Permanent magnet synchronous motor modeling method based on harmonic analysis

Abstract

The invention discloses a permanent magnet synchronous motor modeling method based on harmonic analysis, and belongs to the technical field of power generation, power transformation or power distribution. The method comprises the steps of obtaining flux linkage data changing along with the position of a rotor under different excitation currents, establishing a flux linkage harmonic model representing a flux linkage as a superposition form of a flux linkage fundamental component and a flux linkage harmonic component, representing the flux linkage harmonic model as a function related to the excitation currents and the position of the rotor, and obtaining a lightweight flux linkage harmonic model. Based on an energy conservation relation between mechanical power and electromagnetic power and the lightweight flux linkage harmonic model, establishing an electromagnetic torque harmonic model which is related to excitation current, a rotor position, the number of magnetic pole pairs and a rotor initial position and is in an analytic harmonic superposition function form; a permanent magnet synchronous motor model is established by combining a lightweight flux linkage harmonic model and an electromagnetic torque harmonic model in a harmonic superposition function form, and the purpose of accurately and efficiently obtaining the torque and flux linkage of the motor under different working conditions is achieved.

Description

Technical Field

[0001] The present invention relates to motor control technology, and specifically discloses a modeling method for a permanent magnet synchronous motor based on harmonic analysis, belonging to the technical field of power generation, power transformation or power distribution. Background Art

[0002] Permanent magnet synchronous motors have advantages such as high power density, high efficiency, and good control performance, and have been widely used in electric drive, especially in the field of high-performance electric drive. The motor model is the basis for realizing motor control. Therefore, establishing an accurate mathematical model of the permanent magnet motor is the key to realizing high-performance control.

[0003] For the convenience of analysis, the motor model relied on by traditional permanent magnet synchronous motor control methods makes the following assumptions: the magnetic circuit is linear; the air-gap magnetic field is sinusoidally distributed in space; the influence of stator and rotor surface teeth and slots is not considered.

[0004] By transforming the motor equations in the three-phase stationary coordinate system abc to the two-phase rotating coordinate system dq, the commonly used traditional linear mathematical model of the permanent magnet synchronous motor is obtained, including: the voltage equation shown in Equation (1), the flux linkage equation shown in Equation (2), and the torque equation shown in Equation (3):

[0005]

[0006] In Equations (1) to (3), U d , U q are the equivalent voltages on the d-axis and q-axis; I d , I q are the equivalent currents on the d-axis and q-axis; Λ d , Λ q are the equivalent flux linkages on the d-axis and q-axis; L d , L q are the equivalent inductances on the d-axis and q-axis; R s is the stator resistance; Λ pm is the amplitude of the permanent magnet flux linkage; ω e is the rotor rotational electrical angular velocity, T e is the electromagnetic torque, and P n is the number of pole pairs.

[0007] From the above assumptions and the derived equations, it can be seen that when calculating the flux linkage and electromagnetic torque of the motor using the traditional linear permanent magnet synchronous motor model, the equivalent inductances L d , L q on the d-axis and q-axis, as well as the amplitude Λ pm of the permanent magnet flux linkage, are required as input parameters. During the operation of the permanent magnet synchronous motor, L d , L q , Λ pmIt will change due to various factors such as saturation effect and thermal effect, while the traditional linear permanent magnet synchronous motor model generally takes L d 、L q 、Λ pm The average values of L d0 、L q0 、Λ pm0 within one electrical cycle as the inputs of the model. When L d 、L q 、Λ pm deviates greatly from the average value, it will have a great impact on the overall accuracy of the model.

[0008] At the same time, due to the theoretical assumptions of the traditional model ignoring the influence of stator and rotor slots and assuming that the air-gap magnetic field is sinusoidally distributed in space, the harmonics in the current and voltage during the operation of the motor are ignored, resulting in a large error between the model calculation results and the actual torque and magnetic flux.

[0009] Therefore, scholars at home and abroad have further studied and proposed a more accurate look-up table model. The look-up table model collects the torque and magnetic flux data of the motor at different operating points through experiments or finite element simulation analysis, organizes the data into a table and stores it in the controller. For different inputs, the corresponding torque and magnetic flux are found in the table as outputs. The accuracy of the look-up table model depends on the density of data points. A low-resolution table cannot meet the requirements of precise control, while a high-resolution table will occupy a large storage space in the controller. For inputs not in the table, interpolation processing needs to be carried out first, the response time increases, and the output accuracy is greatly affected by different interpolation methods, which is not conducive to the design of real-time control.

[0010] Therefore, how to establish a high-precision and lightweight permanent magnet synchronous motor model is an urgent problem to be solved. Summary of the Invention

[0011] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a modeling method for permanent magnet synchronous motors based on harmonic analysis. By obtaining the magnetic flux data varying with the rotor position under different excitation currents, and according to the correlation between the harmonics of the magnetic flux of the permanent magnet synchronous motor and the excitation current, a lightweight magnetic flux harmonic model is established. Based on the electromagnetic-mechanical energy conversion mechanism of the permanent magnet synchronous motor and the magnetic flux harmonic model, a torque harmonic model is deduced and established, so as to establish a high-accuracy lightweight permanent magnet synchronous motor model, achieve the invention purpose of accurately and efficiently obtaining the torque and magnetic flux of the motor under different working conditions, provide a model basis for the precise control of the permanent magnet synchronous motor, and solve the technical problems of low accuracy and slow response speed of the traditional permanent magnet synchronous motor model in the permanent magnet synchronous motor control system.

[0012] The present invention adopts the following technical solutions to achieve the above invention purpose:

[0013] A modeling method for permanent magnet synchronous motors based on harmonic analysis, comprising the following steps:

[0014] Step 1: Obtain the flux linkage data varying with the rotor position under different excitation currents;

[0015] Step 2: Establish a flux linkage harmonic model based on the flux linkage data varying with the rotor position under different excitation currents obtained in Step 1. The flux linkage harmonic model represents the flux linkage as a superposition of the fundamental flux linkage component and the harmonic flux linkage components. Both the fundamental flux linkage component and the harmonic flux linkage components are functions related to the rotor position. According to the correlation between each harmonic of the permanent magnet synchronous motor's flux linkage and the excitation current, represent the flux linkage harmonic model as a function related to the excitation current and the rotor position, and obtain a lightweight flux linkage harmonic model;

[0016] Step 3: Based on the energy conservation relationship between mechanical power and electromagnetic power and the lightweight flux linkage harmonic model, establish an electromagnetic torque harmonic model. The electromagnetic torque harmonic model represents the electromagnetic torque as a superposition of the DC component of the electromagnetic torque and the harmonic components of the electromagnetic torque, and deduce and determine the amplitudes and phases of the DC component of the electromagnetic torque and each harmonic component, and represent the electromagnetic torque harmonic model in the form of an analytical harmonic superposition function related to the excitation current, the rotor position, the number of pole pairs, and the initial rotor position;

[0017] Step 4: Based on the lightweight flux linkage harmonic model and the electromagnetic torque harmonic model in the form of an analytical harmonic superposition function, establish a permanent magnet synchronous motor model.

[0018] As a further optimization scheme of a modeling method for permanent magnet synchronous motors based on harmonic analysis, in Step 2, methods including but not limited to discrete cosine transform and Fourier transform are used to establish the flux linkage harmonic model.

[0019] As a further optimization scheme of a modeling method for permanent magnet synchronous motors based on harmonic analysis, in Step 2, the flux linkage harmonic model represents the flux linkage as a superposition of the fundamental flux linkage and the 5th, 7th, 11th, 13th, 23rd, and 25th harmonic components of the flux linkage,

[0020]

[0021] where, Λ a 、Λ b 、Λ c are the flux linkages of phase a, phase b, and phase c respectively, λ k is the amplitude of the kth harmonic of the flux linkage of phase a, is the phase of the kth harmonic of the flux linkage of phase a, and θ e is the rotor position.

[0022] As a further optimization scheme of the permanent magnet synchronous motor modeling method based on harmonic analysis, in step 2, according to the correlation between the magnetic flux harmonics of the permanent magnet synchronous motor and the excitation current, the magnetic flux harmonic model is expressed as a function related to the excitation current and the rotor position, and a lightweight magnetic flux harmonic model is obtained. The specific method is: according to the electromagnetic relationship between the magnetic flux amplitude, the magnetic flux phase and the excitation current, a fitting function is selected to perform nonlinear regression fitting on the magnetic flux amplitude and phase, and a fitting function λ related to the magnetic flux amplitude and the excitation current is obtained. k =f(I d ,I q ) and the flux phase is related to the excitation current The fitting function of the flux amplitude and the excitation current and the fitting function of the flux phase and the excitation current are substituted into the flux harmonic model, where I d ,I q are the d-axis component and q-axis component of the excitation current.

[0023] As a further optimization scheme of the permanent magnet synchronous motor modeling method based on harmonic analysis, in step 3, the expression based on the energy conservation relationship between mechanical power and electromagnetic power in the three-phase coordinate system is: Among them, T e is the electromagnetic torque, P e is the electromagnetic power, ω m is the mechanical angular velocity, are the back electromotive force vectors of phase a, phase b, and phase c respectively, They are the current vectors of phase a, phase b, and phase c respectively.

[0024] As a further optimization scheme of the permanent magnet synchronous motor modeling method based on harmonic analysis, in step 3, the electromagnetic torque harmonic model represents the electromagnetic torque as the superposition of the electromagnetic torque DC component and the harmonic component. The specific method is: substitute the lightweight flux harmonic model into the expression based on the energy conservation relationship between mechanical power and electromagnetic power in the three-phase coordinate system, and Replace with P n , the electromagnetic torque harmonic model represents the electromagnetic torque as the superposition of the electromagnetic torque DC component and the 6th, 12th, and 24th electromagnetic torque harmonic components:

[0025]

[0026] Among them, ω e is the electrical angle, ω e t=θ e , P n is the number of magnetic pole pairs, I a ,I b ,I care the amplitudes of the phase-a, phase-b, and phase-c currents, and \(I\) a = \(I\) b = \(I\) c = \(I\), and \(\psi\) is the initial phase angle of the phase-a current.

[0027] As a further optimization scheme of a permanent magnet synchronous motor modeling method based on harmonic analysis, in step 3, the specific method for deriving and determining the DC component of the electromagnetic torque and the amplitudes and phases of each harmonic component is as follows:

[0028]

[0029] Among them, \(T_0\) is the DC component of the electromagnetic torque, \(T_6\), \(\varphi_6\) are the amplitude and phase of the 6th harmonic of the electromagnetic torque, \(T\) 12 , \(\varphi\) 12 are the amplitude and phase of the 12th harmonic of the electromagnetic torque, \(T\) 24 , \(\varphi\) 24 are the amplitude and phase of the 24th harmonic of the electromagnetic torque.

[0030] As a further optimization scheme of a permanent magnet synchronous motor modeling method based on harmonic analysis, in step 3, the torque harmonic model is expressed as an analytical harmonic superposition function form related to the excitation current, rotor position, number of pole pairs, and initial rotor position, specifically as follows:

[0031]

[0032] An electronic device includes a memory and a processor. A computer program is stored on the memory and runs on the processor. When the processor runs the computer program, it executes the steps of the above-mentioned permanent magnet synchronous motor modeling method.

[0033] A computer-readable storage medium stores a computer program. When the computer program runs, it executes the steps of the above-mentioned permanent magnet synchronous motor modeling method.

[0034] The present invention adopts the above technical solutions and has the following beneficial effects:

[0035] (1) The present invention obtains accurate flux linkage data of a permanent magnet synchronous motor through experiments, and based on the electromagnetic-mechanical energy conversion mechanism of the permanent magnet synchronous motor, establishes an analytical harmonic model of the flux linkage and torque, and further establishes an analytical harmonic model of the permanent magnet synchronous motor. This analytical harmonic model takes into account the harmonic components existing in the motor operation process, is more accurate than the traditional linear model, and is also more lightweight than the traditional look-up table model that stores a large amount of data and performs interpolation processing during the control process, has a shorter response time, reduces the requirements for the controller, and realizes the invention purpose of establishing a permanent magnet synchronous motor model with high accuracy and lightweight.

[0036] (2) The present invention proposes to establish a specific analytical model of a permanent magnet synchronous motor. Compared with the traditional linear model and the abstract look-up table model, different control algorithms can be further optimized and designed based on the analytical model. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flowchart of a method for modeling a permanent magnet synchronous motor based on harmonic analysis proposed by the present invention.

[0038] Figure 2 It is a comparison diagram of the original magnetic flux waveform and the harmonic superposition waveform provided by an embodiment of the present invention.

[0039] Figure 3 It is a fitting effect diagram of the fundamental component of the magnetic flux provided by an embodiment of the present invention.

[0040] Figure 4 It is a fitting effect diagram of the harmonic component of the magnetic flux provided by an embodiment of the present invention.

[0041] Figure 5 It is a comparison diagram of the original electromagnetic torque waveform and the harmonic superposition waveform provided by an embodiment of the present invention.

[0042] Figure 6 It is a schematic diagram of the permanent magnet synchronous motor model based on harmonic analysis in the modeling software provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present invention.

[0044] In view of the deficiencies of the existing permanent magnet synchronous motor models, the present invention proposes a method for modeling a permanent magnet synchronous motor based on harmonic analysis. Through this method, a high-precision and lightweight permanent magnet synchronous motor model can be established.

[0045] The method for modeling a permanent magnet synchronous motor based on harmonic analysis proposed by the present invention is as Figure 1 shown, including Step 1 to Step 4.

[0046] Step 1: Obtain the magnetic flux data varying with the rotor position under different excitation currents

[0047] Obtain the original data of the magnetic flux by testing on the experimental motor platform or in finite element software. In this embodiment, a permanent magnet synchronous motor model is built in the finite element software Ansys Maxwell for simulation, and the simulation parameters are set, including the motor geometric dimensions, material properties, boundary conditions, etc. In this embodiment, current excitation is adopted, and the ranges of the direct-axis current I d and the quadrature-axis current I q are both (0, 500) A, and the step sizes are both 10 A. There are a total of 2601 direct-axis and quadrature-axis current excitation data points at the same rotor position. The selected current range covers the unsaturated region, slightly saturated region, and saturated region of the motor operation. The motor speed is set to 3000 rpm. The stator excitation current frequency is 200 Hz, and a total of 1 electrical cycle is simulated. The rotor rotates through a mechanical angle of 90°, an electrical angle of 360°, and the rotor rotation angle step size is 0.375°. The total number of data points for different direct-axis and quadrature-axis current excitations at all rotor positions is 626841.

[0048] There is no noise interference in the simulation process of this embodiment, so no filtering process is performed. The excitation current step size and rotor rotation angle step size set in this embodiment meet the accuracy requirements, so no higher-resolution interpolation process is performed. In some embodiments, interpolation processing can be performed on the magnetic flux data to improve the data resolution.

[0049] The measured magnetic flux data can be stored through the constructed data table. Compared with the traditional look-up table model, the present invention does not directly store the magnetic flux data table offline or query it online. During the process of measuring the magnetic flux data, the measurement step size, measurement method, interpolation accuracy, interpolation method, fitting accuracy, and fitting method can all be adjusted according to the actual accuracy requirements to meet the accuracy requirements under different working conditions.

[0050] Step 2: Establish a magnetic flux harmonic model

[0051] During the operation of a permanent magnet synchronous motor, due to factors such as the cogging effect, non-sinusoidal distribution of the permanent magnet magnetic field, saturation effect, and thermal effect, high-order harmonics will exist in the magnetic flux. Therefore, the magnetic flux can be expressed as the superposition of the fundamental wave component and each harmonic component, where the fundamental wave component and each harmonic component are all functions of the rotor position. Import the magnetic flux data at all electrical angles under different direct-axis and quadrature-axis current excitations obtained in Step 1 into Matlab for processing. In this embodiment, the fast Fourier transform (FFT) is applied to perform harmonic analysis on the torque and magnetic flux data. It can be obtained that the three-phase magnetic fluxes Λ a , Λ b , Λ c mainly superimpose the 5th, 7th, 11th, 13th, 23rd, and 25th harmonic components on the basis of the fundamental wave component, corresponding to the d-axis and q-axis equivalent magnetic fluxes Λ d , Λ qOn the basis of the DC component, the 6th, 12th, and 24th harmonics are mainly superimposed, and the higher harmonics of different orders have a greater impact on the magnetic flux linkage.

[0052] Harmonic analysis can be carried out by methods including but not limited to Fourier transform, discrete cosine transform, etc.; in the expression of the magnetic flux linkage superimposed on the fundamental component and each harmonic component obtained, the selected basis function and the representation form of each harmonic component include but are not limited to trigonometric functions.

[0053] In this embodiment, taking the specific excitation currents Id = -100A and Iq = 120A as an example, the established magnetic flux linkage harmonic model is shown in Formulas (4) to (6).

[0054]

[0055] In Formulas (4) to (6), Λ a , Λ b , Λ c are the magnetic flux linkages of phase a, phase b, and phase c respectively, λ k is the amplitude of the kth harmonic of the magnetic flux linkage of phase a, is the phase of the kth harmonic of the magnetic flux linkage of phase a, and θ e is the electrical angle, that is, the rotor position.

[0056] In an embodiment of the present invention, there is provided Figure 2 The original waveform of the magnetic flux linkage of phase a shown and the waveform of the magnetic flux linkage of phase a in the form of harmonic superposition shown in Formula (4), where the maximum error is 0.0016 Nm, having high accuracy.

[0057] Under different excitation currents [I d , I q , the amplitude λ k of the kth harmonic of the magnetic flux linkage of phase a and the phase will change, where k = 1, 5, 7, 11, 13, 23, 25. The traditional look-up table model needs to store the amplitude and phase information under different excitation currents in the model. Taking this embodiment as an example, a total of 36,414 amplitude and phase information need to be stored for 2,601 groups of different excitation currents, increasing the demand of the model for storage space and unable to achieve the invention purpose of lightweight. At the same time, for the input current not included in the initial excitation current, the model needs to perform interpolation, reducing the response speed.

[0058] To solve the above problems, the amplitudes and phases of each harmonic of the magnetic flux linkage are expressed as functions of the excitation current, and the model is further parameterized to reduce its demand for storage space and improve the response speed of the model. In this embodiment, a total of 2,601 groups of different direct and quadrature axis excitation currents and the corresponding original data of the amplitude λ k of the kth harmonic of the magnetic flux linkage of phase a and the phase are included According to the electromagnetic relationship among the flux linkage amplitude, phase, and excitation current, a fitting function is selected for λ k , Nonlinear regression fitting is adopted to obtain the fitting function of λ k = f(I d , I q ). The fitting function of

[0059] In an embodiment of the present invention, the fitting effect of the fundamental component amplitude of the flux linkage shown in Figure 3 is provided.

[0060] In an embodiment of the present invention, piecewise fitting or a more complex fitting function is used to fit the more complex (I d , I q ) mapping relationship corresponding to each harmonic component of the flux linkage, and the fitting result shown in Figure 4 is provided.

[0061] Referring to Table 1, the selected fitting function above has a high fitting accuracy for the amplitude and phase of the fundamental component and each harmonic component of the flux linkage. The established flux linkage harmonic model achieves the invention purpose of lightweight on the basis of high accuracy.

[0062] Table 1 Statistical indicators of fitting effect

[0063]

[0064] Step 3: Establish a torque harmonic model

[0065] Based on the fact that the energy conservation relationship between mechanical power and electromagnetic power holds in any coordinate system, the proposed harmonic models of torque and flux linkage also cover various coordinate systems, including but not limited to the three-phase stationary coordinate system, i.e., the abc coordinate system, the two-phase stationary coordinate system, i.e., the αβ coordinate system, and the two-phase rotating coordinate system, i.e., the dq coordinate system; the description method of the rotor position covers different representation methods of the relative positions of the stator and rotor, including but not limited to the electrical angle by which the rotor d-axis leads the stator a-phase winding.

[0066] In the abc coordinate system, the energy relationship between electromagnetic torque and flux linkage can be established as shown in Equation (7).

[0067]

[0068] In Equation (7), P e is the electromagnetic power, ω m is the mechanical angular velocity, are the back electromotive force vectors of phases a, b, and c respectively, are the current vectors of phases a, b, and c respectively.

[0069] Based on the flux linkage harmonic model obtained in Step 2, the harmonic model of torque can be further derived, as shown in Equations (8) to (11):

[0070]

[0071]

[0072] Then,

[0073]

[0074] In Equations (8) to (11), I a , I b , I c are the amplitudes of the phase-a, phase-b, and phase-c currents, and I a = I b = I c = I, and ψ is the initial phase angle of the phase-a current.

[0075] From the above torque harmonic model, it can be seen that the main orders of the torque harmonics are determined by the orders of the flux linkage harmonics and the harmonics of the exciting current. Therefore, the torque can be expressed as the superposition of a DC component and the 6th, 12th, and 24th harmonics. The amplitudes and phases of the main torque harmonics are determined by the amplitudes, phases of the flux linkage harmonics, and motor parameters such as the number of pole pairs, as shown in Equations (12) to (18).

[0076]

[0077]

[0078] In Equations (12) to (18), T0 is the DC component of the torque; T6, φ6 are the amplitude and phase of the 6th harmonic of the torque; T 12 , φ 12 are the amplitude and phase of the 12th harmonic of the torque; T 24 , φ 24 are the amplitude and phase of the 24th harmonic of the torque.

[0079] Convert the abc coordinate system to the dq coordinate system. The amplitude λ k and phase of the kth harmonic of the phase-a flux linkage in the torque harmonic model are expressed as fitting functions of the exciting current [I d , I q through the parameterization method in Step 2. Finally, the torque harmonic model can be expressed as a function of the exciting current [I d , I q , the rotor position θ e , and the number of pole pairs P nAnd the analytical harmonic superposition functions of motor parameters such as the initial rotor position θ0, as shown in Eqs. (19) to (21).

[0080]

[0081] λ k = f(I d , I q )(20)

[0082]

[0083] In Eqs. (19) to (21), k = 1, 5, 7, 11, 13, 23, 25.

[0084] In this embodiment, in Eq. (19), θ0 = 3.75°, P n = 4. In an embodiment of the present invention, there is provided Figure 5 The comparison between the original electromagnetic torque waveform shown and the waveform of the torque harmonic superposition form shown in Eq. (19), where the maximum error is 3.1682 Nm and the relative error is about 2%, having high accuracy.

[0085] Step 4, establish a permanent magnet synchronous motor model

[0086] After implementing the functional expressions of torque and flux linkage with respect to the direct and quadrature axis currents [I d , I q and the rotor position θ e in the control system in the form of software code, it can be embedded into the control system of the permanent magnet synchronous motor to establish a permanent magnet synchronous motor model.

[0087] Referring to Figure 6 , by inputting the direct and quadrature axis currents [I d , I q and the rotor position θ e into the model, and at the same time setting the basic motor parameters such as the number of pole pairs P n , the initial rotor position θ0, etc., the corresponding torque and flux linkage can be calculated to achieve real-time calculation and feedback control. The permanent magnet synchronous motor model established by the method proposed in the present invention can be applied to the design, optimization and performance evaluation of the control system of the permanent magnet synchronous motor, and can achieve the invention purpose of establishing a lightweight permanent magnet synchronous motor model with high accuracy. At the same time, since the constructed model can be represented in an analytical form, it can solve the problems of low accuracy and slow response speed of the permanent magnet synchronous motor model in the permanent magnet synchronous motor control system.

[0088] In the description of this specification, the descriptions referring to terms such as "one embodiment", "example", "specific example", etc. mean that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0089] The above has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and the above embodiments and the descriptions in the specification only illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed.

Claims

1. A permanent magnet synchronous motor modeling method based on harmonic analysis, characterized in that It includes the following steps: Step 1: Obtain the flux linkage data varying with the rotor position under different excitation currents; Step 2: Establish a flux linkage harmonic model based on the flux linkage data varying with the rotor position under different excitation currents obtained in Step 1. The flux linkage harmonic model represents the flux linkage as a superposition of a fundamental flux linkage component and a harmonic flux linkage component. Both the fundamental flux linkage component and the harmonic flux linkage component are functions related to the rotor position. According to the correlation between each harmonic of the permanent magnet synchronous motor's flux linkage and the excitation current, represent the flux linkage harmonic model as a function related to the excitation current and the rotor position, and obtain a lightweight flux linkage harmonic model; Step 3: Based on the energy conservation relationship between the mechanical power and the electromagnetic power and the lightweight flux linkage harmonic model, establish an electromagnetic torque harmonic model. The electromagnetic torque harmonic model represents the electromagnetic torque as a superposition of a DC electromagnetic torque component and a harmonic electromagnetic torque component, and deduce and determine the amplitude and phase of the DC electromagnetic torque component and each harmonic component. Represent the electromagnetic torque harmonic model in the form of an analytical harmonic superposition function related to the excitation current, the rotor position, the number of pole pairs, and the initial rotor position; Step 4: Based on the lightweight flux linkage harmonic model and the electromagnetic torque harmonic model in the form of an analytical harmonic superposition function, establish a permanent magnet synchronous motor model.

2. The permanent magnet synchronous motor modeling method based on harmonic analysis according to claim 1, wherein In Step 2, methods including but not limited to discrete cosine transform and Fourier transform are used to establish the flux linkage harmonic model.

3. The method for modeling a permanent magnet synchronous motor based on harmonic analysis according to claim 2, characterized in that In Step 2, the flux linkage harmonic model represents the flux linkage as a superposition of a fundamental flux linkage and the 5th, 7th, 11th, 13th, 23rd, and 25th harmonic flux linkage components. Among them, Λ a , Λ b , Λ c are the magnetic fluxes of phase a, phase b, and phase c respectively, and λ k is the amplitude of the k-th harmonic of the magnetic flux of phase a, is the phase of the k-th harmonic of the magnetic flux of phase a, and θ e is the rotor position.

4. The method for modeling a permanent magnet synchronous motor based on harmonic analysis according to claim 3, wherein In step 2, according to the correlation between the harmonics of the magnetic flux of the permanent magnet synchronous motor and the excitation current, the magnetic flux harmonic model is expressed as a function related to the excitation current and the rotor position, and a lightweight magnetic flux harmonic model is obtained. The specific method is as follows: According to the electromagnetic relationship between the magnetic flux amplitude, the magnetic flux phase and the excitation current, a fitting function is selected to perform nonlinear regression fitting on the magnetic flux amplitude and phase, and a fitting function λ k = f(I d , I q ) related to the magnetic flux amplitude and the excitation current, and a fitting function of the magnetic flux phase and the excitation current are obtained. Substitute the fitting function related to the magnetic flux amplitude and the excitation current and the fitting function related to the magnetic flux phase and the excitation current into the magnetic flux harmonic model, where I d , I q are the d-axis component and the q-axis component of the excitation current.

5. The modeling method of a permanent magnet synchronous motor based on harmonic analysis according to claim 4, characterized in that, In the said step 3, the expression of the energy conservation relationship between mechanical power and electromagnetic power in the three-phase coordinate system is as follows: where, T e is the electromagnetic torque, P e is the electromagnetic power, ω m is the mechanical angular velocity, are the back electromotive force vectors of phase a, phase b, and phase c respectively, are the current vectors of phase a, phase b, and phase c respectively.

6. The modeling method of a permanent magnet synchronous motor based on harmonic analysis according to claim 5, characterized in that, In the step 3, the electromagnetic torque harmonic model represents the electromagnetic torque as a superposition of the electromagnetic torque DC component and the harmonic components. The specific method is as follows: Substitute the lightweight flux harmonic model into the expression of the energy conservation relationship between the mechanical power and the electromagnetic power in the three-phase coordinate system, and substitute with P n . The electromagnetic torque harmonic model represents the electromagnetic torque as a superposition of the electromagnetic torque DC component and the 6th, 12th, and 24th electromagnetic torque harmonic components: Among them, ω e is the electrical angle, ω e t = θ e , P n is the number of pole pairs, I a , I b , I c are the amplitudes of the currents of phase a, phase b, and phase c, and I a = I b = I c = I, and ψ is the initial phase angle of the current of phase a.

7. The modeling method of a permanent magnet synchronous motor based on harmonic analysis according to claim 6, characterized in that In Step 3, the specific method for deducing and determining the amplitude and phase of the DC electromagnetic torque component and each harmonic component is as follows: Among them, T0 is the DC component of the electromagnetic torque, T6 and φ6 are the amplitude and phase of the 6th harmonic of the electromagnetic torque, T 12 , φ 12 are the amplitude and phase of the 12th harmonic of the electromagnetic torque, T 24 , φ 24 are the amplitude and phase of the 24th harmonic of the electromagnetic torque.

8. The modeling method of a permanent magnet synchronous motor based on harmonic analysis according to claim 7, characterized in that In Step 3, represent the torque harmonic model in the form of an analytical harmonic superposition function related to the excitation current, the rotor position, the number of pole pairs, and the initial rotor position, specifically as:

9. An electronic device includes a memory and a processor. A computer program is stored on the memory and runs on the processor. When the processor runs the computer program, it executes the steps of the permanent magnet synchronous motor modeling method according to any one of claims 1 to 8.

10. A computer-readable storage medium stores a computer program. When the computer program runs, it executes the steps of the permanent magnet synchronous motor modeling method according to any one of claims 1 to 8.

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