Permanent magnet synchronous motor white-box high-frequency impedance modeling method based on small-signal time-harmonic finite element analysis

Abstract

The invention discloses a permanent magnet synchronous motor white-box high-frequency impedance modeling method based on small-signal time-harmonic finite element analysis, and the method comprises the steps: building an electrostatic field finite element model, and calculating static coupling capacitance considering dielectric loss; establishing a static magnetic field finite element model, and calculating the DRT of each finite element grid of the silicon steel sheet; establishing a time-harmonic finite element analysis model containing all copper conductors; setting the coil region as relative complex permeability, and solving the equivalent complex permeability of the coil region; establishing a small-signal time-harmonic finite element model; establishing a time-harmonic electromagnetic finite element model of the end coil, and calculating the inductance and resistance of the end coil related to the frequency; constructing a white-box high-frequency field-path coupling small signal time-harmonic finite element model by utilizing the capacitor considering the dielectric loss, the inductance and the resistance of the end coil and the small signal time-harmonic finite element model; and calculating to obtain differential mode and common mode impedance of the d-axis and the q-axis under different frequencies. According to the method, the HF impedance characteristic of the PMSM can be accurately predicted in the design stage.

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 modulation (PWM) voltage source inverters (VSIs) to dynamically adjust their torque and speed. While inverter power supply brings convenience to motor control, it also introduces many negative effects, including but not limited to PWM-induced losses, sideband vibration and noise, bearing currents, transient overvoltages, and electromagnetic interference (EMI). The application of wide bandgap (SiC, GaN) power electronics with higher switching frequencies in PWM VSIs is beneficial to suppress PWM-induced losses and sideband vibration and noise, but the increase in switching speed will aggravate the problems of bearing currents, transient overvoltages, and electromagnetic interference.

[0003] Accurately modeling the high-frequency (HF) characteristics of PMSM is the basis for evaluating these negative effects and finding effective methods to suppress them. Currently, both gray-box models and white-box models are widely studied as high-frequency modeling methods for motors. The gray-box model has a simple structure and constant parameters, so it is easy to simulate in the frequency domain and time domain. However, some parameters in these models lack clear physical meanings and need to be determined by fitting the measured differential mode (DM) and common mode (CM) impedances, which limits their application in the design stage.

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

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

[0006] 2) The HF eddy current reaction generated in the winding will also cause the winding resistance to increase with increasing frequency, and at the same time hinder the effective passage of magnetic flux through the winding, resulting in a decrease in the internal inductance of the winding. When the winding is composed of multiple round conductors wound in parallel, more mesh elements are required when using FEM to simulate this phenomenon.

[0007] 3) In the case of HF, the eddy current reaction in the silicon steel sheet increases the difficulty of the magnetic flux passing through the silicon steel sheet, resulting in a decrease in the main inductance. Therefore, the proportion of the end leakage reactance in the total inductance increases, and the impact on the high-frequency characteristics of the PMSM cannot be ignored. Accurately calculating the end leakage reactance is a difficult problem in itself; in addition, the end leakage reactance and resistance may also change 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 small-signal THFEA is applied to the HF impedance characteristic modeling of a PMSM. The HF impedance characteristics of the PMSM can be accurately predicted in the design stage, and the influence of parameter changes on the HF characteristics of the PMSM can be analyzed.

[0009] A white box high-frequency impedance modeling method for a permanent magnet synchronous motor based on small signal time-harmonic finite element analysis, characterized in that it comprises 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, the stator, and the rotor;

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

[0012] (3) Establish a static magnetic field finite element model, 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 increment 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, 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, in which the silicon steel material is the frequency-dependent complex incremental tensor magnetic resistivity DRT obtained in step (3), and the coil area material is the equivalent complex magnetic permeability obtained in step (6);

[0017] (8) Establish a time-harmonic electromagnetic field-path coupling finite element model of the end coil and calculate the end coil inductance and resistance that vary with frequency;

[0018] (9) constructing a white box high-frequency field-circuit coupled small signal time-harmonic finite element model of the permanent magnet synchronous motor 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);

[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, firstly calculating the coupling capacitance by electrostatic finite element method, and then directly incorporating these capacitances into the coupled field circuit small signal THFEA model to calculate the HF DM and CM impedances, wherein 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] The present invention considers the frequency-dependent complex incremental tensor magnetoresistance DRT of the capacitance effect, and studies the DM and CM impedances to solve the difficulty 1) mentioned in the background technology. The winding area is modeled by a uniform material with an equivalent complex permeability to solve the difficulty 2) mentioned in the background technology, and an easy-to-implement method to determine the equivalent complex permeability is proposed, which is completely based on numerical solutions. An axisymmetric THFEA model is established to estimate the frequency-dependent end coil inductance and resistance, solving the difficulty 3) mentioned in the background technology.

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

[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, electrostatic field finite element analysis is performed to calculate the surface charges on different boundaries, which are used to calculate the capacitance between the boundary and 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 losses, 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 varies 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 influence of axial segmentation is calculated by multiplying the conductivity of the permanent magnet by a correction coefficient k, where 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] In the formula, represents the resistance change rate, Indicates the rate of change of inductance.

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

[0039] (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 on 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 working 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 the calculation accuracy; a field-circuit coupling finite element analysis is performed at different frequencies 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 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 scanning method to calculate the resistance and inductance at different frequencies when the real part of the complex magnetic permeability of the coil area 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), the real and imaginary parts of the complex permeability of the equivalent winding with the same resistance and inductance obtained in (6-3) are determined using a two-dimensional table lookup method;

[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 constructing 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 targets the difficulties of white-box HF modeling of permanent magnet synchronous motors and 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 220MHz. This method is more suitable for predicting the HF impedance characteristics of PMSMs at the design stage, because the complex magnetic coupling and iron loss resistance in the main magnetic circuit are naturally included in the small-signal model and the frequency-dependent complex DRT is used. In addition, the model can also be used to analyze the impact of parameter changes on the HF characteristics of PMSMs. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A 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 A schematic diagram of the capacitance between any two boundaries when calculating the static coupling capacitance;

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

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

[0053] Figure 6 It 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 region 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] Fig. 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 is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be pointed out that the embodiments described below are intended to facilitate the understanding of the present invention and do not have any limiting effect on the present invention.

[0058] The embodiment of the present invention selects an 8 / 12 IPMSM with concentrated windings as a calculation prototype, and its main parameters for constructing the HF model are shown in Table 1. Figure 1(a) shows a cross section of the prototype, with different colors representing the different 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 without any insulating paper in between.

[0059] Table 1

[0060]

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

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

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

[0064] Each turn of each coil, stator, and rotor is represented by boundaries from 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 other boundaries to zero volts. Then, perform an electrostatic field finite element analysis to calculate the surface charges on different boundaries, which 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. In addition, to take into account 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 in the slot. Since the other capacitance in the end region is much smaller than the capacitance in the slot, it can be ignored.

[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 losses, 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-dependent complex increment tensor magnetic resistivity DRT of each finite element grid of the silicon steel sheet.

[0072] S04, establishing a single slot time-harmonic finite element analysis model including all copper conductors in a slot, and calculating differential mode resistance and inductance, 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 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 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. When μ r r From 0.01 to 1, μ r i THFEA is performed on the single slot equivalent model at different frequencies when changing from -0.5 to 0. Figure 6 The total resistance and inductance of the equivalent coil under the input voltage and calculated current. Then calculate the rate of change of resistance and inductance.

[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] In the formula, 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 Using the two-dimensional table lookup method on the map in , the equivalent complex permeability that makes the equivalent model have the same resistance and inductance change rate can be obtained. The equivalent complex permeability is calculated at different frequencies for the CM and DM cases, and the results are shown in Figure 8 As shown in Figure 2, it can be seen that the equivalent complex permeability calculated in the two cases is very close. Therefore, the average value of these two cases is input into Figure 1 The THFEA model in is used to model the equivalent coil areas. Their variation with frequency is not negligible and will be considered in the small signal THFEA for calculating the CM and DM impedances of the whole 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-dependent 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-path 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 coil shape is assumed to be semicircular, so that the resistance and inductance of the end coil can be calculated using 2D axisymmetric electromagnetic field finite element analysis (THFEA). The average diameter of the semicircle of the end coil is estimated by measuring the distance between the upper and lower coils. Then, an axisymmetric electromagnetic field finite element model of the end coil is established to calculate the inductance and resistance at different 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: Fig. 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 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.

[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 length of the coil to the length of the coil in the slot.

[0091] S10, calculating the field-circuit coupled small signal time-harmonic finite element model formed in step S09, and obtaining the 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 protection scope 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, the stator, and the rotor; (2) converting the static coupling capacitance obtained in step (1) into a capacitance taking into account dielectric loss; (3) Establish a static magnetic field finite element model, 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 increment 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, 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, in which the silicon steel material is the frequency-dependent complex incremental tensor magnetic resistivity DRT obtained in step (3), and the coil area material is the equivalent complex magnetic permeability obtained in step (6); (8) Establish a time-harmonic electromagnetic field-path coupling finite element model of the end coil and calculate the end coil inductance and resistance that vary with frequency; (9) constructing a white box high-frequency field-circuit coupled small signal time-harmonic finite element model of the permanent magnet synchronous motor 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); (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 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 as follows: Each turn of each coil, stator and rotor is represented by boundaries from 1 to x; assuming that the 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 charges on different boundaries. These charges are used to calculate the capacitance between this boundary and other boundaries. Repeat the above process to obtain the capacitance between any two boundaries.

3. The method for white box high-frequency impedance modeling 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 losses, C ∞ , R1 and C1 are calculated as follows: C1=C s -C ∞ R1=1 / (2πf1C1) Where tanδ is the dielectric loss tangent, which varies with frequency f1.

4. The method for white box high-frequency impedance modeling 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 influence of axial segmentation is calculated by multiplying the conductivity of the permanent magnet by a correction coefficient k, where the value of k ranges from 0 to 1.

5. The method for white box high-frequency impedance modeling 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: In the formula, represents the resistance change rate, Indicates the rate of change of inductance.

6. The method for white box high-frequency impedance modeling 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 as follows: (6-1) Establish a physical model of the winding including all copper conductors, and apply a boundary condition of parallel magnetic lines of force on the boundary between the external air and the silicon steel sheet; each conductor is modeled as a conductive finite element conductor; determine the connection method between each finite element conductor according to the actual motor circuit and working conditions, and establish a field-circuit coupling model, that is, a harmonic finite element analysis model; set a fine grid on the conductor boundary to ensure the calculation accuracy; perform field-circuit coupling finite element analysis 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 scanning method to calculate the resistance and inductance at different frequencies when the real part of the complex magnetic permeability of the coil area 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), the real and imaginary parts of the complex permeability of the equivalent winding with the same resistance and inductance obtained in (6-3) are determined using a two-dimensional table lookup method; (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 method for white box high-frequency impedance modeling 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 method for white box high-frequency impedance modeling of a 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 constructing 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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