the leakage magnetic conditions of the flux switching permanent magnet motor are more complicated. In consideration of the solution speed, the embodiment of the present invention simplifies the leakage magnetic conditions to a certain extent, but it can still be considered that the present invention achieves good calculation accuracy and meets the accuracy requirements of the motor analysis and design stage.

[0198] After the magnetic admittance parameters of the stator and rotor core branches reach the convergence conditions, the magnetic induction of the branch can be inferred:

[0199]

[0200] It should be noted that the node magnetic potential method used in the present invention can reduce the number of unknowns. In order to facilitate calculation, when checking the iterative convergence conditions, the program checks and calculates the magnetic admittance value. Therefore, when calculating the eddy current loss of the branch, the inverse of the magnetic admittance of the branch that meets the convergence conditions should be taken to calculate the magnetic impedance of the branch, and then the magnetic induction corresponding to the branch is calculated from the imaginary part of the magnetic impedance. Therefore, based on the vector magnetic circuit theory, the corresponding eddy current loss on each iron core magnetic admittance branch can be calculated. The calculation method is:

[0201]

[0202] Where, ω = 2πf, which is the alternating angular frequency of the magnetic flux in the iron core; is the magnetic induction corresponding to the branch; Φ i is the effective value of the magnetic flux flowing through this branch.

[0203] Figure 10 It is a comparison chart of the eddy current loss calculated by the method of the present invention and the results of the finite element method and experimental measurement. Among them, the finite element software used is JMAG, and the iron loss calculation method is the built-in FFT method of the software, that is, the magnetic flux density in each grid is subjected to fast Fourier decomposition and then superimposed to obtain it. However, when calculating the eddy current loss of each order, this method uses the same eddy current loss coefficient, which cannot accurately describe the harmonic eddy current loss caused by harmonics of each order. When solving the eddy current loss based on the equivalent magnetic network model of magnetic induction, the present invention starts from the principle of eddy current effect, determines the actual value of magnetic induction through iteration, and finally obtains a more accurate eddy current loss. Therefore, the equivalent magnetic network model based on magnetic induction of the present invention is very close to the eddy current loss measured experimentally.

[0204] Based on vector magnetic circuit theory, the present invention utilizes an equivalent magnetic network model to rapidly calculate the electromagnetic performance of a flux-switching permanent magnet motor, significantly reducing computational time and memory usage, and becoming an effective alternative to the finite element method during the motor design and development phase. When the equivalent magnetic network model of the present invention is used, the stator and rotor cores of the flux-switching permanent magnet motor are modeled using a series connection of "magnetic resistance and magnetic induction." This allows the eddy current effects in the motor core to be taken into account when solving for electromagnetic performance, and accurately assesses the eddy current losses of the flux-switching permanent magnet motor.

[0205] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions based on the principles of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for modeling the equivalent magnetic network and calculating eddy current losses of a flux-switching permanent magnet motor, characterized in that: The equivalent magnetic network modeling and eddy current loss calculation method comprises the following steps: Step 1, giving the size parameters of the flux switching permanent magnet motor; Step 2, determining the initial rotor position of the flux switching permanent magnet motor; Step 3: Establish an equivalent magnetic network model, confirm the parameters of each branch, and give the calculated value of the motor stator and rotor core magnetic impedance branch; the equivalent magnetic network model of the flux switching permanent magnet motor consists of four types of branches: the core magnetic impedance branch, the permanent magnet reluctance magnetic potential source branch, the armature winding magnetic potential source branch, and the air reluctance branch; the eddy current effect in the core of the flux switching permanent magnet motor is characterized by the magnetic induction element of the core magnetic impedance branch, and the eddy current loss in the core of the flux switching permanent magnet motor is calculated by the magnetic induction parameters of the core magnetic impedance branch; Step 4: Based on the current rotor position and the preset air gap magnetic resistance calculation interval, the air gap magnetic resistance between any pair of stator and rotor teeth is calculated, and all air gap magnetic permeance branches are generated; Step 5: Based on the nodal magnetic potential method, a nodal magnetic potential equation group is established. The real and imaginary parts of the nodal magnetic potential equation group are separated using the real-domain WZ decomposition method. The separated matrix is ​​numerically solved using successive super-relaxation iterations, and the complex solutions of the nodal magnetic potential equation group are inferred from the calculation results. Step 6: Determine whether the calculation results meet the convergence conditions. If not, adjust the parameters of the core magnetic impedance branch, return to step 3, and re-establish the equivalent magnetic network model until the convergence conditions are met. Step 7: After the branch convergence conditions are met, the calculation results of the current rotor position are stored to determine whether the preset rotor position has been reached. If not, return to step 3 and update the rotor position to simulate the rotation process of the flux switching permanent magnet motor rotor until the preset solution cycle is completed and the electromagnetic performance is output.

2. The method for equivalent magnetic network modeling and eddy current loss calculation of a flux switching permanent magnet motor according to claim 1, characterized in that: Based on the BH curve of the core material, the extrapolation method is used to correct the magnetic resistance value of the core magnetic impedance branch; based on the eddy current effect of the core material, the initial value of the core magnetic induction of the flux switching permanent magnet motor is given according to the magnetic induction value under sinusoidal excitation, and the iterative method is used to continuously approximate the actual value of the magnetic induction of each branch.

3. The method for equivalent magnetic network modeling and eddy current loss calculation of a flux switching permanent magnet motor according to claim 1, characterized in that: Based on the BH curve of the core material, the process of correcting the magnetic resistance value of the core magnetic impedance branch using the extrapolation method includes the following steps: Solve the node magnetic potential equations to obtain the magnetic flux density B(i) of each branch; According to the BH curve, find the magnetic field intensity H(i) corresponding to the calculated magnetic flux density B(i) of each branch, and calculate the magnetic permeability μ k+1 (i); According to the magnetic permeability μ obtained from the table k+1 (i) The permeability μ set when the equivalent magnetic network model was established last time k (i) Make corrections. The correction formula is: Where, the subscript k refers to the number of iterations, and the variable i is the branch number; Substitute the updated magnetic permeability into the core magnetic resistance calculation formula, recalculate the branch parameters, and establish an equivalent magnetic network; Solve the equivalent magnetic network model after updating the parameters, obtain the magnetic flux density of each branch, and find the magnetic permeability according to the BH curve again to determine whether the convergence condition is met. If the condition is met, stop the iteration, otherwise continue to repeat the above process; the convergence judgment condition of the iteration is: |m k+1 (i)-m k (i)|<ε1 Where ε1 is the solution accuracy of magnetic permeability.

4. The method for equivalent magnetic network modeling and eddy current loss calculation of a flux switching permanent magnet motor according to claim 1, characterized in that: The process of correcting the magnetic induction value of the core magnetic impedance branch includes the following steps: Step A1, solve the theoretical calculated value of the core magnetic induction under sinusoidal excitation and use it as the iterative initial value of the branch magnetic induction, marked as Step A2, establishing an equivalent reluctance network of the flux switching permanent magnet motor, establishing a core branch model with the reluctance branch, and calculating the branch reluctance parameters; Step A3, solve the equivalent reluctance network, obtain the calculation results of each core reluctance branch, and calculate the magnetic flux φ and effective value φ of each silicon steel sheet in the core reluctance branch. rms , and the induced voltage dφ / dt caused by eddy current in each silicon steel sheet; Step A4, solve the magnetic induction parameters And determine whether the convergence conditions are met: Where, Δ Fe is the thickness of silicon steel sheet, ε2 is the solution accuracy of branch magnetic induction parameters, magnetic induction parameters The subscript 1 indicates that the magnetic induction parameter is obtained by the first equivalent magnetic network calculation, l and w are the length and height of each silicon steel sheet in the stator tooth area respectively; Step A5, based on the theoretical calculation value of the core magnetic induction under sinusoidal excitation Use the damping method to update the magnetic induction parameters of each branch: in, Indicates the initial value The proportion is 90%, Indicates magnetic induction parameters The proportion is 10%; Step A6: Using the updated magnetic induction parameters of each branch Perform equivalent magnetic network modeling. In this case, each core branch in the model is a magnetic impedance branch with magnetic resistance and magnetic induction in series. After solving the model, determine the convergence conditions: And update the branch magnetic induction parameters: in, Indicates that the theoretical calculated value of magnetic induction accounts for 90%; Indicates magnetic induction parameters The proportion is 10%; If not, return to step A4 until the convergence condition is met, stop the iteration, and save the result.

5. The method for equivalent magnetic network modeling and eddy current loss calculation of a flux switching permanent magnet motor according to claim 4, characterized in that: The magnetic induction of each silicon steel sheet in the stator tooth area is: Among them, P e is the theoretical value of eddy current loss; The magnetic induction parameters of each silicon steel sheet in the rotor tooth core area are: The magnetic induction parameters of each silicon steel sheet in the stator and rotor yoke core area are: Among them, Δ Fe is the thickness of the silicon steel sheet, l and w are the length and height of each silicon steel sheet in the stator tooth area, h, w1 and w2 are the height, upper side length and lower side length of each silicon steel sheet in the rotor tooth area, θ, R1 and R2 are the radian, inner radius and outer radius of each silicon steel sheet in the stator and rotor yoke area, ρ is the electrical conductivity, and its temperature correction formula is: ρ(T)=ρ(T0)[1+α c (T-T0)] Where T0 is the reference temperature, T is the temperature of the motor at rated operation, α c is the temperature coefficient of the core material; The process of calculating branch reluctance parameters includes the following steps: The reluctance parameters of the stator tooth area are: The reluctance parameters of the rotor tooth area are: The reluctance parameters of the stator and rotor yoke area are: Where μ is the relative magnetic permeability, l a is the axial length, l and w are the length and height of each silicon steel sheet in the stator tooth area, h, w1 and w2 are the height, upper side length and lower side length of each silicon steel sheet in the rotor tooth area, θ, R1 and R2 are the radian, inner radius and outer radius of each silicon steel sheet in the stator and rotor yoke area; Based on the vector magnetic circuit theory, the magnetic induction of the core magnetic impedance branch is regarded as the parallel connection of the corresponding magnetic induction of each silicon steel sheet in the area. The initial value of the magnetic impedance parameter of the core magnetic impedance branch is calculated as follows: Where n is the number of stacked silicon steel sheets in the region, and ω = 2πf is the alternating angular frequency of the magnetic flux in the core.

6. The method for equivalent magnetic network modeling and eddy current loss calculation of a flux switching permanent magnet motor according to claim 1, characterized in that: The magnetic admittance value of the iron core magnetic impedance branch is converted by the following formula: Wherein, the subscript x refers to different core regions; ω = 2πf, is the alternating angular frequency of the magnetic flux in the core; j is the imaginary unit; They are the magnetic impedance, magnetic resistance and magnetic induction values ​​corresponding to the core area, are the calculated magnetic admittance, permeance and susceptance values ​​of the corresponding core area respectively.

7. The method for equivalent magnetic network modeling and eddy current loss calculation of a flux switching permanent magnet motor according to claim 1, characterized in that: The established node magnetic potential equations are: The magnetic admittance matrix is a sparse symmetric complex coefficient matrix, and are the node magnetic potential and magnetic flux respectively; when solving, the real domain WZ decomposition method is used to separate the real part and the imaginary part, and the separated matrix is ​​numerically solved by successive super-relaxation iterations, and then the complex solutions of the original node magnetic potential equations are inferred from the calculation results.

8. The method for equivalent magnetic network modeling and eddy current loss calculation of a flux switching permanent magnet motor according to claim 1, characterized in that: The following method is used to calculate the electromagnetic performance of the flux switching permanent magnet motor: The coil flux linkage of the flux switching permanent magnet motor is obtained based on the branch parameters corresponding to the coil enclosed area: Where N is the number of coil turns, and is the magnetic potential at both ends of the branch, is the magnetic admittance of branch i, F m0 (i) is the initial magnetic potential of the branch; Based on the current-flux linkage within one electrical cycle, the electromagnetic torque of the flux-switching permanent magnet motor is calculated by the magnetic common energy method: Where m is the number of motor phases; P r is the number of rotor teeth, that is, the number of pole pairs of the flux switching permanent magnet motor; S i-Ψ It is the integral value of the flux linkage of each phase to the current.

9. The method for equivalent magnetic network modeling and eddy current loss calculation of a flux switching permanent magnet motor according to claim 1, characterized in that: Based on the vector magnetic circuit theory, the eddy current loss corresponding to each core magnetic admittance branch can be calculated using the following method: Where, ω = 2πf is the alternating angular frequency of the magnetic flux in the iron core; is the magnetic induction corresponding to the i-th iron core magnetic admittance branch; φ i is the effective value of the magnetic flux flowing through the i-th iron core magnetic admittance branch.

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