CN105720874A

CN105720874A - Motor air-gap field modeling method based on distribution parameter, and application of the same

Info

Publication number: CN105720874A
Application number: CN201410736628.8A
Authority: CN
Inventors: 钟再敏; 江尚; 张光耀
Original assignee: Tongji University
Current assignee: Valeo Interior Controls Shenzhen Co Ltd
Priority date: 2014-12-04
Filing date: 2014-12-04
Publication date: 2016-06-29
Anticipated expiration: 2034-12-04
Also published as: CN105720874B

Abstract

The invention relates to a motor air-gap field modeling method based on a distribution parameter, and application of the same. The modeling method comprises the steps: 1) selecting a motor working point: respectively dividing the motor practical working ranges of a phase current effective value and a stator current vector relative to a space phase angle of a rotor position d axis, and acquiring the motor current working point under a synchronous rectangular coordinate system according to a magnetomotive force equivalence principle; 2) solving the values for motor air-gap field distribution under each working point; 3) performing fourier series expansion on the values; and 4) fitting a fourier coefficient with a polynomial about the motor current working point, and converting the waveform of the air-gap fields into a mathematical model about quadrature-direct axis current and space mechanical angles. Compared with the prior art, the distribution parameter model for a motor, established by means of the motor air-gap field modeling method based on a distribution parameter can more accurately mathematically descript the motor; and the established model is applied to motor control so that the control accuracy is improved.

Description

Modeling method and application of motor air gap magnetic field based on distributed parameters

技术领域 technical field

本发明涉及永磁同步电机驱动控制技术领域，尤其是涉及一种基于分布参数的电机气隙磁场建模方法及其应用。 The invention relates to the technical field of drive control of permanent magnet synchronous motors, in particular to a method for modeling the air gap magnetic field of a motor based on distributed parameters and its application.

背景技术 Background technique

电动汽车是新能源汽车技术的主要发展方向，而电机驱动系统是电动汽车核心部件。永磁同步电机以其功率密度大、恒转矩的转速范围宽以及效率高等优点受到越来越多的应用。传统的电机控制算法大多采用电感这一集中参数来对电压与磁链方程进行描述，面装式永磁同步电机利用三相绕组之间的自感和互感建立定子坐标系下的电机模型，而凸极式永磁同步电机则采用双轴式理论，通过引入交直轴电感建立转子坐标系下的电机模型。该控制算法需要满足以下关于被控电机的两点假设： Electric vehicles are the main development direction of new energy vehicle technology, and the motor drive system is the core component of electric vehicles. Permanent magnet synchronous motors are used more and more for their advantages of high power density, wide speed range of constant torque and high efficiency. Most of the traditional motor control algorithms use the concentrated parameter of inductance to describe the voltage and flux equations. The surface-mounted permanent magnet synchronous motor uses the self-inductance and mutual inductance between the three-phase windings to establish the motor model in the stator coordinate system. The salient pole permanent magnet synchronous motor adopts the dual-axis theory, and establishes the motor model in the rotor coordinate system by introducing the AC-D axis inductance. The control algorithm needs to satisfy the following two assumptions about the controlled motor:

(1)永磁励磁磁场在空间波形是完全正弦的； (1) The permanent magnet excitation magnetic field is completely sinusoidal in the space waveform;

(2)电机始终工作在非磁饱和区。 (2) The motor always works in the non-magnetic saturation area.

然而由于汽车电驱动系统的特殊性，车用的永磁同步电机无法满足以上两点假设，这使得传统电机算法描述的电机模型将由于电感参数的变化而失真严重，同时其电磁转矩的计算结果也会带有较大的偏差，使其无法满足车用永磁同步电机对转矩精确/快速控制的要求。 However, due to the particularity of the automotive electric drive system, the permanent magnet synchronous motor used in the vehicle cannot satisfy the above two assumptions, which makes the motor model described by the traditional motor algorithm seriously distorted due to the change of the inductance parameter. At the same time, the calculation of the electromagnetic torque The result will also have a large deviation, making it unable to meet the requirements of precise/fast torque control of permanent magnet synchronous motors for vehicles.

本发明，从气隙磁场的数值模型入手，在充分考虑电机定转子结构特征的基础上，计及气隙磁场高次谐波、电机的磁饱和，建立电机的分布参数模型，可以得到更精确的电机数学描述，进而可以得到基于模型的电机控制方法。 In the present invention, starting from the numerical model of the air gap magnetic field, on the basis of fully considering the structural characteristics of the stator and rotor of the motor, taking into account the higher harmonics of the air gap magnetic field and the magnetic saturation of the motor, a distributed parameter model of the motor is established, which can obtain more accurate The mathematical description of the motor, and then the motor control method based on the model can be obtained.

发明内容 Contents of the invention

本发明的目的就是为了克服上述现有技术存在的缺陷而提供一种基于分布参数的电机气隙磁场建模方法及其应用，从气隙磁场的数值模型入手，在充分考虑电机定转子结构特征的基础上，计及气隙磁场高次谐波、电机的磁饱和，建立电机的分布参数模型，更准确地对电机进行数学描述，并将所建立的模型应用于电机控制中，提高了控制精度。 The purpose of the present invention is to provide a method for modeling the air-gap magnetic field of a motor based on distributed parameters and its application in order to overcome the above-mentioned defects in the prior art. Starting from the numerical model of the air-gap magnetic field, fully considering the structural characteristics of the stator and rotor of the motor On the basis of air gap magnetic field higher harmonics and the magnetic saturation of the motor, the distribution parameter model of the motor is established, and the mathematical description of the motor is more accurately described, and the established model is applied to the motor control, which improves the control precision.

本发明的目的可以通过以下技术方案来实现： The purpose of the present invention can be achieved through the following technical solutions:

一种基于分布参数的电机气隙磁场建模方法，包括以下步骤： A method for modeling the air-gap magnetic field of a motor based on distributed parameters, comprising the following steps:

1)选取电机工作点：将相电流有效值I_s和定子电流矢量相对转子位置d轴的空间相位角β的电机实际工作区间分别等分为w_l与w_β份，根据磁动势等效原则获得同步直角坐标系下的电机电流工作点： 1) Select the working point of the motor: divide the actual working range of the motor with the effective value of the phase current I _s and the space phase angle β of the stator current vector relative to the d-axis of the rotor position into w _l and w _β parts respectively, according to the magnetomotive force equivalent The principle is to obtain the motor current operating point in the synchronous Cartesian coordinate system:

${P P}_{m m} = = (({I I}_{d d}^{m m},, {I I}_{q q}^{m m}))$

其中， $I_{d}^{m} = \sqrt{3} I_{s}^{m} \cdot \cos (β^{m}), I_{q}^{m} = \sqrt{3} I_{s}^{m} \cdot \sin (β^{m}),$ β^m分别为第m个工作点的相电流有效值和空间相位角，m＝1，2，...，W，W＝w_l×w_β； in, $I_{d}^{m} = \sqrt{3} I_{the s}^{m} &Center Dot; \cos (β^{m}), I_{q}^{m} = \sqrt{3} I_{the s}^{m} &Center Dot; \sin (β^{m}),$ β ^m is the effective value of the phase current and the space phase angle of the mth working point respectively, m=1, 2,..., W, W=w _l ×w _β ;

2)求取各工作点下电机气隙磁场分布的数值其中，θ_i为相应的空间电角度坐标值，i＝1，2，...，L，L为各工作点所包含的空间电角度个数； 2) Obtain the value of the magnetic field distribution of the air gap of the motor at each operating point Wherein, θ _i is the corresponding space electrical angle coordinate value, i=1, 2, ..., L, L is the number of space electrical angles contained in each working point;

3)对所述数值进行傅里叶级数展开： 3) Carry out Fourier series expansion to described numerical value:

${\overset{^^}{B B}}_{g g}^{m m} ((θ θ)) = = {Σ Σ}_{k k = = 00}^{M m} (({a a}_{k k}^{m m} cos cos k k ((pθ pθ)) + + {b b}_{k k}^{m m} sin sin k k ((pθ pθ))))$

其中，为第m个工作点下的气隙磁场波形的傅里叶拟合，p为电机极对数，M为所选取的傅里叶级数展开阶数，θ为同步直角坐标系下的空间机械角度，为其对应的第k阶傅里叶系数； in, is the Fourier fitting of the air-gap magnetic field waveform at the mth working point, p is the number of pole pairs of the motor, M is the order of the selected Fourier series expansion, θ is the space machine in the synchronous Cartesian coordinate system angle, Its corresponding k-th order Fourier coefficient;

4)以关于电机电流工作点的多项式拟合并将气隙磁场波形转化为关于交直轴电流I_d、I_q以及空间机械角度θ的数学模型： 4) With respect to the motor current operating point polynomial fit of And transform the air-gap magnetic field waveform into a mathematical model about the orthogonal and direct axis currents I _d , I _q and the space mechanical angle θ:

${\overset{&OverBar; &OverBar;}{B B}}_{88} ((X x,, θ θ)) = = [\begin{matrix} C C ((θ θ)) & S S ((θ θ)) \end{matrix}] [\begin{matrix} A A \\ B B \end{matrix}] X x$

其中，为气隙磁场波形函数； in, is the waveform function of the air-gap magnetic field;

C(θ)＝[cos0(pθ)...cosk(pθ)...cosM(pθ)]； C(θ)=[cos0(pθ)...cosk(pθ)...cosM(pθ)];

S(θ)＝[sin0(pθ)...sink(pθ)...sinM(pθ)]； S(θ)=[sin0(pθ)...sink(pθ)...sinM(pθ)];

A＝[α₀，...，α_k，...，α_M]^T，B＝[β₀，...，β_k，...，β_M]^T； A=[α ₀ ,...,α _k ,...,α _M ] ^T , B=[β ₀ ,...,β _k ,...,β _M ] ^T ;

X＝[1，I_d，I_q，I_d ²，I_dI_q，I_q ²，...，I_d ^N，I_d ^N-1I_q，...，I_dI_q ^N-1，I_q ^N]^T； X=[1, I _d , I _q , I _d ² , I _d I _q , I _q ² ,..., I _d ^N , I _d ^N-1 I _q ,..., I _d I _q ^{N- 1} , I _q ^N ] ^T ;

A、B为分布参数，α_k为傅里叶系数的多项式系数向量，β_k为傅里叶系数的多项式系数向量，N为多项式拟合阶数。 A and B are the distribution parameters, and α _k is the Fourier coefficient The polynomial coefficient vector of , β _k is the Fourier coefficient The vector of polynomial coefficients, N is the order of polynomial fitting.

所述求取各工作点下电机气隙磁场分布的数值的方法包括有限元参数仿真法、MEC法或基于Maxwell方程的解析模型法。 The method for calculating the numerical value of the air gap magnetic field distribution of the motor at each working point includes a finite element parameter simulation method, an MEC method or an analytical model method based on Maxwell equation.

所述傅里叶级数展开阶数和多项式拟合阶数根据误差迭代收敛条件选取。 The Fourier series expansion order and the polynomial fitting order are selected according to the error iteration convergence condition.

一种电机定子电流控制方法，包括以下步骤： A motor stator current control method, comprising the following steps:

A1)按权利要求1所述建模方法获得气隙磁场波形函数 A1) obtain the air-gap magnetic field waveform function by the modeling method described in claim 1

A2)根据计算作用在定子截流导体上的总电磁转矩T_e： A2) According to Calculate the total electromagnetic torque T _e acting on the stator intercepting conductors:

${T T}_{e e} = = p p {&Integral; &Integral;}_{00}^{\frac{22 π π}{p p}} {\overset{&OverBar; &OverBar;}{B B}}_{g g} ((X x,, θ θ)) {f f}_{s the s} ((θ θ)) {l l}_{s the s} rdθ rdθ$

其中，p为电机极对数，f_s(θ)为空间每一极内由三相绕组合成的正弦分布的空间磁动势波，l_s为转子轴向长度，r为转子外径，θ为空间机械角度； Among them, p is the number of pole pairs of the motor, f _s (θ) is the space magnetomotive force wave composed of three-phase windings in each pole of space, l _s is the axial length of the rotor, r is the outer diameter of the rotor, θ is the spatial mechanical angle;

A3)将T_e转化为以I_s、β为自变量的转矩表达式Te(I_s，β)； A3) Transform _Te into a torque expression Te(I _s , β) with I _s and β as independent variables;

A4)利用获得不同相电流I_s激励下最大转矩对应的转矩角β的值，再利用坐标变换得到同步坐标系下最大转矩对应的交直轴电流工作点形成最大转矩电流比的定子电流矢量轨迹曲线，并以该曲线控制定子电流。 A4) use Obtain the value of the torque angle β corresponding to the maximum torque under the excitation of different phase currents I _s , and then use the coordinate transformation to obtain the working point of the orthogonal and direct axis current corresponding to the maximum torque in the synchronous coordinate system The stator current vector locus curve of the maximum torque-current ratio is formed, and the stator current is controlled by this curve.

一种基于气隙磁场分布的电机三相定子磁链估计方法，包括以下步骤： A method for estimating motor three-phase stator flux linkage based on air gap magnetic field distribution, comprising the following steps:

B1)按权利要求1所述的建模方法获得气隙磁场波形函数 B1) obtain the air-gap magnetic field waveform function by the modeling method described in claim 1

B2)根据定子三相绕组在空间分布的位置以及转子与定子A轴的夹角θ_r，获得不同时刻下各相磁通量φ_g对应于在空间上的积分上下限[D_P，U_P]； B2) According to the spatial distribution of the three-phase windings of the stator and the angle θ _r between the rotor and the A axis of the stator, the magnetic flux φ _g of each phase at different times corresponds to Integral upper and lower bounds on space [D _P , U _P ];

B3)利用磁通与磁链的固定倍比关系得到三相磁链关于电流跟时间的表达式ψ_P(X，θ_r)： B3) Using the fixed ratio relationship between flux and flux linkage, the expression ψ _P (X, θ _r ) of three-phase flux linkage with respect to current and time is obtained:

${ψ ψ}_{P P} ((X x,, {θ θ}_{r r})) = = {N N}_{s the s} {k k}_{w w 11} {l l}_{s the s} {&Integral; &Integral;}_{{D D.}_{P P}}^{{U u}_{P P}} (({\overset{&OverBar; &OverBar;}{B B}}_{g g} ((X x,, θ θ)) \cdot &Center Dot; ((r r + + \frac{g g}{22})))) dθ dθ$

其中，N_s为定子三相绕组每对极每相串联匝数，k_w1为绕组分布因数，l_s为转子轴向长度，r为转子外径，g为气隙宽度，P＝{A，B，C}，表示当前估计的是P相磁链。 Among them, N _s is the number of turns in series for each pair of poles and each phase of the three-phase stator winding, k _w1 is the winding distribution factor, l _s is the axial length of the rotor, r is the outer diameter of the rotor, g is the air gap width, P={A, B, C}, indicating that the current estimate is the P-phase flux linkage.

与现有技术相比，本发明具有以下有益效果： Compared with the prior art, the present invention has the following beneficial effects:

(1)采用本发明方法所建立的电机气隙磁场模型能够准确地对电机进行描述，能够精确描述考虑气隙磁场高次谐波、电机的磁饱和情况下的电机状态变化以及产生的电磁转矩，能够实现电机的离线或实时仿真。 (1) The air-gap magnetic field model of the motor established by the method of the present invention can accurately describe the motor, and can accurately describe the state change of the motor under the condition of high-order harmonics of the air-gap magnetic field and the magnetic saturation of the motor and the electromagnetic rotation generated. torque, enabling offline or real-time simulation of the motor.

(2)本发明基于分布参数电机气隙磁场模型应用广泛，既可用于电机的最优控制，也可用于故障诊断算法、基于模型的标定、基于模型的解析冗余控制等。 (2) The present invention is widely used based on the distributed parameter motor air-gap magnetic field model, which can be used not only for optimal control of motors, but also for fault diagnosis algorithms, model-based calibration, and model-based analytical redundancy control.

(3)基于本发明分布参数模型的电机三相定子磁链估计方法计算快速，不需要在线对时间积分；计算精确，不依赖定子电阻随温度的变化；计算范围宽，可用于电机所有的速度区间。 (3) The motor three-phase stator flux linkage estimation method based on the distributed parameter model of the present invention is fast in calculation, and does not need to be integrated with time online; the calculation is accurate, and does not depend on the change of the stator resistance with temperature; the calculation range is wide, and can be used for all speeds of the motor interval.

附图说明 Description of drawings

图1是本发明建模方法的流程示意图； Fig. 1 is a schematic flow chart of the modeling method of the present invention;

图2是三相定子坐标系与转子坐标系的关系示意图； Fig. 2 is a schematic diagram of the relationship between the three-phase stator coordinate system and the rotor coordinate system;

图3是本发明中用于具体实施方案的某一个4对极内置式永磁同步电机的有限元仿真模型； Fig. 3 is the finite element simulation model of a certain 4 pairs of poles built-in permanent magnet synchronous motors used in the embodiment of the present invention;

图4是本发明实施例中建模方法与有限元法计算气隙磁场分布结果对比示意图； Fig. 4 is a schematic diagram of the comparison between the modeling method and the finite element method to calculate the air gap magnetic field distribution in the embodiment of the present invention;

其中，(4a)为在工作点(70.4769，25.6515)下的对比图，(4b)为在工作点(112.5000，194.8557)下的对比图，(4c)为在工作点(-402.1733，337.4635)下的对比图； Among them, (4a) is the comparison diagram under the working point (70.4769, 25.6515), (4b) is the comparison diagram under the working point (112.5000, 194.8557), (4c) is the comparison diagram under the working point (-402.1733, 337.4635) comparison chart;

图5是本发明实施例中建模方法与有限元法计算气隙磁链的结果对比示意图； Fig. 5 is a schematic diagram of the comparison between the results of the modeling method and the finite element method for calculating the air gap flux linkage in the embodiment of the present invention;

其中，(5a)～(5c)为A相磁链在三个工作点的对比图，(5d)～(5f)为B相磁链在三个工作点的对比图，(5g)～(5i)为C相磁链在三个工作点的对比图； Among them, (5a)～(5c) are the comparison diagrams of A-phase flux linkage at three operating points, (5d)～(5f) are the comparison diagrams of B-phase flux linkage at three operating points, (5g)～(5i ) is a comparison diagram of C-phase flux linkage at three operating points;

图6是本发明实施例中建模方法与有限元法计算电磁转矩结果对比示意图； Fig. 6 is a schematic diagram of the comparison between the modeling method and the finite element method to calculate the electromagnetic torque results in the embodiment of the present invention;

其中，(6a)为相电流有效值50A时电磁转矩随转矩角β的变化情况，(6b)为相电流有效值150A时电磁转矩随转矩角β的变化情况，(6c)为相电流有效值250A时电磁转矩随转矩角β的变化情况，(6d)为相电流有效值350A时电磁转矩随转矩角β的变化情况； Among them, (6a) is the variation of the electromagnetic torque with the torque angle β when the effective value of the phase current is 50A, (6b) is the variation of the electromagnetic torque with the torque angle β when the effective value of the phase current is 150A, and (6c) is The variation of the electromagnetic torque with the torque angle β when the effective value of the phase current is 250A, (6d) is the variation of the electromagnetic torque with the torque angle β when the effective value of the phase current is 350A;

图7是本发明实施例中建模方法与有限元法计算得的最大转矩/电流比的定子电流矢量轨迹对比示意图。 Fig. 7 is a schematic diagram comparing the stator current vector trajectory of the maximum torque/current ratio calculated by the modeling method and the finite element method in the embodiment of the present invention.

具体实施方式 detailed description

下面结合附图和具体实施例对本发明进行详细说明。本实施例以本发明技术方案为前提进行实施，给出了详细的实施方式和具体的操作过程，但本发明的保护范围不限于下述的实施例。 The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is carried out on the premise of the technical solution of the present invention, and detailed implementation and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

如图1所示，本实施例提供一种基于分布参数的电机气隙磁场建模方法，包括： As shown in Figure 1, this embodiment provides a method for modeling the air gap magnetic field of a motor based on distributed parameters, including:

步骤S1，选取电机工作点：设电机实际工作区间中相电流有效值I_s∈[0I_max]，定子电流矢量i_s相对转子位置d轴的空间相位角β∈[0β_max]。将相电流有效值I_s和定子电流矢量相对转子位置d轴的空间相位角β的电机实际工作区间分别等分为w_l与w_β份，根据磁动势等效原则获得同步直角坐标系下的电机电流工作点： Step S1, select the working point of the motor: set the effective value of the phase current I _s ∈ [0I _max ] in the actual working range of the motor, and the space phase angle β ∈ [0β _max ] of the stator current vector i _s relative to the d-axis of the rotor position. Divide the effective value of the phase current I _s and the space phase angle β of the stator current vector relative to the d-axis of the rotor position, and the actual working range of the motor is divided into w _l and w _β respectively, and according to the equivalent principle of magnetomotive force, obtain the The operating point of the motor current:

${P P}_{m m} = = (({I I}_{d d}^{m m},, {I I}_{q q}^{m m}))$

其中， $I_{d}^{m} = \sqrt{3} I_{s}^{m} \cdot \cos (β^{m}), I_{q}^{m} = \sqrt{3} I_{s}^{m} \cdot \sin (β^{m}),$ β^m分别为第m个工作点的相电流有效值和空间相位角，m＝1，2，...，W，W＝w_l×w_β。 in, $I_{d}^{m} = \sqrt{3} I_{the s}^{m} &Center Dot; \cos (β^{m}), I_{q}^{m} = \sqrt{3} I_{the s}^{m} &Center Dot; \sin (β^{m}),$ β ^m are the effective value of the phase current and the space phase angle of the mth working point respectively, m=1, 2,..., W, W=w _l ×w _β .

步骤S2，求取各工作点下电机气隙磁场分布的数值其中，θ_i为相应的空间电角度坐标值，i＝1，2，...，L。 Step S2, calculate the value of the magnetic field distribution of the air gap of the motor at each operating point Wherein, θ _i is the corresponding space electric angle coordinate value, i=1, 2, . . . , L.

获得气隙磁场分布的数值解的方法包括有限元参数仿真的方法、MEC(magneticequivalentcircuits)以及基于Maxwell方程的解析模型等，本实施例以有限元方法作说明。 The methods for obtaining the numerical solution of the air gap magnetic field distribution include finite element parameter simulation method, MEC (magnetic equivalent circuits) and analytical model based on Maxwell equation, etc. This embodiment uses the finite element method for illustration.

首先利用有限元建立相应的内置式永磁同步电机模型，将步骤S1中得到的电机工作点输入到有限元多参数模型中，通过选取合适的仿真周期与步长进行有限元数值计算。利用脚本文件对有限元数据进行提取跟保存，获得不同工作点下的一周期空间电角度内气隙磁场波形共W条曲线，其中每一条曲线所包含的点数为L。 First, the corresponding built-in permanent magnet synchronous motor model is established by using finite elements, and the motor operating point obtained in step S1 is input into the finite element multi-parameter model, and the finite element numerical calculation is performed by selecting an appropriate simulation cycle and step size. Use the script file to extract and save the finite element data, and obtain a total of W curves of the air-gap magnetic field waveform in a period of space electric angle under different operating points, and the number of points contained in each curve is L.

步骤S3，定子绕组三相电流和永磁体共同励磁下产生气隙磁场，在忽略齿槽效应的情况下，对应于确定的三相电流工作点的气隙磁场将随着转子同步旋转且其分布情况保持不变。由于气隙磁场是空间上周期为的周期函数，可以利用步骤S2中各工作点P_m对应的气隙磁场数值分布作傅里叶级数展开： In step S3, the stator winding three-phase current and the permanent magnet are jointly excited to generate an air-gap magnetic field. In the case of ignoring the cogging effect, the air-gap magnetic field corresponding to the determined three-phase current operating point will rotate synchronously with the rotor and its distribution The situation remains the same. Since the air-gap magnetic field has a spatial period of Periodic function of , you can use the numerical distribution of the air gap magnetic field corresponding to each working point P _m in step S2 Do Fourier series expansion:

其中，为第m个工作点下的气隙磁场波形的傅里叶拟合，p为电机极对数，M为所选取的傅里叶级数展开阶数，θ为同步直角坐标系下的空间机械角度，为其对应的第k阶傅里叶系数。 in, is the Fourier fitting of the air-gap magnetic field waveform at the mth working point, p is the number of pole pairs of the motor, M is the order of the selected Fourier series expansion, θ is the space machine in the synchronous Cartesian coordinate system angle, Its corresponding k-th order Fourier coefficient.

步骤S4，以关于电机电流工作点的多项式拟合每个工作点P_m对应不同的电流激励，进而对应的气隙磁场空间波形的傅里叶近似解不同，即的傅里叶级数展开的系数和可表示为电流坐标(I_d，I_q)的函数： Step S4, with respect to the motor current operating point polynomial fit of Each operating point P _m corresponds to a different current excitation, and then corresponds to the Fourier approximate solution of the space waveform of the air gap magnetic field different, ie The coefficients of the Fourier series expansion of and Can be expressed as a function of current coordinates (I _d , I _q ):

${a a}_{k k}^{m m} = = {f f}_{a a} (({I I}_{d d}^{m m},, {I I}_{q q}^{m m})),, {b b}_{k k}^{m m} = = {f f}_{b b} (({I I}_{d d}^{m m},, {I I}_{q q}^{m m}))$

若对W个工作点下的和值分别用I_d、I_q的N阶多项式拟合，可得到气隙磁场分布的k阶谐波分量对应的傅里叶系数a_k和b_k关于电流工作点I_d、I_q的函数 If for W operating points and The values are fitted by N-order polynomials of I _d and I _q respectively, and the Fourier coefficients a _k and b _k corresponding to the k-order harmonic component of the air gap magnetic field distribution can be obtained as a function of the current operating point I _d and I _q

a_k(I_d，I_q)＝α_kX a _k (I _d , I _q )=α _k X

b_k(I_d，I_q)＝β_kX b _k (I _d , I _q )=β _k X

如果选取的N阶多项式为齐次多项式，则相应的α_k，β_k，X分别表示为： If the selected polynomial of order N is a homogeneous polynomial, the corresponding α _k , β _k , and X are expressed as:

${α α}_{k k} = = [[{α α}_{00}^{k k},, {α α}_{11}^{k k},, . . . . . .,, {α α}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 22}^{k k},, {α α}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 11}^{k k}]]$

${β β}_{k k} = = [[{β β}_{00}^{k k},, {β β}_{11}^{k k},, . . . . . .,, {β β}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 22}^{k k},, {β β}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 11}^{k k}]]$

X＝[1，I_d，I_q，I_d ²，I_d，I_q，I_q ²，...，I_d ^N，I_d ^N-1I_q，...，I_dI_q ^N-1，I_q ^N]^T X=[1, I _d , I _q , I _d ² , I _d , I _q , I _q ² ,..., I _d ^N , I _d ^N-1 I _q ,..., I _d I _q ^{N -1} ，I _q ^N ] ^T

至此，在考虑了I_d、I_q的影响后，可以将气隙磁场波形表示为交直轴电流I_d、I_q以及空间机械角度θ的数学模型： So far, after considering the influence of I _d and I _q , the air gap magnetic field waveform can be expressed as a mathematical model of the orthogonal and direct axis current I _d , I _q and the space mechanical angle θ:

$\begin{matrix} {\overset{&OverBar; &OverBar;}{B B}}_{g g} ((X x,, θ θ)) = = {Σ Σ}_{k k = = 00}^{M m} [[{a a}_{k k} (({I I}_{d d},, {I I}_{q q})) cos cos k k ((pθ pθ)) + + {b b}_{k k} (({I I}_{d d},, {I I}_{q q})) sin sin k k ((pθ pθ))]] \\ = = [\begin{matrix} cos cos 00 ((pθ pθ)) & . . . . . . & cos cos k k ((pθ pθ)) & . . . . . . & cos cos M m ((pθ pθ)) \end{matrix}] [\begin{matrix} {a a}_{00} \\ . . . . . . \\ {a a}_{k k} \\ . . . . . . \\ {a a}_{M m} \end{matrix}] + + [\begin{matrix} sin sin 00 ((pθ pθ)) & . . . . . . & sin sin k k pθ pθ & . . . . . . & sin sin M m ((pθ pθ)) \end{matrix}] [\begin{matrix} {b b}_{00} \\ . . . . . . \\ {b b}_{k k} \\ . . . . . . \\ {b b}_{M m} \end{matrix}] \\ = = \{\begin{matrix} \end{matrix} [\begin{matrix} cos cos 00 ((pθ pθ)) & . . . . . . & cos cos k k ((pθ pθ)) & . . . . . . & cos cos M m ((pθ pθ)) \end{matrix}] [\begin{matrix} {a a}_{00} \\ . . . . . . \\ {a a}_{k k} \\ . . . . . . \\ {a a}_{M m} \end{matrix}] + + [\begin{matrix} sin sin 00 ((pθ pθ)) & . . . . . . & sin sin k k ((pθ pθ)) & . . . . . . & sin sin M m ((pθ pθ)) \end{matrix}] [\begin{matrix} {β β}_{00} \\ . . . . . . \\ {β β}_{k k} \\ . . . . . . \\ {β β}_{M m} \end{matrix}]\} X x \\ = = [[C C {((θ θ))}_{11 \times \times ((M m + + 11))} {A A}_{((M m + + 11)) \times \times \frac{((N N + + 22)) ((N N + + 11))}{22}} + + S S {((θ θ))}_{11 \times \times ((M m + + 11))} {B B}_{((M m + + 11)) \times \times \frac{((N N + + 22)) ((N N + + 11))}{22}}]] {X x}_{\frac{((N N + + 22)) ((N N + + 11))}{22} \times \times 11} \\ = = [\begin{matrix} C C ((θ θ)) & S S ((θ θ)) \end{matrix}] [\begin{matrix} A A \\ B B \end{matrix}] X x \end{matrix}$

式中， In the formula,

C(θ)＝[cos0(pθ)...cosk(pθ)...cosM(pθ)] C(θ)=[cos0(pθ)...cosk(pθ)...cosM(pθ)]

S(θ)＝[sin0(pθ)...sink(pθ)...sinM(pθ)] S(θ)=[sin0(pθ)...sink(pθ)...sinM(pθ)]

$A A = = [\begin{matrix} {a a}_{00} \\ . . . . . . \\ {a a}_{k k} \\ . . . . . . \\ {a a}_{m m} \end{matrix}] = = [\begin{matrix} {α α}_{00}^{00},, {α α}_{11}^{00},, . . . . . .,, {α α}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 22}^{00},, {α α}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 11}^{00} \\ . . . . . . \\ {α α}_{00}^{k k},, {α α}_{11}^{k k},, . . . . . .,, {α α}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 22}^{k k},, {α α}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 11}^{k k} \\ . . . . . . \\ {α α}_{00}^{M m},, {α α}_{11}^{M m},, . . . . . .,, {α α}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 22}^{M m},, {α α}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 11}^{M m} \end{matrix}]$

$B B = = [\begin{matrix} {β β}_{00} \\ . . . . . . \\ {β β}_{k k} \\ . . . . . . \\ {β β}_{m m} \end{matrix}] = = [\begin{matrix} {β β}_{00}^{00},, {β β}_{11}^{00},, . . . . . .,, {β β}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 22}^{00},, {β β}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 11}^{00} \\ . . . . . . \\ {β β}_{00}^{k k},, {β β}_{11}^{k k},, . . . . . .,, {β β}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 22}^{k k},, {β β}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 11}^{k k} \\ . . . . . . \\ {β β}_{00}^{M m},, {β β}_{11}^{M m},, . . . . . .,, {β β}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 22}^{M m},, {β β}_{\frac{((N N + + 22)) ((N N + + 11))}{22} - - 11}^{M m} \end{matrix}]$

A、B为分布参数，其维数均为用以描述气隙磁场空间波形的分布，可以通过选择合适的傅里叶级数级数M和多项式拟合阶数N来保证气隙磁场数学模型的精度和解析方程的简易度。α_k为傅里叶系数的多项式系数向量，β_k为傅里叶系数的多项式系数向量。X为自变量所对应的N阶多项式的基底。 A and B are distribution parameters, and their dimensions are To describe the distribution of the air gap magnetic field space waveform, the accuracy of the mathematical model of the air gap magnetic field and the simplicity of the analytical equation can be ensured by selecting the appropriate Fourier series series M and polynomial fitting order N. α _k is the Fourier coefficient The polynomial coefficient vector of , β _k is the Fourier coefficient A vector of polynomial coefficients for . X is the basis of the Nth degree polynomial corresponding to the independent variable.

在获得气隙磁场模型后还可包括以下步骤： After obtaining the air gap magnetic field model, the following steps can also be included:

步骤S5，根据基于分布参数的电机气隙磁场模型获得电机磁链解析表达式，估计电机三相定子磁链。 In step S5, an analytical expression of the motor flux linkage is obtained according to the motor air-gap magnetic field model based on the distribution parameters, and the three-phase stator flux linkage of the motor is estimated.

气隙磁通量φ_g是气隙磁场强度在空间上的积分，根据A、B、C三相绕组在空间分布位置以及转子位置与定子A轴的夹角θ_r可以分别得到不同时刻通过定子三相绕组的磁场强度空间区间，该区间即为计算各相磁通量的积分上下限[D_P，U_P]，再根据磁通与磁链的固定倍比关系得到A、B、C三相磁链ψ_A，ψ_B，ψ_C的表达式。 The air gap magnetic flux φ _g is the air gap magnetic field strength Integrating in space, according to the spatial distribution positions of the three-phase windings A, B, and C and the angle θ _r between the rotor position and the stator A axis, the spatial intervals of the magnetic field intensity passing through the three-phase windings of the stator at different times can be obtained respectively. This interval is In order to calculate the upper and lower limits of the integral [D _P , _UP ] of the magnetic flux of each phase, the expressions of the three-phase flux linkage ψ _A , ψ _B , and ψ _C of A, B, and C are obtained according to the fixed multiple ratio relationship between the magnetic flux and the flux linkage .

式中，θ_r＝ω_r·t，其中ω_r为转子角速度，t为不同的时刻。 In the formula, θ _r =ω _r ·t, where ω _r is the angular velocity of the rotor, and t is a different moment.

通过改变积分的上下限，同理可以得到通过B、C两相绕组的磁链ψ_B和ψ_C。从ψ_A的表达式中可以看出磁链ψ_B(X，θ_r)和ψ_C(X，θ_r)表达式只需将A相的积分矩阵和替换成以及其中； By changing the upper and lower limits of the integral, the flux linkages ψ _B and ψ _C passing through the B and C two-phase windings can be obtained in the same way. It can be seen from the expression of ψ _A that the expressions of flux linkage ψ _B (X, θ _r ) and ψ _C (X, θ _r ) only need to integrate the integral matrix of phase A and replace with as well as in;

式中，N_s为定子三相绕组每对极每相串联匝数，k_w1为绕组分布因数，l_s为转子轴向长度，r为转子外径，g为气隙宽度。 In the formula, N _s is the number of turns in series for each pair of poles and each phase of the stator three-phase winding, k _w1 is the winding distribution factor, l _s is the axial length of the rotor, r is the outer diameter of the rotor, and g is the air gap width.

基于上述磁链方程可得到电机三相电压方程 Based on the above flux linkage equation, the three-phase voltage equation of the motor can be obtained

$\frac{&PartialD; &PartialD; {ψ ψ}_{P P}}{&PartialD; &PartialD; t t} = = \frac{&PartialD; &PartialD; {ψ ψ}_{P P}}{&PartialD; &PartialD; {θ θ}_{r r}} \cdot &Center Dot; {ω ω}_{r r} = = {U u}_{P P},, P P = = {{A A,, B B,, C C}}$

步骤S6，根据基于分布参数的电机气隙磁场模型获得电机电磁转矩解析表达式。 In step S6, an analytical expression of the electromagnetic torque of the motor is obtained according to the air-gap magnetic field model of the motor based on the distribution parameters.

在空间每一极内由三相绕组合成的正弦分布的空间磁动势波可表示为： The sinusoidally distributed space magnetomotive force wave composed of three-phase windings in each pole of space can be expressed as:

$\begin{matrix} {f f}_{s the s} ((θ θ)) = = \frac{33}{22} {F f}_{s the s} cos cos ((pθ pθ - - β β)) \\ = = \frac{33}{22} \cdot \cdot ((\frac{44}{π π} \frac{N N {k k}_{w w 11}}{22 p p} \sqrt{22} {I I}_{s the s})) \cdot \cdot cos cos ((pθ pθ - - β β)) \\ = = \frac{33 \sqrt{22} {Nk Nk}_{w w 11}}{πp πp} {I I}_{s the s} cos cos ((pθ pθ - - β β)) \end{matrix}$

式中，F_s是单相绕组基波磁动势的幅值，N为每相绕组总串联匝数，I_s为单相电流的有效值，β为定子电流矢量i_s相对转子位置d轴的空间相位角，即转矩角。 In the formula, F _s is the magnitude of the fundamental magnetomotive force of the single-phase winding, N is the total number of series turns of each phase winding, I _s is the effective value of the single-phase current, β is the stator current vector i _s relative to the rotor position d-axis The space phase angle of , that is, the torque angle.

电磁转矩用B_li法来推导，对于任意工作点机械角度微元dθ所对应的气隙长度内所产生的电磁转矩微元dt_e为 The electromagnetic torque is derived by the B _li method, and the electromagnetic torque microelement dt _e generated within the air gap length corresponding to the mechanical angle microelement dθ at any working point is

${dt dt}_{e e} = = Bli bli \cdot &Center Dot; r r = = {\overset{&OverBar; &OverBar;}{B B}}_{g g} ((X x,, θ θ)) {l l}_{s the s} {f f}_{s the s} ((θ θ)) dθ dθ \cdot &Center Dot; r r$

则作用在定子载流导体上的总电磁转矩T_e为 Then the total electromagnetic torque T _e acting on the stator current-carrying conductor is

将代入上述电磁转矩T_e表达式中，可得以I_s，β为自变量的转矩表达式Te(I_s，β)。 Will Substituting the above expression of electromagnetic torque _Te , the torque expression Te(I _s , β) can be obtained with I _s , β as independent variables.

进而，利用可以得出不同相电流I_s激励下最大转矩对应的转矩角β的值，再利用坐标变换得到同步坐标系下最大转矩对应的交直轴电流工作点即最大转矩电流比的定子电流矢量轨迹，电机控制中即可利用该曲线实现转矩/电流比最大的原则来控制定子电流，从而实现电机系统的最优控制。 Furthermore, using The value of the torque angle β corresponding to the maximum torque under the excitation of different phase current I _s can be obtained, and then the working point of the orthogonal and direct axis current corresponding to the maximum torque in the synchronous coordinate system can be obtained by coordinate transformation That is, the stator current vector trajectory of the maximum torque-to-current ratio, which can be used in motor control to control the stator current based on the principle of achieving the maximum torque/current ratio, so as to realize the optimal control of the motor system.

步骤S7，基于分布参数的电机气隙磁场模型的应用。 Step S7, the application of the motor air gap magnetic field model based on the distribution parameters.

利用步骤S5与步骤S6中建立的磁链电压方程和电磁转矩随交直轴电流变化的表达式，除可以用于实现电机的最优控制外，还可以用于建立电机的分布参数模型，该模型能够精确描述考虑气隙磁场高次谐波、电机的磁饱和情况下的电机状态变化以及产生的电磁转矩，通过数值解，能够实现电机的离线或实时仿真。此外，分布参数模型还可以用于实现基于模型的其他应用：包括但不限于故障诊断算法、基于模型的标定、基于模型的解析冗余控制等。 Using the flux linkage voltage equation and the expression of the electromagnetic torque changing with the AC-D axis current established in steps S5 and S6, it can be used to establish the distributed parameter model of the motor in addition to realizing the optimal control of the motor. The model can accurately describe the state change of the motor and the generated electromagnetic torque considering the higher harmonics of the air gap magnetic field and the magnetic saturation of the motor. Through the numerical solution, the offline or real-time simulation of the motor can be realized. In addition, the distributed parameter model can also be used to implement other model-based applications: including but not limited to fault diagnosis algorithms, model-based calibration, model-based analytical redundancy control, etc.

下面给出具体的算例对本发明的结果进行验证。本算例是以某一内置式永磁同步电机的有限元模型为基础，其电机参数如表1所示，其对应的有限元仿真模型如图3所示。 The following specific calculation examples are given to verify the results of the present invention. This calculation example is based on the finite element model of a built-in permanent magnet synchronous motor. The motor parameters are shown in Table 1, and the corresponding finite element simulation model is shown in Figure 3.

表1内置式永磁同步电机基本参数 Table 1 Basic parameters of built-in permanent magnet synchronous motor

本算例充分考虑了电机运行时实际的工作点范围，选取的三相电流幅值区间为0～400A，步长为10A，定子电流矢量i_s与d轴的空间相位角区间为0～180度，步长为10度。利用有限元软件的参数扫描功能，得到0时刻的一对极下气隙磁场的分布形状。采用傅里叶级数展开的阶数为M＝40，多项式拟合阶数为N＝3，对得到的气隙磁场分布进行拟合，得到气隙磁场关于交直轴电流的表达式： This calculation example fully considers the range of the actual working point when the motor is running. The selected three-phase current amplitude range is 0-400A, the step size is 10A, and the space phase angle range between the stator current vector i _s and the d-axis is 0-180 degrees with a step size of 10 degrees. Using the parameter scanning function of the finite element software, the distribution shape of a pair of subpolar air gap magnetic fields at time 0 is obtained. The order of Fourier series expansion is M=40, and the order of polynomial fitting is N=3. The obtained air-gap magnetic field distribution is fitted to obtain the expression of the air-gap magnetic field with respect to the perpendicular axis current:

${\overset{&OverBar; &OverBar;}{B B}}_{g g} ((X x,, θ θ)) = = [\begin{matrix} C C {((θ θ))}_{11 \times \times 4141} & S S {((θ θ))}_{11 \times \times 4141} \end{matrix}] [\begin{matrix} {A A}_{4141 \times \times 1010} \\ {B B}_{4141 \times \times 1010} \end{matrix}] {X x}_{1010 \times \times 11}$

为了反映整个工作点范围内的拟合结果准确度，选取不同工作点下的气隙磁场函数拟合结果与有限元仿真结果作对比，选择的工作点(I_d，I_q)分别为：(70.4769，25.6515)，(112.5000，194.8557)，(-402.1733，337.4635)。各个工作点对应的对比如图4所示，其中横轴为转子坐标系下气隙磁场的机械角度，纵轴为各个不同位置的气隙磁场大小。从图4中可以看出利用傅里叶级数展开和多项式拟合得到的B_g(I_d，I_q，θ)表达式能够非常精确地描述气隙磁场的实际分布情况。 In order to reflect the accuracy of the fitting results within the entire range of operating points, the fitting results of the air-gap magnetic field function under different operating points are selected for comparison with the finite element simulation results. The selected operating points (I _d , I _q ) are: ( 70.4769, 25.6515), (112.5000, 194.8557), (-402.1733, 337.4635). The comparison of each working point is shown in Figure 4, where the horizontal axis is the mechanical angle of the air-gap magnetic field in the rotor coordinate system, and the vertical axis is the magnitude of the air-gap magnetic field at different positions. It can be seen from Fig. 4 that the B _g (I _d , I _q , θ) expression obtained by Fourier series expansion and polynomial fitting can describe the actual distribution of the air gap magnetic field very accurately.

利用电机磁链的解析表达式可以得到在一个电周期内A、B、C三相磁链大小随时间变化的曲线。如图5所示，选取了气隙磁场对比图3中相同的3个工作点(I_d，I_q)，每一行的三个图分别代表一个工作点下的A、B、C三相磁链，其中横轴为一个电周期对应的时间范围，纵轴为不同时刻的三相磁链大小。从图5中可以看出对于每一个电流工作点，A、B、C三相磁链在空间上的相位差均为其电周期的三分之一，这是由定子绕组的空间位置确定的。解析计算与仿真的对比结果显示在各个不同的工作点三相绕组磁链大小在时间和幅值上均有较高的吻合度，这表明本发明得到的磁链解析式能够准确地描述磁链随定子交直轴电流以及时间的变化趋势。 Using the analytical expression of the flux linkage of the motor, the curves of the magnitude of the A, B, and C three-phase flux linkages changing with time can be obtained in one electrical cycle. As shown in Figure 5, the same three operating points (I _d , I _q ) in the comparison of the air gap magnetic field in Figure 3 are selected, and the three figures in each row represent the three-phase magnetic field A, B, and C under one operating point. Chain, where the horizontal axis is the time range corresponding to an electrical cycle, and the vertical axis is the three-phase flux linkage size at different times. It can be seen from Figure 5 that for each current operating point, the spatial phase difference of A, B, and C three-phase flux linkages is one-third of its electrical cycle, which is determined by the spatial position of the stator winding . The comparison results of analytical calculation and simulation show that the magnitude of the three-phase winding flux linkage at each different operating point has a high degree of agreement in time and amplitude, which shows that the flux linkage analytical formula obtained by the present invention can accurately describe the flux linkage Variation trend of stator AC-D axis current and time.

图6反映了相电流分别为50A、150A、250A、350A时电磁转矩随转矩角β的变化情况，从图中可以看出转矩的解析计算结果与有限元仿真结果在相电流较大跟较小时均有着非常高的吻合度，两者之间的误差均控制在2％以内，这表明本发明提供的方法能够精确地计算各个工作点包括饱和区的电机电磁转矩。 Figure 6 reflects the variation of the electromagnetic torque with the torque angle β when the phase currents are 50A, 150A, 250A, and 350A respectively. From the figure, it can be seen that the analytical calculation results of the torque and the finite element simulation results are when the phase current is large Both have a very high degree of coincidence with the smaller time, and the errors between the two are controlled within 2%, which shows that the method provided by the invention can accurately calculate the electromagnetic torque of the motor at each operating point including the saturation region.

图7显示了相电流范围从0～400A时的最大转矩/电流比的定子电流矢量轨迹，从图中可以看出利用本发明中的解析法获得的最大转矩/电流比的交直轴电流工作点具有非常高的准确度，其跟有限元仿真结果的误差均在5％以内，因此可以将其作为电机控制的定子电流最优控制轨迹。 Fig. 7 shows the stator current vector trajectory of the maximum torque/current ratio when the phase current range is from 0 to 400A, from the figure it can be seen that the cross-direction axis current of the maximum torque/current ratio obtained by the analytical method in the present invention working point It has very high accuracy, and its error with the finite element simulation results is within 5%, so it can be used as the optimal control trajectory of the stator current for motor control.

Claims

1. A motor air gap magnetic field modeling method based on distributed parameters, characterized in that, comprising the following steps:

1) Select the working point of the motor: divide the actual working range of the motor with the effective value of the phase current I _s and the space phase angle β of the stator current vector relative to the d-axis of the rotor position into w _I and w _β respectively. The principle is to obtain the motor current operating point in the synchronous Cartesian coordinate system:

{P P}_{m m} = = (({I I}_{d d}^{m m},, {I I}_{q q}^{m m}))

in, β ^m is the effective value of the phase current and the space phase angle of the mth working point respectively, m=1, 2,..., W, W=w _I ×w _β ;

2) Obtain the value of the magnetic field distribution of the air gap of the motor at each operating point Wherein, θ _i is the corresponding space electrical angle coordinate value, i=1, 2, ..., L, L is the number of space electrical angles contained in each working point;

3) Carry out Fourier series expansion to described numerical value:

{\overset{^^}{B B}}_{g g}^{m m} ((θ θ)) = = {Σ Σ}_{k k = = 00}^{M m} (({a a}_{k k}^{m m} cos cos k k ((pθ pθ)) + + {b b}_{k k}^{m m} sin sin k k ((pθ pθ))))

in, is the Fourier fitting of the air-gap magnetic field waveform at the mth working point, p is the number of pole pairs of the motor, M is the order of the selected Fourier series expansion, θ is the space machine in the synchronous Cartesian coordinate system angle, Its corresponding k-th order Fourier coefficient;

4) With respect to the motor current operating point polynomial fit of And transform the air-gap magnetic field waveform into a mathematical model about the orthogonal and direct axis currents I _d , I _q and the space mechanical angle θ:

{\overset{&OverBar; &OverBar;}{B B}}_{g g} ((X x,, θ θ)) = = [\begin{matrix} C C ((θ θ)) & S S ((θ θ)) \end{matrix}] [\begin{matrix} A A \\ B B \end{matrix}] X x

in, is the waveform function of the air-gap magnetic field;

C(θ)=[cos0(pθ)...cosk(pθ)...cosM(pθ)];

S(θ)=[sin0(pθ)...sink(pθ)...sinM(pθ)];

A = [a ₀ , ..., a _k , ..., a _M ] ^T , B = [β ₀ , ..., β _k , ..., β _M ] ^T ;

X x = = {[[11,, {I I}_{d d},, {I I}_{q q},, {I I}_{d d}^{22},, {I I}_{d d} {I I}_{q q},, {I I}_{q q}^{22},, . . . . . .,, {I I}_{d d}^{N N},, {I I}_{d d}^{N N - - 11} {I I}_{q q},, . . . . . .,, {I I}_{d d} {I I}_{q q}^{N N - - 11},, {I I}_{q q}^{N N}]]}^{T T};;

A and B are the distribution parameters, and a _k is the Fourier coefficient The polynomial coefficient vector of , β _k is the Fourier coefficient The vector of polynomial coefficients, N is the order of polynomial fitting.

2. the motor air-gap magnetic field modeling method based on distributed parameters according to claim 1, is characterized in that, the method for obtaining the numerical value of motor air-gap magnetic field distribution under each operating point comprises finite element parameter simulation method, MEC method or analytical model method based on Maxwell equation.

3. The motor air-gap magnetic field modeling method based on distributed parameters according to claim 1, wherein the Fourier series expansion order and polynomial fitting order are selected according to error iteration convergence conditions.

4. A motor stator current control method, is characterized in that, comprises the following steps:

A1) obtain the air-gap magnetic field waveform function by the modeling method described in claim 1

A2) According to Calculate the total electromagnetic torque T _e acting on the stator intercepting conductors:

{T T}_{e e} = = p p {&Integral; &Integral;}_{00}^{\frac{22 x x}{p p}} {\overset{&OverBar; &OverBar;}{B B}}_{g g} ((X x,, θ θ)) {f f}_{s the s} ((θ θ)) {f f}_{s the s} ((θ θ)) {l l}_{s the s} rdθ rdθ

Among them, p is the number of pole pairs of the motor, f _s (θ) is the space magnetomotive force wave composed of three-phase windings in each pole of space, l _s is the axial length of the rotor, r is the outer diameter of the rotor, θ is the spatial mechanical angle;

A3) Transform _Te into a torque expression Te(I _s , β) with I _s and β as independent variables;

A4) use Obtain the value of the torque angle β corresponding to the maximum torque under the excitation of different phase currents I _s , and then use the coordinate transformation to obtain the working point of the orthogonal and direct axis current corresponding to the maximum torque in the synchronous coordinate system The stator current vector locus curve of the maximum torque-current ratio is formed, and the stator current is controlled by this curve.

5. A motor three-phase stator flux linkage estimation method based on air gap magnetic field distribution, is characterized in that, comprises the following steps:

B1) obtain the air-gap magnetic field waveform function by the modeling method described in claim 1

B2) According to the spatial distribution of the three-phase windings of the stator and the angle θ _r between the rotor and the A axis of the stator, the magnetic flux φ _g of each phase at different times corresponds to Integral upper and lower bounds on space [D _P , U _P ];

B3) Using the fixed ratio relationship between flux and flux linkage, the expression ψ _P (X, θ _r ) of three-phase flux linkage with respect to current and time is obtained:

{ψ ψ}_{P P} ((X x,, {θ θ}_{r r})) = = {N N}_{s the s} {k k}_{w w 11} {l l}_{s the s} {&Integral; &Integral;}_{{D D.}_{P P}}^{{U u}_{P P}} (({\overset{&OverBar; &OverBar;}{B B}}_{g g} ((X x,, θ θ)) \cdot \cdot ((r r + + \frac{g g}{22})))) dθ dθ

Among them, N _s is the number of turns in series for each pair of poles and each phase of the three-phase stator winding, k _w1 is the winding distribution factor, l _s is the axial length of the rotor, r is the outer diameter of the rotor, g is the air gap width, P={A, B, C}, indicating that the current estimate is the P-phase flux linkage.