A method for modeling the mathematical model of a motor taking into account inductance harmonics

Abstract

The invention discloses a method for modeling a mathematical model of a motor taking into account inductance harmonics, which relates to the technical field of motor drive and control. A mathematical model taking into account mutual inductance harmonics between an excitation winding and an armature winding and self-inductance harmonics of an excitation winding in a synchronous rotating coordinate system is constructed, and other current differential terms in the AC and DC axis voltage equations and the excitation winding terminal voltage equations are decoupled. The method has clear ideas, is easy to understand and is convenient to operate. The method fully considers the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding, and can accurately reflect the induced pulsating voltage of the excitation winding existing in an electric excitation flux switching motor. At the same time, when the mathematical model is used to simulate the motor control strategy, the use of a finite element analysis method can be avoided, and the simulation time can be saved while ensuring the control simulation accuracy.

Description

Technical Field

[0001] The invention relates to the technical field of motor drive and control, and in particular to a method for building a mathematical model of a motor taking inductance harmonics into account. Background Art

[0002] Permanent magnet motors have the advantages of high power density, high torque density, and high efficiency, so they have attracted widespread attention and are used in new energy vehicles, wind power generation, aerospace, robotics and other fields. However, rare earth permanent magnet materials are expensive, and permanent magnet motors have problems such as difficulty in fault demagnetization, limited weak magnetic speed regulation capability, and irreversible demagnetization at high temperature. The electromagnetic motor uses excitation windings instead of permanent magnets for excitation, which overcomes the inherent defects of permanent magnet motors. The armature winding and excitation winding of the traditional electromagnetic synchronous motor are located on the stator and rotor respectively, and its rotor excitation requires brushes and slip rings, while the armature winding and excitation winding of the electromagnetic flux switching motor are both located on the stator, which can achieve brushless operation, thereby improving operation reliability.

[0003] However, the commonly used mathematical model of the electric excitation flux switching motor currently only considers the fundamental component of the mutual inductance between the armature winding and the excitation winding, ignoring the mutual inductance of each order of harmonics, and regards the self-inductance of the excitation winding as a constant, also ignoring the self-inductance of each order of harmonics, thus failing to accurately reflect the induced pulsating voltage of the excitation winding of the electric excitation flux switching motor. At the same time, when simulating the control strategy of the electric excitation flux switching motor, the commonly used magnetic field-circuit joint simulation (such as ANSYS / Maxwell and Simplorer software joint simulation or ANSYS / Maxwell and MATLAB / Simulink software joint simulation) takes a long time to simulate. Summary of the invention

[0004] In order to solve the deficiencies mentioned in the above background technology, the object of the present invention is to provide a method for modeling a motor mathematical model taking into account inductance harmonics.

[0005] The object of the present invention can be achieved by the following technical solution: a method for modeling a motor mathematical model taking into account inductance harmonics, the method comprising the following steps:

[0006] Construct a mathematical model of the electromagnetic flux switching motor in a three-phase stationary coordinate system, taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding, including the three-phase voltage equation, the excitation winding terminal voltage equation, the three-phase armature winding flux equation, the excitation winding flux equation, the mechanical motion equation and the electromagnetic torque equation;

[0007] Construct the AC / DC dq axis flux equation and the excitation winding flux equation in the synchronous rotating coordinate system, taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding, and substitute them into the dq axis voltage equation, the excitation winding terminal voltage equation and the electromagnetic torque equation in the synchronous rotating coordinate system;

[0008] Eliminate other current differential terms coupled in each voltage equation;

[0009] According to the derived mathematical model of the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding in the synchronous rotating coordinate system, a mathematical model of the electrically excited flux switching motor is built in MATLAB / Simulink, including a voltage / current module, an electromagnetic torque calculation module and a mechanical motion module.

[0010] Preferably, the mutual inductance between the field winding and the armature winding includes fundamental wave and harmonic components of various orders, and the mutual inductance expression is:

[0011]

[0012] Among them, M fa 、M fb and M fc are the mutual inductance between the ABC three-phase winding and the excitation winding, θ is the electrical angle of the rotor position, M sf With M sfi are the amplitudes of the mutual inductance of the fundamental wave and each order harmonic, θ i is the initial phase angle of each order mutual inductance harmonic.

[0013] Preferably, the self-inductance of the excitation winding includes a DC component, a fundamental wave and harmonic components of each order, and the self-inductance expression is:

[0014]

[0015] Among them, L f is the self-inductance of the excitation winding, L ff is the DC component of the excitation winding self-inductance, L ffi is the amplitude of the fundamental wave and each order harmonic self-inductance, θ fi is the initial phase angle of each order of self-inductance harmonics.

[0016] Preferably, the mathematical model of the electromagnetic flux switching motor in a three-phase stationary coordinate system taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding is as follows:

[0017]

[0018] Among them, u s ,i s and ψ sare three-phase voltage, current and flux, u s =[u A u B u C ] T ,i s =[i A i B i C ] T , ψ s =[ψ A ψ B ψ C ] T ; R s =diag([R s R s R s ]) is the resistance matrix of the three-phase armature winding; L ss is the three-phase armature winding inductance matrix; R f is the excitation winding resistance; i f is the excitation current; M sf is the mutual inductance matrix of the armature winding and the excitation winding; L f is the self-inductance of the excitation winding; f is the magnetic flux of the excitation winding; T e is the electromagnetic torque; T L is the load torque; J is the moment of inertia; p n is the number of rotor pole pairs; ω e is the electrical angular velocity; B is the damping coefficient.

[0019] Preferably, the dq-axis flux equation is:

[0020]

[0021] The field winding flux equation is:

[0022]

[0023] Among them, ψ d , q and ψ f are the direct-axis flux, quadrature-axis flux and field winding flux, L d and L q are the direct-axis and quadrature-axis inductances, i d 、i q and i f are the direct axis current, quadrature axis current and excitation current respectively, θ is the electrical angle of the rotor position, M sf 、M sf(3k-1) and M sf(3k+1) are the amplitudes of the fundamental, (3k-1)th and (3k+1)th harmonic mutual inductances, θ 3k-1 and θ3k+1 are the initial phase angles of the (3k-1)th and (3k+1)th mutual inductance harmonics, L ff is the DC component of the excitation winding self-inductance, L ffi is the amplitude of the fundamental wave and each order harmonic self-inductance, θ fi is the initial phase angle of each order of self-inductance harmonics.

[0024] Preferably, the electromagnetic torque equation taking into account the mutual inductance harmonics between the field winding and the armature winding and the self-inductance harmonics of the field winding in the synchronous rotating coordinate system is:

[0025]

[0026] Among them, T e is the electromagnetic torque, p n is the number of rotor pole pairs, L d and L q are the direct-axis and quadrature-axis inductances, i d 、i q and i f are the direct axis current, quadrature axis current and excitation current respectively, θ is the electrical angle of the rotor position, M sf 、M sf(3k-1) and M sf(3k+1) are the amplitudes of the fundamental, (3k-1)th and (3k+1)th harmonic mutual inductances, θ 3k-1 and θ 3k+1 They are the initial phase angles of the (3k-1)th and (3k+1)th mutual inductance harmonics respectively.

[0027] Preferably, the voltage equation at the excitation winding end that eliminates other current differential terms coupled in the voltage equation is:

[0028]

[0029]

[0030] The dq-axis voltage equation that eliminates other current differential terms coupled in the voltage equation is:

[0031]

[0032] in, It can be obtained from (7).

[0033] Preferably, the expressions of the variables K1, K2, K3, K4, K5 and K6 are:

[0034]

[0035] A device comprising:

[0036] one or more processors;

[0037] A memory for storing one or more programs;

[0038] When one or more of the programs are executed by one or more of the processors, the one or more processors implement the motor mathematical modeling method taking inductance harmonics into account as described above.

[0039] A storage medium containing computer executable instructions, wherein the computer executable instructions are used to execute the above-mentioned method for modeling a motor mathematical model taking into account inductance harmonics when executed by a computer processor.

[0040] Beneficial effects of the present invention:

[0041] The method proposed in the present invention has clear ideas, is easy to understand and convenient to operate, fully considers the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding, and can reflect the induced pulsating voltage of the excitation winding in the electric excitation flux switching motor.

[0042] The method proposed in the present invention can avoid the use of finite element method when simulating motor control strategy, thereby saving simulation time while ensuring simulation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0044] Figure 1 The schematic diagram of the modeling principle of the motor mathematical model of the present invention in MATLAB / Simulink;

[0045] Figure 2 The model constructed in MATLAB / Simulink of the present invention and the joint simulation model of ANSYS / Maxwell and Simplorer are shown in the waveform diagram of the induced pulsating voltage of the excitation winding jointly simulated by ANSYS / Maxwell and Simplorer under the condition of keeping the motor control strategy and control parameters consistent;

[0046] Figure 3 The model built in MATLAB / Simulink of the present invention and the joint simulation model of ANSYS / Maxwell and Simplorer are shown in the waveform of the induced pulsating voltage of the excitation winding simulated by MATLAB / Simulink under the condition of keeping the motor control strategy and control parameters consistent;

[0047] Figure 4 A comparison diagram of phase currents between the model built in MATLAB / Simulink of the present invention and the joint simulation model of ANSYS / Maxwell and Simplorer, while keeping the motor control strategy and control parameters consistent;

[0048] Figure 5 This is a comparison chart of the excitation current between the model built in MATLAB / Simulink of the present invention and the ANSYS / Maxwell and Simplorer joint simulation model, while keeping the motor control strategy and control parameters consistent. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] like Figure 1 As shown, a method for modeling a motor mathematical model taking into account inductance harmonics includes the following steps:

[0051] Step 1: Construct a mathematical model of the electromagnetic flux switching motor in a three-phase stationary coordinate system, taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding, including the three-phase voltage equation, the excitation winding terminal voltage equation, the three-phase armature winding flux equation, the excitation winding flux equation, the mechanical motion equation and the electromagnetic torque equation;

[0052] The mutual inductance between the field winding and the armature winding includes the fundamental wave and each order harmonic component. The mutual inductance expression is:

[0053]

[0054] Where θ is the electrical angle of the rotor position, M sf With M sfi are the amplitudes of the mutual inductance of the fundamental wave and each order harmonic, θ i is the initial phase angle of each order mutual inductance harmonic.

[0055] The self-inductance of the excitation winding includes DC component, fundamental wave and harmonic components of each order. The self-inductance expression is:

[0056]

[0057] Among them, L ff is the DC component of the excitation winding self-inductance, L ffi is the amplitude of the fundamental wave and each order harmonic self-inductance, θfi is the initial phase angle of each order of self-inductance harmonics.

[0058] The mathematical model of the electromagnetic flux switching motor in the three-phase stationary coordinate system taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding is:

[0059]

[0060] Among them, u s ,i s and ψ s are three-phase voltage, current and flux, u s =[u A u B u C ] T ,i s =[i A i B i C ] T , ψ s =[ψ A ψ B ψ C ] T ; R s =diag([R s R s R s ]) is the resistance matrix of the three-phase armature winding; L ss is the three-phase armature winding inductance matrix; R f is the excitation winding resistance; i f is the excitation current; M sf is the mutual inductance matrix between the armature winding and the field winding; L f is the self-inductance of the excitation winding; f is the magnetic flux of the excitation winding; T e is the electromagnetic torque; T L is the load torque; J is the moment of inertia; p n is the number of rotor pole pairs; ω e is the electrical angular velocity; B is the damping coefficient.

[0061] Step 2: Construct the dq-axis flux equation and the excitation winding flux equation in the synchronous rotating coordinate system, taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding, and substitute them into the dq-axis voltage equation, the excitation winding terminal voltage equation and the electromagnetic torque equation in the synchronous rotating coordinate system;

[0062] In the synchronous rotating coordinate system, the dq-axis flux equation and the field winding flux equation taking into account the mutual inductance harmonics between the field winding and the armature winding and the self-inductance harmonics of the field winding are:

[0063]

[0064]

[0065] In the synchronous rotating coordinate system, the dq-axis voltage equation and the excitation winding terminal voltage equation taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding are:

[0066]

[0067]

[0068]

[0069] The electromagnetic torque equation taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding in the synchronous rotating coordinate system is:

[0070]

[0071] Step 3: Eliminate other current differential terms coupled in each voltage equation, that is, the dq axis voltage equation and the excitation winding terminal voltage equation only contain di d / dt、di q / dt and di f / dt;

[0072] In order to simplify the expression, variables such as K1, K2, K3, K4, K5 and K6 are introduced:

[0073]

[0074] From (6) and (7), we can get di d / dt and di q / dt About di f The expressions of / dt are shown in (11) and (12).

[0075]

[0076]

[0077] Substituting (11) and (12) into (8), we obtain

[0078]

[0079] Therefore, the excitation winding terminal voltage equation and the dq axis voltage equation can be obtained without coupling other current differential terms, that is, di can be obtained from the dq axis voltage and the excitation winding terminal voltage respectively. d / dt、di q / dt and di f / dt, and then integrate to get the dq axis current and the excitation current.

[0080] Step 4: Based on the derived mathematical model of the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding in the synchronous rotating coordinate system, a mathematical model of the electrically excited flux switching motor is built in MATLAB / Simulink, including a voltage / current module, an electromagnetic torque calculation module, and a mechanical motion module.

[0081] The principle of building a mathematical model of an electrically excited flux switching motor in MATLAB / Simulink is as follows Figure 1 As shown. The mathematical model takes into account the 5th and 7th mutual inductance harmonics between the excitation winding and the armature winding and the 6th harmonic of the self-inductance of the excitation winding. The motor parameters used in the MATLAB / Simulink simulation are all finite element simulation values ​​of the motor under fixed working conditions. The mathematical model that takes into account the 5th and 7th mutual inductance harmonics between the excitation winding and the armature winding and the 6th harmonic of the self-inductance of the excitation winding can further reflect the induced pulsating voltage of the excitation winding.

[0082] Based on the same inventive concept, the present invention also provides a computer device, which includes: one or more processors, and a memory for storing one or more computer programs; the program includes program instructions, and the processor is used to execute the program instructions stored in the memory. The processor may be a central processing unit (CPU), or 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. It is the computing core and control core of the terminal, which is used to implement one or more instructions, specifically for loading and executing one or more instructions in a computer storage medium to implement the above method.

[0083] It needs to be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium, on which a computer program is stored, and the computer program is executed by a processor to execute the above method. The storage medium can adopt any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electrical, magnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples (non-exhaustive list) of computer-readable storage media include: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program, which can be used by an instruction execution system, device or device or used in combination with it.

[0084] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present disclosure. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0085] The above shows and describes the basic principles, main features and advantages of the present disclosure. Those skilled in the art should understand that the present disclosure is not limited by the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present disclosure. Without departing from the spirit and scope of the present disclosure, the present disclosure may have various changes and improvements, and these changes and improvements fall within the scope of the present disclosure to be protected.

Claims

1. A method for modeling a motor mathematical model taking into account inductance harmonics, characterized in that: The method comprises the following steps: Construct a mathematical model of the electromagnetic flux switching motor in a three-phase stationary coordinate system, taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding, including the three-phase voltage equation, the excitation winding terminal voltage equation, the three-phase armature winding flux equation, the excitation winding flux equation, the mechanical motion equation and the electromagnetic torque equation; Construct the AC / DC dq axis flux equation and the excitation winding flux equation in the synchronous rotating coordinate system, taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding, and substitute them into the dq axis voltage equation, the excitation winding terminal voltage equation and the electromagnetic torque equation in the synchronous rotating coordinate system; The electromagnetic torque equation in the synchronous rotating coordinate system taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding is: Among them, T e is the electromagnetic torque, p n is the number of rotor pole pairs, L d and L q are the direct-axis and quadrature-axis inductances, i d 、i q and i f are the direct axis current, quadrature axis current and excitation current respectively, θ is the electrical angle of the rotor position, M sf 、M sf(3k-1) and M sf(3k+1) are the amplitudes of the fundamental, (3k-1)th and (3k+1)th harmonic mutual inductances, θ 3k-1 and θ 3k+1 are the initial phase angles of the (3k-1)th and (3k+1)th mutual inductance harmonics respectively; The voltage equation at the excitation winding end that eliminates other current differential terms coupled in the voltage equation is: Where, L ff is the DC component of the excitation winding self-inductance, L ffi is the amplitude of the fundamental wave and each order harmonic self-inductance, θ fi is the initial phase angle of each order of self-inductance harmonics; The dq-axis voltage equation that eliminates other current differential terms coupled in the voltage equation is: in, It can be obtained from (7); The expressions of the variables K1, K2, K3, K4, K5 and K6 are: Eliminate other current differential terms coupled in each voltage equation; According to the derived mathematical model of the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding in the synchronous rotating coordinate system, a mathematical model of the electrically excited flux switching motor is built in MATLAB / Simulink, including a voltage / current module, an electromagnetic torque calculation module and a mechanical motion module.

2. The method for modeling a motor mathematical model taking into account inductance harmonics according to claim 1, characterized in that: The mutual inductance between the field winding and the armature winding includes fundamental wave and harmonic components of each order, and the mutual inductance expression is: Among them, M fa 、M fb and M fc are the mutual inductance between the ABC three-phase winding and the excitation winding, θ is the electrical angle of the rotor position, M sf With M sfi are the amplitudes of the mutual inductance of the fundamental wave and each order harmonic, θ i is the initial phase angle of each order mutual inductance harmonic.

3. The method for modeling a motor mathematical model taking into account inductance harmonics according to claim 1, characterized in that: The self-inductance of the excitation winding includes a DC component, a fundamental wave and harmonic components of each order. The self-inductance expression is: Among them, L f is the self-inductance of the field winding.

4. The method for modeling a motor mathematical model taking into account inductance harmonics according to claim 1, characterized in that: The mathematical model of the electromagnetic flux switching motor in a three-phase stationary coordinate system, taking into account the mutual inductance harmonics between the excitation winding and the armature winding and the self-inductance harmonics of the excitation winding, is as follows: Among them, u s ,i s and ψ s are three-phase voltage, current and flux, u s =[u A u B u C ] T ,i s =[i A i B i C ] T , ψ s =[ψ A ψ B ψ C ] T ; R s =diag([R s R s R s ]) is the resistance matrix of the three-phase armature winding; L ss is the three-phase armature winding inductance matrix; R f is the resistance of the excitation winding; i f is the excitation current; M sf is the mutual inductance matrix of the armature winding and the excitation winding; L f is the self-inductance of the excitation winding; f is the magnetic flux of the excitation winding; T e is the electromagnetic torque; T L is the load torque; J is the moment of inertia; p n is the number of rotor pole pairs; ω e is the electrical angular velocity; B is the damping coefficient.

5. The method for building a mathematical model of a motor taking into account inductance harmonics according to claim 1, characterized in that: The dq-axis flux equation is: The field winding flux equation is: Among them, ψ d , q and ψ f are the direct-axis flux, quadrature-axis flux and field winding flux, L d and L q are the direct-axis and quadrature-axis inductances, i d 、i q and i f are the direct axis current, quadrature axis current and excitation current respectively, θ is the electrical angle of the rotor position, M sf 、M sf(3k-1) and M sf(3k+1) are the amplitudes of the fundamental, (3k-1)th and (3k+1)th harmonic mutual inductances, θ 3k-1 and θ 3k+1 are the initial phase angles of the (3k-1)th and (3k+1)th mutual inductance harmonics, L ff is the DC component of the excitation winding self-inductance, L ffi is the amplitude of the fundamental wave and each order harmonic self-inductance, θ fi is the initial phase angle of each order of self-inductance harmonics.

6. A device, characterized in that: include: one or more processors; A memory for storing one or more programs; When one or more of the programs are executed by one or more of the processors, the one or more processors implement a method for modeling a motor mathematical model taking into account inductance harmonics as described in any one of claims 1-5.

7. A storage medium containing computer executable instructions, characterized in that: The computer executable instructions are used to execute the method for modeling a motor mathematical model taking into account inductance harmonics as described in any one of claims 1 to 5 when executed by a computer processor.

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