Method and system for verifying mathematical model of high-saturation permanent magnet synchronous motor

Abstract

The invention discloses a verification method and system for a mathematical model of a high-saturation permanent magnet synchronous motor. The method comprises the following steps: constructing the mathematical model of the high-saturation permanent magnet synchronous motor; testing the mathematical model of the high-saturation permanent magnet synchronous motor by adopting motor twin-trawling loading; specifically, in a no-load operation state, a back electromotive force amplitude is obtained, and a permanent magnet flux linkage in a no-load state is calculated; meanwhile, the temperature of the permanent magnet is detected; in a load state, analyzing torque data under different loads, and eliminating temperature influence to obtain variation trends of magnetic linkages under different loads; a high-frequency voltage injection method is adopted, high-frequency voltages with different amplitudes and frequencies are injected into a d axis and a q axis respectively, and the influence of magnetic saturation and desaturation effects on the flux linkage and inductance of the permanent magnet is verified by comparing, identifying and analyzing the change condition of flux linkage components of the d axis and the q axis. The method has the advantages of simple operation, accurate verification and the like.

Description

Technical Field

[0001] The present invention mainly relates to the technical field of permanent magnet synchronous motors, and particularly relates to a method and system for verifying a mathematical model of a high-saturation permanent magnet synchronous motor. Background Art

[0002] Due to the magnetic saturation effect of the motor, the electromagnetic parameters will change non-linearly, which will further affect the output performance and control accuracy of the motor. Therefore, researchers at home and abroad have deeply explored the influence of the magnetic saturation effect on the motor in order to further optimize the design of the motor body or the control algorithm of the drive system, described the magnetic field distribution and magnetic circuit saturation characteristics of the motor under different working conditions, and established a more accurate mathematical model. Among them, the mathematical model considering the magnetic saturation effect is usually established based on physical principles and experimental data, which can predict the influence of the magnetic saturation effect on the motor performance and provide accurate input instructions for the control algorithm to minimize the problems such as errors and performance degradation caused by the magnetic saturation effect.

[0003] In order to analyze the relationship between the electromagnetic parameters and the magnetic saturation effect in the motor, relevant scholars have conducted research from different perspectives. As early as the 1980s, Ahmed M et al. measured the relationship between the power and load angle of a small salient-pole motor through experiments, and verified the saturation effect on the d-axis and q-axis magnetic paths. However, due to the limited experimental conditions at that time, the change trend of the relevant parameters with the magnetic saturation effect was not verified. In order to separately analyze the influence of the magnetic saturation effect on the armature magnetic field or the excitation magnetic field, Yu Shi et al. gave a detailed physical description of the magnetic saturation phenomenon in the PMSM and discussed the causes of the magnetic saturation effect. According to the relationship between the core permeability and the magnetic field strength, a method of decoupling analysis of the armature magnetic flux linkage and the permanent magnet magnetic flux linkage of the PMSM under the saturated state of the core by using the frozen permeability method was proposed. However, this method can only be verified from the simulation perspective, and the influence of magnetic saturation on the permanent magnet magnetic flux linkage has not been directly verified through experiments. Yelong Yu et al. verified through experiments that when vector control is adopted for the PMSM, the negative increase of the d-axis current will cause the dq-axis inductance to increase due to the demagnetization effect. At the same time, when the q-axis current increases, the dq-axis inductance will decrease due to the magnetic saturation effect. However, this method ignores the influence of temperature and magnetic saturation effect on the permanent magnet.

[0004] In summary, the extensive research on the magnetic saturation effect provides important theoretical and technical support for the precise control of PMSM. By deeply studying the mechanism and influence of the magnetic saturation effect, researchers continuously propose innovative designs and control methods to overcome the challenges brought by magnetic saturation. However, for HSPMSM, the changes in motor parameters caused by the magnetic saturation effect are more complex than those of traditional motors, including the change of the permanent magnet flux linkage. So far, there is little research on the influence of the magnetic saturation effect on the permanent magnet flux linkage. How to comprehensively consider the influence of the magnetic saturation effect on parameters and how to verify the mathematical model of HSPMSM through experiments still need further research. Summary of the Invention

[0005] In view of the technical problems existing in the prior art, the present invention provides a verification method and system for the mathematical model of a high-saturation permanent magnet synchronous motor with simple operation and accurate verification.

[0006] To solve the above technical problems, the technical solution proposed by the present invention is as follows:

[0007] A verification method for the mathematical model of a high-saturation permanent magnet synchronous motor includes the steps of:

[0008] Based on the traditional mathematical model of the permanent magnet synchronous motor, considering the parameter changes caused by the magnetic saturation effect, a mathematical model of the high-saturation permanent magnet synchronous motor is constructed;

[0009] Build an IPMSM experimental platform and use motor-to-motor loading to test the mathematical model of the high-saturation permanent magnet synchronous motor. Specifically, in the no-load operation state, obtain the back electromotive force amplitude, calculate the permanent magnet flux linkage at no-load, and simultaneously detect the permanent magnet temperature; in the load state, through the analysis of torque data under different loads, obtain the change trend of the flux linkage under different loads after excluding the temperature influence;

[0010] Adopt the high-frequency voltage injection method, inject high-frequency voltages with different amplitudes and frequencies on the d-axis and q-axis respectively, and through comparison and identification, analyze the change of the dq-axis flux linkage components to verify the influence of magnetic saturation and demagnetization effects on the permanent magnet flux linkage and inductance.

[0011] Preferably, the change of the permanent magnet flux linkage is obtained by directly measuring the torque and current, and the specific calculation formula is:

[0012]

[0013] where Te' is the electromagnetic torque considering the magnetic saturation effect; i q is the q-axis current; p is the number of pole pairs; is the d-axis component of the permanent magnet flux linkage.

[0014] Preferably, the specific process of injecting high-frequency voltages with different amplitudes and frequencies into the d-axis and q-axis respectively by using the high-frequency voltage injection method is as follows:

[0015] Inject a high-frequency voltage with an amplitude of 4V and a frequency of 400Hz into the d-axis, and inject a high-frequency voltage with an amplitude of 4V and a frequency of 500Hz into the q-axis; for the d case where i q = 0 and i > 0, d and for the case where i q < 0 and i = 0, perform identification; where i d , i q are the d-axis and q-axis currents respectively. is the d-axis inductance; the superscript (i d , i q ) represents the real-time values of each parameter under different d-axis and q-axis currents.

[0016] According to the d-axis and q-axis voltage equations, when i d = 0, the influence of the resistance on the d-axis voltage v d can be excluded, and when i q = 0, the influence of the resistance on the q-axis voltage v q can be excluded; calculate the variation of the q-axis component of the permanent magnet flux linkage with i q and the variation of the d-axis component of the permanent magnet flux linkage with i d .

[0017] Draw the conclusion that: will increase with the increase of i q due to the magnetic saturation effect, will increase with the decrease of i d due to the demagnetization saturation effect.

[0018] Preferably, the construction process of the high-saturation permanent magnet synchronous motor mathematical model is as follows:

[0019] Improve the traditional electromagnetic torque mathematical model to obtain the mathematical model of the electromagnetic torque of the HSPMSM in the d-q axis coordinate system as:

[0020]

[0021] In the formula: Te' is the electromagnetic torque considering the magnetic saturation effect; L △ is the difference between the d-axis and q-axis inductances; L d , L q are the d-axis and q-axis inductances respectively; the superscript (i d , i q)Indicates the real-time values of each parameter under different dq-axis currents;

[0022] When considering the phenomenon that the phase of the permanent magnet flux linkage changes due to the magnetic saturation effect, the electromagnetic torque is composed of three torque components, namely:

[0023]

[0024] In the formula: Te' pmd is and i q The d-axis component of the permanent magnet torque generated by the interaction; Te p ' mq is and i d The q-axis component of the permanent magnet torque generated by the interaction; Te' rel is the reluctance torque after considering the magnetic saturation effect; where, when the HSPMSM operates in the motor mode, Te' pmd and Te' rel are positive, while Te' pmq is negative; when using the vector control technology with i d = 0, Te' rel and Te p ' mq are zero, then equation (29) is changed to:

[0025]

[0026] Preferably, the specific process of obtaining equation (29) is as follows:

[0027] The mathematical model of the permanent magnet synchronous motor includes inductance and permanent magnet flux linkage, and its dq-axis voltage equations are as follows:

[0028]

[0029] In the formula: v d , v q are the dq-axis voltages respectively; i d , i q are the dq-axis currents respectively; L d , L q are the dq-axis inductances respectively, specifically:

[0030]

[0031] It can be seen from equation (2) that there are fluxes provided by the armature current and the permanent magnet in the d-axis direction, while there is only the flux provided by the armature current in the q-axis direction. Then the dq-axis flux linkage equations under steady state are:

[0032]

[0033] where: ψ d , ψ q are the total magnetic fluxes of the d - and q - axes respectively; meanwhile, according to the law of conservation of energy, the electromagnetic torque expression of the motor in the dq - axis coordinate system is obtained as:

[0034]

[0035] where: Te is the electromagnetic torque; p is the number of pole pairs;

[0036] In the HSPMSM, the permanent - magnet flux linkage and inductance will change significantly with the change of dq - axis current at the same time; therefore, the parameter changes caused by the magnetic saturation effect need to be considered in the traditional dq - axis mathematical model, and Equation (3) can be rewritten as:

[0037]

[0038] where: the superscript (i d , i q ) represents the real - time values of each parameter under different dq - axis currents;

[0039] Substitute Equation (26) into Equation (4) to improve the traditional electromagnetic torque mathematical model, and the mathematical model of the electromagnetic torque of HSPMSM in the dq - axis coordinate system is obtained as:

[0040]

[0041] where: Te' is the electromagnetic torque considering the magnetic saturation effect.

[0042] Preferably, it can be seen from Equation (4) that the electromagnetic torque output by the PMSM can be divided into two parts, namely, the permanent - magnet torque generated by the interaction between the armature reaction magnetic field and the permanent magnet, and the reluctance torque generated by the interaction between the magnetic field and the rotor with different dq - axis reluctances. The expressions of the two torque components are respectively:

[0043]

[0044] where: L △ is the difference in inductance between the d - and q - axes, that is, L △ = L d - L q ; Te pm , Te rel are the permanent - magnet torque and the reluctance torque respectively; when ψ f and L △ are constant, Te pm is proportional to i q , and Te rel is proportional to the d - and q - axis currents respectively.

[0045] Preferably, during the operation of the motor, the real-time value of the inductance is obtained, and a parameter identification method based on high-frequency voltage injection is adopted;

[0046] It is assumed that the injected high-frequency dq-axis voltages are respectively expressed as:

[0047]

[0048] In the formula: v dh and v qh are respectively the injected high-frequency dq-axis voltages; v dhf , f hd and θ vd are respectively the amplitude, frequency and phase of the injected high-frequency d-axis voltage; v qhf , f hq and θ vq are respectively the voltage, frequency and phase of the injected high-frequency q-axis current; At the same time, the injected high-frequency dq-axis voltages will respectively excite high-frequency dq-axis currents with the same frequency as them, that is:

[0049]

[0050] In the formula: i dh and i qh are respectively the high-frequency dq-axis current signals; i dhf and θ id are respectively the amplitude and phase of the high-frequency d-axis current; i qhf and θ iq are respectively the amplitude and phase of the high-frequency q-axis current;

[0051] The voltage and current in the system are band-pass filtered, and the discrete Fourier transform is used to process the signal to obtain the amplitude and phase of the high-frequency signal; Then, according to the vector relationship, the relationship between the stator resistance R s , the dq-axis inductances and the high-frequency signal is:

[0052]

[0053] The present invention also discloses a computer program product, including a computer program, and the steps of the above-mentioned method are executed when the computer program is run by a processor.

[0054] The present invention further discloses a computer-readable storage medium, on which a computer program is stored, and the steps of the above-mentioned method are executed when the computer program is run by a processor.

[0055] The present invention also discloses a verification system for the mathematical model of a high-saturation permanent magnet synchronous motor, which includes a memory and a processor connected to each other. A computer program is stored on the memory, and when the computer program is run by the processor, it executes the steps of the method described above.

[0056] Compared with the prior art, the advantages of the present invention are as follows:

[0057] The verification method for the mathematical model of the high-saturation permanent magnet synchronous motor of the present invention is based on the traditional mathematical model of the permanent magnet synchronous motor, considering the parameter changes caused by the magnetic saturation effect, and constructs a mathematical model of the high-saturation permanent magnet synchronous motor; builds an IPMSM experimental platform, and uses motor back-to-back loading to test the mathematical model of the high-saturation permanent magnet synchronous motor; specifically, in the no-load operation state, obtains the back electromotive force amplitude, and calculates the permanent magnet flux linkage at no load; and simultaneously detects the temperature of the permanent magnet; in the load state, through the analysis of the torque data under different loads, obtains the change trend of the flux linkage under different loads after excluding the temperature influence; adopts the high-frequency voltage injection method, injects high-frequency voltages with different amplitudes and frequencies on the d-axis and q-axis respectively, and through comparison and identification, analyzes the change of the dq-axis flux linkage components to verify the influence of the magnetic saturation and desaturation effects on the permanent magnet flux linkage and inductance. The method of the present invention is simple to operate and accurate in verification. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is the saturation curve diagram of the PMSM of the present invention.

[0059] Figure 2 It is the magnetic permeability curve diagram of different iron core materials of the present invention.

[0060] Figure 3 It is the dq-axis magnetic circuit diagram of the PMSM of the present invention; (a) is IPMSM; (b) is SPMSM.

[0061] Figure 4 It is the influence diagram of the dq-axis current on the iron core magnetic flux density in the present invention; (a) i d =0, i q =0; (b) i d =-i sr ,i q =0; (c) i d =0, i q =i sr ; (d) i d =-i sr ,i q =i sr .

[0062] Figure 5 It is the change diagram of the dq-axis inductance with the dq-axis current respectively in the present invention; (a) is L d 、Lq With the change of i q variation diagram; (b) is for L d and L q With the change of i d variation diagram.

[0063] Figure 6 This is the vector relationship diagram of high-frequency voltage and current in the present invention.

[0064] Figure 7 This is the parameter identification control block diagram based on high-frequency voltage injection in the present invention.

[0065] Figure 8 This is the irreversible loss and reversible loss diagram in the present invention.

[0066] Figure 9 This is the equivalent magnetic circuit diagram of the PMSM permanent magnet in the present invention.

[0067] Figure 10 This is the schematic diagram of frozen magnetic permeability in the present invention.

[0068] Figure 11 This is the distribution diagram of the magnetic force lines of the permanent magnet in the present invention; (a) is no-load; (b) is load.

[0069] Figure 12 This is the phase diagram of the permanent magnet flux linkage in the present invention.

[0070] Figure 13 This is the variation diagram of the dq-axis components of the permanent magnet flux linkage with the dq-axis current in the present invention; (a) is for ψ fd and ψ fq With the change of i q variation diagram; (b) is for ψ fd and ψ fq With the change of i d variation diagram.

[0071] Figure 14 This is the diagram of the motor test platform in the present invention.

[0072] Figure 15 This is the experimental waveform diagram in the present invention; (a) is the back electromotive force waveform diagram; (b) is the torque waveform diagram.

[0073] Figure 16 This is the permanent magnet temperature diagram in the present invention; (a) is no-load; (b) is iq = 10.

[0074] Figure 17 This is the test diagram at different iq in the present invention; (a) is the measured torque diagram; (b) is the reduced value of the d-axis component of the permanent magnet flux linkage.

[0075] Figure 18It is the dq-axis inductance diagram in the present invention; (a) is the d-axis inductance diagram; (b) is the q-axis inductance diagram.

[0076] Figure 19 It is the dq-axis components of the permanent magnet flux linkage in the present invention; (a) when i d <0 and i q =0, the d-axis component of the permanent magnet flux linkage; (b) when i d =0 and i q >0, the q-axis component of the permanent magnet flux linkage.

[0077] Figure 20 It is the variation of the parameters with the dq-axis current in the present invention; (a) is the parameter Ld; (b) is the parameter Lq; (c) is the parameter ψ fd ; (d) is the parameter ψ fq .

[0078] Figure 21 It is the torque variation diagram with the dq-axis current in the present invention; (a) is Te'; (b) is Te' pmd ; (c) is Te' pmq ; (d) is Te′ rel . Detailed implementation manners

[0079] The present invention will be further described below in conjunction with the accompanying drawings of the specification and specific embodiments.

[0080] On the premise of considering the influence of temperature on the permanent magnet synchronous motor, the present invention constructs a mathematical model of a high magnetic circuit saturation permanent magnet synchronous motor, and directly verifies the influence of the magnetic saturation effect on the permanent magnet flux linkage, as well as the effectiveness and accuracy of the mathematical model of the high magnetic circuit saturation permanent magnet synchronous motor through corresponding experimental methods.

[0081] Specifically, the traditional mathematical model of the current permanent magnet synchronous motor is analyzed as follows:

[0082] 1. Traditional mathematical model of permanent magnet synchronous motor

[0083] The mathematical model of a permanent magnet synchronous motor (Permanent Magnet Synchronous Motor, PMSM) includes inductance and permanent magnet flux linkage. The traditional analysis method is to regard these parameters as constants, and its dq-axis voltage equations are as follows:

[0084]

[0085] In the formula: v d , v q are the dq-axis voltages respectively; i d , i q are the dq-axis currents respectively; L d , Lq They are the d-axis and q-axis inductances respectively, specifically:

[0086]

[0087] It can be seen from Equation (2) that there are fluxes provided by the armature current and the permanent magnet in the d-axis direction, while there is only the flux provided by the armature current in the q-axis direction. Then, the dq-axis flux equations under steady state are:

[0088]

[0089] In the formula: ψ d , ψ q are the total fluxes of the d-axis and q-axis respectively. At the same time, according to the law of conservation of energy, the electromagnetic torque expression of the motor in the dq-axis coordinate system is:

[0090]

[0091] In the formula: Te is the electromagnetic torque; p is the number of pole pairs.

[0092] It can be seen from Equation (4) that the electromagnetic torque output by the PMSM can be divided into two parts, namely, the permanent magnet torque generated by the interaction between the armature reaction magnetic field and the permanent magnet, and the reluctance torque generated by the interaction between the magnetic field and the rotor with different dq-axis reluctances. The expressions of the two torque components are:

[0093]

[0094] In the formula: L △ is the difference between the d-axis and q-axis inductances, that is, L △ = L d - L q ; Te pm , Te rel are the permanent magnet torque and the reluctance torque respectively. When ψ f and L △ are constant, Te pm is proportional to i q , and Te rel is proportional to the d-axis and q-axis currents respectively.

[0095] In fact, during the operation of the motor, different dq-axis currents will result in different saturation degrees of the magnetic circuit, thereby causing changes in inductance and permanent magnet flux linkage. Especially for a High Saturation Permanent Magnet Synchronous Motor (HSPMSM), the variation of electromagnetic parameters with the saturation degree is more complex, which further affects the output performance of the motor. Therefore, in order to achieve high-performance control of HSPMSM, an accurate mathematical model is required as the theoretical basis.

[0096] 2. Analysis of the Saturation Degree of Permanent Magnet Synchronous Motor

[0097] Due to the characteristics of soft magnetic materials, such as high magnetic permeability, low resistivity, and weak remanence, they can generate a strong magnetic induction intensity under the action of a weak external magnetic field, and the magnetism exhibited is temporary. When the external magnetic field is removed, its magnetic field will basically disappear. Therefore, the core material in the motor usually uses soft magnetic materials. However, when the external magnetic field is large, as the carried magnetic flux increases, the core material will gradually saturate, resulting in a decrease in the overall effect of magnetic flux density in the motor, thereby affecting the output performance of the motor.

[0098] The saturation degree of the motor can be reflected by the no-load characteristic curve, or called the saturation curve. For a synchronous motor, making the motor operate at a constant speed and measuring the relationship between the no-load electromotive force and the excitation current can obtain the saturation curve. Since a permanent magnet is used instead of the excitation winding in the rotor of PMSM, the abscissa and ordinate of the saturation curve are equivalently transformed. Assuming that the leakage magnetic flux is ignored, the permanent magnet flux linkage can be equivalently expressed as the product of the excitation current and the d-axis inductance, that is:

[0099] ψ f =L d ·i f (6)

[0100] Where: i f is the equivalent excitation current of the permanent magnet.

[0101] Replace the abscissa of the saturation curve with the permanent magnet flux linkage instead of the excitation current, and the ordinate is converted to the product of the no-load electromotive force and the d-axis inductance, and the saturation curve is drawn by adjusting the remanence of the permanent magnet, as Figure 1 shown.

[0102] From Figure 1 it can be seen that when the given permanent magnet flux linkage is small, the magnetic circuit of the motor is in an unsaturated state, and the saturation curve is a straight line passing through the origin. After extending it, it is called the air-gap line. As the permanent magnet flux linkage increases, the magnetic circuit of the motor gradually saturates, and the saturation curve deviates from the air-gap line. Assuming that the abscissa and ordinate of the motor operating at point c n on the saturation curve are ψfn and E 0n ·L dn , E 0n ·L dn The corresponding point on the air-gap line is b n , b n The corresponding abscissa is ψ fs , using the saturation coefficient K s can reflect the saturation degree of the motor, that is:

[0103]

[0104] For low-saturation motors, K s generally does not exceed 1.25, while for HSPMSM, K s is often greater than 1.25. In addition, the saturation degree of the motor can also be reflected by the magnetic flux density of the iron core. When the HSPMSM operates within the rated range, its iron-core magnetic flux density is usually large. According to the BH curve characteristics of the iron-core material, it can be known that the magnetic permeability of the iron core is low at this time, as Figure 2 shown

[0105] From Figure 2 it can be seen that there is an obvious non-linear relationship between the magnetic permeability and the magnetic field density of different iron-core materials. When the iron-core magnetic flux density is less than 1.5T, the magnetic permeability of the iron core is much greater than the air-gap magnetic permeability. At this time, the iron-core magnetic resistance is much less than the air-gap magnetic resistance. Therefore, the influence brought by the magnetic saturation effect is often ignored. However, for the iron core in the high-saturation state, its iron-core magnetic flux density is often greater than 1.8T, and the iron-core magnetic permeability is close to the air-gap magnetic permeability. Then there is a certain magnetic voltage drop on the iron-core magnetic resistance. At this time, the influence of the magnetic saturation effect on the motor parameters should be considered

[0106] 3. Inductance characteristic analysis and identification

[0107] In PMSM, the difference in the dq-axis magnetic circuits will lead to different dq-axis inductances. Taking the Interior Permanent Magnet Synchronous Motor (IPMSM) as an example, there are only air gaps and iron cores in its q-axis magnetic circuit, while there are permanent magnets in the d-axis magnetic circuit. This makes the magnetic flux in the d-axis direction need to pass through not only the air gap and the iron core but also the permanent magnet. Since the magnetic permeability of the permanent magnet is approximately equal to that of air, it is equivalent to placing a magnetic barrier for magnetic isolation in the d-axis direction, as Figure 3 shown in (a) of

[0108]

[0109] In the formula: Lc is the inductance; R c is the reluctance; N c is the number of winding turns; l c is the length of the magnetic circuit; A c is the average cross-sectional area of the magnetic circuit; μ c is the magnetic permeability in the magnetic circuit.

[0110] According to Equation (8), the inductance is proportional to the square of the number of turns and inversely proportional to the reluctance of the magnetic circuit associated with the winding. Then, the L in the IPMSM d is less than L q . For the surface-mounted permanent magnet synchronous motor (SPMSM), its permanent magnets are usually firmly attached to the rotor surface with special materials, as shown in Figure 3 (b). Ignoring the spacing between the permanent magnets, it can be considered that the SPMSM has a uniform air gap, resulting in equal reluctances of the dq-axis magnetic circuits, and L d and L q are also equal.

[0111] From Figure 3 , it can be seen that the magnetic fluxes of the dq-axis magnetic circuits need to pass through the stator and rotor cores, and the core reluctance will change with the saturation degree, thereby causing the inductance to change. In fact, during the normal operation of the motor, the saturation degree of its core is mainly determined by the stator current. When the motor operates in the motor mode (i d < 0, i q > 0), the influences of the dq-axis currents on the core magnetic flux density are shown in Figure 4 . The parameters of its simulation model are shown in Table 1.

[0112] Table 1 Motor Parameters

[0113]

[0114] Figure 4 In, i sr represents the rated value of the current. By comparing (a) in Figure 4 and (b) in Figure 4 , and by comparing (c) in Figure 4 and (d) in Figure 4 , it can be seen that when a demagnetizing current is given on the d-axis, its magnetic flux direction is opposite to that of the permanent magnet magnetic flux. The direct-axis armature reaction weakens the original motor magnetic field as a whole, reducing the saturation degree of the core and thus reducing the core reluctance. And by comparing (a) in Figure 4 and (c) in Figure 4 , and by comparing (b) in Figure 4 and (d) in Figure 4As can be seen from Fig. (d), when the q-axis current is applied, the cross-axis armature reaction strengthens the original motor magnetic field as a whole, increasing the iron core saturation degree and thus leading to an increase in the iron core magnetic resistance. According to the relationship between magnetic resistance and inductance, it can be obtained that the dq-axis inductance decreases with the increase of i q and increases with the decrease of i d . Assume that Figure 4 the d- or q-axis inductances in Fig. (a)-(d) are L c1 , L c2 , L c3 and L c4 respectively. Then L c3 < L c1 < L c2 and L c3 < L c4 < L c2 .

[0115] Meanwhile, the variation degrees of the dq-axis inductances with the dq-axis current under different saturation coefficients are also different. When K s is 1.05, 1.20 and 1.35, the variations of the dq-axis inductances with the current are as shown in Figure 5 . Among them, the dq-axis inductances under no-load conditions are taken as the reference values respectively, and the current is based on the rated current in Table 1.

[0116] As can be seen from Figure 5 , within the same current range, when K s is close to 1, the variation of the dq-axis inductance is small. Therefore, it can usually be regarded as a constant value. As K s increases, the variation degree of the dq-axis inductance with the current gradually increases. Among them, the variation of the q-axis inductance with the q-axis current is more obvious. Therefore, for some low-saturation motors, the variation of the q-axis inductance needs to be considered. For high-saturation motors, the dq-axis inductances will change significantly at the same time. Therefore, when precisely controlling the HSPMSM, the real-time values of the dq inductances need to be obtained.

[0117] Since during the operation of the motor, the real-time varying inductance is difficult to directly measure, and there is a problem of underdetermined rank in the dq-axis voltage equation, that is, the number of equations is two, while the parameters to be obtained include the dq-axis inductances, stator resistance, permanent magnet flux linkage and other parameters. Therefore, in order to obtain the real-time value of the inductance, a parameter identification method based on high-frequency voltage injection is adopted. Assume that the injected dq-axis high-frequency voltages are respectively expressed as:

[0118]

[0119] where: v dh and v qh are the injected dq-axis high-frequency voltages respectively; v dhf , f hd and θvd are the amplitude, frequency, and phase of the injected d-axis high-frequency voltage; v qhf , f hq and θ vq are the voltage, frequency, and phase of the injected q-axis high-frequency current, respectively; meanwhile, the injected dq-axis high-frequency voltages will respectively excite dq-axis high-frequency currents with the same frequency as them, that is:

[0120]

[0121] In the formula: i dh and i qh are the dq-axis high-frequency current signals respectively; i dhf and θ id are the amplitude and phase of the d-axis high-frequency current respectively; i qhf and θ iq are the amplitude and phase of the q-axis high-frequency current respectively;

[0122] When the amplitude of the high-frequency current is much smaller than the fundamental current amplitude, the change in the dq-axis inductance caused by the high-frequency current is very small. Therefore, at a certain operating point of the motor, it can be considered that the dq-axis inductance does not change due to the injected high-frequency signal. The vector relationship between the high-frequency voltage and the high-frequency current is as Figure 6 shown.

[0123] To extract the high-frequency signal, the voltage and current in the system can be passed through a band-pass filter (BPF), and the discrete Fourier transform (DFT) is used to process the signal to obtain the amplitude and phase of the high-frequency signal. According to the Figure 6 vector relationship in, the relationship between the stator resistance, dq-axis inductance, and the high-frequency signal can be obtained as:

[0124]

[0125] To avoid the injected high-frequency signal affecting the normal operation of the motor, the selected frequency should be greater than the operating frequency of the motor, and the amplitude should be much smaller than the fundamental amplitude. The overall control block diagram is as Figure 7 shown.

[0126] 4. Analysis of the change of permanent magnet flux linkage with dq-axis current

[0127] To ensure the long-term reliable operation of PMSM, it is required that the magnetic properties of the permanent magnet material remain stable. Among them, the main factors affecting the magnetic properties of the permanent magnet material include thermal stability and magnetic stability. Thermal stability refers to the magnetic performance of the permanent magnet material under high-temperature conditions, and magnetic stability refers to the influence of the external magnetic field on the magnetic properties of the permanent magnet material. At present, with the development of permanent magnet materials, permanent magnet materials with high remanence density and high coercivity are usually selected in PMSM design. This kind of permanent magnet material has high magnetic stability and can prevent the demagnetization effect of PMSM caused by demagnetizing current during operation. However, during the actual operation of PMSM, the influence of temperature on the permanent magnet is often inevitable.

[0128] In permanent magnet materials, an increase in temperature will increase the thermal vibration of atoms. This thermal vibration will interfere with the magnetic moment arrangement in the magnetic material, resulting in the random orientation of magnetic moments and the degradation of the magnetic properties of the permanent magnet material. In other words, the thermal motion of atoms hinders the coupling effect (the interaction between particle spin and its motion) between adjacent atomic magnetic moments. When the temperature of the permanent magnet material drops close to absolute zero, i.e., -273 °C (zero Kelvin), the thermal motion of atoms is minimal, making it easier for magnetic moments to be arranged orderly, resulting in the magnetization intensity reaching the maximum value. However, as the temperature rises, until the Curie temperature point, the spin coupling force of magnetic moments is completely destroyed, leading to a slow degradation of the magnetization intensity. Therefore, the magnetic properties of the permanent magnet material will change with the change of the ambient temperature, as Figure 8 shown.

[0129] When the ambient temperature of the permanent magnet material rises, i.e., the temperature rises from t0 to t1, the magnetic density of the permanent magnet material will drop from the original B r0 to B r1 ; and when the temperature drops back to t0 again, the magnetic density will not return to B r0 along the original curve, but will rise to B' r0 . After that, when the ambient temperature changes back and forth between t0 and t1 again, the magnetic density will only change between B' r0 and B r1 . Therefore, the influence of ambient temperature on the magnetic properties of the permanent magnet material can be divided into two parts: irreversible loss and reversible loss.

[0130] (1) Irreversible loss: That is, after the temperature returns to the initial value, the magnetic properties of the permanent magnet material cannot return to the original state. This part of the loss is usually expressed by the loss rate IL(%) as:

[0131]

[0132] The irreversible loss can be further divided into irrecoverable loss and recoverable loss. The irrecoverable loss refers to the loss that the permanent magnet material cannot recover even after being re-magnetized, usually caused by the change of the internal microstructure of the permanent magnet material due to too high environmental temperature. The recoverable loss is the loss that the permanent magnet material can recover after being re-magnetized.

[0133] (2) Reversible loss: This part of the loss refers to the reversible change in the magnetic density or magnetic induction intensity of the permanent magnet material with the repeated change of temperature. Usually, the degree of this reversible change is represented by the temperature coefficient α Br It is expressed as:

[0134]

[0135] According to Equation (12) and Equation (13), it can be obtained that when the temperature of the permanent magnet material rises from t0 to t1, the magnetic density of the permanent magnet can be expressed as:

[0136]

[0137] In practical applications, the permanent magnet material is usually preheated to avoid irreversible loss during the use of the permanent magnet in the motor. Therefore, when driving and controlling the motor, only the reversible loss of the permanent magnet material needs to be considered. At the same time, the relationship between the total magnetic flux provided by the permanent magnet and the magnetic density can be expressed as:

[0138] ψ r =B r A m N (15)

[0139] In the formula: ψ r is the total magnetic flux provided by the permanent magnet; N is the number of turns in series per phase; A m is the cross-sectional area of the magnetic flux provided by the permanent magnet per pole. It can be seen from Equation (15) that ψ r and B r are in a direct proportional relationship. Therefore, when the temperature of the permanent magnet changes, the magnetic flux provided by the permanent magnet will also change accordingly. When the temperature rises from t0 to t1, according to the temperature coefficient, the total magnetic flux provided by the permanent magnet at t1 can be obtained as:

[0140]

[0141] In the formula: ψ r1 and ψ′ r0 are respectively the total magnetic fluxes provided by the permanent magnet material at t1 and t0, corresponding to B r1 and B′ r0 . Among them, the total magnetic flux provided by the permanent magnet includes the virtual internal leakage magnetic flux ψ0 of the permanent magnet and the magnetic flux ψ m provided to the external magnetic circuit, and ψm It is further divided into leakage magnetic linkage ψ σ and air-gap magnetic linkage ψ f , that is:

[0142]

[0143] Since the leakage magnetic linkage does not participate in the process of electromechanical energy conversion, when controlling the motor, the air-gap magnetic linkage provided by the permanent magnet needs to be obtained. In order to analyze the change of the air-gap magnetic linkage provided by the permanent magnet, the equivalent magnetic circuit method is often used. Since the magnetic linkage is proportional to the magnetic flux, the change of the magnetic linkage can be reflected by analyzing the change of the magnetic flux, as Figure 9 shown.

[0144] In Figure 9 , the permanent magnet is equivalent to a constant magnetic flux source Φ r and a constant internal magnetic resistance R0 in parallel. Then the total magnetic flux Φ m provided by the permanent magnet to the external magnetic circuit can be divided into two parts. One part is the main magnetic flux, which can also be called the air-gap magnetic flux Φ f ; the other part is the leakage magnetic flux Φ σ , which does not link with the armature winding turns, and the corresponding magnetic resistance is called the leakage magnetic resistance R σ . Among them, the main magnetic flux corresponds to the main magnetic circuit. The combined magnetic resistance R f in the main magnetic circuit mainly includes the air-gap magnetic resistance, the rotor core magnetic resistance and the stator core magnetic resistance. In actual situations, these three magnetic resistances can be divided into multiple segments and then combined through series and parallel connections. From the previous analysis, it can be seen that the stator and rotor magnetic resistances will change with the saturation degree. Therefore, Φ f will also change with the saturation degree of the iron core. Combining with the definition of magnetic flux, Φ f is expressed as:

[0145] Φ f =b m B r A m (18)

[0146] In the formula: b m is the working coefficient of the permanent magnet and changes with the saturation degree of the iron core. At the same time, ψ f can be expressed as:

[0147] ψ f =b m B r A m N (19)

[0148] Since during the operation of the motor, the saturation degree of the iron core depends on the distribution of the dq-axis currents, the dq-axis currents have an impact on b m and ψ fThe influence can be divided into two points. When i q increases, the saturation degree of the iron core increases accordingly, causing b m to decrease, and then resulting in a decrease in ψ f . When i d increases in the reverse direction, the saturation degree of the iron core decreases accordingly, causing b m to increase, and then resulting in an increase in ψ f . Assume that the temperature of the permanent magnet is t0 when the motor is no-load, and the air-gap magnetic flux provided by the permanent magnet is ψ f '0. The temperature of the permanent magnet is t1 when the motor is loaded, and the air-gap magnetic flux provided by the permanent magnet is ψ f1 , that is:

[0149]

[0150] In the formula: b' m0 and b m1 are the working coefficients of the permanent magnet when the motor is no-load and loaded, respectively.

[0151] Substitute Equation (14) into Equation (20), then the relationship between ψ f '0 and ψ f1 can be expressed as:

[0152]

[0153] It can be seen from Equation (21) that during the operation of the motor, the temperature of the permanent magnet and the saturation degree of the iron core will simultaneously affect the amplitude of the air-gap magnetic flux provided by the permanent magnet.

[0154] At the same time, within the pole width between the magnetomotive force generated by the permanent magnet and the magnetomotive force generated by the stator winding, the magnetic permeability of the stator tooth part where the synthesized air-gap magnetomotive force is located is less than that of the adjacent area. In other words, under the load condition of the motor, the internal magnetic field will be distorted to a certain extent with the change of the armature current, and the distortion degree of the magnetic field will increase with the increase of the saturation degree. When the vector control technology is adopted at this time, the magnetic field provided by the permanent magnet no longer distributes symmetrically along the d-axis as in the no-load state, but is distorted under the influence of the armature current in the load state, resulting in a change in the phase of the permanent magnet magnetic flux.

[0155] Since under the load condition, the magnetic field is jointly generated by the permanent magnet and the armature current, it is difficult to accurately analyze the magnetic field distribution when the permanent magnet acts alone. Therefore, in order to better study the phenomenon of the change in the phase of the permanent magnet magnetic flux, the frozen permeability method is adopted. Assume that the PMSM operates normally under a certain load condition. At this time, the magnetic flux density, magnetic field strength, and magnetic permeability of the iron core are B all , H all and μ all; when the permanent magnet generates a magnetic field alone, the core magnetic flux density, magnetic field strength, and magnetic permeability are B pm , H pm , and μ pm ; when the armature current generates a magnetic field alone, the core magnetic flux density, magnetic field strength, and magnetic permeability are B i , H i , and μ i , as Figure 10 shown.

[0156] From Figure 10 , it can be seen that due to the non-linearity of the BH curve of the core material, the core magnetic permeability when the permanent magnet acts alone, the armature current acts alone, and when both act together is different. Therefore, there is the following relationship between the magnetic fields of the permanent magnet and the armature current superimposed:

[0157]

[0158] The frozen permeability method is to fix the magnetic permeability of the core as μ all , at this time, the core magnetic flux density B pm(FP) when the permanent magnet acts alone and the core magnetic flux density B i(FP) when the armature current acts alone can be respectively expressed as:

[0159]

[0160] And the magnetic flux density generated when the permanent magnet and the armature current act together can be expressed as:

[0161] B i(FP) +B pm(FP) =μ all H i +μ all H pm =μ all H all =B all (24)

[0162] From equations (22) and (24), it can be seen that the frozen permeability method can transform the non-linear problem of the core magnetic flux density into a linear problem, so that the magnetic field generated by the permanent magnet under different loads can be accurately decomposed. For example, when the motor operates under the conditions of i d = 0 and i q = i sr , according to the frozen permeability method, the magnetic field line distribution when the permanent magnet acts alone can be obtained as shown in Figure 11 (b).

[0163] Figure 11 (a) in is the magnetic field line distribution of the permanent magnet under no-load. It can be seen that the magnetic field lines are symmetrically distributed along the d-axis direction under no-load. Compared with the no-load state, Figure 11In (b), the magnetic field lines of the permanent magnet under the load state are significantly shifted. Therefore, it can be shown that in the dq-axis coordinate system, under the load state, in addition to providing magnetic flux in the d-axis direction, the permanent magnet will also generate a certain magnetic flux component in the negative q-axis direction, as Figure 12 shown.

[0164] Assume that when the motor is operating normally under a certain load condition, the phase of the permanent magnet magnetic flux is γ f . Then the relationships between the dq-axis components of the permanent magnet magnetic flux and ψ f can be expressed as:

[0165]

[0166] In the formula: ψ fd , ψ fq are the dq-axis components of the air-gap magnetic flux provided by the permanent magnet respectively; γ f is the angle between ψ f and the d-axis. When i q increases, the degree of magnetic field distortion increases, making γ f become larger, and then resulting in a decrease in ψ fd and an increase in the reverse direction of ψ fq . When i d increases in the reverse direction, the degree of magnetic field distortion decreases, making γ f decrease, and then resulting in an increase in ψ fd and a decrease in the reverse direction of ψ fq .

[0167] In addition, the variation degrees of the dq-axis components of the permanent magnet magnetic flux under different saturation coefficients are also different. Taking the permanent magnet magnetic flux of the motor under no-load with different saturation coefficients as the reference value. When i d = 0, the variation of the dq-axis components of the permanent magnet magnetic flux with i q is as shown in (a) of Figure 13 . When i q = i sr , the variation of the dq-axis components of the permanent magnet magnetic flux with i d is as shown in (b) of Figure 13 .

[0168] As can be seen from Figure 13 , for a low-saturation motor, the variation degrees of the dq-axis components of the permanent magnet magnetic flux with the dq-axis current are relatively small. Therefore, the influence of magnetic saturation effect on the permanent magnet magnetic flux is usually ignored. For a high-saturation motor, the dq-axis components of the permanent magnet magnetic flux will change significantly with the dq-axis current. Therefore, in order to accurately analyze the characteristics of the output torque of HSPMSM and achieve high-performance control, it is necessary to consider the influence of magnetic saturation effect on the permanent magnet magnetic flux.

[0169] 5. dq-Axis Mathematical Model of High-Saturation Permanent Magnet Synchronous Motor

[0170] As can be seen from the previous analysis, in the HSPMSM, the permanent magnet flux linkage and inductance will both change significantly with the change of dq-axis currents. Therefore, the parameter changes caused by the magnetic saturation effect need to be considered in the traditional dq-axis mathematical model, and Equation (3) can be rewritten as:

[0171]

[0172] In the formula: the superscript (i d ,i q ) represents the real-time values of each parameter under different dq-axis currents.

[0173] At the same time, the voltage equations of the dq-axis can be rewritten as:

[0174]

[0175] When the motor is in a steady state and the dq-axis inductance and resistance are known, the dq-axis components of the permanent magnet flux linkage can be obtained by using (27) as:

[0176]

[0177] Substituting Equation (26) into Equation (4) and improving the traditional electromagnetic torque mathematical model, the mathematical model of the electromagnetic torque of the HSPMSM in the dq-axis coordinate system can be obtained as:

[0178]

[0179] In the formula: Te' is the electromagnetic torque considering the magnetic saturation effect. It can be seen from the above formula that when considering the phenomenon that the phase of the permanent magnet flux linkage changes due to the magnetic saturation effect, the electromagnetic torque should be composed of three torque components, namely:

[0180]

[0181] In the formula: Te' pmd is and i q the d-axis component of the permanent magnet torque generated by the interaction; Te p ' mq is and i d the q-axis component of the permanent magnet torque generated by the interaction; Te' rel is the reluctance torque considering the magnetic saturation effect. Among them, when the HSPMSM operates in the motor mode, Te' pmd and Te' rel are positive, while Te' pmq is negative. When using the vector control technology with i d = 0, Te'rel With Te p ' mq being zero, Equation (29) can be rewritten as:

[0182]

[0183] It can be clearly seen from the above equation that, compared with the traditional electromagnetic torque mathematical model, since the amplitude of the permanent magnet flux linkage changes with the saturation degree of the motor, the actual electromagnetic torque and current are no longer in a proportional relationship but a non-linear relationship.

[0184] To verify the HSPMSM mathematical model established above, an embodiment of the present invention correspondingly provides a verification method for the mathematical model of a high-saturation permanent magnet synchronous motor, which specifically includes the steps of:

[0185] Build an IPMSM experimental platform and use the motor-to-motor dragging method for loading, as Figure 14 shown;

[0186] First, both motors on both sides are tested by vector control variable frequency speed regulation with i d = 0. The performance to be tested mainly includes the back electromotive force and load torque under no-load conditions. For the measurement of the back electromotive force, an isolated high-voltage probe is used. The load torque is measured using a high-precision torque sensor with a cut-off frequency of 3K. The analog voltage output signal is collected through a low-voltage probe, and the collected analog signal is converted into a mathematical signal through an oscilloscope again.

[0187] In addition, it can be seen from Equation (31) that at this time, the change of can be obtained by directly measuring the torque and current. However, since the permanent magnet flux linkage is also affected by temperature, in order to verify the influence of magnetic saturation on the permanent magnet flux linkage, the temperature rise of the permanent magnet needs to be measured. For this purpose, the end cover side of the motor is perforated so as to use an infrared temperature sensor to measure the temperature rise of the permanent magnet in real time, as Figure 14 shown. Among them, the parameters of the motor under test are shown in Table 1.

[0188] When the motor speed is the rated speed and it runs under no-load conditions, the amplitude of the back electromotive force is 123.5V, and its waveform is as Figure 15 (a) shown in. According to the back electromotive force formula, the permanent magnet flux linkage under no-load is obtained as 0.227Wb. Taking the motor running at the rated current as an example, when i q = 10, the measured torque is 6.14 Nm, and its torque waveform is as Figure 15 (b) shown in. At this time, the temperature of the permanent magnet under no-load is measured as 29.3 °C by the infrared sensor.

[0189] Then, with i d = 0, iq Taking the motor operating state at i = 10 A as an example, the measured torque is 6.14 Nm; the permanent magnet temperature is 72.7 °C. Compared with the permanent magnet temperature at no-load, the temperature rise is 43.4 °C, as shown in Figure 16 As shown. According to Equation (16), due to the influence of temperature, the total permanent magnet flux linkage is reduced by approximately 0.01 Wb, including and the flux linkages reduced by temperature of two components.

[0190] Assume the value reduced by temperature is 0.01 Wb, and according to Equation (31), at this time is 0.205 Wb. Compared with the permanent magnet flux linkage at no-load, the actual at the load state is reduced by 0.022 Wb. After excluding the influence of temperature, is reduced by 0.012 Wb due to magnetic saturation effect.

[0191] Using the same method to analyze q under different i , where the measured torque is as shown in Figure 17 (a). After excluding the influence of temperature, the flux linkages reduced by magnetic saturation effect under different i q are obtained, as shown in (b). Figure 17 It should be noted that

[0192] in (b), it is assumed that Figure 17 the value changed by temperature is equal to the value of the total permanent magnet flux linkage changed by temperature. Since the total permanent magnet flux linkage will generate a q-axis component, therefore, actually the value changed by temperature will be slightly less than the value of the total permanent magnet flux linkage changed by temperature, and further resulting in that actually the value changed by magnetic saturation effect will be slightly greater than the data in Figure 17 (b).

[0193] In order to further verify that the magnetic saturation effect will cause a q-axis component to be generated in the permanent magnet flux linkage, and to verify the demagnetization effect of the permanent magnet flux linkage. The high-frequency voltage injection method is used to inject a high-frequency voltage with an amplitude of 4 V and a frequency of 400 Hz into the d-axis, and a high-frequency voltage with an amplitude of 4 V and a frequency of 500 Hz into the q-axis. According to Figure 7 respectively identify d when i = 0 and i q > 0 for and i d < 0 and i q = 0 for as shown in Figure 18As shown

[0194] According to the dq-axis voltage equation, when i d = 0, the influence of resistance on v d can be excluded. When i q = 0, the influence of resistance on v q can be excluded. Then, according to Equation (28), the component varies with i q and varies with i d , as Figure 19 shown

[0195] Figure 19 The magnitudes of the dq components of the permanent magnet flux linkage in include both the magnetic saturation effect and the temperature effect. Since temperature causes the magnitude of the permanent magnet flux linkage to decrease, when only considering the magnetic saturation effect, and will have magnitudes slightly larger than those in Figure 19 . However, the following conclusions can still be drawn: will have its magnitude increase with the increase of i q due to the magnetic saturation effect, and will have its magnitude increase with the decrease of i d due to the demagnetization effect.

[0196] Since the above experiments were all carried out when the motor temperature rise was stable, in order to more fully verify the variation trend of the parameters with the magnetic saturation effect, it is necessary to reduce the influence of temperature on the parameters. Assume that the temperature of the permanent magnet does not change significantly in a short period of time. At this time, the parameters are identified, and then the next test is carried out after the motor has cooled down sufficiently. Finally, the identification results of the dq-axis inductance and the dq components of the permanent magnet flux linkage are as Figure 20 shown

[0197] From Figure 20 , it can be seen that the dq-axis inductance and the dq components of the permanent magnet flux linkage will both decrease with the increase of i q and increase with the decrease of i d . The changes in each torque component caused by the change of parameters are as Figure 21 shown

[0198] From Figure 20 and Figure 21 , it can be seen that the changes in inductance and permanent magnet flux linkage will cause each torque component not to change linearly with current, and the magnitude of Te' pmq generated due to the change in the phase of the permanent magnet flux linkage can reach up to 12% of the electromagnetic torque. Therefore, the influence of Te' pmq on the output torque cannot be ignored.

[0199] The experimental results correspond to the conclusions drawn from the previous analysis, and the effectiveness and accuracy of the HSPMSM mathematical model are verified through this experimental method.

[0200] The present invention also discloses a computer program product, including a computer program which, when run by a processor, executes the steps of the method as described above.

[0201] The present invention further discloses a computer-readable storage medium, on which a computer program is stored, and the computer program, when run by a processor, executes the steps of the method as described above.

[0202] The present invention also discloses a verification system for a high-saturation permanent magnet synchronous motor mathematical model, including a memory and a processor connected to each other. A computer program is stored on the memory, and the computer program, when run by the processor, executes the steps of the method as described above.

[0203] The products, media and systems of the present invention correspond to the above method and also have the advantages of the above method.

[0204] The present invention realizes all or part of the processes in the above-described embodiment method, and can also be completed by hardware related to computer program instructions. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-described method embodiment can be realized. Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file or some intermediate form, etc. The computer-readable storage medium includes: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disc, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal, and software distribution medium, etc. The memory is used to store the computer program and / or module, and the processor realizes various functions by running or executing the computer program and / or module stored in the memory, and calling the data stored in the memory. The memory can include high-speed random access memory, and can also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one magnetic disk storage device, flash device, or other volatile solid-state storage devices, etc.

[0205] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. A verification method for the mathematical model of a high-saturation permanent magnet synchronous motor, characterized in that, Including the steps: Based on the traditional mathematical model of the permanent magnet synchronous motor and considering the parameter changes caused by the magnetic saturation effect, a mathematical model of the high-saturation permanent magnet synchronous motor is constructed; Build an IPMSM experimental platform and use motor back-to-back loading to test the mathematical model of the high-saturation permanent magnet synchronous motor; specifically, in the no-load operating state, obtain the back electromotive force amplitude, calculate the permanent magnet flux linkage at no load, and simultaneously detect the permanent magnet temperature; in the load state, analyze the torque data under different loads, and obtain the change trend of the flux linkage under different loads after excluding the temperature influence; Adopt the high-frequency voltage injection method, inject high-frequency voltages with different amplitudes and frequencies on the d-axis and q-axis respectively, and through comparison and identification, analyze the changes of the dq-axis flux linkage components to verify the influence of magnetic saturation and desaturation effects on the permanent magnet flux linkage and inductance.

2. The verification method of the mathematical model of the high-saturation permanent magnet synchronous motor according to claim 1, wherein Obtain the change of the permanent magnet flux linkage by directly measuring the torque and current, and the specific calculation formula is: where Te' is the electromagnetic torque considering the magnetic saturation effect; i q is the q-axis current; p is the number of pole pairs; is the d-axis component of the permanent magnet flux linkage.

3. The verification method of the mathematical model of the high-saturation permanent magnet synchronous motor according to claim 1, characterized in that The specific process of injecting high-frequency voltages with different amplitudes and frequencies on the d-axis and q-axis respectively by adopting the high-frequency voltage injection method is: Inject a high-frequency voltage with an amplitude of 4V and a frequency of 400Hz into the d-axis, and inject a high-frequency voltage with an amplitude of 4V and a frequency of 500Hz into the q-axis; for i d = 0 and i q > 0 and for i d < 0 and i q = 0 for identification; where i d , i q are the dq-axis currents respectively; is the d-axis inductance; the superscript (i d , i q ) represents the real-time values of each parameter under different dq-axis currents; According to the dq-axis voltage equations, when i d = 0, the influence of the resistance on the d-axis voltage v d can be excluded. When i q = 0, the influence of the resistance on the q-axis voltage v q can be excluded; the variation of the q-axis component of the permanent magnet flux linkage with i q and the variation of the d-axis component of the permanent magnet flux linkage with i d are calculated; It is concluded that: its amplitude will increase with the increase of i due to the magnetic saturation effect, q and its amplitude will increase with the decrease of i due to the demagnetization effect. d ​ 4. The verification method of the high-saturation permanent magnet synchronous motor mathematical model according to claim 1 or 2 or 3, characterized in that The construction process of the mathematical model of the high-saturation permanent magnet synchronous motor is: Improve the traditional electromagnetic torque mathematical model, and obtain the mathematical model of the electromagnetic torque of the HSPMSM in the dq-axis coordinate system as: Wherein: Te' is the electromagnetic torque considering the magnetic saturation effect; L △ is the inductance difference between the d and q axes; L d , L q are the d-axis and q-axis inductances respectively; the superscript (i d , i q ) represents the real-time values of each parameter under different d-axis and q-axis currents; When considering the phenomenon that the phase of the permanent magnet flux linkage changes due to the magnetic saturation effect, the electromagnetic torque is composed of three torque components, namely: Where: Te' pmd is the d-axis component of the permanent magnet torque generated by the interaction between q and i p '; Te mq is the q-axis component of the permanent magnet torque generated by the interaction between d and i rel '; Te' pmd is the reluctance torque considering the magnetic saturation effect; where, when the HSPMSM operates in the motor mode, Te' rel is positive, while Te' pmq is negative; when the vector control technology with i d = 0 is adopted, Te' rel and Te p ' mq are zero, then Equation (29) is changed to:

5. The verification method of the mathematical model of the high-saturation permanent magnet synchronous motor according to claim 4, characterized in that The specific process of obtaining Equation (29) is: The mathematical model of the permanent magnet synchronous motor includes inductance and permanent magnet flux linkage, and its dq-axis voltage equation is as follows: where: v d and v q are the d-axis and q-axis voltages respectively; i d and i q are the d-axis and q-axis currents respectively; L d and L q are the d-axis and q-axis inductances respectively, specifically: As can be seen from Equation (2), there is both the flux linkage provided by the armature current and the flux linkage provided by the permanent magnet in the d-axis direction, while there is only the flux linkage provided by the armature current in the q-axis direction. Then the dq-axis flux linkage equation under steady state is: where: ψ d , ψ q are the total magnetic fluxes of the d- and q-axes, respectively; meanwhile, according to the law of conservation of energy, the electromagnetic torque expression of the motor in the dq-axis coordinate system is obtained as follows: In the formula: Te is the electromagnetic torque; p is the number of pole pairs; In the HSPMSM, the permanent magnet flux linkage and inductance will change significantly with the change of the dq-axis current at the same time; therefore, the parameter changes caused by the magnetic saturation effect need to be considered in the traditional dq-axis mathematical model, and then Equation (3) can be rewritten as: where: the superscript (i d , i q ) represents the real-time values of each parameter under different dq-axis currents; Substitute Equation (26) into Equation (4) to improve the traditional electromagnetic torque mathematical model, and obtain the mathematical model of the electromagnetic torque of the HSPMSM in the dq-axis coordinate system as: In the formula: Te' is the electromagnetic torque considering the magnetic saturation effect.

6. The verification method of the mathematical model of the high-saturation permanent magnet synchronous motor according to claim 5, characterized in that As can be seen from Equation (4), the electromagnetic torque output by the PMSM can be divided into two parts, namely the permanent magnet torque generated by the interaction between the armature reaction magnetic field and the permanent magnet, and the reluctance torque generated by the interaction between the magnetic field and the rotor with different dq-axis reluctances. The expressions of the two torque components are respectively: where: L △ is the inductance difference between the d- and q-axes, i.e., L △ = L d - L q ; Te pm , Te rel are the permanent magnet torque and reluctance torque, respectively; when ψ f and L △ are constant, Te pm is proportional to i q , and Te rel is proportional to the d- and q-axis currents, respectively.

7. The verification method of the high-saturation permanent magnet synchronous motor mathematical model according to claim 6, characterized in that Obtain the real-time value of the inductance during the operation of the motor, and adopt the parameter identification method based on high-frequency voltage injection; Assume that the injected dq-axis high-frequency voltages are respectively expressed as: where: v dh and v qh are the high-frequency dq-axis voltages injected respectively; v dhf , f hd and θ vd are the amplitude, frequency and phase of the high-frequency d-axis voltage injected respectively; v qhf , f hq and θ vq are the voltage, frequency and phase of the high-frequency q-axis current injected respectively; meanwhile, the injected high-frequency dq-axis voltages will respectively excite high-frequency dq-axis currents with the same frequencies as them, that is: Where: i dh and i qh are respectively the dq-axis high-frequency current signals; i dhf and θ id are respectively the amplitude and phase of the d-axis high-frequency current; i qhf and θ iq are respectively the amplitude and phase of the q-axis high-frequency current; Filter the voltage and current in the system through a band-pass filter, and use the discrete Fourier transform to process the signal to obtain the amplitude and phase of the high-frequency signal; According to the vector relationship, the stator resistance R can be obtained s , and the relationships between the dq-axis inductances and the high-frequency signals are as follows:

8. A computer program product comprising a computer program, characterized in that, When the described computer program is run by the processor, it executes the steps of the method described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the described computer program is run by the processor, it executes the steps of the method described in any one of claims 1-7.

10. A verification system for the mathematical model of a high-saturation permanent magnet synchronous motor, comprising a memory and a processor connected to each other, wherein a computer program is stored on the memory, and is characterized in that, The computer program, when executed by a processor, performs the steps of the method according to any one of claims 1 to 7.

Images