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

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

Motor gas-gap magnetic field modeling method and application thereof based on distributed constant

Technical field

The present invention relates to permagnetic synchronous motor Drive Control Technique field, especially relate to a kind of motor gas-gap magnetic field modeling method based on distributed constant and application thereof.

Background technology

Electric automobile is the main development direction of new-energy automobile technology, and motor driven systems is electric automobile core component.Permagnetic synchronous motor is big with its power density, the range of speeds width of permanent torque and efficiency advantages of higher are subject to increasing application.Traditional motor control algorithms adopts this lumped parameter of inductance that voltage and flux linkage equations are described mostly, face mounted permagnetic synchronous motor utilizes the self-induction between three-phase windings and mutual inductance to set up the motor model under stator coordinate, salient-pole permanent-magnet synchronous motor then adopts twin axle theoretical, sets up the motor model under rotor coordinate by introducing ac-dc axis inductance.This control algolithm needs to meet 2 hypothesis below in relation to controlled motor:

(1) permanent magnet excitation magnetic field is completely sinusoidal at spatial waveforms；

(2) motor always works in non-magnetic saturation region.

Particularity yet with automobile power drive system, automobile-used permagnetic synchronous motor cannot meet above 2 hypothesis, this make the motor model of conventional motors arthmetic statement by the change due to inductance parameters distortion serious, the result of calculation of its electromagnetic torque also can with bigger deviation simultaneously so that it is cannot meet automobile permanent magnet synchronous motor requirement of accurately/quick control to torque.

The present invention, start with from the numerical model of air-gap field, taking into full account on the basis of electric machine rotor architectural feature, take into account the magnetic saturation of air-gap field higher hamonic wave, motor, set up the distributed parameter model of motor, more accurate motor mathematical description can be obtained, and then the motor control method based on model can be obtained.

Summary of the invention

Defect that the purpose of the present invention is contemplated to overcome above-mentioned prior art to exist and a kind of motor gas-gap magnetic field modeling method based on distributed constant and application thereof are provided, start with from the numerical model of air-gap field, taking into full account on the basis of electric machine rotor architectural feature, take into account the magnetic saturation of air-gap field higher hamonic wave, motor, set up the distributed parameter model of motor, more accurately motor is carried out mathematical description, and the model set up is applied in motor control, improve control accuracy.

The purpose of the present invention can be achieved through the following technical solutions:

A kind of motor gas-gap magnetic field modeling method based on distributed constant, comprises the following steps:

1) motor operating point is chosen: by phase current virtual value I_sW it is divided into respectively with the motor real work interval of the space phase angle β of stator current vector relative rotor position d axle_lWith w_βPart, obtain the current of electric operating point under synchronizing direct angle coordinate system according to magnetomotive force equivalence principle:

$P_m=(I_d^m,I_q^m)$

Wherein, $I_d^m=\sqrt{3}{I}_s^m\·\cos \left({\mathrm{\β}}^m\right),I_q^m=\sqrt{3}{I}_s^m\·\sin \left({\mathrm{\β}}^m\right),$ β^mThe respectively phase current virtual value of m-th operating point and space phase angle, m=1,2 ..., W, W=w_l×w_β；

2) numerical value of motor gas-gap Distribution of Magnetic Field under each operating point is asked forWherein, θ_iFor corresponding space electrical angle coordinate figure, i=1,2 ..., L, L is the space electrical angle number that each operating point comprises；

3) described numerical value is carried out Fourier expansion:

${\hat{B}}_g^m\left(\mathrm{\θ}\right)=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}(a_k^m\cos k\left(\mathrm{p\θ}\right)+b_k^m\sin k\left(\mathrm{p\θ}\right))$

Wherein,For Fourier's matching of the air-gap field waveform under m-th operating point, p is motor number of pole-pairs, and M is selected Fourier expansion exponent number, and θ is the space mechanism angle under synchronizing direct angle coordinate system,Kth rank Fourier coefficient for its correspondence；

4) with about current of electric operating pointFitting of a polynomialAnd air-gap field waveform is converted into about ac-dc axis electric current I_d、I_qAnd the mathematical model of space mechanism angle, θ:

${\stackrel{\‾}{B}}_8(X,\mathrm{\θ})=\left[\begin{array}{cc}C\left(\mathrm{\θ}\right)& S\left(\mathrm{\θ}\right)\end{array}\right]\left[\begin{array}{c}A\\ B\end{array}\right]X$

Wherein,For air-gap field wave function；

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

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

A=[α₀..., α_k..., α_M]^T, B=[β₀..., 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；

A, B are distributed constant, α_kFor Fourier coefficientSystem of polynomials number vector, β_kFor Fourier coefficientSystem of polynomials number vector, N is fitting of a polynomial exponent number.

Described ask for the method for the numerical value of motor gas-gap Distribution of Magnetic Field under each operating point include Parameters of Finite Element simulation method, MEC method or based on Maxwell non trivial solution analyse modelling.

Described Fourier expansion exponent number and fitting of a polynomial exponent number are chosen according to error iteration convergence condition.

A kind of motor stator current control method, comprises the following steps:

A1) air-gap field wave function is obtained by modeling method described in claim 1

A2) basisCalculate and act on total electromagnetic torque T that stator dams on conductor_e:

$T_e=p{\∫}_0^{\frac{2\mathrm{\π}}{p}}{\stackrel{\‾}{B}}_g(X,\mathrm{\θ})f_s\left(\mathrm{\θ}\right)l_s\mathrm{rd\θ}$

Wherein, p is motor number of pole-pairs, f_s(θ) for the space magnetomotive force ripple of each extremely interior Sine distribution synthesized by three-phase windings in space, l_sFor rotor axial length, r is rotor diameter, and θ is space mechanism angle；

A3) by T_eIt is converted into I_s, β be the torque expression formula Te (I of independent variable_s, β)；

A4) utilizeObtain out-of-phase current I_sThe value of the angle of torsion β that the lower torque capacity of excitation is corresponding, recycling coordinate transform obtains the ac-dc axis current work point that torque capacity under synchronous coordinate system is correspondingForm the stator current vector geometric locus of torque capacity current ratio, and with this curve controlled stator current.

A kind of motor threephase stator flux linkage estimation method based on air-gap field distribution, comprises the following steps:

B1) air-gap field wave function is obtained by the modeling method described in claim 1

B2) angle theta according to the three-phase stator winding position in spatial distribution and rotor and stator A axle_r, it is thus achieved that not in the same time under each phase magnetic flux_gCorrespond toRange of integration [D spatially_P, U_P]；

B3) the fixing multiple proportions relation utilizing magnetic flux and magnetic linkage obtains three-phase magnetic linkage about the electric current expression formula ψ with the time_P(X, θ_r):

${\mathrm{\ψ}}_P(X,{\mathrm{\θ}}_r)=N_s{k}_{w1}{l}_s{\∫}_{D_P}^{U_P}({\stackrel{\‾}{B}}_g(X,\mathrm{\θ})\·(r+\frac{g}{2}))\mathrm{d\θ}$

Wherein, N_sExtremely often be in series the number of turn for three-phase stator winding every pair, k_w1For winding distribution factor, l_sFor rotor axial length, r is rotor diameter, and g is width of air gap, P={A, B, C}, and what represent current estimation is P phase magnetic linkage.

Compared with prior art, the method have the advantages that

(1) the motor gas-gap magnetic field model that the inventive method is set up is adopted exactly motor to be described, motor status change in the magnetic saturation situation considering air-gap field higher hamonic wave, motor and the electromagnetic torque produced can accurately be described, it is possible to realize off-line or the real-time simulation of motor.

(2) present invention is widely used based on distributed constant motor gas-gap magnetic field model, can be not only used for the optimum control of motor, it is also possible in fault diagnosis algorithm, based on the demarcation of model, based on solution to model analysis Redundant Control etc..

(3) calculate quickly based on the motor threephase stator flux linkage estimation method of distributed parameter model of the present invention, it is not necessary to online to time integral；Calculate accurately, be independent of stator resistance variation with temperature；Computer capacity width, can be used for all of speed interval of motor.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of modeling method of the present invention；

Fig. 2 is the relation schematic diagram of threephase stator coordinate system and rotor coordinate；

Fig. 3 is the limit element artificial module of some the 4 pairs of pole internal permanent magnet synchronous motor in the present invention for specific embodiments；

Fig. 4 is modeling method and Finite element arithmetic air-gap field distribution results contrast schematic diagram in the embodiment of the present invention；

Wherein, (4a) it is in operating point (70.4769,25.6515) under comparison diagram, (4b) it is in operating point (112.5000,194.8557) under comparison diagram, (4c) it is the comparison diagram under operating point (-402.1733,337.4635)；

Fig. 5 is the Comparative result schematic diagram of modeling method and Finite element arithmetic air gap flux linkage in the embodiment of the present invention；

Wherein, (5a)～(5c) is the A phase magnetic linkage comparison diagram three operating points, (5d)～(5f) is the B phase magnetic linkage comparison diagram three operating points, and (5g)～(5i) is the C phase magnetic linkage comparison diagram three operating points；

Fig. 6 is modeling method and Finite element arithmetic electromagnetic torque Comparative result schematic diagram in the embodiment of the present invention；

Wherein, (6a) time for phase current virtual value 50A, electromagnetic torque is with the situation of change of angle of torsion β, (6b) time for phase current virtual value 150A, electromagnetic torque is with the situation of change of angle of torsion β, (6c) time for phase current virtual value 250A, electromagnetic torque is with the situation of change of angle of torsion β, and when (6d) is for phase current virtual value 350A, electromagnetic torque is with the situation of change of angle of torsion β；

Fig. 7 is the stator current vector track contrast schematic diagram of torque capacity/current ratio that modeling method and Finite element arithmetic obtain in the embodiment of the present invention.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment is carried out premised on technical solution of the present invention, gives detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

As it is shown in figure 1, the present embodiment provides a kind of motor gas-gap magnetic field modeling method based on distributed constant, including:

Step S1, chooses motor operating point: set phase current virtual value I in motor real work interval_s∈[0I_max], stator current vector i_sSpace phase angle β ∈ [0 β of relative rotor position d axle_max].By phase current virtual value I_sW it is divided into respectively with the motor real work interval of the space phase angle β of stator current vector relative rotor position d axle_lWith w_βPart, obtain the current of electric operating point under synchronizing direct angle coordinate system according to magnetomotive force equivalence principle:

$P_m=(I_d^m,I_q^m)$

Wherein, $I_d^m=\sqrt{3}{I}_s^m\·\cos \left({\mathrm{\β}}^m\right),I_q^m=\sqrt{3}{I}_s^m\·\sin \left({\mathrm{\β}}^m\right),$ β^mThe respectively phase current virtual value of m-th operating point and space phase angle, m=1,2 ..., W, W=w_l×w_β。

Step S2, asks for the numerical value of motor gas-gap Distribution of Magnetic Field under each operating pointWherein, θ_iFor corresponding space electrical angle coordinate figure, i=1,2 ..., L.

The method obtaining the numerical solution of air-gap field distribution includes the method for Parameters of Finite Element emulation, MEC (magneticequivalentcircuits) and analyses model etc. based on Maxwell non trivial solution, and the present embodiment explains with Finite Element Method.

Set up corresponding internal permanent magnet synchronous motor model first with finite element, the motor operating point obtained in step S1 is input in finite element multi-parameters model, carry out finite element numerical calculating by choosing suitable emulation cycle with step-length.Script file is utilized to extract with preservation to finite element data, it is thus achieved that air-gap field waveform W bar curve altogether in the periodic spatial electrical angle under different operating point, what each of which curve comprised counts as L.

Step S3, stator winding three-phase current and generation air-gap field under the common excitation of permanent magnet, when ignoring slot effect, the air-gap field of the three-phase current operating point corresponding to determining will remain unchanged along with rotor synchronous rotary and its distribution situation.Owing to air-gap field is that spatially the cycle isPeriodic function, it is possible to use each operating point P in step S2_mCorresponding air-gap field numeric distributionMake Fourier expansion:

${\hat{B}}_g^m\left(\mathrm{\θ}\right)=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}(a_k^m\cos k\left(\mathrm{p\θ}\right)+b_k^m\sin k\left(\mathrm{p\θ}\right))$

Wherein,For Fourier's matching of the air-gap field waveform under m-th operating point, p is motor number of pole-pairs, and M is selected Fourier expansion exponent number, and θ is the space mechanism angle under synchronizing direct angle coordinate system,Kth rank Fourier coefficient for its correspondence.

Step S4, with about current of electric operating pointFitting of a polynomialEach operating point P_mCorresponding different current excitations, and then Fourier's approximate solution of the air-gap field spatial waveforms of correspondenceDifference, namelyThe coefficient of Fourier expansionWithIt is represented by electric current coordinate (I_d, I_q) function:

$a_k^m=f_a(I_d^m,I_q^m),b_k^m=f_b(I_d^m,I_q^m)$

If under W operating pointWithValue uses I respectively_d、I_qN rank fitting of a polynomial, the Fourier coefficient a corresponding to k order harmonic component of air-gap field distribution can be obtained_kAnd b_kAbout current work point I_d、I_qFunction

a_k(I_d, I_q)=α_kX

b_k(I_d, I_q)=β_kX

If the N rank multinomial chosen is quantic, then corresponding α_k, β_k, X is expressed as:

${\mathrm{\α}}_k=[{\mathrm{\α}}_0^k,{\mathrm{\α}}_1^k,...,{\mathrm{\α}}_{\frac{(N+2)(N+1)}{2}-2}^k,{\mathrm{\α}}_{\frac{(N+2)(N+1)}{2}-1}^k]$

${\mathrm{\β}}_k=[{\mathrm{\β}}_0^k,{\mathrm{\β}}_1^k,...,{\mathrm{\β}}_{\frac{(N+2)(N+1)}{2}-2}^k,{\mathrm{\β}}_{\frac{(N+2)(N+1)}{2}-1}^k]$

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

So far, I is being considered_d、I_qImpact after, it is possible to air-gap field waveform table is shown as ac-dc axis electric current I_d、I_qAnd the mathematical model of space mechanism angle, θ:

$\begin{array}{c}{\stackrel{\‾}{B}}_g(X,\mathrm{\θ})=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}[a_k(I_d,I_q)\cos k\left(\mathrm{p\θ}\right)+b_k(I_d,I_q)\sin k\left(\mathrm{p\θ}\right)]\\ =\left[\begin{array}{ccccc}\cos 0\left(\mathrm{p\θ}\right)& ...& \cos k\left(\mathrm{p\θ}\right)& ...& \cos M\left(\mathrm{p\θ}\right)\end{array}\right]\left[\begin{array}{c}{a}_0\\ ...\\ a_k\\ ...\\ a_M\end{array}\right]+\left[\begin{array}{ccccc}\sin 0\left(\mathrm{p\θ}\right)& ...& \sin k\mathrm{p\θ}& ...& \sin M\left(\mathrm{p\θ}\right)\end{array}\right]\left[\begin{array}{c}{b}_0\\ ...\\ b_k\\ ...\\ b_M\end{array}\right]\\ =\left\{\begin{array}{c}\end{array}\left[\begin{array}{ccccc}\cos 0\left(\mathrm{p\θ}\right)& ...& \cos k\left(\mathrm{p\θ}\right)& ...& \cos M\left(\mathrm{p\θ}\right)\end{array}\right]\left[\begin{array}{c}{a}_0\\ ...\\ a_k\\ ...\\ a_M\end{array}\right]+\left[\begin{array}{ccccc}\sin 0\left(\mathrm{p\θ}\right)& ...& \sin k\left(\mathrm{p\θ}\right)& ...& \sin M\left(\mathrm{p\θ}\right)\end{array}\right]\left[\begin{array}{c}{\mathrm{\β}}_0\\ ...\\ {\mathrm{\β}}_k\\ ...\\ {\mathrm{\β}}_M\end{array}\right]\right\}X\\ =[C{\left(\mathrm{\θ}\right)}_{1\×(M+1)}{A}_{(M+1)\×\frac{(N+2)(N+1)}{2}}+S{\left(\mathrm{\θ}\right)}_{1\×(M+1)}{B}_{(M+1)\×\frac{(N+2)(N+1)}{2}}]X_{\frac{(N+2)(N+1)}{2}\×1}\\ =\left[\begin{array}{cc}C\left(\mathrm{\θ}\right)& S\left(\mathrm{\θ}\right)\end{array}\right]\left[\begin{array}{c}A\\ B\end{array}\right]X\end{array}$

In formula,

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

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

$A=\left[\begin{array}{c}{a}_0\\ ...\\ a_k\\ ...\\ a_m\end{array}\right]=\left[\begin{array}{c}{\mathrm{\α}}_0^0,{\mathrm{\α}}_1^0,...,{\mathrm{\α}}_{\frac{(N+2)(N+1)}{2}-2}^0,{\mathrm{\α}}_{\frac{(N+2)(N+1)}{2}-1}^0\\ ...\\ {\mathrm{\α}}_0^k,{\mathrm{\α}}_1^k,...,{\mathrm{\α}}_{\frac{(N+2)(N+1)}{2}-2}^k,{\mathrm{\α}}_{\frac{(N+2)(N+1)}{2}-1}^k\\ ...\\ {\mathrm{\α}}_0^M,{\mathrm{\α}}_1^M,...,{\mathrm{\α}}_{\frac{(N+2)(N+1)}{2}-2}^M,{\mathrm{\α}}_{\frac{(N+2)(N+1)}{2}-1}^M\end{array}\right]$

$B=\left[\begin{array}{c}{\mathrm{\β}}_0\\ ...\\ {\mathrm{\β}}_k\\ ...\\ {\mathrm{\β}}_m\end{array}\right]=\left[\begin{array}{c}{\mathrm{\β}}_0^0,{\mathrm{\β}}_1^0,...,{\mathrm{\β}}_{\frac{(N+2)(N+1)}{2}-2}^0,{\mathrm{\β}}_{\frac{(N+2)(N+1)}{2}-1}^0\\ ...\\ {\mathrm{\β}}_0^k,{\mathrm{\β}}_1^k,...,{\mathrm{\β}}_{\frac{(N+2)(N+1)}{2}-2}^k,{\mathrm{\β}}_{\frac{(N+2)(N+1)}{2}-1}^k\\ ...\\ {\mathrm{\β}}_0^M,{\mathrm{\β}}_1^M,...,{\mathrm{\β}}_{\frac{(N+2)(N+1)}{2}-2}^M,{\mathrm{\β}}_{\frac{(N+2)(N+1)}{2}-1}^M\end{array}\right]$

A, B are distributed constant, and its dimension isIn order to describe the distribution of air-gap field spatial waveforms, it is possible to by selecting suitable Fourier space progression M and fitting of a polynomial exponent number N to ensure the precision of air-gap field mathematical model and the ease of analytic equation.α_kFor Fourier coefficientSystem of polynomials number vector, β_kFor Fourier coefficientSystem of polynomials number vector.X is the polynomial substrate in N rank corresponding to independent variable.

Can comprise the further steps of: after obtaining air-gap field model

Step S5, obtains motor magnetic linkage analytical expression according to the motor gas-gap magnetic field model based on distributed constant, estimates motor threephase stator magnetic linkage.

Air-gap flux amount φ_gIt is air-gap field intensityIntegration spatially, according to A, B, C three-phase windings angle theta in spatial distribution position and rotor-position and stator A axle_rCan respectively obtaining not in the same time by the magnetic field intensity spatial interval of three-phase stator winding, this interval is the range of integration [D calculating each phase magnetic flux_P, U_P], the fixing multiple proportions relation further according to magnetic flux Yu magnetic linkage obtains A, B, C three-phase magnetic linkage ψ_A, ψ_B, ψ_CExpression formula.

In formula, θ_r=ω_rT, wherein ω_rFor rotor velocity, t is the different moment.

By changing the bound of integration, B, C two magnetic linkage ψ of phase winding in like manner can be obtained through_BAnd ψ_C.From ψ_AExpression formula in can be seen that magnetic linkage ψ_B(X, θ_r) and ψ_C(X, θ_r) expression formula only need to by the integration matrix of A phaseWithReplace toAndWherein；

In formula, N_sExtremely often be in series the number of turn for three-phase stator winding every pair, k_w1For winding distribution factor, l_sFor rotor axial length, r is rotor diameter, and g is width of air gap.

Motor three-phase voltage equation can be obtained based on above-mentioned flux linkage equations

$\frac{\∂{\mathrm{\ψ}}_P}{\∂t}=\frac{\∂{\mathrm{\ψ}}_P}{\∂{\mathrm{\θ}}_r}\·{\mathrm{\ω}}_r=U_P,P=\{A,B,C\}$

Step S6, obtains motor electromagnetic torque analytical expression according to the motor gas-gap magnetic field model based on distributed constant.

Space each extremely in the space magnetomotive force ripple of Sine distribution that synthesized by three-phase windings be represented by:

$\begin{array}{c}{f}_s\left(\mathrm{\θ}\right)=\frac{3}{2}{F}_s\cos (\mathrm{p\θ}-\mathrm{\β})\\ =\frac{3}{2}\·\left(\frac{4}{\mathrm{\π}}\frac{N{k}_{w1}}{2p}\sqrt{2}{I}_s\right)\·\cos (\mathrm{p\θ}-\mathrm{\β})\\ =\frac{3\sqrt{2}{\mathrm{Nk}}_{w1}}{\mathrm{\πp}}{I}_s\cos (\mathrm{p\θ}-\mathrm{\β})\end{array}$

In formula, F_sBeing the single-phase magnetomotive amplitude of winding first-harmonic, N is the total turns-in-series of every phase winding, I_sFor the virtual value of monophase current, β is stator current vector i_sThe space phase angle of relative rotor position d axle, i.e. angle of torsion.

Electromagnetic torque B_liMethod is derived, for electromagnetic torque infinitesimal dt produced in the gas length corresponding to any operating point mechanical angle infinitesimal d θ_eFor

${\mathrm{dt}}_e=\mathrm{Bli}\·r={\stackrel{\‾}{B}}_g(X,\mathrm{\θ})l_s{f}_s\left(\mathrm{\θ}\right)\mathrm{d\θ}\·r$

Then act on the total electromagnetic torque T on stator current－carrying conductor_eFor

WillSubstitute into above-mentioned electromagnetic torque T_eIn expression formula, I can be able to_s, β is the torque expression formula Te (I of independent variable_s, β).

And then, utilizeOut-of-phase current I can be drawn_sThe value of the angle of torsion β that the lower torque capacity of excitation is corresponding, recycling coordinate transform obtains the ac-dc axis current work point that torque capacity under synchronous coordinate system is correspondingThe i.e. stator current vector track of torque capacity current ratio, namely motor may utilize this curve and realizes the maximum principle of torque/current ratio to control stator current in controlling, thus realizing the optimum control of electric system.

Step S7, based on the application of the motor gas-gap magnetic field model of distributed constant.

Utilize the magnetic linkage voltage equation set up in step S5 and step S6 and electromagnetic torque with the expression formula of ac-dc axis curent change, except the optimum control that may be used for realizing motor, can be also used for setting up the distributed parameter model of motor, this model can accurately describe the motor status change in the magnetic saturation situation considering air-gap field higher hamonic wave, motor and the electromagnetic torque produced, pass through numerical solution, it is possible to realize off-line or the real-time simulation of motor.Additionally, distributed parameter model can be also used for realizing other application based on model: include but not limited to fault diagnosis algorithm, based on the demarcation of model, based on solution to model analysis Redundant Control etc..

Concrete example result to the present invention is given below be verified.This example is based on the FEM (finite element) model of a certain internal permanent magnet synchronous motor, and its parameter of electric machine is as shown in table 1, and the limit element artificial module of its correspondence is as shown in Figure 3.

Table 1 internal permanent magnet synchronous motor basic parameter

This example has taken into full account operating point range actual when motor runs, and the three-phase current amplitude interval chosen is 0～400A, and step-length is 10A, stator current vector i_sBeing 0～180 degree with the space phase angle range of d axle, step-length is 10 degree.Utilize the parameter scanning function of finite element software, obtain the distribution shape extremely descending air-gap field for a pair in 0 moment.The exponent number adopting Fourier expansion is M=40, and fitting of a polynomial exponent number is N=3, the air-gap field distribution obtained is fitted, obtains the air-gap field expression formula about ac-dc axis electric current:

${\stackrel{\‾}{B}}_g(X,\mathrm{\θ})=\left[\begin{array}{cc}C{\left(\mathrm{\θ}\right)}_{1\×41}& S{\left(\mathrm{\θ}\right)}_{1\×41}\end{array}\right]\left[\begin{array}{c}{A}_{41\×10}\\ B_{41\×10}\end{array}\right]X_{10\×1}$

In order to reflect the fitting result accuracy in whole operating point range, the air-gap field Function Fitting result chosen under different operating point compares with FEM Numerical Simulation, the operating point (I of selection_d, I_q) it is respectively as follows: (70.4769,25.6515), (112.5000,194.8557), (-402.1733,337.4635).As shown in Figure 4, wherein transverse axis is the mechanical angle of air-gap field under rotor coordinate, and the longitudinal axis is the air-gap field size of each diverse location in contrast corresponding to each operating point.As can be seen from Figure 4 the B that Fourier expansion and fitting of a polynomial obtain is utilized_g(I_d, I_q, θ) and expression formula can highly precisely describe the actual distribution situation of air-gap field.

The analytical expression utilizing motor magnetic linkage can obtain the time dependent curve of A, B, C three-phase magnetic linkage size within an electric cycle.As it is shown in figure 5, have chosen 3 operating point (I identical in air-gap field comparison diagram 3_d, I_q), three of every a line figure represent A, B, C three-phase magnetic linkage under an operating point respectively, and wherein transverse axis is time range corresponding to electric cycle, and the longitudinal axis is not three-phase magnetic linkage size in the same time.As can be seen from Figure 5 for each current work point, A, B, C three-phase magnetic linkage phase contrast spatially is 1/3rd of its electricity cycle, and this is to be determined by the locus of stator winding.Analytical Calculation is shown in each different operating point three-phase windings magnetic linkage size from the comparing result of emulation all the higher goodness of fit on time and amplitude, and this shows that the magnetic linkage analytic expression that the present invention obtains can describe magnetic linkage exactly with stator ac-dc axis electric current and the variation tendency of time.

Fig. 6 reflects during phase current respectively 50A, 150A, 250A, 350A electromagnetic torque with the situation of change of angle of torsion β, as can be seen from the figure the analytical Calculation result of torque and FEM Numerical Simulation are relatively big with all there being the very high goodness of fit time less at phase current, error between the two all controls within 2%, and this shows that method provided by the invention can be precisely calculated each operating point and include the motor electromagnetic torque of saturation region.

The stator current vector track of torque capacity/current ratio when Fig. 7 shows phase current scope from 0～400A, as can be seen from the figure utilizes the ac-dc axis current work point of torque capacity/current ratio that the analytic method in the present invention obtainsHaving very high accuracy, it all within 5%, therefore can it can be used as the stator current optimum control track that motor controls with the error of FEM Numerical Simulation.

Claims (5)

1. the motor gas-gap magnetic field modeling method based on distributed constant, it is characterised in that comprise the following steps:

1) motor operating point is chosen: by phase current virtual value I_sW it is divided into respectively with the motor real work interval of the space phase angle β of stator current vector relative rotor position d axle_IWith w_βPart, obtain the current of electric operating point under synchronizing direct angle coordinate system according to magnetomotive force equivalence principle:

$P_m=(I_d^m,I_q^m)$

Wherein, β^mThe respectively phase current virtual value of m-th operating point and space phase angle, m=1,2 ..., W, W=w_I×w_β；

2) numerical value of motor gas-gap Distribution of Magnetic Field under each operating point is asked forWherein, θ_iFor corresponding space electrical angle coordinate figure, i=1,2 ..., L, L is the space electrical angle number that each operating point comprises；

3) described numerical value is carried out Fourier expansion:

${\hat{B}}_g^m\left(\mathrm{\θ}\right)=\underset{k=0}{\overset{M}{\mathrm{\Σ}}}(a_k^m\cos k\left(\mathrm{p\θ}\right)+b_k^m\sin k\left(\mathrm{p\θ}\right))$

Wherein,For Fourier's matching of the air-gap field waveform under m-th operating point, p is motor number of pole-pairs, and M is selected Fourier expansion exponent number, and θ is the space mechanism angle under synchronizing direct angle coordinate system,Kth rank Fourier coefficient for its correspondence；

4) with about current of electric operating pointFitting of a polynomialAnd air-gap field waveform is converted into about ac-dc axis electric current I_d、I_qAnd the mathematical model of space mechanism angle, θ:

${\stackrel{\‾}{B}}_g(X,\mathrm{\θ})=\left[\begin{array}{cc}C\left(\mathrm{\θ}\right)& S\left(\mathrm{\θ}\right)\end{array}\right]\left[\begin{array}{c}A\\ B\end{array}\right]X$

Wherein,For air-gap field wave function；

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

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

A=[a₀..., a_k..., a_M]^T, B=[β₀..., β_k..., β_M]^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 are distributed constant, a_kFor Fourier coefficientSystem of polynomials number vector, β_kFor Fourier coefficientSystem of polynomials number vector, N is fitting of a polynomial exponent number.

2. the motor gas-gap magnetic field modeling method based on distributed constant according to claim 1, it is characterized in that, described in ask for the method for the numerical value of motor gas-gap Distribution of Magnetic Field under each operating point include Parameters of Finite Element simulation method, MEC method or based on Maxwell non trivial solution analyse modelling.

3. the motor gas-gap magnetic field modeling method based on distributed constant according to claim 1, it is characterised in that described Fourier expansion exponent number and fitting of a polynomial exponent number are chosen according to error iteration convergence condition.

4. a motor stator current control method, it is characterised in that comprise the following steps:

A1) air-gap field wave function is obtained by modeling method described in claim 1

A2) basisCalculate and act on total electromagnetic torque T that stator dams on conductor_e:

$T_e=p{\∫}_0^{\frac{2x}{p}}{\stackrel{\‾}{B}}_g(X,\mathrm{\θ})f_s\left(\mathrm{\θ}\right)f_s\left(\mathrm{\θ}\right)l_s\mathrm{rd\θ}$

Wherein, p is motor number of pole-pairs, f_s(θ) for the space magnetomotive force ripple of each extremely interior Sine distribution synthesized by three-phase windings in space, l_sFor rotor axial length, r is rotor diameter, and θ is space mechanism angle；

A3) by T_eIt is converted into I_s, β be the torque expression formula Te (I of independent variable_s, β)；

A4) utilizeObtain out-of-phase current I_sThe value of the angle of torsion β that the lower torque capacity of excitation is corresponding, recycling coordinate transform obtains the ac-dc axis current work point that torque capacity under synchronous coordinate system is correspondingForm the stator current vector geometric locus of torque capacity current ratio, and with this curve controlled stator current.

5. the motor threephase stator flux linkage estimation method based on air-gap field distribution, it is characterised in that comprise the following steps:

B1) air-gap field wave function is obtained by the modeling method described in claim 1

B2) angle theta according to the three-phase stator winding position in spatial distribution and rotor and stator A axle_r, it is thus achieved that not in the same time under each phase magnetic flux_gCorrespond toRange of integration [D spatially_P, U_P]；

B3) the fixing multiple proportions relation utilizing magnetic flux and magnetic linkage obtains three-phase magnetic linkage about the electric current expression formula ψ with the time_P(X, θ_r):

${\mathrm{\ψ}}_P(X,{\mathrm{\θ}}_r)=N_s{k}_{w1}{l}_s{\∫}_{D_P}^{U_P}({\stackrel{\‾}{B}}_g(X,\mathrm{\θ})\·(r+\frac{g}{2}))\mathrm{d\θ}$

Wherein, N_sExtremely often be in series the number of turn for three-phase stator winding every pair, k_w1For winding distribution factor, l_sFor rotor axial length, r is rotor diameter, and g is width of air gap, P={A, B, C}, and what represent current estimation is P phase magnetic linkage.