A mathematical modeling method of an asymmetrical interior permanent magnet motor

Abstract

The application belongs to the technical field of permanent magnet motor modeling, and discloses a mathematical modeling method of an asymmetric interior permanent magnet motor, which specifically comprises the following steps: considering that the permanent magnet axis of the asymmetric interior permanent magnet motor is ahead of the maximum reluctance axis by 45 degrees of electric angle, selecting the permanent magnet axis as a reference direct axis, and establishing an air gap distribution function of the asymmetric interior permanent magnet motor; according to the air gap distribution function, successively establishing winding magnetic potential, magnetic density and flux distribution functions under the action of A-phase, B-phase and C-phase currents, and calculating an inductance matrix of the asymmetric interior permanent magnet motor; performing park transformation on the motor model in a three-phase coordinate system to obtain a mathematical model of the asymmetric interior permanent magnet motor in a corresponding dq coordinate system. The application realizes the establishment of the mathematical model of the asymmetric interior permanent magnet motor considering the magnetic axis offset, and provides a model basis for the control method design and operation performance analysis of the asymmetric interior permanent magnet motor with improved torque component utilization.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet motor modeling technology, specifically relating to a mathematical modeling method for an asymmetric built-in permanent magnet motor. Background Technology

[0002] The modern electric vehicle industry has an urgent need for high-performance, high-quality motors. Compared with induction motors and synchronous reluctance motors, permanent magnet synchronous motors (PMMs) have advantages such as high torque density and high efficiency, and have been widely used in electric vehicles and other industrial fields. In an internal permanent magnet (IPM) motor, the permanent magnet is located inside the rotor, providing reluctance torque through the difference in inductance between the direct and quadrature axes. However, because traditional IPM motors typically employ a symmetrical rotor structure, the current angle corresponding to the peak permanent magnet torque and the peak reluctance torque theoretically differs by 45°, resulting in a combined torque that is less than the algebraic sum of the torque components, leading to low torque component utilization. Furthermore, rare-earth permanent magnet materials are expensive, increasing the manufacturing cost of permanent magnet motors and hindering large-scale application and promotion. How to effectively improve torque component utilization and reduce the amount of rare-earth permanent magnet materials used has become a hot topic in the motor industry.

[0003] To improve torque density, Professor TAL ipo of the University of Wisconsin-Madison proposed an asymmetric rotor structure IPM motor. This motor achieves an asymmetric rotor structure through a hybrid rotor structure or auxiliary magnetic barriers, resulting in peak permanent magnet torque and peak reluctance torque at similar current angles. This improves the utilization rate of the motor's torque components and further enhances its torque density. However, current research mainly focuses on the structural design and optimization for improving motor torque density; mathematical models applicable to the operation and control analysis of asymmetric built-in permanent magnet motors are still lacking.

[0004] Because the maximum reluctance axis of a traditional IPM motor is aligned with the permanent magnet axis, while the maximum reluctance axis of an asymmetric built-in permanent magnet motor is offset from the permanent magnet axis, it is difficult to analyze the novel asymmetric built-in permanent magnet motor using the mathematical model of a traditional permanent magnet motor. Existing literature analyzes the torque components of asymmetric motors based on different reference coordinate systems, but there is still a lack of mathematical models for voltage and flux linkage of asymmetric built-in permanent magnet motors, which brings difficulties to the design of control methods and the analysis of the operating performance of such motors. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a mathematical modeling method for asymmetric built-in permanent magnet motors, which solves the problem of establishing mathematical models for voltage and flux linkage in existing technologies.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A mathematical modeling method for an asymmetric built-in permanent magnet motor, specifically including the following steps:

[0008] Considering that the permanent magnet axis of the asymmetric built-in permanent magnet motor leads the maximum reluctance axis by 45° electrical angle, the permanent magnet axis is selected as the reference direct axis, and the air gap distribution function of the asymmetric built-in permanent magnet motor is established.

[0009] Based on the air gap distribution function, the winding magnetomotive force, magnetic flux density and magnetic flux distribution functions under the action of phase A, phase B and phase C current are established in sequence, and the inductance matrix of the asymmetric built-in permanent magnet motor is calculated.

[0010] A Parker transformation is performed on the motor model in the three-phase coordinate system to obtain the mathematical model of the asymmetric built-in permanent magnet motor in the corresponding dq coordinate system.

[0011] Furthermore, the air gap distribution function of the asymmetric built-in permanent magnet motor is as follows:

[0012]

[0013] In the formula, β r β represents the spatial electrical angle from the stator to the reference q-axis. s The spatial electrical angle from the stator to the a-phase axis represents the rotor position θ. r The angle from the reference q-axis to the a-phase axis is used to represent the length. α1 represents the reciprocal average of the maximum and minimum air gap lengths, and α2 represents the parameter controlling the maximum and minimum air gap lengths. The maximum air gap length is (α1-α2). -1 The minimum air gap length is (α1+α2). -1 .

[0014] Furthermore, the winding magnetomotive force distribution functions under the action of phase A, phase B, and phase C currents are as follows:

[0015]

[0016]

[0017]

[0018] In the formula, MMF as MMF bs and MMF cs These are the winding magnetomotive force distribution functions under the action of phase A, phase B, and phase C currents, respectively, N. s Indicates the number of stator turns per phase, i a i b and i c This represents the phase current.

[0019] Furthermore, the air gap magnetic flux density distribution function under single-phase current is as follows:

[0020]

[0021]

[0022]

[0023] In the formula, B as B bs and B cs These are the air gap magnetic flux density distribution functions under the action of phase A, phase B, and phase C currents, respectively, and μ0 is the air permeability.

[0024] Furthermore, the flux linkage of phase A winding under the action of phase A, phase B, and phase C currents is as follows:

[0025]

[0026]

[0027]

[0028] In the formula, ψ aa , ψ ab and ψ ac These are the flux linkages of phase A windings under the action of phase A, phase B, and phase C currents, respectively, L. ls Let l represent the leakage inductance of the phase winding, l be the length of the motor core, r be the outer radius of the rotor, ζ represent the lower limit of the integral for calculating the winding flux linkage, and ψ be calculated. aa When ζ = -π / 2, calculate ψ ab When ζ=-π / 2-2π / 3, calculate ψ ac When ζ = -π / 2 - 4π / 3.

[0029] Furthermore, the inductor matrix of the asymmetric built-in permanent magnet motor is as follows:

[0030]

[0031] In the formula, φ r =2π / 3, L abc L represents the inductance matrix per phase. ms L represents the average self-inductance of each phase winding. δ This represents the amplitude of the fundamental component of the self-inductance of each phase winding.

[0032] Furthermore, by performing a Parker transformation on the motor model in the three-phase coordinate system, the flux linkage equation, stator voltage equation, and torque equation in the corresponding dq coordinate system are obtained as follows:

[0033]

[0034]

[0035]

[0036] In the formula L s L represents the self-inductance of the dq axis. Δ Indicates mutual inductance along the dq axis. ψ m ψ represents permanent magnet flux linkage. d and ψ q These represent the stator dq axis flux linkages, u and u, respectively. d and u q These represent the stator dq-axis voltages, i and i, respectively. d and i q Representing the stator dq-axis currents, r s T represents the stator phase resistance, ω represents the rotor electrical angular velocity, and T represents the rotor phase resistance. e This represents electromagnetic torque, and P represents the number of poles of the motor.

[0037] The beneficial effects of this invention are:

[0038] 1. The method of this invention provides a mathematical model for an asymmetric built-in permanent magnet motor with an offset between the permanent magnet axis and the reluctance axis. Compared with the prior art, which only analyzes the torque characteristics of the asymmetric motor, this invention establishes a comprehensive mathematical model of the motor and provides a model basis for the design of control methods and the analysis of the operating performance of the asymmetric built-in permanent magnet motor with improved torque component utilization.

[0039] 2. The method of this invention uses the permanent magnet axis as the reference axis. Compared with the mathematical modeling method that uses the maximum reluctance axis as the reference axis, this modeling form has advantages in i. d When the value is 0, it is the maximum torque per ampere (MTPA) output control, which simplifies the complexity of MTPA control and the design of speed controllers. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart of the mathematical modeling method of the present invention;

[0042] Figure 2 This is a schematic diagram of the axes of the two-pole asymmetric built-in permanent magnet motor with the permanent magnet axis as the reference straight axis according to the present invention. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] In the description of this invention, it should be understood that the terms "opening", "upper", "lower", "thickness", "top", "middle", "length", "inner", "around", etc., which indicate orientation or positional relationship, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the components or elements referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as limiting this invention.

[0045] like Figure 1 As shown, this invention provides a technical method, relating to a mathematical modeling method for an asymmetric built-in permanent magnet motor, specifically including the following steps:

[0046] S1. Considering that the permanent magnet axis of the asymmetric built-in permanent magnet motor leads the maximum reluctance axis by 45° electrical angle, the permanent magnet axis is selected as the reference direct axis, and the air gap distribution function of the asymmetric built-in permanent magnet motor is established.

[0047] S2. Based on the air gap distribution function, establish the magnetomotive force, magnetic flux density, and magnetic flux linkage functions in sequence, and calculate the inductance matrix of the asymmetric built-in permanent magnet motor.

[0048] S3. Perform Parker transformation on the motor model in the three-phase coordinate system to obtain the mathematical model of the asymmetric built-in permanent magnet motor in the corresponding dq coordinate system.

[0049] The present invention provides a mathematical model for an asymmetric built-in permanent magnet motor with an offset between the permanent magnet axis and the reluctance axis. Compared with the prior art, which only analyzes the torque characteristics of the asymmetric motor, this invention establishes a comprehensive mathematical model of the motor. At the same time, it provides a model basis for the design of control methods and the analysis of the operating performance of the asymmetric built-in permanent magnet motor with improved torque component utilization.

[0050] The method of this invention uses the permanent magnet axis as the reference axis. Compared with mathematical modeling methods that use the maximum reluctance axis as the reference axis, this modeling form has advantages in i. d When the value is 0, it is the maximum torque per ampere (MTPA) output control, which simplifies the complexity of MTPA control and the design of speed controllers.

[0051] In step S1, the permanent magnet axis is selected as the reference direct axis direction, combined with... Figure 2The diagram shows the axes of a two-pole asymmetric built-in permanent magnet motor, with rotor position θ. r Expressed as the angle from the reference q-axis to the a-phase axis, β r β represents the spatial electrical angle from the stator to the q-axis. s Let represent the spatial electrical angle from the stator to the a-phase axis. Considering that the permanent magnet axis of the asymmetric built-in permanent magnet motor leads the maximum reluctance axis by 45° electrical angle, the air gap distribution function of the asymmetric built-in permanent magnet motor is established as follows:

[0052]

[0053] In the formula, α1 represents the reciprocal average of the maximum and minimum air gap lengths, α2 represents the parameter controlling the maximum and minimum air gap lengths, and the maximum air gap length is (α1-α2). -1 The minimum air gap length is (α1+α2). -1 .

[0054] In step S2, obtaining the inductance matrix of the asymmetric built-in permanent magnet motor mainly includes the following steps:

[0055] S21. Establish the winding magnetomotive force distribution functions under the action of phase A, phase B, and phase C currents respectively:

[0056]

[0057]

[0058]

[0059] In the formula, MMF as MMF bs and MMF cs These are the winding magnetomotive force distribution functions under the action of phase A, phase B, and phase C currents, respectively, N. s Indicates the number of stator turns per phase, i a i b and i c This represents the phase current.

[0060] S22. Combining equations (1)-(4), establish the air gap magnetic flux density distribution function under single-phase current:

[0061]

[0062]

[0063]

[0064] In the formula, B as B bs and B csThese are the air gap magnetic flux density distribution functions under the action of phase A, phase B, and phase C currents, respectively, where μ0 is the air permeability.

[0065] S23. Combining equations (5)-(7), calculate the flux linkage of phase A winding under single-phase current:

[0066]

[0067]

[0068]

[0069] In the formula, ψ aa , ψ ab and ψ ac These are the flux linkages of phase A windings under the action of phase A, phase B, and phase C currents, respectively, L. ls Let l represent the leakage inductance of the phase winding, l be the length of the motor core, r be the outer radius of the rotor, ζ represent the lower limit of the integral for calculating the winding flux linkage, and ψ be calculated. aa When ζ = -π / 2, calculate ψ ab When ζ=-π / 2-2π / 3, calculate ψ ac When ζ = -π / 2 - 4π / 3; similarly, the flux linkages of the B-phase and C-phase windings can be obtained;

[0070] S24. Combining equations (8)-(10), the inductance matrix of the asymmetric built-in permanent magnet motor is calculated as follows:

[0071]

[0072] In the formula, φ r =2π / 3, L abc L represents the inductance matrix per phase. ms L represents the average self-inductance of each phase winding. δ Indicates the amplitude of the fundamental component of the self-inductance of each phase winding:

[0073] L ms =μ0N s 2 πrlα1 (12)

[0074]

[0075] In step S3, the flux linkage equation and voltage equation in the three-phase coordinate system are as follows:

[0076]

[0077]

[0078] In the formula ψ m ψ represents permanent magnet flux linkage. abcIndicates the stator three-phase flux linkage, i abc U represents the three-phase stator current. abc Represents the three-phase stator voltage, r s Indicates the stator phase resistance;

[0079] The Parker transformation matrix for transforming the various physical quantities of the motor from the stator three-phase coordinate system to the rotor coordinate system is as follows:

[0080]

[0081] By performing a Parker transformation on the motor model in the three-phase coordinate system, the flux linkage equation, stator voltage equation, and torque equation in the corresponding dq coordinate system are obtained as follows:

[0082]

[0083]

[0084]

[0085] In the formula L s L represents the self-inductance of the dq axis. Δ Indicates mutual inductance along the dq axis. ψ m ψ represents permanent magnet flux linkage. d and ψ q These represent the stator dq axis flux linkages, u and u, respectively. d and u q These represent the stator dq-axis voltages, i and i, respectively. d and i q Representing the stator dq-axis current, ω represents the rotor electric angular velocity, and T represents the rotor electric angular velocity. e This represents electromagnetic torque, and P represents the number of poles of the motor.

[0086] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0087] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A mathematical modeling method for an asymmetric built-in permanent magnet motor, characterized in that, Specifically, the following steps are included: Considering that the permanent magnet axis of the asymmetric built-in permanent magnet motor leads the maximum reluctance axis by 45° electrical angle, the permanent magnet axis is selected as the reference direct axis, and the air gap distribution function of the asymmetric built-in permanent magnet motor is established. Based on the air gap distribution function, the winding magnetomotive force, magnetic flux density and magnetic flux distribution functions under the action of A-phase, B-phase and C-phase currents are established in sequence, and the inductance matrix of the asymmetric built-in permanent magnet motor is calculated. Perform a Parker transformation on the motor model in the three-phase coordinate system to obtain the corresponding dq Mathematical model of an asymmetric built-in permanent magnet motor in a coordinate system; The air gap distribution function of the asymmetric built-in permanent magnet motor is as follows: (1) In the formula, βr Indicates stator to reference q Spatial electrical angle of the axis, βs Indicates stator to a Spatial electrical angle of phase axis, rotor position θr Use reference q Axis to a Expressed by the angle of the phase axis. α 1 represents the reciprocal average of the maximum and minimum air gap lengths. α 2 represents the parameter controlling the maximum and minimum air gap lengths, where the maximum air gap length is... The minimum air gap length is ; The winding magnetomotive force distribution functions under the action of phase A, phase B, and phase C currents are as follows: (2) (3) (4) In the formula, MMF as MMF bs and MMF cs These are the winding magnetomotive force distribution functions under the action of phase A, phase B, and phase C currents, respectively. Ns Indicates the number of stator turns per phase. ia , ib and ic This represents the phase current.

2. The mathematical modeling method for the asymmetric built-in permanent magnet motor according to claim 1, characterized in that, The air gap magnetic flux density distribution function under single-phase current is as follows: (5) (6) (7) In the formula, Bas , Bbs and Bcs These are the air gap magnetic flux density distribution functions under the action of phase A, phase B, and phase C currents, respectively. μ 0 represents the permeability of air.

3. The mathematical modeling method for the asymmetric built-in permanent magnet motor according to claim 2, characterized in that, The flux linkage of phase A winding under the action of phase A, phase B, and phase C currents is as follows: (8) (9) (10) In the formula, ψaa , ψab and ψac These are the magnetic flux linkages of the A-phase winding under the action of A-phase, B-phase, and C-phase currents, respectively. Lls Indicates leakage inductance of the phase winding. l The length of the motor core. r The outer radius of the rotor. ζ This indicates the lower limit of integration for calculating winding flux linkage. ψaa hour ,calculate ψab hour ,calculate ψac hour .

4. The mathematical modeling method for the asymmetric built-in permanent magnet motor according to claim 3, characterized in that, The inductor matrix of the asymmetric built-in permanent magnet motor is as follows: (11) In the formula, , Labc This represents the inductance matrix for each phase. Lms This represents the average self-inductance of each phase winding. Lδ This represents the amplitude of the fundamental component of the self-inductance of each phase winding.

5. The mathematical modeling method for the asymmetric built-in permanent magnet motor according to claim 1, characterized in that, Perform a Parker transformation on the motor model in the three-phase coordinate system to obtain the corresponding dq The flux linkage equation, stator voltage equation, and torque equation in the coordinate system are as follows: (17) (18) (19) In the formula Ls express dq Shaft self-inductance, L Δ represents dq Shaft mutual inductance, , ; ψm Indicates permanent magnet flux linkage. ψ d and ψq They represent the stator. dq Axial magnetic flux, ud and uq They represent the stator. dq shaft voltage, id and iq They represent the stator. dq shaft current, rs Indicates the stator phase resistance. ω Indicates the rotor's electric angular velocity. Te Indicates electromagnetic torque. P This indicates the number of poles of the motor.

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