CN103853891A - Finite element analysis-based variable-element permanent magnet synchronous motor modeling method - Google Patents

Abstract

The invention relates to a finite element analysis-based variable-element permanent magnet synchronous motor modeling method which comprises the following steps of constructing a three-dimensional finite element electromagnetic field simulation model of a permanent magnet synchronous motor, and performing transient field road coupling analysis on the three-dimensional finite element electromagnetic field simulation model to obtain a large quantity of characteristic parameters; creating an improved permanent magnet synchronous motor voltage equation and a torque equation; constructing a simulation model of the permanent magnet synchronous motor according to an improved permanent magnet synchronous motor math model; leading all the obtained characteristic parameters into corresponding ports of the simulation model to construct a finite element analysis-based variable-element permanent magnet synchronous motor dynamic simulation model. The permanent magnet synchronous motor model modeled by the method disclosed by the invention comprehensively considers the magnetic field saturation effect, the d-q axis cross coupling effect, the eddy current effect, the hysteresis effect and the like; the instantaneity is considered, and the accuracy of the permanent magnet synchronous motor model is improved; the permanent magnet synchronous motor model is particularly suitable for the research on the dynamic processes such as power failure-bepelt and three-phase sudden short circuit of the permanent magnet synchronous motor.

Description

A kind of variable element permasyn morot modeling method based on finite element analysis

Technical field

The invention belongs to the modeling method of motor, be specifically related to a kind of variable element permasyn morot modeling method based on finite element analysis.

Background technology

Permasyn morot is because of features such as its volume are little, performance is good, simple in structure, reliability is high, output torque is large, be subject to extensive concern, application scenario and the field of especially at robot, space flight and aviation, precision electronic device equipment etc., motor performance, control accuracy being had relatively high expectations.The drive motor of the large inertia load such as high ferro locomotive, electric automobile and large scale screw propeller also progressively develops into permasyn morot from induction motor.And the dynamic process time such as throwing, three-phase suddenly-applied short circuit of permanent magnet synchronous electric tester in power-down state-is heavily short, model and parameter change greatly, realize effective control of dynamic process, need to set up the dynamic model fast, accurately of being convenient to carry out electromagnetic field analysis so that the basis of analysis to be provided.

Conventional motor modeling method has two kinds at present: Analysis of Magnetic Circuit model and field analysis model (being limited element calculation model).Traditional d-q axle Analysis of Magnetic Circuit model based on two reaction theory, there is the feature easy, simulation velocity is fast of calculating, but the fundametal compoment of its consideration motor inductance and air gap flux linkage and do not consider harmonic effects, ignore the impact of magnetic field saturation effect, the effect of d-q between centers cross-couplings, eddy current loss and magnetic hysteresis loss, be difficult to meet the needs of dynamic process analysis.And magnetic field analysis model adopts the method for finite element analysis to carry out Electromagnetic Calculation completely, although the accurate subdivision of grid can obtain high-precision electromagnetic field model, but large, the consuming time length of calculated amount, cannot be used for the real-time control of motor, and between motor internal parameter, electromagnetic relationship embodiment is clear and definite not, is unfavorable for research and analysis.

Summary of the invention

The technical matters solving

For fear of the deficiencies in the prior art part, the present invention proposes a kind of variable element permasyn morot modeling method based on finite element analysis, magnetic field saturation effect, d-q axle cross-coupling effect, eddy current and hysteresis effect can be considered to improve the accuracy of existing permasyn morot model, and permasyn morot inductance, resistance, magnetic linkage, the isoparametric variation of moment of inertia can easily be embodied.

Technical scheme

A variable element permasyn morot modeling method based on finite element analysis, is characterized in that step is as follows:

Step 1: according to the structural parameters of designed permasyn morot, set up the three-dimensional finite element electromagnetic-field simulation model of permasyn morot;

Step 2: adopt finite element transient field road coupling analytical method to carry out transient state Coupled field and circuit analysis to realistic model, obtain the d-axis synchronous inductance value L of permasyn morot under different cross, straight shaft currents _dd, quadrature axis synchronous inductance value L _qq, the mutual inductance value L of quadrature axis in d-axis _dqmutual inductance value L with d-axis in quadrature axis _qd, the phase resistance value R of permasyn morot and permanent magnet flux linkage value ψ under different temperatures _f;

Step 3: the virtual damping winding inductance value of the quadrature axis L that then calculates interior eddy current of electric cycle of equivalent motor and magnetic hysteresis loss sum _qQ, resistance value R _qwith the virtual damping winding inductance value of d-axis L _dD, resistance value R _d:

$R_D=-\frac{K_{D}f{L}_{\mathrm{dD}}\sin \left(\mathrm{\Δ}{\mathrm{\θ}}_D\right)}{{K_D}^2-2K_D\cos \left(\mathrm{\Δ}{\mathrm{\θ}}_D\right)+1}$

$R_Q=-\frac{K_{Q}f{L}_{\mathrm{qQ}}\sin \left(\mathrm{\Δ}{\mathrm{\θ}}_Q\right)}{{K_Q}^2-2K_Q\cos \left(\mathrm{\Δ}{\mathrm{\θ}}_Q\right)+1}$

$L_{\mathrm{DD}}=-\frac{K_D{L}_{\mathrm{dD}}(K_D-\cos \left(\mathrm{\Δ}{\mathrm{\θ}}_D\right))}{{K_D}^2-2K_D\cos \left(\mathrm{\Δ}{\mathrm{\θ}}_D\right)+1}$

$L_{\mathrm{QQ}}=-\frac{K_Q{L}_{\mathrm{qQ}}(K_Q-\cos \left(\mathrm{\Δ}{\mathrm{\θ}}_Q\right))}{{K_Q}^2-2K_Q\cos \left(\mathrm{\Δ}{\mathrm{\θ}}_Q\right)+1}$

Wherein:

ψ _d' the synthetic magnetic linkage of three-phase while maintaining static for the directed lower rotor part of d-axis, ψ _dthe synthetic magnetic linkage of three-phase while rotation with rated speed for the directed lower rotor part of d-axis, ψ _q' the synthetic magnetic linkage of three-phase while maintaining static for the directed lower rotor part of quadrature axis, ψ _qthe synthetic magnetic linkage of three-phase while rotation with rated speed for the directed lower rotor part of quadrature axis, Δ θ _dfor ψ _d' and ψ _dphase differential, Δ θ _qfor ψ _q' and ψ _qphase differential, f is power frequency, L _dDfor the amplitude of mutual inductance between synchronous motor stator phase winding and the virtual damping winding of d-axis, L _qQfor the amplitude of mutual inductance between synchronous motor stator phase winding and the virtual damping winding of quadrature axis;

Step 4: calculate d-axis permanent magnetism magnetic linkage ψ _dpmwith quadrature axis permanent magnetism magnetic linkage ψ _qpm:

ψ _dpm=（0.8～1.2）*ψ _f，

ψ _qpm=（0.8～1.2）*ψ _f，

Wherein: ψ _ffor permasyn morot saturation coefficient;

Determine permasyn morot mechanical friction loss P _msstray loss P during with motor output rated power _sN:

$P_{\mathrm{ms}}=\frac{(1\%~5\%)*(1-\mathrm{\η})*P}{\mathrm{\η}}$

$P_{\mathrm{sN}}=\frac{(0.5\%~3\%)*P}{\mathrm{\η}}$

Wherein: η is motor operational efficiency, P is motor rated power;

Step 5: the motor characteristic parameter obtaining with step 2～step 4, builds permasyn morot voltage equation and torque equation:

Permasyn morot voltage equation is:

$\left\{\begin{array}{c}{U}_d={\mathrm{Ri}}_d+L_{\mathrm{dd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}+L_{\mathrm{dq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}+L_{\mathrm{dD}}\frac{{\mathrm{di}}_D}{\mathrm{dt}}-\mathrm{\&omega;}(L_{\mathrm{qq}}{i}_q+L_{\mathrm{qd}}{i}_d+{\mathrm{\&psi;}}_{\mathrm{qpm}}+L_{\mathrm{qQ}}{i}_Q)\\ U_q={\mathrm{Ri}}_q+L_{\mathrm{qq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}+L_{\mathrm{qd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}+L_{\mathrm{qQ}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}+\mathrm{\&omega;}(L_{\mathrm{dd}}{i}_d+L_{\mathrm{dq}}{i}_q+{\mathrm{\&psi;}}_{\mathrm{dpm}}+L_{\mathrm{dD}}{i}_D)\\ 0=R_D{i}_D+L_{\mathrm{DD}}\frac{{\mathrm{di}}_D}{\mathrm{dt}}+L_{\mathrm{dD}}\frac{{\mathrm{di}}_{\mathrm{<figure-callout\; id="0"\; label="d\; dt"\; filenames="HDA0000480089990000013.png,HDA0000480089990000031.png"\; state="\{\{state\}\}">d</figure-callout>}}}{\mathrm{dt}}\\ 0=R_Q{i}_Q+L_{\mathrm{QQ}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}+L_{\mathrm{qQ}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}\end{array}\right.;$

Permasyn morot torque equation is:

$\begin{array}{c}{T}_e=\frac{P_{\mathrm{out}}}{{\mathrm{\&omega;}}_m}=\frac{3}{2}p[(L_{\mathrm{dd}}-L_{\mathrm{qq}})i_d{i}_q+({\mathrm{\&psi;}}_{\mathrm{dpm}}{i}_q-{\mathrm{\&psi;}}_{\mathrm{qpm}}{i}_d)+(L_{\mathrm{dq}}{i}_q^2-L_{\mathrm{qd}}{i}_d^2)+(L_{\mathrm{dD}}{i}_D{i}_q-L_{\mathrm{qQ}}{i}_Q{i}_d)]\\ -[T_{\mathrm{ms}}+\frac{(i_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000480089990000021.png,HDA0000480089990000032.png"\; state="\{\{state\}\}">d</figure-callout>}}^2+i_q^2)P_{\mathrm{sN}}}{{\mathrm{\&omega;}}_m}+\frac{3}{2}p(L_{\mathrm{DD}}-L_{\mathrm{QQ}})i_D{i}_Q];\end{array}$

Step 6: utilize Electric Machine Control class simulation software MATLAB/Simulink to build permasyn morot voltage equation and torque equation in step 5, obtain the model of the variable element permasyn morot dynamic simulation modeling based on finite element analysis.

Described L _dDfor d-axis synchronous inductance L _dd1% of mean value.

Described L _qQfor quadrature axis synchronous inductance L _qq1% of mean value.

Beneficial effect

A kind of variable element permasyn morot modeling method based on finite element analysis that the present invention proposes, carry out permasyn morot Ontology Modeling according to the result of motor electromagnetic emulation, consider magnetic field saturation effect, d-q axle cross-coupling effect, the impact on motor body parameter and electromagnetic torque of eddy current and hysteresis effect, by inputting variable motor inductance, resistance, the parameters such as magnetic linkage and the relative constant parameter that changes less equivalent loss, both can simulate accurately real electrical machinery runnability, can input again the motor inductance of any amplitude, resistance, the parameters such as permanent magnetism magnetic linkage, the impact of the variation of the parameter of electric machine on control performance under research motor limit running status, and can reach the real-time control of motor.

Compared with prior art, the beneficial effect of the method is:

1, by the accurate parameter of electric machine value of input FEM (finite element) calculation gained, can consider the variation of impact, transient reactance and the subtransient reactance of eddy effect, the higher hamonic wave of saturation, d-q axle cross-coupling effect, slot effect, permanent magnet and the rotor core in magnetic field, more approach real electrical machinery running status, improved the accuracy of permasyn morot performance analysis;

2, the impact of mechanical loss, stray loss, iron loss and the copper loss of having considered motor on electromagnetic torque;

3, the traditional normal value inductance, resistance, permanent magnetism magnetic linkage, the moment of inertia parameter that are encapsulated in motor model are become to the parameter that can be inputted by outside port, amplitude can change arbitrarily;

4, by the parameter of electric machine of certain limit under input limits duty, the impact on Electric Machine Control performance after can simulating real electrical machinery and changing with external working environment;

5, in popular position Sensorless Control necessary parameter identification, variable element permasyn morot Dynamic Simulation Model based on finite element analysis can, by changing arbitrarily the size of parameter of electric machine amplitude, be determined the loose property of holding back of Identification of parameter, accuracy and rapidity;

6, for the Electric Machine Control mode (as Direct Torque Control, ANN (Artificial Neural Network) Control) that need to use motor body parameter, the variable element permasyn morot Dynamic Simulation Model based on finite element analysis can be connected to desired parameters in control module easily;

7, the input voltage port of the variable element permasyn morot Dynamic Simulation Model based on finite element analysis is line of electric force type, can directly be connected with the inverter of line of electric force type port, without again building inverter bridge with discrete component.

Brief description of the drawings

Fig. 1 is the variable element permasyn morot Dynamic Simulation Model modeling process flow diagram based on finite element analysis;

Fig. 2 is the variable element permasyn morot three-dimensional finite element transient field analysis chart based on finite element analysis;

Fig. 3 is the curve map that cross, straight axle synchronous inductance and cross-couplings inductance change with cross, straight shaft current;

Fig. 4 is that variable element permasyn morot realistic model and the parameter based on finite element analysis arranges figure;

Fig. 5 is the variable element permasyn morot voltage equation module map based on finite element analysis;

Fig. 6 is the variable element permasyn morot torque equation module map based on finite element analysis;

Fig. 7 is the variable element permasyn morot dynamic process simulation result based on finite element analysis.

Embodiment

Now in conjunction with the embodiments, the invention will be further described for accompanying drawing:

Fig. 1 is the variable element permasyn morot modeling process flow diagram based on finite element analysis.Below in conjunction with accompanying drawing, taking a set of 30KW non-salient pole permanent magnet synchronous motor as example, list in detail variable element permasyn morot modeling method and process based on finite element analysis:

1. according to the structural parameters of designed permasyn morot, model comprises the permasyn morot three-dimensional finite element spatial structure of winding overhang, define afterwards the material properties of each structure division, external circuit connected mode is set, finite element calculation of boundary conditions is set, finally motor model is carried out to mesh generation, can carry out the calculating of transient state Coupled field and circuit analysis.Permasyn morot three-dimensional finite element three-dimensional structure diagram as shown in Figure 2.

2. by finite element transient state Coupled field and circuit analysis, can directly obtain the d-axis synchronous inductance value L of permasyn morot _dd, quadrature axis synchronous inductance value L _qq, the mutual inductance value L of quadrature axis in d-axis _dqmutual inductance value L with d-axis in quadrature axis _qd.Because of armature mmf difference under the cross, straight shaft current of difference, armature reacting field degree of saturation difference in motor, cause reactance of armature reaction difference, the cross, straight axle synchronous inductance of gained and cross-couplings inductance value are the binary functions of quadrature axis electric current, direct-axis current, as shown in Figure 3.Phase resistance value R, the permanent magnet flux linkage value ψ of permasyn morot _fand the unary between temperature also can directly obtain.

3. pass through to introduce d-axis field ratio of damping K for virtual damping winding inductance, the resistance value of eddy current and magnetic hysteresis loss sum in the electric cycle of equivalent motor _d, quadrature axis field ratio of damping K _qdetermine.Be specially:

wherein ψ _d' the synthetic magnetic linkage of three-phase while maintaining static for the directed lower rotor part of d-axis, ψ _dthe synthetic magnetic linkage of three-phase while rotation with rated speed for the directed lower rotor part of d-axis, ψ _q' the synthetic magnetic linkage of three-phase while maintaining static for the directed lower rotor part of quadrature axis, ψ _qthe synthetic magnetic linkage of three-phase while rotation with rated speed for the directed lower rotor part of quadrature axis.If Δ θ _dfor ψ _d' and ψ _dphase differential, Δ θ _qfor ψ _q' and ψ _qphase differential:

$R_D=-\frac{K_{D}f{L}_{\mathrm{dD}}\sin \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_D\right)}{{K_D}^2-2K_D\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_D\right)+1}---\left(1\right)$

$R_Q=-\frac{K_{Q}f{L}_{\mathrm{qQ}}\sin \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_Q\right)}{{K_Q}^2-2K_Q\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_Q\right)+1}---\left(2\right)$

$L_{\mathrm{DD}}=-\frac{K_D{L}_{\mathrm{dD}}(K_D-\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_D\right))}{{K_D}^2-2K_D\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_D\right)+1}---\left(3\right)$

$L_{\mathrm{QQ}}=-\frac{K_Q{L}_{\mathrm{qQ}}(K_Q-\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_Q\right))}{{K_Q}^2-2K_Q\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_Q\right)+1}---\left(4\right)$

Wherein: R _dfor the virtual damping winding resistance of d-axis, R _qfor the virtual damping winding resistance of quadrature axis, L _dDfor the self-induction of the virtual damping winding of d-axis, L _qQfor the self-induction of the virtual damping winding of quadrature axis, f is power frequency, L _dDfor the amplitude of mutual inductance between synchronous motor stator phase winding and the virtual damping winding of d-axis, L _qQfor the amplitude of mutual inductance between synchronous motor stator phase winding and the virtual damping winding of quadrature axis.Because of L _dD, L _qQbe virtual amount, the present invention adopts 1% of d-axis synchronous inductance mean value to determine L _dD, adopt 1% of quadrature axis synchronous inductance mean value to determine L _qQ.

4. the asymmetric meeting of magnetic circuit that permanent magnet causes because magnetic circuit is saturated causes d-axis permanent magnetism magnetic linkage ψ _dpmwith quadrature axis permanent magnetism magnetic linkage ψ _qpmamplitude difference, the present invention adopts saturation coefficient to take into account this impact, that is:

ψ _dpm=（0.8～1.2）*ψ _f (5)

ψ _qpm=（0.8～1.2）*ψ _f (6)

5. establish P _msfor permasyn morot mechanical friction loss, P _sNstray loss during for motor output rated power, the present invention adopts experience factor to take into account the impact of loss on motor performance, that is:

$P_{\mathrm{ms}}=\frac{(1\%~5\%)*(1-\mathrm{\&eta;})*P}{\mathrm{\&eta;}}---\left(7\right)$

$P_{\mathrm{sN}}=\frac{(0.5\%~3\%)*P}{\mathrm{\&eta;}}---\left(8\right)$

Wherein: η is motor operational efficiency, P is motor rated power.

6. according to the basic electromagnetic relation of permasyn morot, consider the characteristic parameter of reflection electric machine non-linear characteristic, classical permagnetic synchronous motor voltage equation is improved.The permagnetic synchronous motor voltage equation that the present invention proposes is as follows:

$\left\{\begin{array}{c}{U}_d={\mathrm{Ri}}_d+L_{\mathrm{dd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}+L_{\mathrm{dq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}+L_{\mathrm{dD}}\frac{{\mathrm{di}}_D}{\mathrm{dt}}-\mathrm{\&omega;}(L_{\mathrm{qq}}{i}_q+L_{\mathrm{qd}}{i}_d+{\mathrm{\&psi;}}_{\mathrm{qpm}}+L_{\mathrm{qQ}}{i}_Q)\\ U_q={\mathrm{Ri}}_q+L_{\mathrm{qq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}+L_{\mathrm{qd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}+L_{\mathrm{qQ}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}+\mathrm{\&omega;}(L_{\mathrm{dd}}{i}_d+L_{\mathrm{dq}}{i}_q+{\mathrm{\&psi;}}_{\mathrm{dpm}}+L_{\mathrm{dD}}{i}_D)\\ 0=R_D{i}_D+L_{\mathrm{DD}}\frac{{\mathrm{di}}_D}{\mathrm{dt}}+L_{\mathrm{dD}}\frac{{\mathrm{di}}_{\mathrm{<figure-callout\; id="0"\; label="d\; dt"\; filenames="HDA0000480089990000013.png,HDA0000480089990000031.png"\; state="\{\{state\}\}">d</figure-callout>}}}{\mathrm{dt}}\\ 0=R_Q{i}_Q+L_{\mathrm{QQ}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}+L_{\mathrm{qQ}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}\end{array}\right.---\left(9\right)$

It should be noted that: the permagnetic synchronous motor voltage equation that the present invention proposes is not only applicable to the non-salient pole permanent magnet synchronous motor in embodiment, is equally applicable to salient-pole permanent-magnet synchronous motor; Be not only applicable to the permagnetic synchronous motor of undamped winding on rotor, be equally applicable to have on rotor the permagnetic synchronous motor of damping winding, now, L _dDfor the self-induction sum of the virtual damping winding of d-axis of d-axis damping winding and equivalent loss, L _qQfor the self-induction sum of the virtual damping winding of quadrature axis of quadrature axis damping winding and equivalent loss, R _dfor d-axis damping winding and the virtual damping winding resistance of d-axis sum, R _qfor quadrature axis damping winding and the virtual damping winding resistance of quadrature axis sum.

7. for taking into account the impact of the loss of electric machine on permasyn morot electromagnetic torque, the present invention does following derivation to electromagnetic torque equation.

The power input of permagnetic synchronous motor is:

$P_{\mathrm{in}}=\frac{3}{2}(U_d{i}_d+U_q{i}_q)=P_{\mathrm{out}}+P_{\mathrm{ms}}+P_s+P_{\mathrm{Fe}}+P_{\mathrm{cu}}---\left(10\right)$

In formula: P _outfor output power of motor; P _msfor electromechanics loss; P _sfor stray loss of motor; P _fefor motor iron loss, i.e. eddy current loss and magnetic hysteresis loss sum; P _cufor motor copper loss.Wherein:

$P_{\mathrm{cu}}=P_{\mathrm{cu}\_\mathrm{stator}}+P_{\mathrm{cu}\_\mathrm{rotor}}=R(i_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000480089990000021.png,HDA0000480089990000032.png"\; state="\{\{state\}\}">d</figure-callout>}}^2+i_q^2)+R_{\mathrm{<figure-callout\; id="2"\; label="D\; i\; D"\; filenames="HDA0000480089990000021.png,HDA0000480089990000032.png"\; state="\{\{state\}\}">D</figure-callout>}}{i}_D^{}{}_2^{}+R_Q{i}_Q^2---\left(11\right)$

$\begin{array}{c}{P}_{\mathrm{out}}+P_{\mathrm{ms}}+P_s+P_{\mathrm{Fe}}\\ =\frac{3}{2}\mathrm{\&omega;}[(L_{\mathrm{dd}}-L_{\mathrm{qq}})i_d{i}_q+({\mathrm{\&psi;}}_{\mathrm{dpm}}{i}_q-{\mathrm{\&psi;}}_{\mathrm{qpm}}{i}_d)+\left(L_{\mathrm{dq}}{i}_d^2\right)+(L_{\mathrm{dD}}{i}_D{i}_q-L_{\mathrm{qQ}}{i}_Q{i}_d)]\\ +L_{\mathrm{dq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}{i}_d+L_{\mathrm{qd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}{i}_q+L_{\mathrm{dd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}{i}_d+L_{\mathrm{qq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}{i}_q+L_{\mathrm{dD}}\frac{{\mathrm{di}}_D}{\mathrm{dt}}{i}_d+L_{\mathrm{qQ}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}{i}_q\\ \&ap;\frac{3}{2}\mathrm{\&omega;}[(L_{\mathrm{dd}}-L_{\mathrm{qq}})i_d{i}_q+({\mathrm{\&psi;}}_{\mathrm{dpm}}{i}_q-{\mathrm{\&psi;}}_{\mathrm{qpm}}{i}_d)+(L_{\mathrm{dd}}{i}_d^2-L_{\mathrm{qd}}{i}_d^2)+(L_{\mathrm{dD}}{i}_D{i}_q-L_{\mathrm{qQ}}{i}_Q{i}_d)]\end{array}---\left(12\right)$

$\begin{array}{c}\frac{P_{\mathrm{ms}}+P_s+P_{\mathrm{Fe}}}{{\mathrm{\&omega;}}_m}=\frac{P_{\mathrm{ms}}}{{\mathrm{\&omega;}}_m}+\frac{({\mathrm{<figure-callout\; id="2"\; label="i\; d"\; filenames="HDA0000480089990000021.png,HDA0000480089990000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_d^{}+i_q^2)P_{\mathrm{sN}}}{{\mathrm{\&omega;}}_m}+\frac{\frac{3}{2}\mathrm{\&omega;}(L_{\mathrm{DD}}-L_{\mathrm{QQ}})i_D{i}_Q}{{\mathrm{\&omega;}}_m}\\ =\frac{P_{\mathrm{ms}}}{{\mathrm{\&omega;}}_m}+\frac{({\mathrm{<figure-callout\; id="2"\; label="i\; d"\; filenames="HDA0000480089990000021.png,HDA0000480089990000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_d^{}+i_q^2)P_{\mathrm{sN}}}{{\mathrm{\&omega;}}_m}+\frac{3}{2}p(L_{\mathrm{DD}}-L_{\mathrm{QQ}})i_D{i}_Q\end{array}---\left(13\right)$

The electromagnetic torque of motor is:

$\begin{array}{c}{T}_e=\frac{P_{\mathrm{out}}}{{\mathrm{\&omega;}}_m}=\frac{3}{2}p[(L_{\mathrm{dd}}-L_{\mathrm{qq}})i_d{i}_q+({\mathrm{\&psi;}}_{\mathrm{dpm}}{i}_q-{\mathrm{\&psi;}}_{\mathrm{qpm}}{i}_d)+(L_{\mathrm{dq}}{i}_q^2-L_{\mathrm{qd}}{i}_d^2)+(L_{\mathrm{dD}}{i}_D{i}_q-L_{\mathrm{qQ}}{i}_Q{i}_d)]\\ -[\frac{P_{\mathrm{ms}}}{{\mathrm{\&omega;}}_m}+\frac{({\mathrm{<figure-callout\; id="2"\; label="i\; d"\; filenames="HDA0000480089990000021.png,HDA0000480089990000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_d^{}+i_q^2)P_{\mathrm{sN}}}{{\mathrm{\&omega;}}_m}+\frac{3}{2}p(L_{\mathrm{DD}}-L_{\mathrm{QQ}})i_D{i}_Q]\end{array}---\left(14\right)$

In formula: ω _mfor rotor mechanical angular velocity, P is motor number of pole-pairs.

8. supplement the equation of motion of motor can carry out building of permasyn morot Dynamic Simulation Model, T in formula _lfor electric motor load torque, J is the moment of inertia sum of motor and load.The cross, straight axle synchronous inductance obtaining by FEM (finite element) calculation and cross-couplings inductance value utilization two dimension table look-up module are input to the inductance input port of variable element permasyn morot realistic model; Temperature variant resistance value, permanent magnet flux linkage value utilize one dimension table look-up module to be input to resistance, the magnetic linkage input port of variable element permasyn morot realistic model; Each constant parameter and other motor body constant parameters for the equivalent loss of electric machine are inputted by packaged parameter setting module; Electric motor load torque, moment of inertia can need input arbitrarily according to actual measurement or emulation experiment.The variable element permasyn morot Dynamic Simulation Model based on finite element analysis of building and parameter setting thereof as shown in Figure 4, voltage equation and torque equation module that Fig. 5 and Fig. 6 are the variable element permasyn morot Dynamic Simulation Model inside based on finite element analysis of building according to formula (1), formula (6).

For feasibility of the present invention is described, 30KW permasyn morot model in above-described embodiment is carried out to simulating, verifying.Motor main design parameters is: number of pole-pairs P=4, rated voltage 233V, rated current 98A, rated speed 3000rpm, torque at rated load 95.6Nm.Empty load of motor starts, in the time of 0.1s, add nominal load, the parameter waveform figure such as three-phase current in this process, three-phase voltage, rotating speed, torque as shown in Figure 7, visible, motor output parameter and design parameter have good consistance, have proved the correctness of the variable element permasyn morot Dynamic Simulation Model based on finite element analysis of setting up.

Claims (3)

1. the variable element permasyn morot modeling method based on finite element analysis, is characterized in that step is as follows:

Step 1: according to the structural parameters of designed permasyn morot, set up the three-dimensional finite element electromagnetic-field simulation model of permasyn morot;

Step 2: adopt finite element transient field road coupling analytical method to carry out transient state Coupled field and circuit analysis to realistic model, obtain the d-axis synchronous inductance value L of permasyn morot under different cross, straight shaft currents _dd, quadrature axis synchronous inductance value L _qq, the mutual inductance value L of quadrature axis in d-axis _dqmutual inductance value L with d-axis in quadrature axis _qd, the phase resistance value R of permasyn morot and permanent magnet flux linkage value ψ under different temperatures _f;

Step 3: the virtual damping winding inductance value of the quadrature axis L that then calculates interior eddy current of electric cycle of equivalent motor and magnetic hysteresis loss sum _qQ, resistance value R _qwith the virtual damping winding inductance value of d-axis L _dD, resistance value R _d:

$R_D=-\frac{K_{D}f{L}_{\mathrm{dD}}\sin \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_D\right)}{{K_D}^2-2K_D\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_D\right)+1}$

$R_Q=-\frac{K_{Q}f{L}_{\mathrm{qQ}}\sin \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_Q\right)}{{K_Q}^2-2K_Q\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_Q\right)+1}$

$L_{\mathrm{DD}}=-\frac{K_D{L}_{\mathrm{dD}}(K_D-\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_D\right))}{{K_D}^2-2K_D\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_D\right)+1}$

$L_{\mathrm{QQ}}=-\frac{K_Q{L}_{\mathrm{qQ}}(K_Q-\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_Q\right))}{{K_Q}^2-2K_Q\cos \left(\mathrm{\&Delta;}{\mathrm{\&theta;}}_Q\right)+1}$

Wherein:

ψ _d' the synthetic magnetic linkage of three-phase while maintaining static for the directed lower rotor part of d-axis, ψ _dthe synthetic magnetic linkage of three-phase while rotation with rated speed for the directed lower rotor part of d-axis, ψ _q' the synthetic magnetic linkage of three-phase while maintaining static for the directed lower rotor part of quadrature axis, ψ _qthe synthetic magnetic linkage of three-phase while rotation with rated speed for the directed lower rotor part of quadrature axis, Δ θ _dfor ψ _d' and ψ _dphase differential, Δ θ _qfor ψ _q' and ψ _qphase differential, f is power frequency, L _dDfor the amplitude of mutual inductance between synchronous motor stator phase winding and the virtual damping winding of d-axis, L _qQfor the amplitude of mutual inductance between synchronous motor stator phase winding and the virtual damping winding of quadrature axis;

Step 4: calculate d-axis permanent magnetism magnetic linkage ψ _dpmwith quadrature axis permanent magnetism magnetic linkage ψ _qpm:

ψ _dpm=（0.8～1.2）*ψ _f，

ψ _qpm=（0.8～1.2）*ψ _f，

Wherein: ψ _ffor permasyn morot saturation coefficient;

Determine permasyn morot mechanical friction loss P _msstray loss P during with motor output rated power _sN:

$P_{\mathrm{ms}}=\frac{(1\%~5\%)*(1-\mathrm{\&eta;})*P}{\mathrm{\&eta;}}$

$P_{\mathrm{sN}}=\frac{(0.5\%~3\%)*P}{\mathrm{\&eta;}}$

Wherein: η is motor operational efficiency, P is motor rated power;

Step 5: the motor characteristic parameter obtaining with step 2～step 4, builds permasyn morot voltage equation and torque equation:

Permasyn morot voltage equation is:

$\left\{\begin{array}{c}{U}_d={\mathrm{Ri}}_d+L_{\mathrm{dd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}+L_{\mathrm{dq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}+L_{\mathrm{dD}}\frac{{\mathrm{di}}_D}{\mathrm{dt}}-\mathrm{\&omega;}(L_{\mathrm{qq}}{i}_q+L_{\mathrm{qd}}{i}_d+{\mathrm{\&psi;}}_{\mathrm{qpm}}+L_{\mathrm{qQ}}{i}_Q)\\ U_q={\mathrm{Ri}}_q+L_{\mathrm{qq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}+L_{\mathrm{qd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}+L_{\mathrm{qQ}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}+\mathrm{\&omega;}(L_{\mathrm{dd}}{i}_d+L_{\mathrm{dq}}{i}_q+{\mathrm{\&psi;}}_{\mathrm{dpm}}+L_{\mathrm{dD}}{i}_D)\\ 0=R_D{i}_D+L_{\mathrm{DD}}\frac{{\mathrm{di}}_D}{\mathrm{dt}}+L_{\mathrm{dD}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}\\ 0=R_Q{i}_Q+L_{\mathrm{QQ}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}+L_{\mathrm{qQ}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}\end{array}\right.;$

Permasyn morot torque equation is:

$\begin{array}{c}{T}_e=\frac{P_{\mathrm{out}}}{{\mathrm{\&omega;}}_m}=\frac{3}{2}p[(L_{\mathrm{dd}}-L_{\mathrm{qq}})i_d{i}_q+({\mathrm{\&psi;}}_{\mathrm{dpm}}{i}_q-{\mathrm{\&psi;}}_{\mathrm{qpm}}{i}_d)+(L_{\mathrm{dq}}{i}_q^2-L_{\mathrm{qd}}{i}_d^2)+(L_{\mathrm{dD}}{i}_D{i}_q-L_{\mathrm{qQ}}{i}_Q{i}_d)]\\ -[T_{\mathrm{ms}}+\frac{(i_d^2+i_q^2)P_{\mathrm{sN}}}{{\mathrm{\&omega;}}_m}+\frac{3}{2}p(L_{\mathrm{DD}}-L_{\mathrm{QQ}})i_D{i}_Q];\end{array}$

Step 6: utilize Electric Machine Control class simulation software MATLAB/Simulink to build permasyn morot voltage equation and torque equation in step 5, obtain the model of the variable element permasyn morot dynamic simulation modeling based on finite element analysis.

2. the variable element permasyn morot modeling method based on finite element analysis according to claim 1, is characterized in that: described L _dDfor d-axis synchronous inductance L _dd1% of mean value.

3. the variable element permasyn morot modeling method based on finite element analysis according to claim 1, is characterized in that: described L _qQfor quadrature axis synchronous inductance L _qq1% of mean value.

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