Modeling method of permanent magnet synchronous motor agent model in eccentric state

Abstract

This invention discloses a modeling method for a proxy model of a permanent magnet synchronous motor under eccentric conditions. First, a mathematical model of the eccentric motor proxy model is established, including the permanent magnet flux linkage and no-load back EMF, flux linkage model, voltage model, electromagnetic torque, and torque balance equations. Then, no-load back EMF, permanent magnet flux linkage, and dq-axis inductance data are obtained through finite element simulation, and harmonic fitting is performed on the permanent magnet flux linkage. Next, a multi-dimensional parameterized lookup table covering eccentricity type and degree, speed, torque, and rotor position angle is constructed. The lookup table and interpolation algorithm are integrated into the simulation platform to form a high-fidelity proxy model module that can be called in real time. Finally, the model accuracy is verified by comparison with finite element simulation and experimental data. This invention achieves high-precision and rapid mapping of the electromagnetic characteristics of eccentric motors, balancing modeling accuracy, efficiency, and versatility.

Description

Technical Field

[0001] This invention belongs to the field of motor fault modeling and diagnosis technology, specifically relating to a modeling method for a proxy model of a permanent magnet synchronous motor under eccentric conditions. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs), with their high power density, high efficiency, and high-precision control characteristics, have become core drive components for high-end equipment such as new energy vehicles and aerospace. However, due to limitations in processing equipment precision and technological level, deviations in the coaxiality of the stator and rotor are inevitable. As operating time increases, the motor is subjected to the combined effects of mechanical shock, alternating high and low temperatures, and load fluctuations, which can easily amplify the degree of eccentricity, leading to a vicious cycle of eccentricity-vibration-wear-severe eccentricity. This results in various problems such as mechanical structural damage, deterioration of vibration and noise, and degradation of motor performance and control capabilities. Therefore, establishing an effective mathematical model to describe the electromagnetic characteristics of a motor in an eccentric state and revealing the intrinsic relationship between eccentricity parameters and electromagnetic parameters is of significant theoretical and engineering value for achieving early diagnosis and fault-tolerant control of eccentricity faults.

[0003] Currently, the main methods for modeling and analyzing eccentrically faulted motors include analytical modeling, equivalent magnetic circuit method, improved winding function method, and finite element method. The literature [Liu Ronghui, Liu Jinkun, Zhang Junda. Analytical Model of Air Gap Magnetic Field of Halbach Array Surface-Mounted Permanent Magnet Motor Based on Hyperbolic Cotangent Transform [J]. Journal of Electrical Engineering, 2023, 38(06):1433-1446] proposes an analytical method based on a combination of hyperbolic cotangent transform and sub-region model. By introducing a relative permeability function to correct the influence of stator slotting, it achieves accurate calculation of the air gap magnetic field under rotor eccentricity. However, this method usually requires linearization assumptions about the magnetic circuit structure, neglecting nonlinear effects such as magnetic saturation and cross-coupling. In automotive applications, the motor's magnetic circuit is deeply saturated, and the dq-axis cross-coupling effect is significant. The analytical model's calculation accuracy is limited in this scenario, making it difficult to effectively reproduce the motor's electromagnetic characteristics.

[0004] The literature [Q Li, C Ma, P Wang, et al. Analytical model for IPMSMs with mixed eccentricity considering the effect of eccentricity on core saturation[J].IEEE Transactions on Transportation Electrification, 2025, 11(1): 3159-3168] proposes an analytical model for an embedded permanent magnet synchronous motor considering mixed eccentricity. This model adopts an improved equivalent magnetic circuit method, introduces the equivalent air gap reluctance after eccentricity, and combines a two-layer iterative algorithm to solve the time-varying non-uniform saturation characteristics of the inner and outer magnetic bridges, which can calculate the no-load magnetic field distribution under large eccentricity. The literature [Liu Kai, Zhang Bingyi, Feng Guihong. Research on Eccentric Inductance Parameters of Permanent Magnet Synchronous Motor Based on Asymmetric Winding Function Method [J]. Journal of Electrical Engineering, 2020, 35(S2):387-394+431] proposes the asymmetric winding function method, which improves the traditional winding function by introducing harmonic magnetomotive force distortion coefficient, and establishes an inductance calculation model of eccentric motor including air gap radius, inverse permeability function and winding turn function, and analyzes the variation law of inductance with eccentricity and rotor position. However, these two methods have obvious limitations: first, the model parameters increase sharply with the complexity of the working conditions, and the expressions are too cumbersome, which is not conducive to analysis and application; second, it is difficult to effectively accommodate the high-order harmonic effects introduced by frequency conversion power supply, and the accuracy and applicability in frequency conversion drive scenarios are insufficient.

[0005] The literature [Pérez R, Cros J, Picard M. Real-Time Modeling of Static, Dynamic and Mixed Eccentricity in Permanent Magnet Synchronous Machines [J].Machines, 2025, 13(2): 120] proposes a parametric modeling method based on finite element data and bilinear interpolation for rapid simulation of eccentricity faults in permanent magnet synchronous motors. This model can calculate parameters such as inductance and flux linkage in real time and reproduce the voltage and current waveforms under eccentricity faults. However, the accuracy of this model is highly dependent on the density and distribution of finite element sample points, and it mainly considers the influence of rotor position on electromagnetic parameters. Its ability to uniformly represent magnetic saturation effects and different types of eccentricity is limited.

[0006] It is evident that existing methods still have shortcomings in terms of modeling accuracy, efficiency, and versatility. Designing a high-precision modeling method suitable for eccentric faults in automotive permanent magnet synchronous motors, which can maintain excellent modeling accuracy and versatility while considering magnetic circuit saturation and cross-coupling effects, presents a considerable challenge. Summary of the Invention

[0007] In view of the above, the present invention provides a modeling method for a proxy model of a permanent magnet synchronous motor under eccentric conditions. The algorithm is simple, easy to implement, and can achieve universal modeling for different types and degrees of eccentricity.

[0008] A modeling method for a proxy model of a permanent magnet synchronous motor under eccentric conditions includes the following steps: (1) Establish a proxy model for an eccentric motor that considers magnetic circuit saturation and cross-coupling effects, including permanent magnet flux linkage and no-load back EMF, flux linkage model, voltage model, electromagnetic torque model and torque balance equation; (2) Based on the eccentric motor proxy model, the electromagnetic data of the motor is obtained by finite element simulation, including no-load back EMF and inductance data, and then the permanent magnet flux containing harmonics is obtained by fitting the no-load back EMF. (3) Preprocess the inductance data and construct a multi-dimensional parameterized inductance lookup table covering eccentric state, motor speed, reference torque and mechanical position angle; (4) The control structure based on the eccentric motor proxy model is constructed using the multidimensional parameterized inductance lookup table and the fitted permanent magnet flux linkage, and then integrated into the electric vehicle permanent magnet synchronous motor field orientation control system.

[0009] Furthermore, the expressions for the permanent magnet flux linkage and the no-load back EMF in step (1) are as follows: , in: These are three-phase permanent magnet flux linkages subjected to eccentric modulation under no-load conditions. and These are the direct-axis stator flux linkage and quadrature-axis stator flux linkage under eccentric modulation under no-load conditions, respectively. k The harmonic order is odd. N The highest harmonic order, The rotor electrical angle position and , p This represents the number of pole pairs of the motor. The mechanical angular velocity of the rotor. t For time, and They are respectively k Amplitude and initial phase of the secondary permanent magnet flux linkage harmonics These are the three-phase no-load back EMFs under eccentric modulation under no-load conditions. and These are the direct-axis no-load back EMF and quadrature-axis no-load back EMF modulated by eccentricity under no-load conditions, respectively. T PARK This is the Park transformation matrix (first two rows). and They are respectively k The amplitude and initial phase of the no-load back EMF harmonic.

[0010] Furthermore, the expression for the magnetic flux linkage model in step (1) is as follows: in: These are the flux linkages of the three-phase stator windings. and These are direct-axis stator flux linkage and quadrature-axis stator flux linkage, respectively. These are the three-phase stator currents, These are the self-inductance coefficients of the three-phase stator windings. The DC component of self-inductance. For leakage inductance, The amplitude of the second harmonic component of the self-inductance. The mutual inductance coefficient of phase A stator winding relative to phase B stator winding. The mutual inductance coefficient of phase B stator winding relative to phase A stator winding is given. The mutual inductance coefficient between the B-phase stator winding and the C-phase stator winding. The mutual inductance coefficient between the C-phase stator winding and the B-phase stator winding. The mutual inductance coefficient of the C-phase stator winding relative to the A-phase stator winding is given. The mutual inductance coefficient of phase A stator winding relative to phase C stator winding. and The amplitudes of the DC component and the second harmonic component of the mutual inductance are respectively. , .

[0011] Furthermore, the expression for the voltage model in step (1) is as follows: in: These are the three-phase stator voltages. and These are the direct-axis voltage and the quadrature-axis voltage, respectively. This refers to the stator phase resistance.

[0012] Furthermore, the expressions for the electromagnetic torque model and torque balance equation in step (1) are as follows: in: For electromagnetic torque, J Let be the moment of inertia of the motor. D The friction torque coefficient is proportional to the motor speed. T L For load torque, and These are the direct-axis current and the quadrature-axis current, respectively.

[0013] Furthermore, the permanent magnet flux linkage expression obtained in step (2) is as follows: in: Eccentric states ST The three-phase permanent magnet linkage below, and Eccentric states ST Lower direct-axis permanent magnet flux linkage and quadrature-axis permanent magnet flux linkage and Eccentric states ST Down k Amplitude and initial phase of the secondary permanent magnet flux linkage harmonics, eccentric state ST There are 11 types, where H represents the unbiased state. This indicates a static eccentricity state with an eccentricity of 10%. This indicates a static eccentricity state with an eccentricity of 20%. This indicates a static eccentricity state with an eccentricity of 30%. This indicates a static eccentricity state with an eccentricity of 40%. This indicates a static eccentricity state with an eccentricity of 50%. This indicates a dynamic eccentricity state with an eccentricity of 10%. This indicates a dynamic eccentricity state with an eccentricity of 20%. This indicates a dynamic eccentricity state with an eccentricity of 30%. This indicates a dynamic eccentricity state with an eccentricity of 40%. This indicates a dynamic eccentricity state with an eccentricity of 50%.

[0014] Further, the inductance data in step (3) includes quadrature-axis inductance, direct-axis inductance, and cross-saturated mutual inductance. First, based on the range of values ​​for eccentricity, motor speed, reference torque, and mechanical position angle, the node vectors corresponding to eccentricity, motor speed, reference torque, and mechanical position angle are obtained through discretization. Then, five-dimensional data lists are established for quadrature-axis inductance, direct-axis inductance, and cross-saturated mutual inductance respectively (together forming a multi-dimensional parameterized inductance lookup table). Any element in the five-dimensional data list... L LUT ( v , j , q , m ) indicates the different eccentricity state values Motor speed n、 Reference torque and mechanical position angle The corresponding inductance value below.

[0015] Furthermore, the construction of the five-dimensional data list employs a four-dimensional linear interpolation algorithm, calculating normalized interpolation coefficients for each dimension. A continuous inductive surface is obtained through weighted fusion of 16 grid vertices, with the adjacent node index set as (…). v , j , q , m )and( v +1, j +1, q +1, m +1), then the inductance interpolation expression is as follows: in: Represents adjacent nodes on the inductor surface ( v , j , q , m )and( v +1, j +1, q +1, m The inductance interpolation between +1) is at any input point The output inductance value at the following conditions Represents the corresponding node in the five-dimensional data list ( v +1, j +1, q +1, m +1) inductance value, b 1, b 2, b 3,b 4∈{0,1} represents the flags indicating whether the grid vertex is on the left or right in the four dimensions of eccentric state, motor speed, reference torque, and mechanical position angle, respectively. A value of 0 represents the left side and a value of 1 represents the right side. f 1, f 2, f 3, f 4 represents the normalized distance in four dimensions: eccentric state, motor speed, reference torque, and mechanical position angle. w The weights of the grid vertices, v , j , q , m These represent the node indices in the node vectors corresponding to the eccentric state, motor speed, reference torque, and mechanical position angle, respectively. and These represent the first node in the vector corresponding to the eccentric state. v The and the first v +1 element value, and These represent the first node in the node vector corresponding to the motor speed. j The and the first j +1 element value, and These represent the first node in the reference torque corresponding to the node vector. q The and the first q +1 element value, and These represent the first node in the node vector corresponding to the mechanical position angle. m The and the first m +1 element value.

[0016] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described modeling method for a proxy model of a permanent magnet synchronous motor under eccentric conditions.

[0017] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the modeling method for the proxy model of a permanent magnet synchronous motor under the aforementioned eccentric state.

[0018] Based on the above technical solution, the present invention has the following beneficial technical effects: 1. By constructing a multidimensional parametric lookup table and a four-dimensional linear interpolation algorithm, the relative error between the electromagnetic parameters output by the surrogate model and the finite element reference solution is far less than 10%, which meets engineering requirements and significantly improves computational efficiency compared to the traditional finite element model.

[0019] 2. The model of this invention covers 11 eccentric states, including static eccentricity and dynamic eccentricity, as well as various operating conditions. It can uniformly characterize the changes in electromagnetic characteristics under different types and degrees of eccentricity, providing effective support for the general modeling of eccentricity faults.

[0020] 3. This invention fully considers the effects of magnetic circuit saturation and cross-coupling, and completely preserves the harmonic characteristics of the dq-axis cross-coupled inductance and permanent magnet flux linkage. Experimental verification shows that the model can effectively reflect the influence of nonlinear factors such as magnetic circuit saturation and cross-coupling on electromagnetic parameters. Attached Figure Description

[0021] Figure 1 The diagrams show stator and rotor structures with different eccentricity types in embodiments of the present invention, where (a) corresponds to the state without eccentricity, (b) corresponds to the state of static eccentricity, and (c) corresponds to the state of dynamic eccentricity. O S For the stator center, O R Center of the rotor O w It is the center of rotor rotation.

[0022] Figure 2 This is a schematic diagram of the design process of a high-precision proxy model for an eccentric motor in an embodiment of the present invention.

[0023] Figure 3 This is a three-dimensional diagram of the dq-axis current lookup table data in an embodiment of the present invention.

[0024] Figure 4 The diagram shows the structure of the high-precision proxy model of the eccentric motor in this embodiment of the invention, where (a) corresponds to the flux linkage model structure, (b) corresponds to the voltage model structure, and (c) corresponds to the electromagnetic torque model structure.

[0025] Figure 5 This is a control block diagram in an embodiment of the present invention, showing the integration of an eccentric motor proxy model into the field orientation control system of a permanent magnet synchronous motor for electric vehicles.

[0026] Figure 6 This is a schematic diagram of the verification process for the eccentric motor proxy model in an embodiment of the present invention.

[0027] Figure 7 This is a schematic diagram comparing the fitting degree of the permanent magnet flux linkage of the eccentric motor proxy model (Simulink) and the finite element model (FEA) under no-load operation at a speed of 1500 r / min in an embodiment of the present invention. (a) corresponds to the static eccentricity state of 40%, and (b) corresponds to the dynamic eccentricity state of 40%. The blue dashed line corresponds to Simulink, and the orange solid line corresponds to FEA.

[0028] Figure 8This is a schematic diagram comparing the d-axis flux linkage of the surrogate model (Simulink) and the finite element model (FEA) with a static eccentricity of 40% under different torques at a speed of 1500 r / min in an embodiment of the present invention. (a) and (b) are the d-axis and q-axis flux linkages under no-load operation, respectively; (c) and (d) are the d-axis and q-axis flux linkages under a torque of 100 Nm, respectively; and (e) and (f) are the d-axis and q-axis flux linkages under a torque of 320 Nm, respectively. The blue dashed line corresponds to Simulink, and the orange solid line corresponds to FEA.

[0029] Figure 9 This is a schematic diagram comparing the d-axis flux linkage of the surrogate model (Simulink) and the finite element model (FEA) with a dynamic eccentricity of 40% under different torques at a speed of 1500 r / min in an embodiment of the present invention. (a) and (b) are the d-axis and q-axis flux linkages under no-load operation, respectively; (c) and (d) are the d-axis and q-axis flux linkages under a torque of 100 Nm, respectively; and (e) and (f) are the d-axis and q-axis flux linkages under a torque of 320 Nm, respectively. The blue dashed line corresponds to Simulink, and the orange solid line corresponds to FEA.

[0030] Figure 10 This is a comparative schematic diagram of the dq-axis inductance of the eccentric motor proxy model (Simulink) and the finite element model (FEA) in an embodiment of the present invention at a speed of 1500 r / min and a torque of 100 Nm. In this diagram, (a) and (b) are the direct-axis inductances at static eccentricity of 40% and dynamic eccentricity of 40%, respectively; (c) and (d) are the quadrature-axis inductances at static eccentricity of 40% and dynamic eccentricity of 40%, respectively; and (e) and (f) are the mutual inductances at static eccentricity of 40% and dynamic eccentricity of 40%, respectively. The blue dashed line corresponds to Simulink, and the orange solid line corresponds to FEA.

[0031] Figure 11 The A-phase stator current of the eccentric motor proxy model in this embodiment of the invention is shown under different torques at a speed of 1500 r / min. I a The spectrum diagram shows the A-phase stator current spectrum under a load of 100 Nm, with static eccentricity of 40% and dynamic eccentricity of 40%, respectively. I a =109, THD=0.28%; (c) and (d) are the stator current spectra of phase A under a load of 200Nm and static and dynamic eccentricity conditions of 40% and 40%, respectively. I a =216, THD=0.24%; (e) and (f) are the A-phase stator current spectra under a load of 400Nm and static eccentricity of 40% and dynamic eccentricity of 40%, respectively. I a =446, THD=0.12%, THD represents total harmonic distortion.

[0032] Figure 12 This diagram illustrates the comparison of d-axis flux linkages at different currents and rotor position angles using a surrogate model (Simulink) and an experiment with a 40% static eccentricity eccentricity eccentric motor in this embodiment of the invention. (a) shows the comparison results of d-axis flux linkages at different rotor position angles; (b) shows the comparison results of q-axis flux linkages at different rotor position angles; (c) shows the three-dimensional comparison results of d-axis flux linkages at different currents and rotor position angles; and (d) shows the three-dimensional comparison results of q-axis flux linkages at different currents and rotor position angles. The blue dashed lines correspond to Simulink, the orange solid lines correspond to Experiment, the red blocks correspond to Simulink, and the blue blocks correspond to Experiment.

[0033] Figure 13 This diagram illustrates the comparison of d-axis flux linkages at different currents and rotor position angles using a surrogate model (Simulink) and an experiment with a 40% dynamic eccentricity eccentricity eccentric motor in this embodiment of the invention. (a) shows the comparison results of d-axis flux linkages at different rotor position angles; (b) shows the comparison results of q-axis flux linkages at different rotor position angles; (c) shows the three-dimensional comparison results of d-axis flux linkages at different currents and rotor position angles; and (d) shows the three-dimensional comparison results of q-axis flux linkages at different currents and rotor position angles. The blue dashed lines correspond to Simulink, the orange solid lines to Experiment, the red blocks to Simulink, and the blue blocks to Experiment. Detailed Implementation

[0034] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] This implementation method uses a built-in permanent magnet synchronous motor with a rated power of 110kW, rated torque of 406Nm, rated speed of 2650r / min, and 4 pole pairs as an example to explain in detail the modeling method of the IPMSM (built-in permanent magnet synchronous motor) surrogate model under eccentric faults. The specific process is as follows: Figure 2 As shown: (1) Definition of the eccentric motor proxy model structure.

[0036] 1.1 Permanent magnet flux linkage and no-load back EMF.

[0037] No-load conditions ( i Under condition =0), the air gap magnetic field is determined solely by the permanent magnet magnetomotive force. F R Excitation, radial air gap magnetic flux density B r ( θ, t )= F R ( θ , t ) Λ ( θ , t When eccentricity occurs, the air gap permeability... Λ ( θ , t It exhibits a periodic modulation effect. At this point, in the three-phase stationary coordinate system, the flux linkage between the stator winding and the permanent magnet is no longer an ideal sinusoidal function, but rather exhibits characteristics containing a series of harmonic components modulated by eccentricity: in: k =1,3,5,… represent the harmonic orders; N The highest harmonic order; θ Re = pω R t This refers to the rotor's electrical angle position; p For extreme logarithms, ω R The mechanical angular velocity of the rotor rotation; ψ fk and θ fk They are respectively k The amplitude and initial phase of the secondary permanent magnet flux linkage harmonics are both related to the eccentricity. e The function.

[0038] The three-phase no-load back EMF can be expressed as: in: u 0,k and θ k for k The amplitude and initial phase of the no-load back EMF harmonic; the subscript 0 indicates no-load.

[0039] Applying the Park transformation to the three-phase no-load back EMF, the expression for the no-load back EMF in the rotor field-oriented dq coordinate system is: in: h =1,2,3,… are positive integers. N 1 is N The maximum value of , then the harmonic order in the three-phase stationary coordinate system k It can be represented as k= 6 h±1, "+1" corresponds to positive sequence harmonics (e.g., 7th, 13th), and "-1" corresponds to negative sequence harmonics (e.g., 5th, 11th); after Park transformation to the dq synchronous rotating coordinate system, these harmonics will appear as 6. h Sub-pulse component.

[0040] 1.2 Magnetic flux linkage model.

[0041] The expression for the flux linkage of the stator winding in a three-phase stationary coordinate system is: in: These are the magnetic flux linkages of the stator windings in a three-phase stationary coordinate system. These are the three-phase stator currents, L AA , L BB , L CC These are the self-inductance coefficients of each winding. L a0 The DC component of self-inductance. L a1 For leakage inductance, L a2 The amplitude of the second harmonic component of the self-inductance. M AB , M BA , M AC , M CA , M CB , M BC The mutual inductance coefficient of the two windings. M a0 = L a0 / 2、 M a2 = L a2 These represent the DC component and second harmonic component amplitudes of the mutual inductance, respectively. It should be noted that the self-inductance and mutual inductance coefficients mentioned above are all related to the eccentricity. e The function.

[0042] The flux linkage equation of the stator winding in the three-phase stationary coordinate system is transformed by Park, and then expressed as follows in the rotor field-oriented dq coordinate system: in: and These are the direct-axis and quadrature-axis stator flux linkages, respectively. L d and L q These are direct-axis and quadrature-axis inductors, respectively. L dq and L qd For cross-saturated mutual inductance, and Do not use direct-axis or quadrature-axis permanent magnet flux linkages. T PARK The first two rows of the Park transformation matrix T IPARK These are the first two columns of the Park inverse transformation matrix.

[0043] 1.3 Voltage Model.

[0044] In a three-phase stationary coordinate system, the stator voltage expression is: in: This refers to the stator phase resistance.

[0045] The stator voltage equations in the three-phase stationary coordinate system are transformed using the Park transformation. Then, in the rotor field-oriented dq coordinate system, the voltage equation expression is: in: and These are the direct-axis and quadrature-axis voltages, respectively.

[0046] 1.4 Electromagnetic torque model.

[0047] According to the principle of conservation of energy, electromagnetic torque T e The expression is: In the rotor magnetic field-oriented dq coordinate system, the expression for electromagnetic torque is: 1.5 Torque balance equation.

[0048] in: For electromagnetic torque, J The moment of inertia of the unit; D The friction torque coefficient is proportional to the rotational speed; T L This represents the load torque.

[0049] (2) High-fidelity data acquisition and post-processing.

[0050] Based on the ANSYS Maxwell platform, this implementation method establishes IPMSM motor models with different degrees of eccentricity. Figure 1 The stator and rotor structures of the motor under different eccentric states are shown, and their relative eccentricity is defined as: in: and These are static eccentricity and dynamic eccentricity, respectively. It is the air gap distance between the inner surface of the stator and the outer surface of the rotor under eccentric conditions.

[0051] The type and degree of eccentricity in constructing the finite element model of an eccentric motor are represented as follows: To simplify the description, variables are used below. ST The dataset is uniformly identified using the formula {H, s10, s20, s30, s40, s50, d10, d20, d30, d40, d50}, where H represents no eccentricity, s represents static eccentricity, and d represents dynamic eccentricity, with the numbers corresponding to the percentage values ​​of the eccentricity rate. The dataset construction method is explained below based on finite element simulation results.

[0052] 2.1 No-load back EMF data acquisition and processing.

[0053] When the motor is unloaded and its rotational angular velocity is ω R Under the given conditions, finite element simulation was used to obtain three-phase no-load back EMF data of the motor under no-eccentricity and different degrees of dynamic and static eccentricity, with a sampling frequency of [missing information]. f c The waveform period is p If there are one fundamental frequency cycle (i.e., one mechanical cycle), then the signal sequence formed by the back electromotive force data can be represented as: In the formula: m =1,2,…, L θ For sampling sequence number, L θ = 2 pf c / ω RThis represents the total number of sampling points. It should be noted that, for simplicity, the superscripts of each data element in the formula are... ST Omitted writing.

[0054] Fourier series fitting was performed on the above three-phase no-load back EMF simulation data to obtain the amplitude and phase of each back EMF harmonic. A suitable highest harmonic order was then selected. N This ensures that the absolute error between the Fourier series fitting result and the original finite data satisfies the error limit ± σ Requirements (e.g., ±5%). Further calculations were performed on the amplitude and initial phase of each harmonic of the permanent magnet flux linkage under different degrees of dynamic and static eccentricity, resulting in the table functions shown in Tables 1 and 2: Table 1: Definition of harmonic amplitude results of permanent magnet flux linkage under different degrees of eccentricity Table 2: Definitions of the initial phase results of permanent magnet flux harmonics under different degrees of eccentricity The constructed three-phase permanent magnet flux linkage is as follows: in: Different ST The time-fitted three-phase permanent magnet flux linkage.

[0055] Perform a Park transformation on the three-phase permanent magnet flux linkage, and then... p The permanent magnet flux linkage waveform (i.e., one mechanical cycle) is sampled for one fundamental cycle, with a total number of sampling points of [number missing]. L θ The flux linkage along the dq axis is obtained as follows: in: and Let be the components of the permanent magnet flux linkage along the dq axes, respectively. In this case, the permanent magnet flux linkage along the quadrature and direct axes is written with respect to the mechanical position angle. θ R Degree of eccentricity ST The data is presented in a three-dimensional list format.

[0056] 2.2 Inductance matrix data acquisition and processing based on operating conditions.

[0057] Taking automotive applications as an example, automakers currently mainly use offline calibration to establish command current lookup tables for different torque and speed requirements, and then combine interpolation and current closed-loop control to achieve stable and reliable MTPA (maximum torque-to-current ratio) and field weakening control. Figure 3 The experimental motor lookup table data for peak power and peak speed of 160kW and 10000r / min in this embodiment is provided. Based on this lookup table, for any reference command torque... Tref and motor speed n ( n =30 ω R / The corresponding dq-axis current reference value can be determined by interpolation. i dref , i qref That is: By employing the inverse Park transformation, the dq-axis current command is transformed to a three-phase stationary coordinate system, resulting in the current source excitation used for Maxwell finite element simulation: Finite element simulation was used to calculate different... T ref , n Under operating conditions, motors with no eccentricity and different degrees of dynamic and static eccentricity L AA , L BB , L CC , M AB (= M BA ), M BC (= M CB ), M CA (= M AC Data, assuming the data sampling frequency is... f c Data length is p One fundamental frequency period, that is: It should be noted that, in order to simplify the expression of the superscript ST of each data element in the above formula and omit the writing of the operating conditions, we can further obtain: In other words, inductance can be written with respect to the mechanical position angle. θ R Degree of eccentricity ST Operating conditions T ref , n The data is presented in a five-dimensional data list format.

[0058] (3) High-dimensional data list interpolation method.

[0059] set up L ε , L n and L T These represent the degree of eccentricity and the total number of speed and torque decomposition points in the dq-axis current lookup table (LUT), respectively. L ε The total number of points is 6, corresponding to ST ={H, s10, s20, s30, s40, s50} and ST ={H, d10, d20, d30, d40, d50}, and write the vectors of each node as: in: These are the node vectors representing the eccentricity, rotational speed, torque, and mechanical position angle of the lookup table, respectively. v =1,2,…, L ε , j =1,2,…, L n , q =1,2,…, L T , m =1,2,…, L θ This is the node sequence number.

[0060] Based on the above node definition, the acquired inductance matrix data is written in the form of a five-dimensional data table: Among them: elements in the five-dimensional data table L LUT ( v , j , q , m This indicates that for different degrees of static or dynamic eccentricity, at different speeds... n j Torque reference value T refq and mechanical position angle θ Rm The inductance value below, i.e. L d-LUT ( v , j , q , m ), L q-LUT ( v ,j , q , m ), L dq-LUT ( v , j , q , m ), L qd-LUT ( v , j , q , m ).

[0061] To achieve smooth querying in a continuous input space, this implementation uses a four-dimensional linear interpolation algorithm. Normalized interpolation coefficients are calculated for each dimension, and a continuous inductive surface is obtained through weighted fusion of 16 grid vertices. For any input point ( ε ST , n , T ref , θ R The 16 vertices of the grid cell in which it resides can be indexed using binary indices. b 1, b 2, b 3, b 4) indicates that, among which b 1, b 2, b 3, b 4∈{0,1} represents that the vertex is located "left" (0) or "right" (1) in the dimensions of eccentricity, rotational speed, torque, and mechanical position angle, respectively. Let the index of the adjacent breakpoint be ( v , j , q , m )and( v +1, j +1, q +1, m +1), then the interpolated output is: The weights of each vertex are determined by the normalized distances of the input points in each dimension. The weights are defined as follows: w The expression is: The normalized distance expressions for each dimension are: (4) Eccentric motor proxy model and model integration.

[0062] 4.1 Eccentric motor proxy model.

[0063] Based on the parameterized lookup table constructed above, and according to the mathematical relationships defined in step (1), the control structure of the general eccentric motor surrogate model (EMSM) is built, as follows: Figure 4 As shown.

[0064] 4.2 Model Integration.

[0065] The aforementioned eccentric motor proxy model is integrated into the field-oriented control (FOC) system of a permanent magnet synchronous motor in an electric vehicle, forming a simulation model containing an eccentric motor, a SiC (silicon carbide) power converter, and torque open-loop + current closed-loop vector control, such as... Figure 5 As shown.

[0066] (5) Simulation platform verification and experimental verification.

[0067] 5.1 Simulation platform verification.

[0068] To evaluate the eccentric motor proxy model constructed in this invention, a simulation verification platform was established in this embodiment. This platform uses a high-fidelity eccentric fault motor model built with the finite element software ANSYS Maxwell as a benchmark. Verification is achieved by comparing its output with the proxy model built in Matlab / Simulink under the same operating conditions. The verification process is as follows: Figure 6 As shown.

[0069] Figure 7 The results show the comparison of permanent magnet flux linkage fitting degree under no-load operation at a speed of 1500 r / min. Figure 8 and Figure 9 The results show the comparison of dq axis flux linkage output by the Simulink proxy model and the finite element model at steady-state operating points of 1500 r / min and torques of 0 Nm, 100 Nm and 320 Nm, respectively. 0 Nm and 100 Nm correspond to the working conditions at the lookup table interpolation points, while 320 Nm corresponds to the working conditions at the non-interpolation points. Figure 10 The inductance calculation results of the finite element model and the surrogate model at a speed of 1500 r / min and a torque of 100 Nm are selected, and the relative error is defined. σ As an accuracy evaluation index, its expression is: in: These represent the real-time dynamic parameters of the surrogate model, the finite element method, and the experimental baseline solution, respectively. The baseline physical quantities can be represented as electromagnetic parameters such as dq-axis inductance, permanent magnet flux linkage, and dq-axis flux linkage. A relative error threshold is set based on engineering application requirements. σ max ≤10%.

[0070] Based on the relative error evaluation index in the above formula, Tables 3 and 4 respectively present the statistical results of the relative errors between the dynamic electromagnetic parameters output by the surrogate model and the reference solution at 1500 r / min and three load conditions under static and dynamic eccentricity.

[0071] Table 3: Error Analysis of the Surrogate Model and the Finite Element Model under 40% Static Eccentricity Table 4: Error Analysis of the Surrogate Model and the Finite Element Model under 40% Dynamic Eccentricity By comparing the simulation curves of the surrogate model and the finite element reference, it can be seen that the two exhibit a high degree of consistency in waveform phase and amplitude. Further error analysis shows that the maximum time-varying error of each dynamic parameter is significantly lower than the preset error threshold. The above simulation comparison and error analysis results jointly verify that the surrogate model of the present invention can effectively characterize the nonlinear electromagnetic characteristics of static and dynamic eccentric motors under various operating conditions.

[0072] Furthermore, based on the Simulink platform and using the eccentric motor surrogate model established in this invention, the spectrum analysis of the A-phase stator current under three typical operating conditions—1500 r / min and loads of 100 Nm, 200 Nm, and 400 Nm—was performed. The results are as follows: Figure 11 As shown, under static eccentricity, all three load points exhibit obvious characteristic sideband components, but their amplitude gradually decreases with increasing load; under dynamic eccentricity, the sideband components at each load point are not obvious. The above comparison demonstrates that the surrogate model of this invention can effectively distinguish the differences in current harmonic response between static and dynamic eccentricity faults, verifying its accurate characterization capability for the electromagnetic characteristics of different eccentricity types.

[0073] Computational efficiency is a core indicator for evaluating the engineering practicality of the surrogate model. To quantify its advantages, this embodiment selects typical working conditions and compares simulations using a finite element model and the surrogate model established in this invention. The finite element model, based on the ANSYS Maxwell platform and employing a transient field solver, has an average simulation time of 45 minutes per run. The surrogate model, based on the Matlab / Simulink platform, has an average simulation time of only 3 seconds for the same task. The comparison results show that the computational speed of the surrogate model is approximately three orders of magnitude faster than that of the traditional finite element model.

[0074] 5.2 Experimental verification.

[0075] Figure 12 and Figure 13The results show the comparison between the dq-axis flux linkage of the eccentric motor surrogate model and the experimentally measured flux linkage at different currents and rotor position angles. The simulated flux linkage values ​​of the eccentric surrogate model of this invention are in good agreement with the experimental values, and have high accuracy, thus verifying its effective characterization ability of the nonlinear electromagnetic characteristics of the eccentric motor.

[0076] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A method for modeling a proxy model of a permanent magnet synchronous motor in an eccentric state, characterized in that, Includes the following steps: (1) Establish a proxy model for an eccentric motor that considers magnetic circuit saturation and cross-coupling effects, including permanent magnet flux linkage and no-load back EMF, flux linkage model, voltage model, electromagnetic torque model and torque balance equation; (2) Based on the eccentric motor proxy model, the electromagnetic data of the motor is obtained by finite element simulation, including no-load back EMF and inductance data, and then the permanent magnet flux containing harmonics is obtained by fitting the no-load back EMF. (3) Preprocess the inductance data and construct a multi-dimensional parameterized inductance lookup table covering eccentric state, motor speed, reference torque and mechanical position angle; (4) The control structure based on the eccentric motor proxy model is constructed using the multidimensional parameterized inductance lookup table and the fitted permanent magnet flux linkage, and then integrated into the electric vehicle permanent magnet synchronous motor field orientation control system.

2. The modeling method of the proxy model of the permanent magnet synchronous motor in the eccentric state according to claim 1, characterized in that, The expressions for the permanent magnet flux linkage and the no-load back EMF in step (1) are as follows: ， wherein: λd, λqare the three-phase permanent magnet flux linkages under no-load condition modulated by eccentricity, respectively, λd, λqare the direct-axis stator flux linkage and quadrature-axis stator flux linkage under no-load condition modulated by eccentricity, respectively, k p is the harmonic number and is odd, N pmaxis the highest harmonic number, θeis the rotor electrical angular position and p p is the number of motor pole pairs, ωr is the rotor rotating mechanical angular velocity, t t is time, λd, λqare the three-phase no-load back EMF under no-load condition modulated by eccentricity, respectively, k λd, λqare the direct-axis no-load back EMF and quadrature-axis no-load back EMF under no-load condition modulated by eccentricity, respectively, PARK is the Park transformation matrix, λd, λqare the three-phase no-load back EMF under no-load condition modulated by eccentricity, respectively, k λd, λqare the direct-axis no-load back EMF and quadrature-axis no-load back EMF under no-load condition modulated by eccentricity, respectively.​​​​​​​ 3. The method of claim 2, wherein the method further comprises: The expression for the magnetic flux linkage model in step (1) is as follows: wherein: λd, λqare the magnetic flux linkage of the three-phase stator windings, respectively, λd, λqare the magnetic flux linkage of the three-phase stator windings, respectively, id, iqare the three-phase stator currents, respectively, Ld, Lqare the self-inductance of the three-phase stator windings, respectively, .​​​​​​​​​​​​​ 4. The modeling method for the surrogate model of a permanent magnet synchronous motor under eccentric conditions according to claim 3, characterized in that, The expression for the voltage model in step (1) is as follows: in: These are the three-phase stator voltages. and These are the direct-axis voltage and the quadrature-axis voltage, respectively. This refers to the stator phase resistance.

5. The modeling method for the surrogate model of a permanent magnet synchronous motor under eccentric conditions according to claim 3, characterized in that, The expressions for the electromagnetic torque model and torque balance equation in step (1) are as follows: in: For electromagnetic torque, J Let be the moment of inertia of the motor. D The friction torque coefficient is proportional to the motor speed. T L For load torque, and These are the direct-axis current and the quadrature-axis current, respectively.

6. The modeling method for the surrogate model of a permanent magnet synchronous motor under eccentric conditions according to claim 2, characterized in that, The permanent magnet flux linkage expression obtained by fitting in step (2) is as follows: in: Eccentric states ST The three-phase permanent magnet linkage below, and Eccentric states ST Lower direct-axis permanent magnet flux linkage and quadrature-axis permanent magnet flux linkage and Eccentric states ST Down k Amplitude and initial phase of the secondary permanent magnet flux linkage harmonics, eccentric state ST There are 11 types, where H represents the unbiased state. This indicates a static eccentricity state with an eccentricity of 10%. This indicates a static eccentricity state with an eccentricity of 20%. This indicates a static eccentricity state with an eccentricity of 30%. This indicates a static eccentricity state with an eccentricity of 40%. This indicates a static eccentricity state with an eccentricity of 50%. This indicates a dynamic eccentricity state with an eccentricity of 10%. This indicates a dynamic eccentricity state with an eccentricity of 20%. This indicates a dynamic eccentricity state with an eccentricity of 30%. This indicates a dynamic eccentricity state with an eccentricity of 40%. This indicates a dynamic eccentricity state with an eccentricity of 50%.

7. The modeling method for the surrogate model of a permanent magnet synchronous motor under eccentric conditions according to claim 1, characterized in that: The inductance data in step (3) includes quadrature-axis inductance, direct-axis inductance, and cross-saturated mutual inductance. First, based on the range of values ​​for eccentricity, motor speed, reference torque, and mechanical position angle, the node vectors corresponding to eccentricity, motor speed, reference torque, and mechanical position angle are obtained through discretization. Then, five-dimensional data lists are established for quadrature-axis inductance, direct-axis inductance, and cross-saturated mutual inductance, respectively. Any element in the five-dimensional data list... L LUT ( v , j , q , m ) indicates the different eccentricity state values Motor speed n、 Reference torque and mechanical position angle The corresponding inductance value below.

8. The modeling method for the surrogate model of a permanent magnet synchronous motor under eccentric conditions according to claim 7, characterized in that: The five-dimensional data list is constructed using a four-dimensional linear interpolation algorithm. Normalized interpolation coefficients are calculated for each dimension, and a continuous inductive surface is obtained through weighted fusion of 16 grid vertices. The adjacent node index is set as (…). v , j , q , m )and( v +1, j +1, q +1, m +1), then the inductance interpolation expression is as follows: in: Represents adjacent nodes on the inductor surface ( v , j , q , m )and( v +1, j +1, q +1, m The inductance interpolation between +1) is at any input point The output inductance value at the following conditions Represents the corresponding node in the five-dimensional data list ( v +1, j +1, q +1, m +1) inductance value, b 1, b 2, b 3, b 4∈{0,1} represents the flags indicating whether the grid vertex is on the left or right in the four dimensions of eccentric state, motor speed, reference torque, and mechanical position angle, respectively. A value of 0 represents the left side and a value of 1 represents the right side. f 1, f 2, f 3, f 4 represents the normalized distance in four dimensions: eccentric state, motor speed, reference torque, and mechanical position angle. w The weights of the grid vertices, v , j , q , m These represent the node indices in the node vectors corresponding to the eccentric state, motor speed, reference torque, and mechanical position angle, respectively. and These represent the first node in the vector corresponding to the eccentric state. v The and the first v +1 element value, and These represent the first node in the node vector corresponding to the motor speed. j The and the first j +1 element value, and These represent the first node in the reference torque corresponding to the node vector. q The and the first q +1 element value, and These represent the first node in the node vector corresponding to the mechanical position angle. m The and the first m +1 element value.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: The processor is used to execute the computer program to implement the modeling method for the surrogate model of the permanent magnet synchronous motor in the eccentric state as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements the modeling method for the surrogate model of the permanent magnet synchronous motor in the eccentric state as described in any one of claims 1 to 8.

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