CN103853891B - A kind of variable element permasyn morot modeling method based on finite element analysis - Google Patents

Abstract

The present invention relates to a kind of variable element permasyn morot modeling method based on finite element analysis, comprise the following steps: set up the three-dimensional finite element electromagnetic-field simulation model of permasyn morot, and it is carried out transient state Coupled field and circuit analysis, to obtain a large amount of characteristic parameter；Create the permasyn morot voltage equation and torque equation improved；According to the permasyn morot mathematical model improved, build the phantom of permasyn morot；Obtained each characteristic parameter is passed through the corresponding port of phantom, completes building of variable element permasyn morot Dynamic Simulation Model based on finite element analysis.The permasyn morot model of the present invention can consider the effects such as magnetic field saturation effect, d q axle cross-coupling effect, eddy current and magnetic hysteresis, improve the accuracy of existing permasyn morot model while taking into account real-time, be particularly well-suited to permagnetic synchronous motor power-off heavily throw, the research of the dynamic process such as three-phase suddenly-applied short circuit.

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 permanent-magnet synchronous based on finite element analysis Motor modeling method.

Background technology

Permasyn morot because its volume is little, performance is good, the feature such as simple in construction, reliability are high, output torque is big, Receive extensive concern, especially at robot, space flight and aviation, precision electronic device equipment etc. to motor performance, control Application scenario that required precision processed is higher and field.The large inertia such as high ferro locomotive, electric automobile and large scale propeller are born The driving motor carried the most progressively develops into permasyn morot from induction conductivity.And permagnetic synchronous motor power-off-weight The dynamic process times such as throwing, three-phase suddenly-applied short circuit are short, model and Parameters variation big, effective control of dynamic process to be realized System, needs to set up the dynamic model fast, accurately being convenient for electromagnetic field analysis to provide the basis analyzed.

The most conventional motor modeling method has two kinds: Analysis of Magnetic Circuit model and field analysis model (i.e. FEM calculation mould Type).Traditional d-q axle Analysis of Magnetic Circuit model based on two-reaction system, has that calculating is easy, simulation velocity is fast Feature, but it considers that motor inductances and the fundametal compoment of air gap flux linkage do not account for harmonic effects, have ignored magnetic field The impact of saturation effect, d-q between centers cross-couplings effect, eddy-current loss and magnetic hystersis loss, it is difficult to meet dynamic process The needs analyzed.And magnetic field analysis model uses the method for finite element analysis to carry out Electromagnetic Calculation completely, although net The accurate subdivision of lattice is obtained in that high-precision electromagnetic field model, but computationally intensive, the longest, it is impossible to for motor Real-time control, and between motor internal parameter, electromagnetic relationship embodies clear and definite not, is unfavorable for research and analysis.

Summary of the invention

Solve the technical problem that

In place of the deficiencies in the prior art, it is same that the present invention proposes a kind of variable element permanent magnetism based on finite element analysis Step motor modeling method, it is possible to consider magnetic field saturation effect, d-q axle cross-coupling effect, eddy current and magnetic hysteresis Effect with improve existing permasyn morot model accuracy, and can easily embody permasyn morot inductance, The isoparametric change of resistance, magnetic linkage, rotary inertia.

Technical scheme

A kind of variable element permasyn morot modeling method based on finite element analysis, it is characterised in that step is as follows:

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

Step 2: use finite element transient field road coupling analytical method that phantom is carried out transient state Coupled field and circuit analysis, Obtain direct-axis synchronous inductance value L of permasyn morot under different cross, straight shaft current_dd, quadrature axis synchronous inductance value L_qq、 The quadrature axis mutual inductance value L in d-axis_dqWith the d-axis mutual inductance value L in quadrature axis_qd, permasyn morot under different temperatures Phase resistance value R and permanent magnet flux linkage value ψ_f；

Step 3: then calculate in equivalence one electric cycle of motor the quadrature axis automatic virtual blocks of eddy current and magnetic hystersis loss sum around Group inductance value L_QQ, resistance value R_QWith d-axis automatic virtual blocks winding inductance value 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' it is that the three-phase that d-axis orients when lower rotor part maintains static synthesizes magnetic linkage, ψ_DThree-phase synthesis magnetic linkage when rotating with rated speed for d-axis orientation lower rotor part, ψ_Q' fix for quadrature axis orientation lower rotor part Three-phase synthesis magnetic linkage when not turning, ψ_QThree-phase synthesis magnetic linkage when rotating with rated speed for quadrature axis orientation lower rotor part, Δθ_DFor ψ_D' and ψ_DPhase contrast, Δ θ_QFor ψ_Q' and ψ_QPhase contrast, f is power frequency, L_dDFor synchronous motor The amplitude of mutual inductance, L between stator phase winding and d-axis automatic virtual blocks winding_qQVirtual with quadrature axis for synchronous motor stator phase winding The amplitude of mutual inductance between Damper Winding；

Step 4: calculate d-axis permanent magnet flux linkage ψ_dpmWith quadrature axis permanent magnet flux 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 that permasyn morot mechanical friction is lost P_msWith stray loss P during 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 obtained with step 2～step 4, build permasyn morot voltage equation and Torque equation:

Permasyn morot voltage equation is:

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

Permasyn morot torque equation is:

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

Step 6: utilize motor to control class simulation software MATLAB/Simulink to the synchronous permanent-magnet motor in step 5 Machine voltage equation and torque equation are built, and obtain variable element permasyn morot based on finite element analysis dynamic The model of simulation modeling.

Described L_dDFor direct-axis synchronous inductance L_ddThe 1% of meansigma methods.

Described L_qQFor quadrature axis synchronous inductance L_qqThe 1% of meansigma methods.

Beneficial effect

A kind of based on finite element analysis the variable element permasyn morot modeling method that the present invention proposes, according to motor The result of Electromagnetic Simulation carries out permasyn morot Ontology Modeling, it is contemplated that magnetic field saturation effect, d-q axle intersection coupling Close effect, eddy current with hysteresis effect to motor body parameter and the impact of electromagnetic torque, by the motor electricity that input is variable The constant parameter of the equivalence loss that the parameters such as sense, resistance, magnetic linkage are less with relative change, both can simulate reality accurately Motor runnability, can input again the parameters such as the motor inductances of any amplitude, resistance, permanent magnet flux linkage, studies motor pole The change of the parameter of electric machine impact on control performance under limit running status, and can reach the real-time control of motor.

Compared with prior art, the having the beneficial effects that of the method:

1, by input FEM calculation gained accurate parameter of electric machine value, can consider magnetic field saturation, D-q axle cross-coupling effect, slot effect, permanent magnet and the eddy current effect of rotor core, the impact of higher hamonic wave, Transient reactance and the change of subtransient reactance, closer to real electrical machinery running status, improve permasyn morot and move The accuracy that state is analyzed；

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

3, traditional constant value inductance being encapsulated in motor model, resistance, permanent magnet flux linkage, rotary inertia parameter are become The parameter that can be inputted by outside port, amplitude can arbitrarily change；

4, by the parameter of electric machine a range of under input limits duty, real electrical machinery can be simulated with extraneous work Make the impact on motor control performance after environmental change；

5, for parameter identification necessary in popular position Sensorless Control, change based on finite element analysis is joined Number permasyn morot Dynamic Simulation Model can determine parameter identification by arbitrarily changing the size of parameter of electric machine amplitude Algorithm hold back scattered property, accuracy and rapidity；

6, for needing to use the motor control mode (such as Direct Torque Control, ANN Control) of motor body parameter, Desired parameters can be connected to control by based on finite element analysis variable element permasyn morot Dynamic Simulation Model easily In molding block；

7, the input voltage port of variable element permasyn morot Dynamic Simulation Model based on finite element analysis is electric power Line type, can directly inverter with power line types port be connected, it is not necessary to again build inverter bridge with discrete component.

Accompanying drawing explanation

Fig. 1 is variable element permasyn morot Dynamic Simulation Model modeling procedure figure based on finite element analysis；

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

Fig. 3 is the curve chart that cross, straight axle synchronous inductance changes with cross, straight shaft current with cross-couplings inductance；

Fig. 4 is variable element permasyn morot phantom based on finite element analysis and parameter arranges figure；

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

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

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

Detailed description of the invention

In conjunction with embodiment, accompanying drawing, the invention will be further described:

Fig. 1 is variable element permasyn morot modeling procedure figure based on finite element analysis.Below in conjunction with the accompanying drawings, with As a example by a set of 30KW non-salient pole permanent magnet synchronous motor, list variable element permanent-magnet synchronous based on finite element analysis in detail Motor modeling method and process:

1., according to the structural parameters of designed permasyn morot, initially set up the permanent-magnet synchronous including winding overhang Motor three-dimensional finite element stereochemical structure, defines the material properties of each structure division afterwards, arranges external circuit connection side Formula, arranges finite element calculation of boundary conditions, finally motor model is carried out mesh generation, can carry out transient field road coupling Close analytical calculation.Permasyn morot three-dimensional finite element three-dimensional structure diagram is as shown in Figure 2.

2., by finite element transient state Coupled field and circuit analysis, the direct-axis synchronous inductance value of permasyn morot can be directly obtained L_dd, quadrature axis synchronous inductance value L_qq, the quadrature axis mutual inductance value L in d-axis_dqWith the d-axis mutual inductance value L in quadrature axis_qd。 Because under different cross, straight shaft currents, armature mmf is different, the armature reacting field degree of saturation in motor is different, causes electricity Reactance of armature reaction is different, and i.e. gained cross, straight axle synchronous inductance and cross-couplings inductance value are quadrature axis current, direct-axis current Binary function, as shown in Figure 3.Phase resistance value R of permasyn morot, permanent magnet flux linkage value ψ_fAnd between temperature Unary also can directly obtain.

3. eddy current and the automatic virtual blocks winding inductance of magnetic hystersis loss sum, resistance value within equivalence one electric cycle of motor By introducing d-axis field damped coefficient K_D, quadrature axis field damped coefficient K_QDetermine.Particularly as follows: Wherein ψ_D' orient three-phase synthesis magnetic linkage when lower rotor part maintains static, ψ for d-axis_DUnder orienting for d-axis Three-phase synthesis magnetic linkage when rotor rotates with rated speed, ψ_Q' orient three-phase synthesis when lower rotor part maintains static for quadrature axis Magnetic linkage, ψ_QThree-phase synthesis magnetic linkage when rotating with rated speed for quadrature axis orientation lower rotor part.If Δ θ_DFor ψ_D' and ψ_D's Phase contrast, Δ θ_QFor ψ_Q' and ψ_QPhase contrast, then:

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

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

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

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

Wherein: R_DFor d-axis automatic virtual blocks winding resistance, R_QFor quadrature axis automatic virtual blocks winding resistance, L_DDEmpty for d-axis Intend the self-induction of Damper Winding, L_QQFor the self-induction of quadrature axis automatic virtual blocks winding, f is power frequency, L_dDFor synchronous motor The amplitude of mutual inductance, L between stator phase winding and d-axis automatic virtual blocks winding_qQVirtual with quadrature axis for synchronous motor stator phase winding The amplitude of mutual inductance between Damper Winding.Because of L_dD、L_qQBeing virtual amount, the present invention uses direct-axis synchronous inductance meansigma methods 1% determines L_dD, use the 1% of quadrature axis synchronous inductance meansigma methods to determine L_qQ。

4. the asymmetric meeting of magnetic circuit that permanent magnet causes because magnetic circuit is saturated causes d-axis permanent magnet flux linkage ψ_dpmWith quadrature axis permanent-magnet magnetic Chain ψ_qpmAmplitude is different, and the present invention uses saturation coefficient meter and this impact, it may be assumed that

ψ_dpM=(0.8～1.2) * ψ_f (5)

ψ_qpm=(0.8～1.2) * ψ_f (6)

5. set P_msIt is lost for permasyn morot mechanical friction, P_sNStray loss during rated power is exported for motor, The present invention uses empirical coefficient meter and the loss impact on motor performance, it may be assumed that

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

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

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

6. according to the basic electromagnetic relation of permasyn morot, it is contemplated that the feature ginseng of reflection electric machine non-linear characteristic Number, improves classical permagnetic synchronous motor voltage equation.The permagnetic synchronous motor voltage equation that the present invention proposes As follows:

$\left\{\begin{array}{c}{U}_d={\mathrm{Ri}}_d+L_{\mathrm{dd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}+L_{\mathrm{dq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}+L_{\mathrm{dD}}\frac{{\mathrm{di}}_D}{\mathrm{dt}}-\mathrm{\ω}(L_{\mathrm{qq}}{i}_q+L_{\mathrm{qd}}{i}_d+{\mathrm{\ψ}}_{\mathrm{qpm}}+L_{\mathrm{qQ}}{i}_Q)\\ U_q={\mathrm{Ri}}_q+L_{\mathrm{qq}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}+L_{\mathrm{qd}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}+L_{\mathrm{qQ}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}+\mathrm{\ω}(L_{\mathrm{dd}}{i}_d+L_{\mathrm{dq}}{i}_q+{\mathrm{\ψ}}_{\mathrm{dpm}}+L_{\mathrm{dD}}{i}_D)\\ 0=R_D{i}_D+L_{\mathrm{DD}}\frac{{\mathrm{di}}_D}{\mathrm{dt}}+L_{\mathrm{dD}}\frac{{\mathrm{di}}_d}{\mathrm{dt}}\\ 0=R_Q{i}_Q+L_{\mathrm{QQ}}\frac{{\mathrm{di}}_Q}{\mathrm{dt}}+L_{\mathrm{qQ}}\frac{{\mathrm{di}}_q}{\mathrm{dt}}\end{array}\right.---\left(9\right)$

It should be understood that the non-salient pole that the permagnetic synchronous motor voltage equation that the present invention proposes is applicable not only in embodiment Formula permagnetic synchronous motor, is equally applicable to salient-pole permanent-magnet synchronous motor；It is applicable not only to undamped winding on rotor Permagnetic synchronous motor, is equally applicable on rotor the permagnetic synchronous motor having Damper Winding, now, L_DDHinder for d-axis The self-induction sum of the d-axis automatic virtual blocks winding that Buddhist nun's winding is lost with equivalence, L_QQFor quadrature axis Damper Winding and equivalence loss The self-induction sum of quadrature axis automatic virtual blocks winding, R_DFor d-axis Damper Winding and d-axis automatic virtual blocks winding resistance sum, R_QFor quadrature axis Damper Winding and quadrature axis automatic virtual blocks winding resistance sum.

7., for meter and the loss of electric machine impact on permasyn morot electromagnetic torque, electromagnetic torque equation is made by the present invention Following derivation.

The input power 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_msIt is lost for electromechanics；P_sFor stray loss of motor；P_FeFor motor Iron loss, i.e. eddy-current loss and magnetic hystersis loss sum；P_cuFor copper wastage.Wherein:

$P_{\mathrm{cu}}=P_{\mathrm{cu}\_\mathrm{stator}}+P_{\mathrm{cu}\_\mathrm{rotor}}=R(i_d^2+i_q^2)+R_D{i}_D^2+R_Q{i}_Q^2---\left(11\right)$

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

$\begin{array}{c}\frac{P_{\mathrm{ms}}+P_s+P_{\mathrm{Fe}}}{{\mathrm{\ω}}_m}=\frac{P_{\mathrm{ms}}}{{\mathrm{\ω}}_m}+\frac{(i_d^2+i_q^2)P_{\mathrm{sN}}}{{\mathrm{\ω}}_m}+\frac{\frac{3}{2}\mathrm{\ω}(L_{\mathrm{DD}}-L_{\mathrm{QQ}})i_D{i}_Q}{{\mathrm{\ω}}_m}\\ =\frac{P_{\mathrm{ms}}}{{\mathrm{\ω}}_m}+\frac{(i_d^2+i_q^2)P_{\mathrm{sN}}}{{\mathrm{\ω}}_m}+\frac{3}{2}p(L_{\mathrm{DD}}-L_{\mathrm{QQ}})i_D{i}_Q\end{array}---\left(13\right)$

Then the electromagnetic torque of motor is:

$\begin{array}{c}{T}_e=\frac{P_{\mathrm{out}}}{{\mathrm{\ω}}_m}=\frac{3}{2}p[(L_{\mathrm{dd}}-L_{\mathrm{qq}})i_d{i}_q+({\mathrm{\ψ}}_{\mathrm{dpm}}{i}_q-{\mathrm{\ψ}}_{\mathrm{qpm}}{i}_d)+(L_{\mathrm{dq}}{i}_q^2-L_{\mathrm{qd}}{i}_d^2)+(L_{\mathrm{dD}}{i}_D{i}_q-L_{\mathrm{qQ}}{i}_Q{i}_d)]\\ -[\frac{P_{\mathrm{ms}}}{{\mathrm{\ω}}_m}+\frac{(i_d^2+i_q^2)P_{\mathrm{sN}}}{{\mathrm{\ω}}_m}+\frac{3}{2}p(L_{\mathrm{DD}}-L_{\mathrm{QQ}})i_D{i}_Q]\end{array}---\left(14\right)$

In formula: ω_mFor rotor mechanical angle speed, P is motor number of pole-pairs.

8. supplement the equation of motion of motorThen can carry out permasyn morot Dynamic Simulation Model Build, T in formula_LFor electric motor load torque, J is the rotary inertia sum of motor and load.Obtained by FEM calculation To cross, straight axle synchronous inductance and cross-couplings inductance value utilize two dimension table look-up module to be input to variable element permanent magnet synchronous electric The inductance input port of motivation phantom；The resistance value, the permanent magnet flux linkage value that vary with temperature utilize one-dimensional mould of tabling look-up Block is input to the resistance of variable element permasyn morot phantom, magnetic linkage input port；For the equivalence loss of electric machine Each constant parameter and other motor body constant parameters inputted by packaged parameter setting module；Motor load turns Square, rotary inertia can need arbitrarily input according to actual measurement or emulation experiment.Change based on the finite element analysis ginseng built Number permasyn morot Dynamic Simulation Models and parameter arrange as shown in Figure 4, Fig. 5 Yu Fig. 6 be according to formula (1), The voltage equation within variable element permasyn morot Dynamic Simulation Model based on finite element analysis that formula (6) is built With torque equation module.

For the feasibility of the present invention is described, 30KW permasyn morot model in above-described embodiment is carried out emulation and tests Card.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, and adds nominal load when 0.1s, during this The parameter waveform figures such as three-phase current, three-phase voltage, rotating speed, torque are as shown in Figure 7, it is seen that, motor output parameter with Design parameter has good concordance, it was demonstrated that the variable element permasyn morot of based on finite element analysis set up moves The correctness of state phantom.

Claims (3)

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

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

Step 2: use finite element transient field road coupling analytical method that phantom is carried out transient state Coupled field and circuit analysis, Obtain direct-axis synchronous inductance value L of permasyn morot under different cross, straight shaft current_dd, quadrature axis synchronous inductance value L_qq、 The quadrature axis mutual inductance value L in d-axis_dqWith the d-axis mutual inductance value L in quadrature axis_qd, permasyn morot under different temperatures Phase resistance value R and permanent magnet flux linkage value ψ_f；

Step 3: then calculate in equivalence one electric cycle of motor the quadrature axis automatic virtual blocks of eddy current and magnetic hystersis loss sum around Group inductance value L_QQ, resistance value R_QWith d-axis automatic virtual blocks winding inductance value L_DD, resistance value R_D:

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

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

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

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

Wherein:ψ_D' orient three-phase synthesis magnetic linkage when lower rotor part maintains static for d-axis, ψ_DThree-phase synthesis magnetic linkage when rotating with rated speed for d-axis orientation lower rotor part, ψ_Q' fix for quadrature axis orientation lower rotor part Three-phase synthesis magnetic linkage when not turning, ψ_QThree-phase synthesis magnetic linkage when rotating with rated speed for quadrature axis orientation lower rotor part, Δθ_DFor ψ_D' and ψ_DPhase contrast, Δ θ_QFor ψ_Q' and ψ_QPhase contrast, f is power frequency, L_dDFor synchronous motor The amplitude of mutual inductance, L between stator phase winding and d-axis automatic virtual blocks winding_qQVirtual with quadrature axis for synchronous motor stator phase winding The amplitude of mutual inductance between Damper Winding；

Step 4: calculate d-axis permanent magnet flux linkage ψ_dpmWith quadrature axis permanent magnet flux 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 that permasyn morot mechanical friction is lost P_msWith stray loss P during motor output rated power_sN:

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

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

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

Step 5: the motor characteristic parameter obtained with step 2～step 4, build permasyn morot voltage equation and Torque equation:

Permasyn morot voltage equation is:

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

Permasyn morot torque equation is:

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

Wherein, d, q represent motor quadrature axis and d-axis, and R represents motor stator resistance, i_d、i_qRepresent that motor is handed over straight Shaft current, ω represents motor angular rate, P_outRepresenting output power of motor, p represents motor number of pole-pairs, ω_mFor turning Handset tool angular velocity, T_msRepresent frictional damping torque, i_D, i_QRepresent automatic virtual blocks winding ac-dc axis electric current；

Step 6: utilize motor to control class simulation software MATLAB/Simulink to the synchronous permanent-magnet motor in step 5 Machine voltage equation and torque equation are built, and obtain variable element permasyn morot based on finite element analysis dynamic The model of simulation modeling.

Variable element permasyn morot modeling method based on finite element analysis, its feature the most according to claim 1 It is: described L_dDFor direct-axis synchronous inductance L_ddThe 1% of meansigma methods.

Variable element permasyn morot modeling method based on finite element analysis, its feature the most according to claim 1 It is: described L_qQFor quadrature axis synchronous inductance L_qqThe 1% of meansigma methods.