Consideration electric suspension / generation coupling magnetic suspension motor accurate modeling method, system

Abstract

The application provides a kind of accurate modeling method and system of magnetic suspension motor considering electric / suspension / power generation coupling, constructs the mathematical model of instantaneous electromagnetic torque of motor, the mathematical model of suspension force and the mathematical model of power generation, obtains the control component of suspension current in the electric state from the mathematical model of instantaneous electromagnetic torque and the mathematical model of suspension force, obtains the control component of suspension current in the power generation state from the mathematical model of power generation and the mathematical model of instantaneous electromagnetic torque.The application simultaneously considers the coupling of torque current freewheeling and suspension current in the electric state, the coupling of suspension current and excitation current in the power generation state, and can adjust suspension current in real time in the electric state and the power generation state, realizes the stable suspension of motor in two states.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mathematical modeling, and particularly relates to a magnetic suspension motor accurate modeling method and system considering electric / suspension / power generation coupling. BACKGROUND

[0002] When the magnetic suspension motor is applied to a flywheel battery, when the flywheel system is in an electric state, for any phase winding, the winding works as a torque-related break, and the next working state of the winding is a suspension phase, at this time, the torque current freewheeling of the winding will be coupled with the suspension current passed through when the winding works as a suspension phase; when the flywheel system is in a power generation state, for any phase winding, the winding works as a suspension phase for a period of time and needs to provide excitation current in advance for the power generation state, at this time, the suspension current of the winding will be coupled with the excitation current. The coupling phenomenon will cause the suspension force to pulsate, and the suspension state of the magnetic suspension motor is unstable. SUMMARY

[0003] In view of the deficiencies in the prior art, the application provides a magnetic suspension motor accurate modeling method and system considering electric / suspension / power generation coupling, which solves the coupling problem.

[0004] The application achieves the above technical objective through the following technical means.

[0005] The magnetic suspension motor accurate modeling method considering electric / suspension / power generation coupling comprises the following steps.

[0006] An instantaneous electromagnetic torque mathematical model of the motor is constructed, and the instantaneous electromagnetic torque mathematical model is obtained by taking the partial derivative of the magnetic field energy storage with respect to the rotor position angle;

[0007] A suspension force mathematical model of the motor is constructed, and the suspension force mathematical model is obtained by taking the derivative of the radial suspension magnetic field energy variation of each phase winding with respect to the air gap size variation;

[0008] A motor power generation mathematical model is constructed, and the motor power generation mathematical model is: Wherein U is the power generation output voltage, i G is the excitation current, R represents the winding resistance, ψ represents the excitation flux linkage, and t represents time;

[0009] The torque current freewheeling i T of the four windings is obtained according to the instantaneous electromagnetic torque mathematical model; T The i F is taken as the bias current component I1 of the suspension current i F of the suspension phase, the control current component i1 of the suspension current i F is obtained according to the suspension force mathematical model, and the i1 is taken as the control component of the suspension current in the electric state;

[0010] According to the mathematical model of the motor, the exciting current i G , the i G is the suspension current flowing into the suspension phase F , the bias current component I2 of the suspension current i F is obtained according to the mathematical model of the suspension force, and the i2 is taken as the control component of the suspension current in the power generation state.

[0011] In a further aspect, the mathematical model of the instantaneous electromagnetic torque is specifically:

[0012]

[0013] wherein T represents torque, W1 represents the radial torque magnetic field energy of the four windings, θ represents the rotor position angle, J(θ) represents the motor torque coefficient, i M represents the torque current of any winding, and i M = i T .

[0014] In a further aspect, the radial torque magnetic field energy W1 is specifically:

[0015]

[0016] wherein i1, i2, i3 and i4 represent the torque currents of the four windings in each phase winding, and i1=i2=i3=i4; L1, L2, L3 and L4 represent the self-inductance of the four windings in any phase winding; M αβ represents the mutual inductance between the four windings in any phase winding, and α and β represent winding numbers, and α and β take values of 1, 2, 3 and 4, and α≠β.

[0017] In a further aspect, the self-inductance and mutual inductance satisfy:

[0018]

[0019] wherein N represents the number of turns of the winding, P1, P2, P3 and P4 represent the air gap permeance under the four stator poles of each phase winding, P represents the total air gap permeance under the four stator poles of each phase winding, and P=P1+P2+P3+P4.

[0020] In a further aspect, the total air gap permeance satisfies:

[0021]

[0022] wherein a is a constant, μ0 represents the vacuum permeability, l represents the length of the motor core, g represents the air gap length, r represents the arc radius of the stator pole, and θ represents the rotor position angle.

[0023] Further technical solutions, the suspension force mathematical model is:

[0024]

[0025]

[0026]

[0027] Wherein, F represents the suspension force, F1 represents the force at air gap 1, F2 represents the force at air gap 2, B1 represents the magnetic induction at air gap 1, B2 represents the magnetic induction at air gap 2, H1 represents the magnetic field intensity at air gap 1, H2 represents the magnetic field intensity at air gap 2, S is the single stator pole cross-sectional area, x0 is the rotor displacement, g is the air gap length, μ0 is the vacuum permeability, N is the winding number, I is the bias current component of the suspension current, and i is the control component of the suspension current.

[0028] Further technical solutions, the magnetic suspension motor is applied to the flywheel battery, the working range of each phase winding in the motor state is 45° mechanical angle, and the working range of each phase winding in the generator state is 45° mechanical angle.

[0029] In the motor state, the inductance rising area winding in the range of 0°-22.5° mechanical angle generates torque as a torque phase, and the inductance flat area winding in the range of 22.5°-45° mechanical angle generates suspension force as a suspension phase.

[0030] In the generator state, the inductance flat area winding in the range of 0°-22.5° mechanical angle generates suspension force as a suspension phase, and the inductance falling area winding in the range of 22.5°-45° mechanical angle controls power generation as a power generation phase.

[0031] A system of a magnetic suspension motor precise modeling method, comprising:

[0032] A mathematical model construction module is configured to construct an instantaneous electromagnetic torque mathematical model, a suspension force mathematical model and a motor power generation mathematical model.

[0033] A suspension current control component solving module is configured to solve the control component of the suspension current in the motor state according to the instantaneous electromagnetic torque mathematical model and the suspension force mathematical model, and solve the control component of the suspension current in the generator state according to the suspension force mathematical model and the motor power generation mathematical model.

[0034] An electronic device comprises a memory and a processor;

[0035] The memory is configured to store a computer program;

[0036] The processor is configured to execute the computer program and realize the above-mentioned magnetic suspension motor precise modeling method when the computer program is executed.

[0037] A storage medium, the storage medium stores a computer program, the computer program is executed by a processor to make the processor execute the above-mentioned magnetic suspension motor precise modeling method.

[0038] The application has the advantages that: the application considers the coupling conditions of the torque current freewheeling and the suspension current when the winding is in the motoring state, and considers the coupling conditions of the suspension current and the excitation current when the winding is in the generating state, and the actual working process of the motor is considered more comprehensively; in the motoring state, the instantaneous electromagnetic torque mathematical model and the suspension force mathematical model are combined to solve the control component of the suspension current in the motoring state; in the generating state, the suspension force mathematical model and the motor generating mathematical model are combined to solve the control component of the suspension current in the generating state; the suspension current can be adjusted in real time in the motoring state and the generating state, the motor stable suspension in the two states is realized, and the coupling problems in the two states are solved; on the basis of improving the accuracy of the mathematical model, the motor control performance based on the model can also be greatly improved. BRIEF DESCRIPTION OF DRAWINGS

[0039] Fig. 1(a) is a curve diagram of A, B phase winding inductance of the double 8 / 4 magnetic suspension motor according to the application;

[0040] Fig. 1(b) is a curve diagram of C, D phase winding inductance of the double 8 / 4 magnetic suspension motor according to the application;

[0041] Fig. 2(a) is a motoring working state diagram of the double 8 / 4 magnetic suspension motor;

[0042] Fig. 2(b) is a generating working state diagram of the double 8 / 4 magnetic suspension motor;

[0043] Fig. 3(a) is an equivalent magnetic circuit diagram of the torque system of the double 8 / 4 magnetic suspension motor;

[0044] Fig. 3(b) is a simplified magnetic circuit diagram of the torque system of the double 8 / 4 magnetic suspension motor;

[0045] Figure 4 Fig. 4 is a segmentation diagram of the air gap permeance of the torque system of the double 8 / 4 magnetic suspension motor;

[0046] Figure 5 Fig. 5 is a suspension force generation mechanism diagram of the double 8 / 4 magnetic suspension motor;

[0047] Figure 6 Fig. 6 is an excitation circuit principle diagram of the double 8 / 4 magnetic suspension motor in the generating state. DETAILED DESCRIPTION

[0048] The application will be further described below in combination with the drawings and specific embodiments, but the protection scope of the application is not limited thereto.

[0049] As shown in Fig. 1(a), (b), the double 8 / 4 magnetic suspension motor has A-phase, B-phase, C-phase and D-phase four-phase windings, each phase winding is composed of four windings, when the double 8 / 4 magnetic suspension motor is applied to the flywheel battery, the working range of each phase winding in the motoring state is 45° mechanical angle, and the working range in the generating state is 45° mechanical angle; the inductance rising area winding in the 0°-22.5° mechanical angle range in the motoring state generates torque as the torque phase, and the inductance flat area winding in the 22.5°-45° mechanical angle range generates suspension force as the suspension phase; the inductance flat area winding in the 0°-22.5° mechanical angle range in the generating state generates suspension force as the suspension phase, and the inductance falling area winding in the 22.5°-45° mechanical angle range generates electricity as the generating phase.

[0050] As shown in Fig. 2(a), in the motoring state, the torque phase control is turned off at the end of the inductance rising area (i.e. 22.5° mechanical angle), and the torque current of the four windings of the torque phase continues to flow i T The four windings of the suspension phase in the inductance flat area (i.e. in the 22.5°-45° mechanical angle range) pass through the suspension current i F There is coupling; as shown in Fig. 2(b), in the generating state, the motor generates suspension force F as the suspension phase in the inductance flat area (i.e. in the 0°-22.5° mechanical angle range), and the four windings of the suspension phase need to provide excitation current i G in advance before entering the inductance falling area (i.e. before 22.5° mechanical angle), at this time, the suspension phase has an advance excitation conduction mechanical angle θ1 (0<θ1<22.5°) before 22.5° mechanical angle, and the suspension current i F The excitation current i G There is coupling in the (22.5°-θ1)-22.5° mechanical angle range.

[0051] As shown in Fig. 3(a), the torque system equivalent magnetic circuit diagram of the double 8 / 4 magnetic suspension motor, the four windings of each phase generate torque flux together, as shown in Fig. 3(b), the torque system simplified magnetic circuit diagram of the double 8 / 4 magnetic suspension motor, from the simplified magnetic circuit diagram, it can be obtained that:

[0052]

[0053] In the formula, N is the number of turns of the winding, i1, i2, i3, i4 are the torque currents of the four windings of each phase, and i1=i2=i3=i4, φ1, φ2, φ3, φ4 are the magnetic fluxes of the four windings of each phase, P1, P2, P3, P4 are the air gap permeances under the four stator poles of each phase;

[0054] Solving the equation of formula (1), it can be obtained that:

[0055]

[0056] In the formula, P is the total air gap permeance of four stator poles in each phase, i.e. P=P1+P2+P3+P4;

[0057] According to formula (2), the air gap flux can be expressed in matrix form as:

[0058]

[0059] In addition, because:

[0060] ψ=Nφ (4)

[0061] In the formula, ψ represents the magnetic linkage of the motor, and φ represents the air gap flux;

[0062] According to formula (3) and formula (4), the magnetic linkage of each phase winding can be obtained as:

[0063]

[0064] The relationship between the magnetic linkage of each phase winding and the current of each phase and the inductance between the four windings of each phase can be expressed as:

[0065]

[0066] In the formula, L1, L2, L3, and L4 represent the self-inductance of the four windings of each phase, M αβ is the mutual inductance between the four windings of each phase, and α and β are the winding numbers. There are four windings in each phase, so α and β can take values of 1, 2, 3, and 4, and α≠β;

[0067] According to the above formula (5) and formula (6), the self-inductance between the windings of each phase can be obtained as:

[0068]

[0069] According to the above formula (5) and formula (6), the mutual inductance between the windings of each phase can be obtained as:

[0070]

[0071] As Figure 4 shown in the air gap magnetic circuit partition diagram of the double 8 / 4 magnetic suspension motor, the permeance can be divided into three parts: the air gap permeance of the overlapping part of the stator pole and the rotor pole is P1, the air gap permeance of the edge magnetic circuit of the lower oval is P2, and the air gap permeance of the edge magnetic circuit of the upper oval is P3. The air gap permeance of the edge magnetic circuit has the following relationship:

[0072]

[0073] Wherein, constant a = 1.49, μ0 is the vacuum permeability, l is the motor core length, σ is the short axis radius of the edge magnetic circuit of the ellipse, g is the air gap length, and the value of k in the figure is determined by the ratio of σ to g.

[0074] Then the air gap edge permeance P2, P3 can be obtained by integrating formula (9) :

[0075]

[0076] Wherein, r is the stator pole arc radius, θ is the rotor position angle, and σ = rθ;

[0077] The air gap permeance P1 at the alignment position of the stator pole and the rotor pole is:

[0078]

[0079] Then the total air gap permeance can be obtained by summing formula (10) and formula (11) :

[0080]

[0081] From formula (12), the air gap permeance under the four stator poles of each phase winding is respectively:

[0082]

[0083] Wherein, x1, y1 are the rotor displacement in the radial x direction and y direction of the motor;

[0084] When any phase is conducting as a torque phase, the radial torque field energy storage of the motor can be represented as:

[0085]

[0086] The instantaneous electromagnetic torque mathematical model of any phase as a torque winding can be obtained by taking the partial derivative of its radial magnetic field energy storage with respect to the rotor position angle θ, and then the motor torque can be obtained from formula (14) :

[0087]

[0088] Wherein, i M is the motor torque current, and i1 = i2 = i3 = i4 = i M ; J(θ) is the motor torque coefficient, which is related to the rotor position angle, and can be represented as:

[0089]

[0090] As shown in Figure 5 , when each phase is a suspension winding, first, the bias current component I of the suspension current is input, the magnetic flux density at each place in the air gap is the same, and the rotor remains balanced. It is known that the air gap flux density expression is:

[0091]

[0092] where B is the air-gap flux density, N is the number of turns of the winding, and I is the bias current;

[0093] The magnetic field in the air gap is uniform, and the expression of the radial levitation magnetic field energy of a single stator pole is:

[0094]

[0095] where W2 represents the radial levitation magnetic field energy, S is the cross-sectional area of a single stator pole, H is the magnetic field strength in the air gap, V is the air gap volume corresponding to S for a single magnetic pole, and g is the air gap length;

[0096] Figure 5 The levitation force generated by the motor is decomposed into the x direction and the y direction, and it is assumed that the rotor has a displacement x0 (known) in the x direction, x0 << g, so that air gap 1 is increased to g+x0 and air gap 2 is reduced to g-x0. At this time, in order to maintain the balance of the rotor, a control current component i needs to be passed through the levitation winding again, so that i4 = I+i and i2 = I-i. At this time, the current i4 passed through the winding at air gap 1 is different from the current i2 passed through the winding at air gap 2, so the force F1 generated at air gap 1 and the force F2 generated at air gap 2 can be obtained from formula (18) as follows:

[0097]

[0098]

[0099] where W air1 represents the radial levitation magnetic field energy at air gap 1, W air2 represents the radial levitation magnetic field energy at air gap 2, B1 represents the magnetic induction strength at air gap 1, B2 represents the magnetic induction strength at air gap 2, H1 represents the magnetic field strength at air gap 1, H2 represents the magnetic field strength at air gap 2, F1 represents the force at air gap 1, F2 represents the force at air gap 2, F represents the levitation force, I is the bias current component of the levitation current, and i is the control component of the levitation current.

[0100] At this time, an x positive direction levitation force is generated, and the levitation force model can be obtained from formula (19) as follows:

[0101]

[0102] The linearization processing is performed on formula (20), Taylor series expansion is performed, and the second-order and higher infinitesimal quantities are omitted:

[0103] F = k x x0+k i i (21)

[0104] In the formula, The suspension forces in the x negative direction, y positive direction and y negative direction are the same as the above principle and derivation process, which will not be described here.

[0105] When the double 8 / 4 magnetic suspension motor is in the electric state, after the winding torque phase ends, the torque current control is turned off, and the torque current i T of the four windings (i.e., the torque current of the four windings) can be obtained according to the torque T and the torque mathematical model (formula (15)). T When the torque current i F is used as the bias current component I1 of the suspension current i , the control current component i1 required at this time can be obtained according to the suspension force mathematical model (formula (21)) according to the size of the required suspension force F of the motor.

[0106] Figure 6 As shown in the excitation circuit diagram of the motor when generating electricity, it can be seen from the figure that:

[0107] U=i G R-e (22)

[0108]

[0109] The relationship between the generated output voltage and the excitation current in the power generation mathematical model can be obtained from formula (22) and formula (23):

[0110]

[0111] In the formula, U is the generated output voltage, i G is the excitation current, R represents the winding resistance, ψ represents the excitation flux, and t represents time.

[0112] When the double 8 / 4 magnetic suspension motor is in the generating state, the excitation current i G is first obtained according to formula (24) from the generated output voltage U, and the value of i G is used as the bias current component I2 of the suspension current i F , and the control current component i2 of the suspension current i F at this time is obtained from the suspension force mathematical model (formula (21)) according to the size of the required suspension force F, so that the suspension force F of the motor remains unchanged while the excitation is normal.

[0113] The application also provides a double 8 / 4 magnetic suspension motor precise modeling system, comprising:

[0114] A mathematical model construction module is used to construct the instantaneous electromagnetic torque mathematical model, the suspension force mathematical model and the motor power generation mathematical model.

[0115] The suspension current control component solving module solves the control component of the suspension current in the motoring state according to the instantaneous electromagnetic torque mathematical model and the suspension force mathematical model, and solves the control component of the suspension current in the power generation state according to the suspension force mathematical model and the motor power generation mathematical model.

[0116] Based on the same inventive concept as the accurate modeling method of the dual 8 / 4 magnetic suspension motor considering the motoring / suspension / power generation coupling, the present application also provides an electronic device comprising one or more processors and one or more memories, the memories storing computer readable codes, wherein the computer readable codes, when executed by the one or more processors, perform the implementation of the accurate modeling method of the dual 8 / 4 magnetic suspension motor considering the motoring / suspension / power generation coupling. The memories can include non-volatile storage media and internal memories; the non-volatile storage media can store an operating system and computer readable codes. The computer readable codes include program instructions that, when executed, can cause the processor to perform any of the accurate modeling methods of the dual 8 / 4 magnetic suspension motor considering the motoring / suspension / power generation coupling. The processor is used to provide computing and control capabilities to support the operation of the entire electronic device. The memories provide an environment for the computer readable codes in the non-volatile storage media to run, and the computer readable codes, when executed by the processor, can cause the processor to perform any of the accurate modeling methods of the dual 8 / 4 magnetic suspension motor considering the motoring / suspension / power generation coupling.

[0117] It should be understood that the processor can be a central processing unit (CPU), and the processor can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor.

[0118] The computer readable storage medium can be an internal storage unit of the electronic device in the foregoing embodiments, such as a hard disk or a memory of the computer device. The computer readable storage medium can also be an external storage device of the electronic device, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the electronic device.

[0119] The above embodiments are preferred embodiments of the present application, but the present application is not limited to the above embodiments, and any obvious modifications, replacements or variations made by those skilled in the art without departing from the spirit of the present application shall fall within the scope of protection of the present application.

Claims

1. A method for precise modeling of an electric / magnetic levitation / generation coupled magnetic levitation motor, comprising: constructing a mathematical model of instantaneous electromagnetic torque of the motor, the mathematical model of instantaneous electromagnetic torque being obtained by partial derivation of magnetic field energy storage with respect to a rotor position angle; constructing a mathematical model of levitation force of the motor, the mathematical model of levitation force being obtained by derivation of energy variation of a radial levitation magnetic field generated by four windings of each phase winding with respect to air gap size variation; the mathematical model of instantaneous electromagnetic torque is specifically: the radial torque magnetic field energy storage W1 is: the self-inductance and mutual inductance satisfy: wherein N is a winding number, P1, P2, P3 and P4 are air gap permeances under four stator poles of each phase winding, and P is a total air gap permeance under four stator poles of each phase winding, and P = P1 + P2 + P3 + P4; the total air gap permeance satisfies: wherein a is a constant, μ0 is a vacuum permeability, l is a motor core length, g is an air gap length, r is a stator pole arc radius, and θ is a rotor position angle; the mathematical model of levitation force is: wherein F represents the levitation force, F1 represents a force at air gap 1, F2 represents a force at air gap 2, B1 represents a magnetic induction intensity at air gap 1, B2 represents a magnetic induction intensity at air gap 2, H1 represents a magnetic field intensity at air gap 1, H2 represents a magnetic field intensity at air gap 2, S is a single stator pole cross-sectional area, x0 is a rotor displacement, g is an air gap length, μ0 is a vacuum permeability, N is a winding number, I is a bias current component of a levitation current, and i is a control component of the levitation current. The double 8 / 4 magnetic levitation motor is applied to a flywheel battery, a working range of each phase winding in an electric state is 45° mechanical angle, and a working range of each phase winding in a generation state is 45° mechanical angle; in the electric state, the inductance rising region winding in a 0°-22.5° mechanical angle range generates torque, and the inductance flat region winding in a 22.5°-45° mechanical angle range generates levitation force; in the generation state, the inductance flat region winding in the 0°-22.5° mechanical angle range generates levitation force, and the inductance falling region winding in the 22.5°-45° mechanical angle range controls generation. The method comprises: a mathematical model construction module, configured to construct the mathematical model of instantaneous electromagnetic torque, the mathematical model of levitation force and a motor generation mathematical model; and a levitation current control component solving module, configured to solve the control component of the levitation current in the electric state according to the mathematical model of instantaneous electromagnetic torque and the mathematical model of levitation force, and solve the control component of the levitation current in the generation state according to the mathematical model of levitation force and the motor generation mathematical model. A motor generation mathematical model is constructed, and the motor generation mathematical model is: Wherein U is a generation output voltage, i G is an excitation current, R represents a winding resistance, ψ represents an excitation flux linkage, and t represents time. The torque current i of the four windings is obtained according to the instantaneous electromagnetic torque mathematical model T The i T The suspension current i of the suspension phase is inputted F The bias current component I1 of the suspension current i is obtained according to the suspension force mathematical model F The control current component i1 of the suspension current i is obtained according to the suspension force mathematical model The excitation current i G The i G The control current component i2 of the levitation current i F The control current component i2 of the levitation current i F The control current component i2 of the levitation current i 2. The method of claim 1, wherein, The method comprises a memory and a processor; where T is the torque, W1 represents the radial torque magnetic field energy generated by the four windings, θ represents the rotor position angle, J(θ) is the motor torque coefficient, i M is the torque current of any winding, and i M = i T .

3. The method of claim 2, wherein, The memory is configured to store a computer program; wherein: i1, i2, i3, i4 are the torque currents of the four windings in each phase winding, and i1=i2=i3=i4; L1, L2, L3, L4 represent the self-inductance of the four windings in any phase winding; M αβ is the mutual inductance between the four windings in any phase winding, and α and β are the winding numbers, α and β taking values of 1, 2, 3, 4, and α≠β.

4. The method of claim 3, wherein, The processor is configured to execute the computer program and implement the method for precise modeling of the magnetic levitation motor according to any one of claims 1-7 when the computer program is executed. The storage medium stores a computer program, and the computer program causes the processor to execute the method for precise modeling of the magnetic levitation motor according to any one of claims 1-7 when the computer program is executed by the processor.

5. The method of claim 4, wherein, ​ ​ 6. The method of claim 1, wherein, ​ ​ 7. The method of claim 1, wherein, ​ ​ ​ 8. A system for accurate modeling of a magnetic levitation motor based on the method of any one of claims 1-7, characterized in that, ​ ​ ​ 9. An electronic device, comprising: ​ ​ ​ 10. A storage medium, characterized by ​

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