A permanent magnet synchronous motor modeling method and system based on vector magnetic circuit theory

Abstract

The application discloses a permanent magnet synchronous motor modeling method and system based on a vector magnetic circuit theory, and belongs to the field of motor and magnetic circuit theory application; the modeling method comprises the following steps: establishing a motor magnetic impedance model; calculating motor armature winding magnetic motive force; calculating armature winding flux linkage according to the motor magnetic impedance model and the armature winding magnetic motive force; calculating permanent magnet magnetic motive force according to a motor permanent magnet flux linkage nominal value and the motor magnetic impedance model; calculating permanent magnet flux linkage according to the motor magnetic impedance model and the permanent magnet magnetic motive force; obtaining motor stator flux linkage by using a superposition theorem according to the armature winding flux linkage and the permanent magnet flux linkage; and establishing a permanent magnet synchronous motor mathematical model based on the vector magnetic circuit theory and considering eddy current reaction according to a motor stator voltage equation. Compared with a traditional permanent magnet motor model, the modeling method has clear physical meaning, can accurately consider the motor cross / straight axis cross-coupling influence caused by the eddy current reaction, and has higher accuracy.

Description

Technical Field

[0001] This invention belongs to the field of motor and magnetic circuit theory application, specifically involving a modeling method and system for permanent magnet synchronous motors based on vector magnetic circuit theory. Background Technology

[0002] Compared to induction motors, permanent magnet synchronous motors (PMSMs) offer advantages such as high power density, high efficiency, and superior control performance, leading to their widespread application in electric drives, particularly high-performance electric drives. The mathematical model of the motor is fundamental to motor control; therefore, establishing an accurate mathematical model of the PMSM is crucial for achieving high-performance control. However, existing PMSM modeling methods often fail to account for the effects of eddy current reactions, resulting in discrepancies between the theoretical and practical models, especially in high-speed motor applications where iron losses are relatively high. While methods such as state observers are commonly used to correct or compensate for these unconsidered factors, the introduction of observers limits further improvements in control performance. Therefore, researching PMSM modeling methods that incorporate eddy current reactions is of significant value.

[0003] Existing modeling methods for permanent magnet motors that consider eddy current reactions typically introduce an equivalent iron loss resistance branch into the motor's equivalent circuit model to simulate eddy current losses, and then obtain the equivalent iron loss resistance value through methods such as experimental data fitting. However, this type of modeling method suffers from unclear physical meaning, requires a large amount of experimental data to obtain a relatively accurate motor model, and the established motor model is usually only applicable to steady-state analysis. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a modeling method and system for permanent magnet synchronous motors based on vector magnetic circuit theory.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory includes the following steps:

[0007] Establish the motor magnetoresistance model;

[0008] Calculate the magnetomotive force of the motor armature winding;

[0009] Calculate the armature winding flux linkage based on the motor magnetoresistance model and the armature winding magnetomotive force;

[0010] Calculate the permanent magnet magnetomotive force based on the nominal value of the permanent magnet flux linkage and the magnetic impedance model of the motor;

[0011] Calculate the permanent magnet flux linkage based on the motor magnetoresistance model and permanent magnet magnetomotive force;

[0012] Based on the armature winding flux linkage and the permanent magnet flux linkage, the superposition theorem is used to obtain the stator flux linkage of the motor.

[0013] A motor model is established based on the motor stator voltage equation and the motor stator flux linkage.

[0014] Furthermore, the equivalent magnetic circuit diagram corresponding to the motor magnetoresistance model includes magnetoresistance, magnetic induction, and source magnetomotive force, wherein the source magnetomotive force includes armature and permanent magnet magnetomotive force.

[0015] The motor's magnetic impedance model is as follows:

[0016]

[0017]

[0018]

[0019] Among them, F m It is the source magnetomotive force, R m It is magnetic reluctance, L m φ is magnetic flux; N is the equivalent number of turns of the winding corresponding to the magnetic circuit under study, and L is magnetic flux. e N is the winding inductance corresponding to the magnetic circuit under study; i R is the equivalent number of core turns corresponding to eddy current losses. i It is the equivalent core resistance corresponding to eddy current loss;

[0020] The magnetic induction L m The following formula can be used to adjust the operating frequency:

[0021]

[0022] Where ω is the actual electrical frequency, ω N It is the rated electrical frequency.

[0023] Furthermore, the formula for calculating the magnetomotive force of the armature winding is:

[0024]

[0025] in, It is the armature winding magnetomotive force vector, F d It is the magnetomotive force component of the d-axis armature winding, F q It is the magnetomotive force component of the q-axis armature winding, and j is the imaginary unit of the complex number.

[0026] Furthermore, the formula for calculating the armature winding flux linkage is:

[0027]

[0028]

[0029] Among them, R md and R mq These are the d-axis and q-axis reluctance, respectively. It is the armature flux linkage vector, and k is the combined value of variables that are difficult to measure.

[0030] Furthermore, the formula for calculating the permanent magnet magnetomotive force is:

[0031]

[0032] in, It is the rated flux linkage amplitude given on the nameplate. It is the permanent magnet magnetomotive force vector, ω N It is the rated electrical frequency of the motor.

[0033] Furthermore, the formula for calculating the permanent magnet flux linkage is:

[0034]

[0035] in, It is a permanent magnet flux linkage vector.

[0036] Furthermore, the formula for calculating the stator flux linkage of the motor is:

[0037]

[0038] in, It is the stator flux linkage vector.

[0039] Furthermore, the motor model expression is as follows:

[0040]

[0041]

[0042] Furthermore, the estimation formula for the value of k is:

[0043]

[0044] Where, k N For the nominal value of k, ω N ω is the rated electrical frequency of the motor, i is the actual electrical frequency of the motor, and i is the rated electrical frequency of the motor. dN and i qN These are the rated d-axis and q-axis currents of the motor, R s It is the stator resistance, ψ fN It is the rated permanent magnet flux linkage amplitude, L d and L q These are the inductances of the motor's d-axis and q-axis, respectively.

[0045] A modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory includes:

[0046] Magnetoresistive model building unit: Establishing the motor magnetoresistive model;

[0047] Armature winding magnetomotive force calculation unit: Calculates the magnetomotive force of the motor armature winding;

[0048] Armature winding flux linkage calculation unit: Calculates armature winding flux linkage based on motor magnetoresistance model and armature winding magnetomotive force;

[0049] Permanent magnet magnetomotive force calculation unit: Calculates permanent magnet magnetomotive force based on the nominal value of permanent magnet flux linkage and the motor magnetic impedance model;

[0050] Permanent magnet flux linkage calculation unit: Calculates permanent magnet flux linkage based on motor magnetic impedance model and permanent magnet magnetomotive force;

[0051] Stator flux linkage calculation unit: Based on the armature winding flux linkage and permanent magnet flux linkage, the superposition theorem is used to obtain the stator flux linkage of the motor;

[0052] And the motor model building unit: Based on the motor stator voltage equation and the motor stator flux linkage, a motor model is established.

[0053] The beneficial effects of this invention are:

[0054] (1) This invention establishes a motor magnetoresistance model and uses the influence of magnetometer and eddy current reaction in magnetic circuit theory on the motor model. Compared with the traditional modeling method of directly connecting the equivalent iron loss resistor across the equivalent circuit of the motor, the modeling method proposed in this invention has clear physical meaning.

[0055] (2) In the modeling method of permanent magnet synchronous motor considering eddy current reaction proposed in this invention, the model parameters can be estimated by the parameters provided by the motor nameplate. Compared with the traditional modeling method that requires a lot of experiments and data fitting, the modeling method proposed in this invention has stronger practicality because the model parameters are easy to obtain.

[0056] (3) Based on the motor magnetic impedance model, the modeling method proposed in this invention takes into account the influence of the cross coupling of the motor dq axis caused by eddy current reaction more comprehensively, which is more accurate than the traditional modeling method based on equivalent iron loss resistance. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1This is a flowchart of the permanent magnet synchronous motor modeling method of the present invention;

[0059] Figure 2 This is the equivalent circuit diagram of a permanent magnet motor that does not take eddy current reaction into account.

[0060] Figure 3 This is the equivalent circuit diagram of a traditional permanent magnet motor that takes into account eddy current reaction.

[0061] Figure 4 This is the equivalent magnetic circuit diagram corresponding to the magnetoresistance model of a permanent magnet motor;

[0062] Figure 5 It is the equivalent circuit diagram of the motor obtained by the modeling method of permanent magnet synchronous motor with eddy current reaction based on vector magnetic circuit theory;

[0063] Figure 6 This is a vector diagram of a permanent magnet motor that does not take eddy current reaction into account.

[0064] Figure 7 It is a vector diagram of a permanent magnet motor that takes into account eddy current reaction based on vector magnetic circuit theory;

[0065] Figure 8 This is an example of a control block diagram for model predictive control based on a permanent magnet synchronous motor model that takes into account eddy current reaction, using vector magnetic circuit theory.

[0066] Figure 9 It applies a permanent magnet synchronous motor model based on vector magnetic circuit theory and considering eddy current reaction to... Figure 8 The simulated speed waveform of the motor during the starting process after the model predictive control is shown.

[0067] Figure 10 It applies a permanent magnet synchronous motor model based on vector magnetic circuit theory and considering eddy current reaction to... Figure 8 The simulated torque waveform of the motor starting process after model predictive control is shown.

[0068] Figure 11 It applies a permanent magnet synchronous motor model based on vector magnetic circuit theory and considering eddy current reaction to... Figure 8 The simulated stator current waveform during motor startup is shown after the model predictive control is implemented.

[0069] Figure 12 The simulation waveforms show the stator current prediction error using a motor model that does not consider eddy current reaction and a permanent magnet synchronous motor model that considers eddy current reaction based on vector magnetic circuit theory.

[0070] Figure 13The figures show the current prediction error curves for a three-phase motor prototype using a DSP controller without considering eddy current reaction under different speed and torque conditions, and for a permanent magnet synchronous motor model based on vector magnetic circuit theory that considers eddy current reaction proposed in this patent. Detailed Implementation

[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] like Figure 2 The equivalent circuit diagram of the motor model, neglecting eddy current reaction, is shown. In this diagram, the equivalent circuits for the dq axes consist of resistors, inductors, and potentials connected in series. Based on the equivalent circuit structure, the following motor model can be obtained:

[0073]

[0074] Among them, u d and u q These are the d-axis and q-axis stator voltages, i d and i q These are the d-axis and q-axis stator currents, respectively, L d and L q These are the d-axis and q-axis inductances, R s It is the stator resistance, ψ f It is a permanent magnet flux linkage, ω is the electric angular frequency; the coupling potential E along the d-axis d =-ωL q i q The coupling potential E along the q-axis q =ωL d i d +ωψ f .

[0075] like Figure 2 The equivalent circuit of a traditional permanent magnet motor that considers eddy current reaction is shown. This type of model directly connects an equivalent iron loss resistor in parallel with the inductance and electromotive force branches (i.e., the induced electromotive force branch) to account for eddy current reaction. However, the equivalent iron loss resistor in parallel usually needs to be obtained through a large number of experimental tests and fitting. Based on the equivalent circuit, the motor model shown in Equation (2) can be obtained:

[0076]

[0077] Among them, R iIt is the equivalent iron loss resistance; it should be noted that the current in equation (2) does not include the current flowing through the equivalent iron loss resistance, and cannot be directly used in actual analysis; therefore, in order to simplify the analysis, the modeling method of permanent magnet motor based on the equivalent iron loss resistance is usually applicable to steady-state analysis.

[0078] Unlike traditional motor modeling methods that indirectly reflect eddy current reaction through equivalent circuits, vector magnetic circuit theory allows for direct modeling of eddy current reaction in the magnetic circuit using magnetic flux density, thus possessing a more explicit physical meaning. The modeling assumptions of the permanent magnet synchronous motor modeling method based on vector magnetic circuit theory, which considers eddy current reaction, include the following:

[0079] (1) Ignore spatial harmonics and assume that the winding magnetomotive force is distributed sinusoidally along the air gap;

[0080] (2) Ignore the magnetic circuit saturation effect, that is, the self-inductance of each winding and the mutual inductance between windings are constant;

[0081] (3) Hysteresis loss is not taken into account;

[0082] (4) Ignore the effects of temperature rise and frequency on the motor body parameters;

[0083] (5) Assume that the permeability inside the permanent magnet is the same as that of air, and assume that the permanent magnet flux is constant.

[0084] (6) Assume that the equivalent number of core turns corresponding to eddy current loss is constant.

[0085] like Figure 1 As shown, a modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory includes the following steps:

[0086] S1. Establish the motor magnetic impedance model and use the influence of magnetometer and eddy current reaction in magnetic circuit theory on the motor model.

[0087] like Figure 4 The equivalent magnetic circuit diagram corresponding to the permanent magnet motor magnetoresistance model shown includes magnetoresistance, magnetic induction, and source magnetomotive force, which includes the armature and permanent magnet magnetomotive force.

[0088] Based on the equivalent magnetic circuit, the magnetic impedance model of the motor can be obtained:

[0089]

[0090] Among them, F m It is the source magnetomotive force, R m Here, Lm is magnetic reluctance, φ is magnetic flux, and Lm is magnetic induction. Magnetic reluctance can be calculated using the following formula:

[0091]

[0092] Where N is the equivalent number of turns of the winding corresponding to the magnetic circuit under study, and L e This is the winding inductance corresponding to the magnetic circuit under study; the magnetic inductance can be calculated using the following formula:

[0093]

[0094] Where, N i R is the equivalent number of core turns corresponding to eddy current losses. i This refers to the equivalent core resistance corresponding to eddy current losses; both are motor parameters under rated operating conditions. Considering the skin effect, the equivalent core resistance can be corrected according to the operating frequency using the following formula:

[0095]

[0096] Where ω is the actual electrical frequency, ω N It is the rated electrical frequency.

[0097] S2, calculate the dq-axis magnetomotive force generated by the motor armature winding; the calculation formula is as follows:

[0098]

[0099] in, It is the armature winding magnetomotive force vector, F d It is the magnetomotive force component of the d-axis armature winding, F q It is the magnetomotive force component of the q-axis armature winding, and j is the imaginary unit of the complex number.

[0100] S3, calculate the armature winding flux linkage based on the motor magnetoresistance model established in S1 and the armature winding magnetomotive force in S2; the calculation process is as follows:

[0101]

[0102] Among them, R md and R mq These are the d-axis and q-axis reluctance, respectively. It is the armature flux linkage vector; the variables in the flux linkage equation that are difficult to measure in practice are combined and denoted as k:

[0103]

[0104] The final expression for the armature winding flux linkage is then obtained as follows:

[0105]

[0106] S4. Calculate the permanent magnet magnetomotive force based on the nominal value of the permanent magnet flux linkage and the magnetic impedance model of the motor.

[0107] Generally, the permanent magnet flux linkage given on the motor nameplate corresponds to the amplitude of the permanent magnet flux linkage under rated operating conditions. Since the d-axis position of the motor is determined by the coincidence of the neutral line of the permanent magnet poles and the neutral line of the windings, the permanent magnet magnetomotive force vector is always located on the d-axis. Due to the influence of magnetic induction, the permanent magnet flux linkage will lag behind the d-axis. To calculate the permanent magnet flux linkage vector under arbitrary frequency operating conditions, the quantity in the magnetic circuit that does not change with frequency, i.e., the magnetomotive force, should be calculated first.

[0108]

[0109] in, It is the rated flux linkage amplitude given on the nameplate. It is the permanent magnet magnetomotive force vector, ω N It is the rated electrical frequency of the motor.

[0110] S5, calculate the permanent magnet flux linkage along the dq axis based on the motor magnetoresistance model and the permanent magnet magnetomotive force in S4; the calculation formula is:

[0111]

[0112] in, It is a permanent magnet flux linkage vector.

[0113] S6, based on the armature winding flux linkage calculated in S3 and the permanent magnet flux linkage calculated in S5, the stator flux linkage of the motor is obtained using the superposition theorem; the calculation formula is as follows:

[0114]

[0115] in, It is the stator flux linkage vector, ψ sd ψ is the d-axis component of the stator flux linkage vector. sq It is the q-axis component of the stator flux linkage vector.

[0116] S7. Based on the stator voltage equation and the stator flux calculated in S6, establish the motor model;

[0117] The general form of the motor voltage equation is shown below:

[0118]

[0119] Substituting the stator flux vector calculated in the aforementioned steps yields the following voltage equation, which is the mathematical model of the permanent magnet synchronous motor based on vector magnetic circuit theory and considering eddy current reaction provided by this invention:

[0120]

[0121]

[0122] The method for calculating the model parameter k in this invention is as follows:

[0123] For the undetermined parameter k in the equation, the power conservation can be used to approximate the estimate based on the iron loss of the motor. Based on the power conservation of the magnetic circuit, the parameter k can be calculated according to equations (17)-(20), where the subscript N indicates that the variable is the rated value. It should be noted that the permanent magnet flux value in the nameplate is the amplitude, while the stator flux Φ in the power calculation is the effective value. It can be seen that, in order to estimate, the stator flux is calculated using a motor model that does not consider the eddy current reaction.

[0124]

[0125] Among them, P ironlossN It is the rated iron loss of the motor, k. N For the nominal value of k, ω N ω is the rated electrical frequency of the motor, and L is the actual electrical frequency of the motor. mN It is the rated equivalent magnetic induction of the motor, Φ N Motor equivalent magnetic flux, i dN and i qN These are the rated d-axis and q-axis currents of the motor, R s It is the stator resistance, ψ fN It is the rated permanent magnet flux linkage amplitude, L d and L q These are the d-axis and q-axis inductances of the motor, respectively, and m is the number of phases of the motor.

[0126] Based on the assumption that the iron loss and copper loss of the motor are equal under rated operating conditions, the iron loss of the permanent magnet motor is calculated as follows:

[0127]

[0128] Then k under rated operating conditions N The expression is:

[0129]

[0130] Finally, considering the skin effect, the expression for parameter k at any frequency is shown in equation (20).

[0131]

[0132] The equivalent circuit diagram of the permanent magnet synchronous motor obtained by the modeling method of the permanent magnet synchronous motor considering eddy current reaction based on vector magnetic circuit theory is as follows: Figure 5 As shown; including stator winding resistance R s d-axis resistance R caused by eddy current reaction dv d-axis inductance L considering eddy current reaction dv The coupling potential E, taking into account the eddy current reaction, dv d-axis stator voltage u d q-axis resistance R caused by eddy current reaction qvq-axis inductance L considering eddy current reaction qv The coupling potential E, taking into account the eddy current reaction, qv and q-axis stator voltage u q .from Figure 5 It can be seen that both the d-axis and q-axis circuits introduce new coupling potentials, which, along with... Figure 2 and Figure 3 The equivalent circuits shown are significantly different.

[0133] In this invention, the vector diagram of the permanent magnet motor, which does not take into account eddy current reaction, is as follows: Figure 6 As shown, this includes the rotor position angle θ and the permanent magnet flux vector. Armature flux vector Stator flux linkage vector Stator current vector and stator voltage vector from Figure 6 It can be seen that in the vector diagram of a permanent magnet motor without considering the reaction of eddy currents, the permanent magnet flux linkage and the permanent magnet magnetomotive force are in the same direction, both located in the d-axis direction; and the direction of the armature flux linkage depends only on the direction of the stator current and the inductance value.

[0134] In this invention, a vector diagram of a permanent magnet motor considering eddy current reaction is used based on vector magnetic circuit theory, such as... Figure 7 As shown, this includes the rotor position angle θ and the permanent magnet flux vector. Armature flux vector Stator flux linkage vector Stator current vector and stator voltage vector from Figure 7 It can be seen that in the vector diagram of a permanent magnet motor considering eddy current reaction based on vector magnetic circuit theory, the permanent magnet flux linkage lags behind the direction of the permanent magnet magnetomotive force, that is, it lags behind the d-axis direction. Simultaneously, the armature flux linkage direction relative to... Figure 6 There is also a lag; the lag in the phases of the armature flux linkage and permanent magnet flux linkage directly reflects whether or not the influence of eddy current reaction on the motor model is taken into account.

[0135] In this invention, an embodiment of a model-based motor control algorithm, based on vector magnetic circuit theory and considering eddy current reaction, is applied. Figure 8 As shown, it includes: a speed closed-loop PI regulator, a model predictive control module, a three-phase two-level inverter, a three-phase permanent magnet synchronous motor, a coordinate transformation module, a control delay compensating current prediction, a position encoder, and a speed calculation module; Model-based motor control algorithms usually require discretization of the motor model, as shown in equations (21)-(24); For ease of representation, some variables in equations (15) and (16) of the motor model are defined as variables shown in equation (21);

[0136]

[0137] The motor model can then be represented as:

[0138]

[0139] Furthermore, the motor equations are rearranged into differential form:

[0140]

[0141] The Euler method is used to discretize equation (23) to obtain the discrete motor model shown in equation (24).

[0142]

[0143] The results of Simulink simulation verification of this invention are as follows: Figures 9 to 12 As shown. Figure 9 It applies a permanent magnet synchronous motor model based on vector magnetic circuit theory and considering eddy current reaction to... Figure 8 The simulated waveform of the motor speed during the starting process after predictive control of the model is shown. Figure 10 It applies a permanent magnet synchronous motor model based on vector magnetic circuit theory and considering eddy current reaction to... Figure 8 The torque simulation waveform of the motor starting process after predictive control of the model is shown. Figure 11 It applies a permanent magnet synchronous motor model based on vector magnetic circuit theory and considering eddy current reaction to... Figure 8 The simulated stator current waveform during motor startup is shown after model predictive control. The simulation results show that during motor startup, the torque rapidly rises to its maximum value, causing the speed acceleration to reach its maximum value. Once the speed approaches the reference speed, the torque gradually decreases to its steady-state value under the action of the speed closed-loop PI regulator, and the startup process meets expectations. Figure 12 These are simulation waveforms of stator current prediction errors using a model of a permanent magnet synchronous motor that neglects eddy current reaction and a model of a permanent magnet synchronous motor that considers eddy current reaction based on vector magnetic circuit theory. From... Figure 12 It can be seen that when using a model that does not consider eddy current reaction to predict the stator current, the prediction result has a large steady-state error, which leads to a decrease in control performance. However, when using a permanent magnet synchronous motor model based on vector magnetic circuit theory that considers eddy current reaction to predict the stator current, the steady-state error of the current prediction is significantly reduced, proving that the model constructed by the modeling method of this invention has higher prediction accuracy than the model constructed by traditional modeling methods.

[0144] The experimental verification results of this invention regarding current prediction are as follows: Figure 13 As shown. Figure 13The figures show the current prediction error curves for a three-phase motor prototype using a DSP controller without considering eddy current reaction under different speed and torque conditions, and for a permanent magnet synchronous motor model based on vector magnetic circuit theory and considering eddy current reaction proposed in this patent. The expression for the vector magnitude of the current prediction error is shown in equation (25).

[0145]

[0146] The parameters of the permanent magnet motor in the experiment are as follows: 10 pole pairs, q-axis inductance of 10.588 mH, d-axis inductance of 8.422 mH, permanent magnet flux linkage of 0.101065 Wb, stator resistance of 0.427 Ω, and sampling frequency of 5 kHz. Figure 13 It can be seen that the model constructed by the modeling method of this invention has higher prediction accuracy than the model constructed by traditional modeling methods.

[0147] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0148] The foregoing 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 to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory, characterized in that, Includes the following steps: Establish the motor magnetoresistance model; Calculate the magnetomotive force of the motor armature winding; Calculate the armature winding flux linkage based on the motor magnetoresistance model and the armature winding magnetomotive force; Calculate the permanent magnet magnetomotive force based on the nominal value of the permanent magnet flux linkage and the magnetic impedance model of the motor; Calculate the permanent magnet flux linkage based on the motor magnetoresistance model and permanent magnet magnetomotive force; Based on the armature winding flux linkage and the permanent magnet flux linkage, the superposition theorem is used to obtain the stator flux linkage of the motor. A motor model is established based on the motor stator voltage equation and the motor stator flux linkage; The equivalent magnetic circuit diagram corresponding to the motor magnetoresistance model includes magnetoresistance, magnetic induction, and source magnetomotive force, which includes armature and permanent magnet magnetomotive force. The motor's magnetic impedance model is as follows: Where Fm is the source magnetomotive force, Rm is the reluctance, Lm is the magnetic induction, and φ is the magnetic flux; N is the equivalent number of turns of the winding corresponding to the magnetic circuit under study, Le is the winding inductance corresponding to the magnetic circuit under study; Ni is the equivalent number of core turns corresponding to eddy current loss, and Ri is the equivalent core resistance corresponding to eddy current loss. The magnetic induction Lm can be corrected according to the operating frequency using the following formula: Where ω is the actual electrical frequency and ωN is the rated electrical frequency.

2. The modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory according to claim 1, characterized in that, The formula for calculating the magnetomotive force of the armature winding is: in, It is the magnetomotive force vector of the armature winding. Fd yes d Magnetomotive force component of the armature winding. Fq yes q Magnetomotive force component of the armature winding. j It is the imaginary unit of complex numbers, and id and iq are the stator currents on the d-axis and q-axis, respectively.

3. The modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory according to claim 2, characterized in that, The formula for calculating the armature winding flux linkage is: Where Rmd and Rmq are the d-axis and q-axis reluctances, respectively. is the armature flux linkage vector, k is the combined value of variables that are difficult to measure, and Ld and Lq are the d-axis and q-axis inductances, respectively.

4. The modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory according to claim 3, characterized in that, The formula for calculating the permanent magnet magnetomotive force is: in, It is the rated flux linkage amplitude given on the nameplate. ωN is the permanent magnet magnetomotive force vector, and ωN is the rated electrical frequency of the motor.

5. The modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory according to claim 4, characterized in that, The formula for calculating the permanent magnet flux linkage is: in, It is a permanent magnet flux linkage vector.

6. The modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory according to claim 5, characterized in that, The formula for calculating the stator flux linkage of the motor is: in, It is the stator flux linkage vector.

7. The modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory according to claim 6, characterized in that, The motor model expression is: Among them, u d and u q These are the d-axis and q-axis stator voltages, respectively, R s It is the stator resistor.

8. The modeling method for permanent magnet synchronous motors based on vector magnetic circuit theory according to claim 5, characterized in that, The k The formula for estimating the value is: in, k N for k The rated value, ω N It is the rated electrical frequency of the motor. ω It is the actual electrical frequency of the motor. i dN and i qN These are the rated values ​​of the motor. d shaft and q shaft current, R s It is the stator resistance. ψ fN It is the rated permanent magnet flux linkage amplitude. L d and L q They are motors d shaft and q Shaft inductance.

9. A permanent magnet synchronous motor modeling system based on vector magnetic circuit theory, comprising the method described in any one of claims 1-8, characterized in that, include: Magnetoresistive model building unit: Establishing the motor magnetoresistive model; Armature winding magnetomotive force calculation unit: Calculates the magnetomotive force of the motor armature winding; Armature winding flux linkage calculation unit: Calculates armature winding flux linkage based on motor magnetoresistance model and armature winding magnetomotive force; Permanent magnet magnetomotive force calculation unit: Calculates permanent magnet magnetomotive force based on the nominal value of permanent magnet flux linkage and the motor magnetic impedance model; Permanent magnet flux linkage calculation unit: Calculates permanent magnet flux linkage based on motor magnetic impedance model and permanent magnet magnetomotive force; Stator flux linkage calculation unit: Based on the armature winding flux linkage and permanent magnet flux linkage, the superposition theorem is used to obtain the stator flux linkage of the motor; And the motor model building unit: Based on the motor stator voltage equation and the motor stator flux linkage, a motor model is established.

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