Equivalent magnetic circuit modeling method of surface-mounted permanent magnet synchronous motor

Abstract

The invention discloses an equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor, and belongs to the technical field of calculation, reckoning or counting. The magnetic circuit model constructed by the method comprises two mutually coupled subsystems of a permanent magnet equivalent magnetic circuit and a permanent magnet outer magnetic circuit, the permanent magnet magnetic circuit is characterized by demagnetization characteristics of ferromagnetic materials, the outer magnetic circuit adopts a nonlinear magnetic resistance network and a magnetic induction element for collaborative modeling, and the magnetic induction element realizes parameter correction through eddy current effect iteration. By establishing an interaction mechanism of a permanent magnet demagnetization curve and a characteristic curve of an external magnetic circuit, accurate solving of a permanent magnet working point is realized by adopting a numerical iteration method. According to the method, the influence of eddy current loss on the main magnetic flux is fully considered in model establishment, and the calculation precision of the magnetic circuit model in motor performance analysis is effectively improved.

Description

Technical Field

[0001] The present invention relates to magnetic circuit modeling technology, and more specifically, discloses a method for modeling the equivalent magnetic circuit of a surface-mounted permanent magnet synchronous motor, belonging to the technical field of calculation, estimation or counting. Background Art

[0002] As high-speed motor systems evolve toward ultra-high speeds and ultra-high power densities, surface-mounted permanent magnet synchronous motors (SPMSMs), with their low inertia and high dynamic response, have become core drive units in cutting-edge applications such as high-speed centrifugal compressors and flywheel energy storage systems. However, under extreme speed conditions, high-frequency harmonic magnetic fields cause exponentially increasing eddy current and hysteresis losses in the core, leading to exacerbated localized magnetic flux saturation in the core, causing an additional temperature rise of 15%-30% and material insulation degradation. Furthermore, core saturation distorts the air gap magnetic field waveform, causing torque output fluctuations and energy efficiency degradation, directly threatening system operational stability.

[0003] Traditional magnetic circuit theory, based on the linear reluctance model, simplifies magnetic circuit analysis through lumped parameters. While this allows for rapid calculations in engineering design, its fundamental flaw lies in its ability to only describe the amplitude relationship between the magnetomotive force and the magnetic flux, while failing to characterize the phase difference and nonlinear coupling effects between the two. Under high-speed or heavy-load conditions, motor core saturation, eddy current losses, and hysteresis effects significantly increase. Traditional methods, ignoring these factors, lead to large deviations in the calculation of magnetic flux density distribution, severely impacting torque prediction accuracy and loss assessment reliability, hindering the reliability design and ultimate performance breakthroughs of high-speed motors. There is an urgent need to construct a refined model that integrates eddy current analytical calculations with multi-physics coupling of magnetic circuits to accurately quantify and actively suppress eddy current losses.

[0004] Therefore, for surface-mounted permanent magnet motors, it is particularly important at this stage to develop an equivalent magnetic circuit model that combines solution time and solution accuracy, and can take into account the influence of eddy current loss in the calculation of electromagnetic properties such as magnetic flux, while accurately calculating eddy current loss. Summary of the Invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned background technology and provide an equivalent magnetic circuit modeling method for a surface-mounted permanent magnet synchronous motor, which can quickly and accurately evaluate the torque performance and eddy current loss of the permanent magnet synchronous motor, effectively improve the calculation accuracy of the magnetic circuit model in motor analysis, and solve the technical problems that the traditional equivalent magnetic circuit model ignores the spatial distribution characteristics of the eddy current path and the multi-physical field coupling effect, resulting in large loss prediction deviations and distorted modeling of the core saturation effect under high-speed conditions, realize refined magnetic circuit modeling under high-speed conditions, and provide a reliable theoretical basis for motor torque fluctuation suppression and energy efficiency optimization.

[0006] The present invention adopts the following technical solutions to achieve the above-mentioned purpose: An equivalent magnetic circuit modeling method for a surface-mounted permanent magnet synchronous motor includes: Step 1: Obtain initialization parameters of the surface-mounted permanent magnet synchronous motor; Step 2: Obtain the initial value of the permanent magnet working point by the interaction mechanism between the permanent magnet demagnetization curve and the permanent magnet external magnetic circuit characteristic curve, and calculate the total magnetic flux, leakage magnetic flux and air gap main magnetic flux based on the initial value of the permanent magnet working point; Step 3: Establish a motor equivalent magnetic circuit model including a permanent magnet equivalent magnetic circuit and a permanent magnet external magnetic circuit based on the magnetic flux path. The permanent magnet external magnetic circuit includes: a leakage magnetic circuit, an air gap magnetic circuit, and an iron core magnetic impedance network. The magnetic resistance in the motor equivalent magnetic circuit model is given according to the total magnetic flux, leakage magnetic flux, and air gap main magnetic flux calculated in step 2, and the magnetic induction in the permanent magnet external magnetic circuit is iteratively optimized. Step 4, calculating the leakage permeance and the main permeance from the magnetic voltage drop of each magnetic component in the external magnetic circuit of the permanent magnet, and calculating the current operating point of the permanent magnet according to the per-unit values ​​of the leakage permeance and the main permeance; Step 5: When the difference between the current working point of the permanent magnet and the initial value of the permanent magnet working point meets the convergence condition, the iterative process ends; otherwise, the process returns to step 2, updates the initial value of the permanent magnet working point to the current working point of the permanent magnet, and iterates again until the convergence condition is met. Step 6: Calculate the electromagnetic performance parameters of the motor according to the current operating point of the permanent magnet that meets the convergence condition.

[0007] As a further optimization scheme for the equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor, the surface-mounted permanent magnet synchronous motor initialization parameters obtained in step 1 include: motor geometric parameters, distributed topology of stator windings, and core material. BH curve.

[0008] As a further optimization scheme for the equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor, step 2 is specifically as follows: Step 2A, determine whether the motor is running under load. If the motor is running without load, go to step 2B. If the motor is running under load, go to step 2C. Step 2B, combine the normalized permanent magnet working equation and the external magnetic circuit characteristic equation, and solve the permanent magnet no-load working point ( b m0， h m0 ) as the initial value of the permanent magnet working point, , calculate the total magnetic flux generated by the permanent magnet when no-load based on the permanent magnet no-load operating point , leakage flux and air gap main flux , ,in, b m0is the per-unit value of the magnetic flux density generated by the permanent magnet when it is no-load, h m0 is the per-unit value of the magnetic field intensity generated by the permanent magnet when it is unloaded, is the per-unit value of the main magnetic flux when no-load, f m0 is the per-unit value of the permanent magnet's magnetomotive force when it is no-load, is the per-unit value of the equivalent magnetic permeability of the permanent magnet external magnetic circuit, B r is the residual magnetic induction intensity, A m is the cross-sectional area of ​​the permanent magnet perpendicular to the magnetization direction; Step 2C: Calculate the direct-axis armature magnetic potential based on the distributed topology of the stator winding f ad , taking into account the direct-axis armature magnetic potential f ad The magnetic potential modulation effect is used to modify the magnetic potential balance equation, and the load operating point of the permanent magnet is solved by the modified magnetic potential balance equation ( b mN， h mN ), , take the load operating point of the permanent magnet as the initial value of the permanent magnet operating point, and calculate the total magnetic flux generated by the permanent magnet when loaded according to the load operating point of the permanent magnet , leakage flux and air gap main flux , .

[0009] As a further optimization scheme for the equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor, step 3 is specifically as follows: Step 3A, characterizing the permanent magnet equivalent magnetic circuit by a permanent magnet internal resistance connected in parallel at both ends of the permanent magnet magnetic flux source, characterizing the leakage magnetic circuit by a leakage magnetic resistance connected in parallel at both ends of the permanent magnet internal resistance, characterizing the air gap magnetic circuit by an air gap magnetic resistance connected in series at both ends of the iron core magnetic flux path, characterizing the stator tooth magnetic impedance network by two magnetic resistance-magnetic induction series branches connected in series on the stator tooth magnetic flux path, and characterizing the stator yoke magnetic impedance network by a magnetic resistance-magnetic induction series branch connected in series on the stator yoke magnetic flux path. The stator tooth magnetic impedance network and the stator yoke magnetic impedance network constitute the iron core magnetic impedance network; Step 3B, according to the core material BHThe internal resistance of the permanent magnet is given by the curve characteristic, the leakage magnetic reluctance is given according to the leakage magnetic flux and the corresponding magnetic flux density, the air gap magnetic reluctance is given according to the main magnetic flux of the air gap and the corresponding magnetic flux density, the stator tooth magnetic reluctance is given according to the stator tooth size parameters and the corresponding magnetic flux density, and the stator yoke magnetic reluctance is given according to the stator yoke size parameters and the corresponding magnetic flux density, wherein the magnetic flux density corresponding to the stator teeth is calculated based on the main magnetic flux and the stator tooth size parameters, and the magnetic flux density corresponding to the stator yoke is calculated based on the main magnetic flux and the stator yoke size parameters; In step 3C, the equivalent magnetic inductions of the stator teeth and the stator yoke under sinusoidal magnetic field excitation are the stator tooth magnetic induction and the stator yoke magnetic induction initial values, respectively, and the stator tooth magnetic induction and the stator yoke magnetic induction are iteratively optimized.

[0010] As a further optimization scheme for the equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor, step 3C is specifically as follows: Step 3C1, calculating the equivalent magnetic induction of the silicon steel sheets of the stator teeth and stator yoke under sinusoidal magnetic field excitation based on the geometric parameters of the motor, and obtaining the initial values ​​of the stator tooth magnetic induction and the stator yoke magnetic induction; Step 3C2: Based on the initial values ​​of the magnetic induction of the stator teeth and stator yoke, the nonlinear equations of the magnetic circuit model at the permanent magnet operating point are solved simultaneously to calculate the magnetic flux density and magnetic field intensity of the stator teeth, the magnetic flux density and magnetic field intensity of the stator yoke, and the effective value of the air gap magnetic flux; Step 3C3, according to the calculation results of step 3C2, solving the lumped magnetic induction parameters of the stator teeth and the lumped magnetic induction parameters of the stator yoke; Step 3C4: When the error between the currently solved stator tooth lumped magnetic induction parameters and the previously solved stator tooth lumped magnetic induction parameters approaches 0 and the error between the currently solved stator yoke lumped magnetic induction parameters and the previously solved stator yoke lumped magnetic induction parameters approaches 0, the currently solved stator tooth lumped magnetic induction parameters and the stator yoke lumped magnetic induction parameters are taken as the final solution; otherwise, return to step 3C2, update the initial values ​​of the stator tooth magnetic induction and the stator yoke magnetic induction to the currently solved stator tooth lumped magnetic induction parameters and the stator yoke lumped magnetic induction parameters, and perform iterative calculation again.

[0011] As a further optimization scheme for the equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor, in step 3C1, the equivalent magnetic induction of the silicon steel sheet of the stator teeth under sinusoidal magnetic field excitation is , the equivalent magnetic induction of the stator yoke silicon steel sheet excited by the sinusoidal magnetic field is , where L eq is the equivalent magnetic induction of the silicon steel sheet in the stator teeth under sinusoidal magnetic field excitation, a 、 b 、 h are the thickness, width and length of the silicon steel sheet respectively, is the resistivity of silicon steel sheet, L eqyis the equivalent magnetic induction of the stator yoke sector silicon steel sheet excited by the sinusoidal magnetic field, 、 R 1. R 2 is the included angle and inner and outer radius of the sector-shaped silicon steel sheet of the stator yoke.

[0012] As a further optimization scheme for the equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor, step 3C3 solves the stator tooth lumped magnetic induction parameters and the stator yoke lumped magnetic induction parameters based on the calculation results of step 3C2. Specifically, , ,in, For the k The calculated stator tooth lumped magnetic induction parameters are: For the k The lumped magnetic induction parameters of the stator yoke calculated this time are: B t is the magnetic flux density of the stator teeth, B j is the magnetic flux density of the stator yoke, is the effective value of the air gap flux.

[0013] As a further optimization scheme for the equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor, the motor electromagnetic performance parameters calculated in step 6 according to the current operating point of the permanent magnet under the convergence condition include but are not limited to: the fundamental amplitude of the back electromotive force when the motor is no-load and the stator eddy current loss.

[0014] As a further optimization scheme for the equivalent magnetic circuit modeling method of surface-mounted permanent magnet synchronous motor, The fundamental amplitude of the back electromotive force when the motor is unloaded is , E 0 is the fundamental amplitude of the back electromotive force when the motor is unloaded, f is the frequency of the fundamental back EMF, N is the number of series turns of each phase winding, K dp is the winding factor, is the air gap flux waveform coefficient, , is the polar arc coefficient; The stator eddy current loss is , P L is the stator eddy current loss, is the alternating angular frequency of the magnetic flux in the core, is the lumped magnetic induction value of the core, is the effective value of the magnetic flux flowing through the core.

[0015] An electronic device includes a memory and a processor. The memory stores a computer program that runs on the processor. When the processor runs the computer program, the steps of the above-mentioned equivalent magnetic circuit modeling method are executed.

[0016] Compared with the existing equivalent magnetic circuit model based on a single magnetoresistive element, the technical solution provided by the present invention has the following beneficial effects: (1) The equivalent magnetic circuit modeling method of the surface-mounted permanent magnet synchronous motor of the present invention adds a magnetic induction element to the traditional equivalent magnetic circuit modeling method, constructs the eddy current effect model of the core material through the magnetic resistance-magnetic induction coupling model, realizes the characterization of the nonlinear coupling effect inside the motor, and takes the influence of the eddy current effect on the magnetic flux into consideration in the magnetic circuit modeling.

[0017] (2) The equivalent magnetic circuit model of the surface-mounted permanent magnet synchronous motor of the present invention establishes a complex domain analytical model of the magnetomotive force-flux vector based on the phase lag characteristics of the magnetic induction by adding magnetic induction elements. The amplitude and phase relationship between the magnetomotive force and the magnetic flux is fully considered in the magnetic circuit iteration, realizing the law characterization of the core loss angle. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The figure is a schematic diagram of the stator slot type and dimensions of a surface-mounted high-speed permanent magnet synchronous motor provided in one embodiment of the present invention.

[0019] Figure 2 Schematic diagram of calculating the magnetic induction of the core laminations in the stator tooth region provided in one embodiment of the present invention.

[0020] Figure 3 Schematic diagram of calculating the magnetic induction of the core laminations in the stator yoke region provided in one embodiment of the present invention.

[0021] Figure 4 Schematic diagram of an equivalent magnetic circuit model of a surface-mounted high-speed permanent magnet synchronous motor provided in one embodiment of the present invention.

[0022] FIG5( a ) is a flow chart of the method for establishing the equivalent magnetic circuit model of the surface-mounted permanent magnet synchronous motor proposed in the present invention; FIG5( b ) is a flow chart of the iterative calculation of the magnetic induction of the core branch proposed in the present invention.

[0023] Figure 6 It is a comparison diagram between the no-load characteristics calculated by the method of the present invention and the finite element analysis results.

[0024] FIG7( a ) is a comparison diagram of the back electromotive force calculated by the method of the present invention and the finite element analysis results; FIG7( b ) is a comparison diagram of the eddy current loss calculated by the method of the present invention and the finite element analysis results.

[0025] Figure 8 This is a comparison diagram of the d-axis magnetic flux calculated by the method of the present invention and the finite element analysis results. DETAILED DESCRIPTION

[0026] The following examples may enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0027] The present invention provides a method for modeling the equivalent magnetic circuit of a surface-mounted permanent magnet synchronous motor. The magnetic circuit model constructed by this method includes two mutually coupled subsystems: a permanent magnet equivalent magnetic circuit and a permanent magnet external magnetic circuit. The permanent magnet equivalent magnetic circuit is characterized by the demagnetization characteristics of ferromagnetic materials, and the permanent magnet external magnetic circuit is collaboratively modeled using a nonlinear reluctance network and an inductor element, wherein the inductor element is parameter-corrected through iteration of the eddy current effect. By establishing an interactive mechanism between the permanent magnet demagnetization curve and the characteristic curve of the external magnetic circuit, a numerical iteration method is used to accurately solve the permanent magnet operating point. Experimental verification shows that the calculation results of this method are in good agreement with the finite element and experimental measurement results.

[0028] This paper uses a 2-pole surface-mounted high-speed permanent magnet synchronous motor as an example to verify the above-mentioned equivalent magnetic circuit modeling method. Figure 1 Figure 1 is a schematic diagram of the stator slot type and dimensions of the 2-pole surface-mount high-speed permanent magnet synchronous motor. Table 1 shows the specific dimension data of the stator slot type.

[0029] <![CDATA[Slot depth h s0 / mm]]> 0.75 <![CDATA[Tooth boot depth h s1 / mm]]> 0.225 <![CDATA[Tooth groove depth h s2 / mm]]> 10.57 <![CDATA[Top height of the groove h s3 / mm]]> 4 <![CDATA[Slot width b s0 / mm]]> 2 <![CDATA[Tooth groove width b s1 / mm]]> 4.61 <![CDATA[Stator tooth width b t1 / mm]]> 1.25 Silicon steel sheet model 20JNEH1200 The embodiment of the present invention divides the motor structure into three parts based on the topological structure of the two-pole surface-mounted high-speed permanent magnet synchronous motor and the material properties of each part: the permanent magnet magnetic potential source part, the main magnetic circuit part including the air gap magnetic resistance and the iron core magnetic impedance, and the leakage magnetic circuit part. The calculation of the parameters of each of the above branches is explained below.

[0030] First, the parameter calculation method of the permanent magnet magnetic potential source is explained. In a permanent magnet synchronous motor, the permanent magnet often operates in the linear region of the demagnetization curve. The linearized mathematical model can be established as follows: (1) In formula (1), B is the magnetic flux density; B r is the residual magnetic induction intensity, that is, the value of the magnetic induction intensity when the magnetic field intensity is zero, the unit is T; H c is the magnetic induction coercive force, that is, the value of the magnetic field intensity when the magnetic induction intensity is zero, the unit is A / m; is the magnetic permeability of vacuum; is the relative recoil permeability; H is the magnetic field strength.

[0031] Formula (1) can be simplified as: (2) Multiply both ends of formula (2) by the length in the magnetization direction h m have to: (3) In formula (3), F m is the magnetic potential of the permanent magnet, F c is the virtual intrinsic magnetomotive force, A m is the cross-sectional area of ​​the permanent magnet perpendicular to the magnetization direction, R m is the magnetic resistance of the permanent magnet, is the total magnetic flux of the motor.

[0032] Secondly, the parameters of the magnetic resistance part in the magnetic circuit model are calculated based on the flux continuity theorem and the B = / S Calculate the air gap flux density in the motor B δ , stator tooth flux density B t , stator yoke magnetic flux density B j .

[0033] Made of iron core material BH The curve obtains the magnetic field strength corresponding to the magnetic flux density at this time, and according to the magnetic flux path in the motor, the magnetic path length of each part is calculated. L ,Depend on F=HL Calculate the magnetic voltage drop of each nonlinear magnetic resistance element of the motor core, including the air gap magnetic potential F δ , stator teeth magnetic voltage drop F t , stator yoke magnetic voltage drop F j The main magnetic flux through the air gap Divide by the sum of the magnetic potentials on the magnetic circuit to get the total permeability of the main magnetic circuit .

[0034] Furthermore, the leakage permeance can be obtained from the leakage coefficient, that is, (4) In formula (4), is the magnetic flux leakage coefficient, is the per-unit value of leakage magnetic permeability.

[0035] In order to solve the problem of non-sinusoidal distortion of the core magnetic flux waveform caused by the stator salient pole effect, the present invention proposes a magnetic induction calculation method based on eddy current field iterative correction. First, the equivalent magnetic induction of the stator tooth silicon steel sheet under sinusoidal magnetic flux excitation is used as the initial value of the stator tooth magnetic induction element. Combining Faraday's law of electromagnetic induction and Ohm's law, the mapping relationship between the induced voltage, eddy current density and power loss in the silicon steel sheet is established. According to the geometric dimensions of the stator tooth silicon steel sheet, such as Figure 2 As shown, the equivalent magnetic induction L of the silicon steel sheet in the stator teeth under sinusoidal magnetic field excitation can be obtained. eq for: (5) In formula (5), a 、 b 、 h are the thickness, width and length of the silicon steel sheet respectively, is the resistivity of silicon steel sheet.

[0036] Accordingly, the equivalent magnetic induction of the stator yoke sector silicon steel sheet under sinusoidal magnetic flux excitation is taken as the initial value of the stator yoke magnetic induction element, and according to the geometric dimensions of the stator yoke sector silicon steel sheet, as follows: Figure 3 As shown, the equivalent magnetic induction L of the sector-shaped silicon steel sheet of the stator yoke under sinusoidal excitation is eqy The calculation formula is as follows: (6) In formula (6), 、 R 1. R 2 is the included angle and inner and outer radius of the fan-shaped silicon steel sheet of the yoke.

[0037] For the laminated core of the motor, assuming that the magnetic field of all single cores is the same, the lumped magnetic induction parameter of the corresponding part of the motor can be regarded as the parallel connection of the corresponding magnetic induction of each silicon steel sheet. Therefore, the initial value of the magnetic reactance parameter X in the core magnetic impedance model is: (7) In formula (7), n is the number of silicon steel sheets stacked, is the alternating angular frequency of the magnetic flux in the core, , is the lumped magnetic induction value of the core.

[0038] Based on the geometric parameters of the core laminations and the resistivity characteristics of the material, the initial value of the eddy current loss in the core is calculated using formula (8), and the eddy current energy distribution law is quantified. Subsequently, the magnetic induction parameters of each magnetic circuit branch of the core are dynamically adjusted through an iterative algorithm, which can gradually approximate the eddy current effect corresponding to the nonlinear magnetic flux density waveform under actual working conditions. Formula (8) is: (8) By connecting the magnetic guide and the magnetic induction element in the embodiment of the present invention, the following can be constructed: Figure 4 The equivalent magnetic circuit model of the permanent magnet synchronous motor is shown. Figure 4 middle, is the magnetic flux corresponding to the permanent magnet, R m is the internal resistance of the permanent magnet, is the total magnetic flux of the motor, is the leakage magnetic reluctance, is the air gap reluctance, R t is the stator tooth reluctance, L t is the stator tooth magnetic induction, R j is the stator yoke reluctance, L j is the stator yoke magnetic induction.

[0039] At this point, the basic framework for equivalent magnetic circuit modeling based on magnetic induction has been established. The next step is to solve this model and, based on this, further solve the electromagnetic performance of the permanent magnet synchronous motor. The iterative approach to establishing the equivalent magnetic circuit model proposed in this invention is shown in Figure 5(a). The main steps are: Step 1: Provide the basic geometric parameters of the motor, the distributed topology of the stator winding and the core material BH Curve; Step 2: Initialize the permanent magnet operating point of the motor to be, and calculate the total magnetic flux of the motor according to the initial value of the permanent magnet operating point , leakage flux and air gap main flux ; Step 3: Establish a motor equivalent magnetic circuit model that includes the permanent magnet equivalent magnetic circuit and the permanent magnet external magnetic circuit: Step 3A: Build Figure 4 The motor equivalent magnetic circuit model shown is characterized by the permanent magnet internal resistance connected in parallel at both ends of the permanent magnet flux source, the leakage magnetic circuit is characterized by the leakage magnetic resistance connected in parallel at both ends of the permanent magnet internal resistance, the air gap magnetic circuit is characterized by the air gap magnetic resistance connected in series at both ends of the iron core magnetic flux path, the stator tooth magnetic impedance network is characterized by two magnetic resistance-magnetic induction series branches connected in series on the stator tooth magnetic flux path, and the stator yoke magnetic impedance network is characterized by a magnetic resistance-magnetic induction series branch connected in series on the stator yoke magnetic flux path. The stator tooth magnetic impedance network and the stator yoke magnetic impedance network constitute the iron core magnetic impedance network, and the leakage magnetic circuit, the air gap magnetic circuit and the iron core magnetic impedance network constitute the permanent magnet external magnetic circuit; Step 3B: According to the core material BH The curve characteristic is formula (3) given the internal resistance of the permanent magnet; the total magnetic flux corresponding to the initial value of the permanent magnet working point obtained in step 2 is , leakage flux and air gap main flux Given a magnetic resistance value in the external magnetic circuit of the permanent magnet of the motor, the magnetic resistance value in the external magnetic circuit of the permanent magnet includes leakage magnetic resistance, air gap magnetic resistance, stator tooth magnetic resistance, and stator yoke magnetic resistance. The leakage magnetic resistance is given according to the leakage magnetic flux and the corresponding magnetic flux density. The air gap magnetic resistance is given according to the air gap main magnetic flux and the corresponding magnetic flux density. The stator tooth magnetic resistance is given according to the stator tooth size parameters and the stator tooth magnetic flux density. The stator yoke magnetic resistance is given according to the stator yoke size parameters and the stator yoke magnetic flux density. The magnetic flux density of the stator teeth is calculated based on the main magnetic flux and the tooth size parameters, and the magnetic flux density of the stator yoke is calculated based on the main magnetic flux and the yoke size parameters. Step 3C: Using the equivalent magnetic inductions of the stator teeth and stator yoke under sinusoidal magnetic field excitation as the initial values ​​of the stator tooth magnetic induction and the stator yoke magnetic induction, the stator tooth magnetic induction and the stator yoke magnetic induction are iteratively optimized through the eddy current effect. The eddy current effect in the stator and rotor cores of the permanent magnet motor is reflected by the magnetic induction elements in the core magnetic impedance network. Step 4: Obtain the leakage permeance and main permeance of the motor from the magnetic voltage drop of each magnetic resistance and magnetic induction element in the permanent magnet external magnetic circuit, and calculate the per-unit value of the leakage permeance and the per-unit value of the main magnetic permeability Then the current operating point of the motor permanent magnet is obtained; Step 5: Determine whether the difference between the current motor operating point calculated in step 4 and the initial value of the permanent magnet operating point meets the convergence condition. If so, the iterative process is completed; if not, return to step 2, update the initial value of the permanent magnet operating point to the current permanent magnet operating point, and then iterate again. Repeat steps 2 to 5 until the convergence condition is met.

[0040] Step 6: After the convergence conditions of the motor are met, the electromagnetic performance parameters of the motor can be calculated based on the permanent magnet operating point that meets the convergence conditions. The electromagnetic performance parameters include but are not limited to the back electromotive force fundamental amplitude and stator eddy current loss when the motor is no-load.

[0041] The permanent magnet operating point is essentially the geometric intersection of the permanent magnet demagnetization curve and the characteristic curve of the external magnetic circuit. Its coordinate solution represents the steady-state equilibrium condition of the magnetic circuit system. By establishing the interaction mechanism between the permanent magnet demagnetization curve and the characteristic curve of the permanent magnet external magnetic circuit, the permanent magnet operating point is solved by combining the permanent magnet demagnetization curve and the characteristic curve of the permanent magnet external magnetic circuit. Step 2 is specifically as follows: Step 2A, determine whether the motor is running under load. If the motor is running without load, go to step 2B. If the motor is running under load, go to step 2C. Step 2B: The motor is in no-load condition. The normalized permanent magnet working equation and the external magnetic circuit characteristic equation are combined to obtain: (9) In formula (9), f m0is the per-unit value of the permanent magnet's magnetomotive force when it is no-load, is the per-unit value of the main magnetic flux when no-load, is the per-unit value of the main magnetic permeance, is the per-unit value of leakage magnetic permeability, is the per-unit value of the equivalent magnetic permeability of the permanent magnet external magnetic circuit; Solving formula (9) yields: (10) In formula (10), b m0 is the per-unit value of the magnetic flux density generated by the permanent magnet when it is no-load, h m0 is the per-unit value of the magnetic field intensity generated by the permanent magnet when it is unloaded, ( b m0， h m0 ) is the no-load operating point of the permanent magnet, based on which the total magnetic flux generated by the permanent magnet when no-load can be obtained , leakage flux and air gap main flux : (11) Step 2C: The motor is in load condition. Under load condition, the direct axis armature magnetic potential must be taken into account. f ad The magnetic potential modulation effect of the direct-axis armature magnetic potential f ad Calculated based on the distributed topology of the stator winding; according to the principle of magnetic field superposition, the external magnetic circuit characteristic curve produces an axial offset, and the offset is determined by the leakage flux coefficient Corrected equivalent magnetic potential f adn =f ad / The modified magnetic potential balance equation can be expressed as: (12) In formula (12), f mN is the per-unit value of the permanent magnet's magnetomotive force when loaded, It is the per-unit value of the main magnetic flux when loaded.

[0042] Solving formula (12) yields: (13) In formula (13), b mN is the per-unit value of the magnetic flux density generated by the permanent magnet when loaded, h mN is the per-unit value of the magnetic field strength generated by the permanent magnet when loaded, (b mN， h mN ) is the load operating point of the permanent magnet, based on which the total magnetic flux generated by the permanent magnet under load can be obtained , leakage flux and air gap main flux : (14) Based on the above overall iterative approach, the process of iterating the core magnetic induction elements representing eddy current loss, i.e., the stator tooth magnetic induction and the stator yoke magnetic induction, toward the true value in the embodiment of the present invention is shown in FIG5( b ). Step 3C is specifically as follows: Step 3C1: Calculate the theoretical initial values ​​of the magnetic induction elements of the stator teeth and yoke under sinusoidal magnetic field excitation using the core size parameters and equations (5) and (6); Step 3C2: Add the stator teeth and yoke magnetic induction elements after assigning theoretical initial values ​​to the magnetic impedance model of the stator core, and solve the nonlinear equations of the magnetic circuit model at the permanent magnet working point. Solve equation (10) when no-load and solve equation (13) when loaded to calculate the magnetic flux density of the stator teeth at this time. B t and magnetic field strength H t , magnetic flux density of the stator yoke B j and magnetic field strength H j , and the effective value of the air gap flux at this time ; Step 3C3: Based on the calculation results of 3C2, the lumped magnetic induction parameters of the stator teeth and stator yoke are obtained: (15) (16) In formula (15) and formula (16), a 、 b 、 h are the thickness, width and length of the silicon steel sheet respectively, is the resistivity of silicon steel sheet, For the k The calculated total magnetic induction value of the stator teeth is: For the k The calculated lumped magnetic induction value of the stator yoke; Step 3C4: Compare and The error between and Is the error between them close to 0? If not, return to step A2 and update the initial values ​​of the magnetic induction elements of the stator teeth and yoke to and And perform iterative calculation again; otherwise, complete the iteration and obtain the final magnetic induction value of the iron core magnetic impedance network.

[0043] In order to verify the effectiveness of the proposed equivalent magnetic circuit modeling method for a surface-mounted permanent magnet synchronous motor, the present invention established an example Figure 1 The equivalent magnetic circuit model of the surface-mounted high-speed permanent magnet synchronous motor is shown in the figure, and the electromagnetic parameters of the motor are solved using this model to prove that the present invention has high accuracy in solving motor performance and calculating core eddy current loss.

[0044] When the motor is running at no load, the static magnetic circuit parameters obtained from the equivalent magnetic circuit model including the magnetic induction element are compared and analyzed with the finite element simulation. The fundamental amplitude of the back EMF when the motor is running at no load can be calculated using the following formula: (17) In formula (17), f is the frequency of the fundamental back EMF, N is the number of series turns of each phase winding, K dp is the winding factor, is the air gap flux waveform coefficient, which comprehensively reflects the pole arc coefficient Correction effect on the sinusoidality of air gap flux. The calculation formula is: (18) Figure 6 The comparison diagram of the no-load characteristics calculated by the method of the present invention and the finite element analysis results respectively compares the no-load air gap tangential flux density of the motor at rated speed. B R0 , no-load back electromotive force E 0 and stator iron loss P Fe0 By comparing the three main parameters, it can be found that after adding the magnetic induction element to the magnetic circuit, the calculated values ​​of the no-load air gap flux density and back electromotive force are slightly improved, especially the no-load air gap flux density, which is closer to the calculation results obtained by finite element simulation; the change in core loss is larger than the other two, because the eddy current loss value iteratively calculated by the magnetic induction element is more accurate, so the iron loss obtained on this basis is almost consistent with that calculated by finite element simulation.

[0045] By further changing the parameters of the magnetic circuit, the no-load back electromotive force and eddy current loss can be compared over a wider speed range. Based on the vector magnetic circuit theory, the eddy current loss corresponding to the stator teeth and stator yoke can be calculated separately. The calculation formula is: (19) In formula (19), is the alternating angular frequency of the magnetic flux in the core; is the lumped magnetic induction value of the corresponding part of the core, is the effective value of the magnetic flux flowing through the core. When the eddy current loss of the stator teeth is taken into account, Take the lumped magnetic induction parameters of the stator teeth, Take the effective value of the magnetic flux flowing through the stator teeth; when taking into account the eddy current loss of the stator yoke, Take the lumped magnetic induction parameters of the stator yoke, Take the effective value of the magnetic flux flowing through the stator yoke.

[0046] Figure 7(a) compares the back EMF calculated by the method of the present invention with the results of finite element analysis, and Figure 7(b) compares the eddy current loss calculated by the method of the present invention with the results of finite element analysis. The vector magnetic circuit iteration algorithm shows excellent accuracy in the no-load back EMF waveform. At the same time, when calculating eddy current loss, the results obtained by the vector magnetic circuit iteration algorithm are more accurate than those of the equivalent magnetic circuit method, almost completely overlapping with the results of finite element simulation, with a maximum error of only 0.3%. The change trend is also completely consistent with the finite element simulation, achieving a more rigorous magnetic circuit iteration process.

[0047] When the motor is running under load, if the load current remains at rated working condition, the continuous increase of motor speed will lead to a significant increase of eddy current loss. Figure 8 As shown in the figure, as the speed increases, the nonlinear growth of eddy current loss directly leads to d The traditional equivalent magnetic circuit model cannot accurately describe the physical process of axial flux attenuation due to the lack of dynamic loss coupling mechanism. The eddy current effect coupling modeling method based on magnetic induction elements realizes the magnetic circuit analysis and calculation of this phenomenon by adding representative eddy current losses into the iterative process of magnetic flux.

[0048] Based on vector magnetic circuit theory, the present invention utilizes an equivalent magnetic circuit model to quickly and accurately calculate the electromagnetic performance of a permanent magnet synchronous motor. This significantly reduces computational time and memory usage compared to finite element simulation. Compared to traditional equivalent magnetic circuit models, this method takes into account the nonlinear coupling effects within the motor, enabling more accurate calculations of motor performance parameters. Using the equivalent magnetic circuit model of the present invention, the core portion of the permanent magnet synchronous motor is modeled using a "reluctance-induction" series connection. This allows for the consideration of the impact of eddy current loss on magnetic flux distribution and more accurate calculations of eddy current loss.

[0049] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed in the present invention should be included in the protection scope recorded in the claims.

Claims

1. A method for modeling an equivalent magnetic circuit of a surface-mounted permanent magnet synchronous motor, characterized in that: include: Step 1: Obtain initialization parameters of the surface-mounted permanent magnet synchronous motor; Step 2: Obtain the initial value of the permanent magnet working point by the interaction mechanism between the permanent magnet demagnetization curve and the permanent magnet external magnetic circuit characteristic curve, and calculate the total magnetic flux, leakage magnetic flux and air gap main magnetic flux based on the initial value of the permanent magnet working point; Step 3: Establish a motor equivalent magnetic circuit model including a permanent magnet equivalent magnetic circuit and a permanent magnet external magnetic circuit based on the magnetic flux path. The permanent magnet external magnetic circuit includes a leakage magnetic circuit, an air gap magnetic circuit, and an iron core magnetic impedance network. The magnetic resistance in the motor equivalent magnetic circuit model is given according to the total magnetic flux, leakage magnetic flux, and air gap main magnetic flux calculated in step 2, and the magnetic induction in the permanent magnet external magnetic circuit is iteratively optimized. Step 4, calculating the leakage permeance and the main permeance from the magnetic voltage drop of each magnetic component in the external magnetic circuit of the permanent magnet, and calculating the current operating point of the permanent magnet according to the per-unit values ​​of the leakage permeance and the main permeance; Step 5: When the difference between the current working point of the permanent magnet and the initial value of the permanent magnet working point meets the convergence condition, the iterative process ends; otherwise, the process returns to step 2, updates the initial value of the permanent magnet working point to the current working point of the permanent magnet, and iterates again until the convergence condition is met. Step 6: Calculate the electromagnetic performance parameters of the motor according to the current operating point of the permanent magnet that meets the convergence condition.

2. The equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor according to claim 1, characterized in that: The surface-mounted permanent magnet synchronous motor initialization parameters obtained in step 1 include: motor geometric parameters, a distributed topology of the stator winding, and a BH curve of the core material.

3. The equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2A, determine whether the motor is running under load. If the motor is running without load, go to step 2B. If the motor is running under load, go to step 2C. Step 2B, combine the normalized permanent magnet working equation and the external magnetic circuit characteristic equation, and solve the permanent magnet no-load working point (b m0， h m0 ) as the initial value of the permanent magnet working point, , calculate the total magnetic flux generated by the permanent magnet when no-load based on the permanent magnet no-load operating point , leakage flux and air gap main flux , Among them, b m0 is the per-unit value of the magnetic flux density generated by the permanent magnet when it is no-load, h m0 is the per-unit value of the magnetic field intensity generated by the permanent magnet when it is unloaded, is the per-unit value of the main magnetic flux when no-load, f m0 is the per-unit value of the permanent magnet magnetomotive force when no load is applied, λ n B is the per-unit value of the equivalent magnetic permeability of the permanent magnet external magnetic circuit, r is the residual magnetic induction intensity, A m is the cross-sectional area of ​​the permanent magnet perpendicular to the magnetization direction; Step 2C: Calculate the direct-axis armature magnetic potential f based on the distributed topology of the stator winding. ad , taking into account the direct-axis armature magnetic potential f ad The magnetic potential modulation effect is used to modify the magnetic potential balance equation, and the load operating point of the permanent magnet is solved by the modified magnetic potential balance equation (b mN， h mN ), , take the load operating point of the permanent magnet as the initial value of the permanent magnet operating point, and calculate the total magnetic flux generated by the permanent magnet when loaded according to the load operating point of the permanent magnet , leakage flux and air gap main flux , , where b mN is the per-unit value of the magnetic flux density generated by the permanent magnet when loaded, h mN is the per-unit value of the magnetic field strength generated by the permanent magnet when loaded, is the per-unit value of the main magnetic flux when loaded, f mN is the per-unit value of the permanent magnet's magnetomotive force when loaded, is the corrected equivalent magnetic potential, , is the magnetic flux leakage coefficient.

4. The equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3A: characterizing the permanent magnet equivalent magnetic circuit by a permanent magnet internal resistance connected in parallel at both ends of the permanent magnet magnetic flux source, characterizing the leakage magnetic circuit by a leakage magnetic resistance connected in parallel at both ends of the permanent magnet internal resistance, characterizing the air gap magnetic circuit by an air gap magnetic resistance connected in series at both ends of the iron core magnetic flux path, characterizing the stator tooth magnetic impedance network by two magnetic resistance-magnetic induction series branches connected in series on the stator tooth magnetic flux path, and characterizing the stator yoke magnetic impedance network by a magnetic resistance-magnetic induction series branch connected in series on the stator yoke magnetic flux path. The stator tooth magnetic impedance network and the stator yoke magnetic impedance network constitute the iron core magnetic impedance network; Step 3B, determining the internal resistance of the permanent magnet according to the BH curve characteristics of the core material, determining the leakage magnetic reluctance according to the leakage magnetic flux and the corresponding magnetic flux density, determining the air gap magnetic reluctance according to the air gap main magnetic flux and the corresponding magnetic flux density, determining the stator tooth magnetic reluctance according to the stator tooth size parameters and the corresponding magnetic flux density, and determining the stator yoke magnetic reluctance according to the stator yoke size parameters and the corresponding magnetic flux density, wherein the magnetic flux density corresponding to the stator teeth is calculated based on the main magnetic flux and the stator tooth size parameters, and the magnetic flux density corresponding to the stator yoke is calculated based on the main magnetic flux and the stator yoke size parameters; In step 3C, the equivalent magnetic inductions of the stator teeth and the stator yoke under sinusoidal magnetic field excitation are the stator tooth magnetic induction and the stator yoke magnetic induction initial values, respectively, and the stator tooth magnetic induction and the stator yoke magnetic induction are iteratively optimized.

5. The equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor according to claim 4, characterized in that: The step 3C is specifically as follows: Step 3C1, calculating the equivalent magnetic induction of the silicon steel sheets of the stator teeth and stator yoke under sinusoidal magnetic field excitation based on the geometric parameters of the motor, and obtaining the initial values ​​of the stator tooth magnetic induction and the stator yoke magnetic induction; Step 3C2, based on the initial values ​​of the magnetic induction of the stator teeth and stator yoke, simultaneously solve the nonlinear equations of the magnetic circuit model of the permanent magnet operating point to calculate the magnetic flux density and magnetic field intensity of the stator teeth, the magnetic flux density and magnetic field intensity of the stator yoke, and the effective value of the air gap magnetic flux; Step 3C3, solving the lumped magnetic induction parameters of the stator teeth and the lumped magnetic induction parameters of the stator yoke based on the calculation results of step 3C2; Step 3C4: When the error between the currently solved stator tooth lumped magnetic induction parameters and the previously solved stator tooth lumped magnetic induction parameters approaches 0 and the error between the currently solved stator yoke lumped magnetic induction parameters and the previously solved stator yoke lumped magnetic induction parameters approaches 0, the currently solved stator tooth lumped magnetic induction parameters and the stator yoke lumped magnetic induction parameters are taken as the final solution; otherwise, return to step 3C2, update the initial values ​​of the stator tooth magnetic induction and the stator yoke magnetic induction to the currently solved stator tooth lumped magnetic induction parameters and the stator yoke lumped magnetic induction parameters, and perform iterative calculation again.

6. The equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor according to claim 5, characterized in that: In step 3C1, the equivalent magnetic induction of the stator teeth silicon steel sheet under the sinusoidal magnetic field excitation is The equivalent magnetic induction of the stator yoke silicon steel sheet excited by the sinusoidal magnetic field is , where L eq is the equivalent magnetic induction of the silicon steel sheet in the stator teeth under sinusoidal magnetic field excitation, a, b, and h are the thickness, width, and length of the silicon steel sheet respectively. is the resistivity of silicon steel sheet, L eqy is the equivalent magnetic induction of the stator yoke sector silicon steel sheet excited by a sinusoidal magnetic field, θ, R1, and R2 are the angle and inner and outer radii of the stator yoke sector silicon steel sheet.

7. The equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor according to claim 6, characterized in that: In step 3C3, based on the calculation results of step 3C2, the lumped magnetic induction parameters of the stator teeth and the lumped magnetic induction parameters of the stator yoke are solved, specifically: , ,in, is the lumped magnetic induction parameter of the stator teeth calculated for the kth time, is the lumped magnetic induction parameter of the stator yoke calculated for the kth time, B t is the magnetic flux density of the stator teeth, B j is the magnetic flux density of the stator yoke, is the effective value of the air gap flux.

8. The equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor according to claim 7, characterized in that: The electromagnetic performance parameters of the motor calculated in step 6 according to the current working point of the permanent magnet under the convergence condition include but are not limited to: the fundamental amplitude of the back electromotive force when the motor is no-load and the stator eddy current loss.

9. The equivalent magnetic circuit modeling method of a surface-mounted permanent magnet synchronous motor according to claim 8, characterized in that: The fundamental amplitude of the back electromotive force when the motor is unloaded is , E0 is the fundamental amplitude of the back electromotive force when the motor is unloaded, f is the frequency of the fundamental back electromotive force, N is the number of series turns of each phase winding, K dp is the winding factor, is the air gap flux waveform coefficient, , α i is the polar arc coefficient; The stator eddy current loss is , P L is the stator eddy current loss, is the alternating angular frequency of the magnetic flux in the core, is the lumped magnetic induction value of the core, is the effective value of the magnetic flux flowing through the core.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program running on the processor, and the processor executes the steps of the equivalent magnetic circuit modeling method according to claim 1 when running the computer program.

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