White-box high-frequency impedance modeling method for permanent magnet synchronous motors based on small-signal time-harmonic finite element analysis

Abstract

The present invention discloses a white-box high-frequency impedance modeling method for a permanent magnet synchronous motor based on small-signal time-harmonic finite element analysis, comprising: establishing an electrostatic field finite element model to calculate a static coupling capacitance taking into account dielectric loss; establishing a static magnetic field finite element model to calculate the DRT of each finite element grid of a silicon steel sheet; establishing a time-harmonic finite element analysis model including all copper conductors; setting the coil region to a relative complex permeability to solve for the coil region equivalent complex permeability; establishing a small-signal time-harmonic finite element model; establishing a time-harmonic electromagnetic finite element model of the end coil to calculate the frequency-dependent end coil inductance and resistance; constructing a white-box high-frequency field-circuit coupling small-signal time-harmonic finite element model using the capacitance, end coil inductance and resistance taking into account dielectric loss, and the small-signal time-harmonic finite element model; and calculating the differential mode and common mode impedance at different frequencies of the d and q axes. The present invention can accurately predict the HF impedance characteristics of a PMSM during the design phase.

Description

Technical Field

[0001] The present invention belongs to the field of motor design, and in particular relates to a white-box high-frequency impedance modeling method for a permanent magnet synchronous motor based on small-signal time-harmonic finite element analysis. Background Art

[0002] Today, most permanent magnet synchronous motors (PMSMs) use pulse-width modulated (PWM) voltage source inverters (VSIs) to dynamically adjust their torque and speed. While inverter power supply facilitates motor control, it also introduces numerous negative impacts, including but not limited to PWM-induced losses, sideband vibration and noise, bearing currents, transient overvoltages, and electromagnetic interference (EMI). The use of wide-bandgap (SiC, GaN) power electronics with higher switching frequencies in PWM VSIs helps suppress PWM-induced losses, sideband vibration, and noise, but the increased switching speed exacerbates bearing currents, transient overvoltages, and EMI.

[0003] Accurately modeling the high-frequency (HF) characteristics of PMSMs is fundamental to assessing these negative impacts and identifying effective methods to mitigate them. Currently, both gray-box and white-box models are being widely studied as HF modeling approaches for motors. Gray-box models, with their simple structure and constant parameters, facilitate simulation in both the frequency and time domains. However, some parameters in these models lack clear physical meaning and must be determined by fitting measured differential-mode (DM) and common-mode (CM) impedances, limiting their application during the design phase.

[0004] White-box models can be used during the design phase because all parameters are obtained using the finite element method (FEM) or analytical methods based on the motor's physical parameters. Currently, the main approach for constructing white-box HF models is based on transmission line models. This involves first calculating capacitance through electrostatic finite element analysis (FEA), then dynamically simulating the magnetic field to determine the frequency-dependent self-inductance, mutual inductance, and resistance. Finally, a complete circuit HF model is created in circuit simulation software such as SPICE. We call this a three-step approach. Due to the complexity of the motor structure and HF phenomena, the resulting circuit models can be quite complex. Furthermore, their overall computational accuracy is not particularly satisfactory. The main difficulties in accurately establishing white-box HF models of PMSMs are reflected in the following aspects.

[0005] 1) At high frequencies, the magnetic permeability of silicon steel sheets is not only affected by saturation but also varies with frequency. Furthermore, the magnetic permeability varies across different regions of the core. This causes the self-inductance, mutual inductance, and iron loss resistance of permanent magnet synchronous motors to vary with frequency and the core's saturation state, making them difficult to simulate using circuit simulation alone.

[0006] 2) HF eddy currents generated in the windings also cause the winding resistance to increase with frequency. This also hinders the efficient flow of magnetic flux through the windings, reducing the winding's internal inductance. When the windings consist of multiple strands of circular conductors wound in parallel, more mesh elements are required when simulating this phenomenon using FEM.

[0007] 3) At high frequencies, eddy currents in the silicon steel sheets complicate the passage of magnetic flux through them, reducing the main inductance. Consequently, the proportion of the terminal leakage reactance in the total inductance increases, significantly impacting the high-frequency characteristics of the PMSM. Accurately calculating the terminal leakage reactance is inherently challenging; furthermore, the terminal leakage reactance and resistance can also vary with frequency. Summary of the Invention

[0008] The present invention provides a white-box high-frequency impedance modeling method for a permanent magnet synchronous motor based on small-signal time-harmonic finite element analysis. Aiming at the difficulties in white-box HF modeling of a permanent magnet synchronous motor, the present invention applies small-signal THFEA to the HF impedance characteristic modeling of a PMSM. This method can accurately predict the HF impedance characteristics of a PMSM during the design phase and simultaneously analyze the influence of parameter changes on the HF characteristics of the PMSM.

[0009] A white box high-frequency impedance modeling method for a permanent magnet synchronous motor based on small signal time-harmonic finite element analysis is characterized by comprising the following steps:

[0010] (1) Establishing an electrostatic field finite element model and calculating the static coupling capacitance; the static coupling capacitance includes the capacitance between the coil, stator, and rotor;

[0011] (2) converting the static coupling capacitance obtained in step (1) into a capacitance that takes dielectric loss into account;

[0012] (3) Establish a static magnetic field finite element model to calculate and determine the DC bias magnetic induction intensity of each finite element grid of the silicon steel sheet; and further determine the frequency-dependent complex incremental tensor magnetic resistivity (DRT) of each finite element grid of the silicon steel sheet;

[0013] (4) Establish a single-slot time-harmonic finite element analysis model containing all copper conductors in the slot, and calculate the differential mode resistance and inductance, and common mode resistance and inductance at different frequencies;

[0014] (5) Set the coil area to relative complex permeability and solve the rate of change of resistance and inductance;

[0015] (6) Combine steps (4) and (5) to calculate the equivalent complex magnetic permeability of the coil area;

[0016] (7) Establishing a small signal time-harmonic finite element model of a permanent magnet synchronous motor, wherein the silicon steel material in the model is the frequency-variable complex incremental tensor magnetic resistivity DRT obtained in step (3), and the coil region material is the equivalent complex magnetic permeability obtained in step (6);

[0017] (8) Establish a time-harmonic electromagnetic field-circuit coupled finite element model of the end coil and calculate the frequency-dependent inductance and resistance of the end coil;

[0018] (9) using the capacitance obtained in step (2), the end coil inductance and resistance obtained in step (8), and the small signal time-harmonic finite element model obtained in step (7), a white box high-frequency field-circuit coupled small signal time-harmonic finite element model of the permanent magnet synchronous motor is constructed;

[0019] (10) Calculate the field-circuit coupled small signal time-harmonic finite element model formed in step (9) to obtain the differential mode and common mode impedances at different frequencies of the d and q axes.

[0020] The present invention proposes an innovative two-step method. First, the coupling capacitance is calculated by electrostatic finite element method. Then, these capacitances are directly incorporated into the coupled field circuit small-signal THFEA model to calculate the HF DM and CM impedances. The small-signal THFEA first performs static magnetic field FEA to determine the DC bias magnetic induction intensity of each unit of the silicon steel sheet. On this basis, the frequency-dependent complex incremental tensor magnetoresistance (DRT) of each unit can be determined and then submitted to the THFEA program to consider the hysteresis, eddy current and saturation effects of the silicon steel sheet.

[0021] This paper addresses the DM and CM impedances by considering the frequency-dependent complex delta tensor magnetoresistance (DRT) of capacitance effects, resolving the difficulty 1 mentioned in the previous article. It also addresses the difficulty 2) mentioned in the previous article by modeling the winding region with a uniform material having an equivalent complex permeability. A readily implementable method for determining the equivalent complex permeability is proposed, based entirely on numerical solutions. An axisymmetric THFEA model is developed to estimate the frequency-dependent end-coil inductance and resistance, resolving the difficulty 3) mentioned in the previous article.

[0022] The specific process of step (1) is:

[0023] Each turn of each coil, stator, and rotor is represented by boundaries from 1 to x. Assuming that parallel conductors belonging to the same turn have the same voltage, one boundary is set to 1 volt and the other boundaries are set to zero volts. Then, an electrostatic field finite element analysis is performed to calculate the surface charge on different boundaries. These charges are used to calculate the capacitance between the boundary and the other boundaries. The above process is repeated to obtain the capacitance between any two boundaries.

[0024] In step (2), the static coupling capacitance is converted into a capacitance that takes dielectric loss into account, specifically:

[0025] In the circuit model, a static coupling capacitor C s Converted to parallel C ∞ Branch and R1C1 branch; C∞ is the high frequency capacitor, R1 and C1 are used to model dielectric loss, C ∞ , R1 and C1 are calculated as follows:

[0026]

[0027] C1=C s -C ∞

[0028] R1=1 / (2πf1C1)

[0029] Where tanδ is the dielectric loss tangent, which changes with frequency f1.

[0030] In step (3), when establishing the static magnetic field finite element model, each permanent magnet block is modeled as a solid conductor with zero net current constraint, and the correction coefficient k is multiplied by the permanent magnet conductivity to calculate the effect of axial segmentation, and the value of k ranges from 0 to 1.

[0031] In step (5), when using the single slot model, the resistance and inductance of a slot are calculated as follows:

[0032] R1=P cop / |I| 2

[0033] L1=Im(V / / ) / (2πf)

[0034] Where V and I are the voltage of the AC voltage source and the current of the ammeter, respectively; |I| is the RMS value of I; P cop is the total loss of all copper conductors calculated using the time-harmonic finite element analysis model; f is the frequency of the time-harmonic finite element analysis model; when f is 1 Hz, the calculated resistance and inductance are considered to be DC values; the rate of change of resistance and inductance with frequency is defined as follows:

[0035]

[0036]

[0037] Where, represents the resistance change rate, Indicates the rate of change of inductance.

[0038] The specific process of step (6) is:

[0039] (6-1) A physical model of the winding containing all copper conductors is established, and a boundary condition of parallel magnetic field lines is applied at the boundary between the external air and the silicon steel sheet. Each conductor is modeled as a conductive finite element conductor. The connection method between each finite element conductor is determined based on the actual motor circuit and operating conditions, and a field-circuit coupling model, that is, a harmonic finite element analysis model, is established. A fine grid is set on the conductor boundary to ensure calculation accuracy. At different frequencies, a field-circuit coupling finite element analysis is performed to calculate the total resistance and inductance.

[0040] (6-2) Establish an equivalent winding model using complex magnetic permeability. The circuit topology and boundary conditions of this model are the same as those of the field-circuit coupling model in (6-1), except that the winding is modeled using a thin wire finite element region with complex magnetic permeability.

[0041] (6-3) Use a sweeping method to calculate the resistance and inductance at different frequencies when the real part of the complex permeability of the coil region in (6-2) changes from 0.01 to 1 and the imaginary part changes from -0.5 to 0;

[0042] (6-4) Based on the actual resistance and inductance calculated at different frequencies in (6-1), a two-dimensional lookup table method is used to determine the real and imaginary parts of the complex permeability of the equivalent winding with the same resistance and inductance obtained in (6-3);

[0043] (6-5) For common-mode and differential-mode operating conditions, repeat (6-1) to (6-4) respectively, calculate the equivalent complex permeability at different frequencies, and use the average value under the two operating conditions as the equivalent complex permeability for subsequent modeling of the entire motor.

[0044] In step (9), when constructing a white box high-frequency field-circuit coupled small signal time-harmonic finite element model of a permanent magnet synchronous motor, in the circuit model, the end capacitance of the coil is obtained through the electrostatic field, or an equivalent method is used to multiply the turn-to-turn capacitance of the same coil by the ratio of the total length of the coil to the length of the coil in the slot.

[0045] In the process of building all finite element models, a complete model is established, or a 1 / n finite element model is established according to the structural characteristics of the motor to reduce the solution time.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] This method addresses the difficulties of white-box HF modeling of permanent magnet synchronous motors (PMSMs). It applies small-signal time-harmonic field finite element analysis (THFEA) to model the high-frequency (HF) impedance characteristics of permanent magnet synchronous motors (PMSMs) up to 220 MHz. This method is more suitable for predicting the HF impedance characteristics of PMSMs during the design phase because the complex magnetic coupling and iron loss resistance in the main magnetic circuit are naturally included in the small-signal model and a frequency-dependent complex DRT is used. Furthermore, this model can be used to analyze the impact of parameter variations on the PMSM's HF characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of a prototype machine used for modeling in an embodiment of the present invention;

[0049] Figure 2 This is a flow chart of a white-box high-frequency impedance modeling method for a permanent magnet synchronous motor based on small-signal time-harmonic finite element analysis according to an embodiment of the present invention;

[0050] Figure 3 Schematic diagram of the capacitance between any two boundaries when calculating static coupling capacitance;

[0051] Figure 4 Schematic diagram for converting static coupling capacitance into capacitance considering dielectric loss;

[0052] Figure 5 This is the coupled field circuit diagram of the single-slot physical model;

[0053] Figure 6 is the coupled field circuit diagram of the single-slot equivalent model;

[0054] Figure 7 is the resistance and inductance change ratio obtained by scanning THFEA with different complex permeabilities in the coil area of ​​the equivalent model when f is 1 MHz;

[0055] Figure 8 are the real and imaginary parts of the equivalent relative complex permeability in the coil area.

[0056] Figure 9 Schematic diagram of a white-box high-frequency field-circuit coupled small-signal time-harmonic finite element model constructed for an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be noted that the following examples are intended to facilitate understanding of the present invention and do not have any limiting effect on the present invention.

[0058] In the embodiment of the present invention, an 8 / 12 IPMSM with concentrated windings is selected as a calculation prototype. The main parameters used to construct the HF model are shown in Table 1. Figure 1(a) shows a cross-section of the prototype, with different colors representing the number of coil turns in each slot. Figure 1 (b) shows a picture of the stator. It can be seen that the coils of different phases are arranged in a top-to-bottom manner in a single slot, with no insulation paper in between.

[0059] Table 1

[0060]

[0061] like Figure 2 As shown in FIG, a flowchart of a white box high-frequency impedance modeling method for a permanent magnet synchronous motor based on small signal time-harmonic finite element analysis is shown, which includes the following steps:

[0062] S01, establishing an electrostatic field finite element model and calculating the static coupling capacitance; the static coupling capacitance includes the capacitance between the coil, the stator, and the rotor.

[0063] To calculate the capacitance between the coils, stator, and rotor, a two-dimensional electrostatic field finite element model is first created. It is assumed that the gaps between the conductors are filled with insulating varnish, and the relative permittivity of both the insulating layer and the conductor insulation is set to 3.5. In this case, the very thin insulation layer on the conductor surface does not require special modeling. The relative permittivity of the wedge-shaped slot liner and wedge shape is also set to 3.5 to simplify the process. The slot insulation thickness is set to 0.6 mm.

[0064] Each turn of each coil, stator, and rotor is represented by boundaries 1 to 20. Assume that the 13 parallel conductors belonging to the same turn have the same voltage. Set one boundary to 1 volt and the others to zero volts. Then, perform an electrostatic finite element analysis to calculate the surface charge on the different boundaries. These charges are used to calculate the capacitance between the boundary and the other boundaries. Repeat the above process to obtain the capacitance between any two boundaries, such as Figure 3 As shown. Furthermore, to account for the end coils, the turn-to-turn capacitance of the same coil is multiplied by the ratio of the total coil length to the coil length within the slot. Since the additional capacitance in the end region is much smaller than the capacitance within the slot, it can be neglected.

[0065] S02, converting the static coupling capacitance obtained in step S01 into a capacitance taking dielectric loss into consideration.

[0066] like Figure 4 As shown, a static coupling capacitor C is added to the circuit model. s Converted to parallel C ∞ Branch and R1C1 branch; C ∞ is the high frequency capacitor, R1 and C1 are used to model dielectric loss, C ∞ , R1 and C1 are calculated as follows:

[0067]

[0068] C1=C s -C ∞

[0069] R1=1(2πf1C1)

[0070] Where tanδ is the dielectric loss tangent, which varies with frequency f1. When f1 is 1MHz, tanδ is set to 0.15. Finally, for different C s , we can calculate C ∞ , R1 and C1.

[0071] S03, establishing a static magnetic field finite element model, calculating and determining the DC bias magnetic induction intensity of each finite element grid of the silicon steel sheet; and further determining the frequency-varying complex incremental tensor magnetic resistivity DRT of each finite element grid of the silicon steel sheet.

[0072] S04: Establish a single-slot time-harmonic finite element analysis model that includes all copper conductors in the slot, and calculate the differential mode resistance and inductance, and common mode resistance and inductance at different frequencies.

[0073] At the boundary between air and silicon steel sheet, the magnetic field lines are assumed to be perpendicular to the boundary. Each conductor is modeled as a solid finite element conductor. The 13 conductors belonging to the same number of turns are connected in parallel, and all windings in one slot are connected in series, as shown in Figure 1. Figure 5 When CM current flows through the coils, the direction of the current in the Ap coil is opposite to that in the Cn coil; however, in the case of DM current flow, they will have different directions. Both cases will be solved by adjusting the C N The calculation is performed based on the positive direction of the regional current. A fine mesh is set on the conductor boundaries to ensure calculation accuracy. Coupled field-path THFEA is calculated at different frequencies to calculate the total resistance and inductance.

[0074] S05, set the coil area to relative complex permeability and solve the rate of change of resistance and inductance.

[0075] The real part of the relative complex permeability of the coil area is expressed in μ r r The imaginary part is represented by μ r i . indicates that when μ r r From 0.01 to 1, μ r i When the frequency changes from -0.5 to 0, THFEA is performed on the single tank equivalent model at different frequencies. Figure 6 The total resistance and inductance of the equivalent coil under the input voltage and calculated current are then calculated. The rate of change of resistance and inductance is then calculated.

[0076] When using the single-slot model, the resistance and inductance of a slot are calculated as follows:

[0077] R1=P cop I 2

[0078] L1=Im(V / I) / (2πf)

[0079] Where V and I are the voltage of the AC voltage source and the current of the ammeter, respectively; |I| is the RMS value of I; P cop is the total loss of all copper conductors calculated using the time-harmonic finite element analysis model; f is the frequency of the time-harmonic finite element analysis model; when f is 1 Hz, the calculated resistance and inductance are considered to be DC values; the rate of change of resistance and inductance with frequency is defined as follows:

[0080]

[0081]

[0082] Where, represents the resistance change rate, Indicates the rate of change of inductance.

[0083] S06, combining steps S04 and S05 to calculate the equivalent complex magnetic permeability of the coil area.

[0084] According to R1 rat and L1 rat The calculation results at 1MHz are Figure 7 The equivalent complex permeability that makes the equivalent model have the same resistance and inductance change rate can be obtained by using the two-dimensional table lookup method on the map in . The equivalent complex permeability is calculated at different frequencies for the CM and DM cases, and the results are shown in the figure. Figure 8 As shown in Figure 2, it can be seen that the equivalent complex permeabilities calculated in the two cases are very close. Therefore, the average value of these two cases is input into Figure 1 The THFEA model in

[15] is used to model the equivalent coil area. Their frequency variation is not negligible and will be considered in the small signal THFEA to calculate the CM and DM impedances of the entire machine.

[0085] S07, establishing a small signal time-harmonic finite element model of the permanent magnet synchronous motor, in which the silicon steel material is the frequency-variable complex incremental tensor magnetic resistivity DRT obtained in step S03, and the coil area material is the equivalent complex magnetic permeability obtained in step S06.

[0086] S08, establish a time-harmonic electromagnetic field-circuit coupling finite element model of the end coil and calculate the inductance and resistance of the end coil that vary with frequency.

[0087] For simplicity, the end coils are assumed to be semicircular. This allows the calculation of their resistance and inductance using two-dimensional axisymmetric electromagnetic finite element analysis (THFEA). The average diameter of the end coil semicircle is estimated by measuring the distance between the upper and lower coils. An axisymmetric electromagnetic finite element model of the end coils is then developed to calculate their inductance and resistance at various frequencies.

[0088] S09, using the capacitance obtained in step S02, the end coil inductance and resistance obtained in step S08, and the small signal time-harmonic finite element model obtained in step S07, a white box high frequency field-circuit coupled small signal time-harmonic finite element model of the permanent magnet synchronous motor is constructed. Finally, the obtained white box high frequency field-circuit coupled small signal time-harmonic finite element model is as follows: Figure 9 shown.

[0089] In the circuit model, the end capacitance of the coil is obtained through the electrostatic field, or by using the equivalent method, multiplying the inter-turn capacitance of the same coil by the ratio of the total coil length to the coil length in the slot.

[0090] The end capacitance of the coil is obtained by electrostatic field, or by using the equivalent method, multiplying the turn-to-turn capacitance of the same coil by the ratio of the total coil length to the coil length in the slot.

[0091] S10 , calculating the field-circuit coupled small signal time-harmonic finite element model formed in step S09 to obtain differential mode and common mode impedances at different frequencies of the d and q axes.

[0092] The embodiments described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A white box high-frequency impedance modeling method for permanent magnet synchronous motor based on small signal time-harmonic finite element analysis, characterized in that: The following steps are involved: (1) Establishing an electrostatic field finite element model and calculating the static coupling capacitance; the static coupling capacitance includes the capacitance between the coil, stator, and rotor; (2) converting the static coupling capacitance obtained in step (1) into a capacitance that takes dielectric loss into account; (3) Establish a static magnetic field finite element model to calculate and determine the DC bias magnetic induction intensity of each finite element grid of the silicon steel sheet; and further determine the frequency-dependent complex incremental tensor magnetic resistivity (DRT) of each finite element grid of the silicon steel sheet; (4) Establish a single-slot time-harmonic finite element analysis model containing all copper conductors in the slot, and calculate the differential mode resistance and inductance, and common mode resistance and inductance at different frequencies; (5) Set the coil area to relative complex permeability and solve the rate of change of resistance and inductance; (6) Combine steps (4) and (5) to calculate the equivalent complex magnetic permeability of the coil area; (7) Establishing a small signal time-harmonic finite element model of a permanent magnet synchronous motor, wherein the silicon steel material in the model is the frequency-variable complex incremental tensor magnetic resistivity DRT obtained in step (3), and the coil region material is the equivalent complex magnetic permeability obtained in step (6); (8) Establish a time-harmonic electromagnetic field-circuit coupled finite element model of the end coil and calculate the frequency-dependent inductance and resistance of the end coil; (9) using the capacitance obtained in step (2), the end coil inductance and resistance obtained in step (8), and the small signal time-harmonic finite element model obtained in step (7), a white box high-frequency field-circuit coupled small signal time-harmonic finite element model of the permanent magnet synchronous motor is constructed; (10) Calculate the field-circuit coupled small signal time-harmonic finite element model formed in step (9) to obtain the differential mode and common mode impedances at different frequencies of the d and q axes.

2. The white box high-frequency impedance modeling method of a permanent magnet synchronous motor based on small signal time-harmonic finite element analysis according to claim 1 is characterized in that: The specific process of step (1) is: Each turn of each coil, stator, and rotor is represented by boundaries from 1 to x. Assuming that parallel conductors belonging to the same turn have the same voltage, one boundary is set to 1 volt and the others are set to zero volts. Then, an electrostatic finite element analysis is performed to calculate the surface charges on the different boundaries. These charges are used to calculate the capacitance between that boundary and the other boundaries. Repeat the above process to obtain the capacitance between any two boundaries.

3. The white box high-frequency impedance modeling method of a permanent magnet synchronous motor based on small signal time-harmonic finite element analysis according to claim 1 is characterized in that: In step (2), the static coupling capacitance is converted into a capacitance that takes dielectric loss into account, specifically: In the circuit model, a static coupling capacitor C s Converted to parallel C ∞ Branch and R1C1 branch; C ∞ is the high frequency capacitor, R1 and C1 are used to model dielectric loss, C ∞ , R1 and C1 are calculated as follows: C1=C s -C ∞ R1=1 / (2πf1C1) Where tanδ is the dielectric loss tangent, which changes with frequency f1.

4. The white box high-frequency impedance modeling method of a permanent magnet synchronous motor based on small signal time-harmonic finite element analysis according to claim 1 is characterized in that: In step (3), when establishing the static magnetic field finite element model, each permanent magnet block is modeled as a solid conductor with zero net current constraint, and the correction coefficient k is multiplied by the permanent magnet conductivity to calculate the effect of axial segmentation, and the value of k ranges from 0 to 1.

5. The white box high-frequency impedance modeling method of a permanent magnet synchronous motor based on small signal time-harmonic finite element analysis according to claim 1 is characterized in that: In step (5), when using the single slot model, the resistance and inductance of a slot are calculated as follows: R1=P cop / |I| 2 L1=Im(V / I) / (2πf) Where V and I are the voltage of the AC voltage source and the current of the ammeter, respectively; |I| is the RMS value of I; P cop is the total loss of all copper conductors calculated using the time-harmonic finite element analysis model; f is the frequency of the time-harmonic finite element analysis model. When f is 1 Hz, the calculated resistance and inductance are considered to be DC values. The rate of change of resistance and inductance with frequency is defined as follows: Where, represents the resistance change rate, Indicates the rate of change of inductance.

6. The white box high-frequency impedance modeling method of a permanent magnet synchronous motor based on small signal time-harmonic finite element analysis according to claim 1 is characterized in that: The specific process of step (6) is: (6-1) A physical model of the winding containing all copper conductors is established, and a boundary condition of parallel magnetic lines of force is applied to the boundary between the external air and the silicon steel sheet; each conductor is modeled as a conductive finite element conductor; the connection method between each finite element conductor is determined according to the actual motor circuit and operating conditions, and a field-circuit coupling model, that is, a harmonic finite element analysis model, is established; a fine grid is set on the conductor boundary to ensure calculation accuracy; a field-circuit coupling finite element analysis is performed at different frequencies to calculate the total resistance and inductance; (6-2) Establish an equivalent winding model using complex magnetic permeability. The circuit topology and boundary conditions of this model are the same as those of the field-circuit coupling model in (6-1), except that the winding is modeled using a thin wire finite element region with complex magnetic permeability. (6-3) Use a sweeping method to calculate the resistance and inductance at different frequencies when the real part of the complex permeability of the coil region in (6-2) changes from 0.01 to 1 and the imaginary part changes from -0.5 to 0; (6-4) Based on the actual resistance and inductance calculated at different frequencies in (6-1), a two-dimensional lookup table method is used to determine the real and imaginary parts of the complex permeability of the equivalent winding with the same resistance and inductance obtained in (6-3); (6-5) For common-mode and differential-mode operating conditions, repeat (6-1) to (6-4) respectively, calculate the equivalent complex permeability at different frequencies, and use the average value under the two operating conditions as the equivalent complex permeability for subsequent modeling of the entire motor.

7. The white box high-frequency impedance modeling method of a permanent magnet synchronous motor based on small signal time-harmonic finite element analysis according to claim 1 is characterized in that: In step (9), when constructing a white box high-frequency field-circuit coupled small signal time-harmonic finite element model of a permanent magnet synchronous motor, in the circuit model, the end capacitance of the coil is obtained through the electrostatic field, or an equivalent method is used to multiply the turn-to-turn capacitance of the same coil by the ratio of the total length of the coil to the length of the coil in the slot.

8. The white box high-frequency impedance modeling method for permanent magnet synchronous motor based on small signal time-harmonic finite element analysis according to claim 1 is characterized in that: In the process of building all finite element models, a complete model is established, or a 1 / n finite element model is established according to the structural characteristics of the motor to reduce the solution time.

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