8/13/2019 A New Simulation Model of BLDC Motor With Real Back EMF Waveform

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A New Simulation Model of BLDC M otor W ith Real Back EMF WaveformY. S. Jeon, H. S Mok, G . Choe, D. K. Kim*, J. S Ryu**Dept. of Electrical Eng. Konkuk Univ., Komotek*, Jasontech**

Abstract- A BLDC motor with the characteristics of highspeed and high'power density has been more widely used inindustrial area. As for the design of motor drive system,simulation method has been nearly used as the drive system an dthe controller of BLDC motor have become more complicatedand precise. The torque characteristic of BLDC motor is veryimportant factor in the design of motor drive system, so it isnecessary to predict the precise value of torque, which isdetermined by the waveform of back EMF. The conventionalsimulation model of BLDC motor is obtained by approximationof real back EM F waveform to ideal trapezoidal waveform. B utas the shapes of slot, skew and magnet of BLDC motor arevarious subject to design purposes, the real back EMFwaveform is at some degree deviated from the ideal trapezoidalwaveform. As a result, when using the ideal trapezoidalwaveform, the er ro r occurs. In consequence, in ord er to lessensuch an error, the model of BLDC motor with real back EMFwaveform is needed instead of its approximation model. In th ispaper, for the reduction of err or in simulation, a new simulationmodel of BLDC motor with nearly real back EMF waveform isproposed and through the simulation, the validity of theproposed m odel is shown for three-phase BLDC motor.

I. INTRODUCTIONBLDC M otor has advantage of long lifetime, faster responseand capability of high-speed drive in comparison with DCMotor and has been more widely used in industrial area inline with the development of power switching device,microprocessor and digital technology.Generally, the torque of the BLDC motor is mainly

influenced by the waveform of back EMF and hence it isneeded to predict its precise back EMF. On the other hand, toanalyze the characteristics of BLDC motor systems as well asthe other motor drive systems, computer simulation toolssuch as IsSpice, PSIM, PSpice, and Saver are widely used.And the model of back EMF approximated to idealtrapezoidal waveform in BLDC motor system has beengenerally used in com puter simulation tools.Fig.1 shows the waveforms of back EMF, torque andcurrent simulated by IsSpice, which is a computer simulationtool used widely to analyze general electrical or electroniccircuits, and in this figure the back EMF of BLDC isapproximated to' deal trapezoidal waveform.But as the shapes of slot, skew and magnet of BLDC m otor

are vaned subject to design purposes, the waveform of realback EMF is at some degree deviated from the idealtrapezoidal waveform as shown in Fig. 2. Consequently, th eerror could be occured between real value and the sim ulationresult when using t he m odel of ideal trapezoidal method.So in order to obtain accurate motor characteristics insimulation, a simulation model with nearly real back EM F is

Fig. 1. Back EMF, phase current and torque output usingconventional model by IsSpice.

Fig. 2. The measured real back EM F waveform of BLDCmotor.required. Another problem in simulation of BLDC motor isthat it is almost impossible to simulate transientcharacteristics because the error is maximized when thetrapezoidal model is used in transient state. Therefore, tosolve this problem, the model having back EMF waveformsimilar to the real is also needed. In this paper, for 3-phase,4-pole, Y-connected permanent magnet BLDC motor, a newmodel of BLDC motor is proposed and it is shown that themodeled back EMF waveform is accorded with the real backEMF.

11 Modeling of 3-Phase BLDC motorIn the proposed model o f BL DC m otor, the back EMF andtorque constant is represented s he function of rotor positionfo r restoring real waveform. Equation s of armature windingan d torque are used in modeling of 3-phase BLDC motor.The equation of each armature winding could berepresented as (l), (2), 3) on the assumption that mutualinductance is constant while moto r is revolving.

didtV a = R I a + L - + E a

0-7803-6561-5/00/$10.00 2000 IEEE~~

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8/13/2019 A New Simulation Model of BLDC Motor With Real Back EMF Waveform

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(2)(3

dibv =m +L EbdtdidtV, = RI - L E ,

where, L, = L, =L , = L : armature inductance [HIR =Rb =R , = R : armature resistance [Q]V : erminal voltage [VII :phase current [A]E : ba ck EM F [VI

3-phase BLDC motor, the back EM F is related to a functionof rotor position and th e back EMF of each phase has 120phase angle difference so its equation of each phase shou ld beas follows. Fig. 3. The model of 3-phase BLDC m otor.

(4)( 5 )6 )

Hence, by using the above eq uations, the model of BL DCmotor could be obtained represented as Fig. J This isconstructed by ISpice circuit model and consist of armatureequation, torque equation and electrical angle generation partwith mechanical angle accor ding angular velocity. Theta-a,theta-b and theta-c are used to restore the real back EM Fwaveform and E a,E b and Ec is the restored back EM F in Fig. 3.   Restoring method will be discussed at next chapter.here, K E , : back EMF constant of one phase

111.Restoration of Back EMF wavefo rmorque constant also could be represented as K, f3)satisfiing K T e )= K E 0 ) . Thus, torque output of eachphase should be expressed as follows. For restoring the back EMF waveform similar to the real, theFFT (Fast Fourier Transform) and IFFT (Inverse FFT)met hod are used in this paper. First of all, Fourier series isrepresented like (12) and the back EMF waveform of onepole-pair could be transposed to Fourier series by FFTmethod.

The coeficient b, is 0 at all integer and a, is 0 at evennumber in 3-phase BLDC motor because the back EMFwaveform of BLDC motor is quarter-wave sym metry.

Tu 4=K q @ ) I , t )21t

2a

7)( 8 )

9 )

T b t ) = K z e--) lb f)

T,W =K q 6+,v, 0where, Kq orque constant of one phaseGenerally as reluctance torque is small, total torque outputcan be represented as summation of that of each phase.Equation (1 0) represents the total torque output.

T E = Tu+ Tb +T (10)where, T E : otal torque output p . m ]

In the meanwhile, the equation of mechanical part isrepresented as follows.(11)

TL oad torque l?Jin]J : rotor inertia [kgm2]B : damping constant

d odtT -TL = J- Bowhere,

i i ----7A, %

md r b M r tFig. 4 The model restoring nonlinear back EMF waveform

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Fig. shows the model restoring nonlinear back EMFwave form of one phase till 23'Th harmonics. Each electricalangle according to motor position are multiplied with eachcoefficient and summ ed. Input voltage

where U : elec. degree

300 [VI

In this model, 8 has the value as (13), (14) and (15) at eachphase.

Armature resistanceArmature self inductance

P2P2

e =e X-e =e,x--12oo

0.388 [Q]2.28 [mH]

P2

ec=e X +120where 8, , 8, c input of IFFT mo L-

Armature mutual inductanceK T G

(13)14)15)

[elec. degree]

0.56 [mH]1

8, Mechanical angle of rotor [mech. degree]Load torque

IV. Simulation Result

5 [

is need to know real back EMF waveform and other motorparameter for simulation. This could be mainly obtainedobtained measurement or calculation at motor design step.Am ong o f them, calculation m ethod is generally used, for thepurpose of simulation is to confirm the design of motor andcontroller at design step. Especially back EMF waveformshould be known for analyzing torque, speed and othercharacteristic of motor and it could be obtained mostly withFEM (finite element method).

Design of Motor usingsoftware tool

Calculatethe back EMFwaveform using FEM-

I

Model generation suitablefor simulationtool

IDynamic simulationof

Designed motor -

Calculate the coefficient forIFFT with FFI' of waveform

Restore the back EMF waveformaccordingto rotor angle

Peak value of back EMFPeak value of torque constant INumber of polesInertia of rotor 2 x103[kgm2]

In this paper, Design of motor was performed with MotorExpert that is a design tool for various motors. Back E M Fwaveform and other motor parameters were calculated withMotor Expert using FEM and the parameter of proposedmodel, especially coefficient of FFT calculated withMESPICE that is Motor Expert module. The library forvarious simulation tools according to various parameters isobtained with MESPICE. The proposed model was made tothe library of ISPICE with parameter and coefficientcalculated by M otor Expert.Table. 1 shows simulation parameters. And open loopcontrol is adopted as a control method to compare thesimulation results for the conventional and propose d mo del.Fig.6 represents a comparison of the simulation results forthe conventional and proposed model. In this figure, (a)shows a simulation result using conventional model and (b)proposed model that restores back EMF waveform similar tothe real of Fig. 2.   It can be notified that the back EM Fwaveform by proposed model could be restored very similarto the real waveform in Fig. 2. 

In comparison of two models, simulated torque outputthrough the conventional model has larger torque ripple thanthat through proposed model. And speed in convention almodel is lower than that in proposed model at same loadtorque because the average value of back EMF inconventional model is higher than the real value. It could beknown that the simulated results of conventional andproposed model are very different and the proposed modelcould obtain the more precise s imulation result.

Fig.5 Simulation procedure

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8/13/2019 A New Simulation Model of BLDC Motor With Real Back EMF Waveform

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lm ICrU Q.l(b)Fig.6 Comparison of the simulation results for conventionaland the proposed model. (a) Back EMF, phase current andtorque output using conventional model with load torque

5[ ] 384[rad/sec]. (b) Back EMF, phase current and torqueoutput using proposed model with load torque 5[Nm],424[rad/sec].

V. ConclusionA new BLDC motor model with the precise back EMFwaveform restored by FFT and IFFT method is proposed toimprove simulation result of BLDC motor. Through thesimulation results, it is proved that the back EMF waveformwith proposed model could be reconstructed to any waveform

real waveform calculated by FEM. Thus it is possible tosimulate the dynamic characteristic of motor with real backEM F w aveform according to various shape of slot, skew andmagnet and designer could be able to design for various case.In addition to that, the more practical and precise speed andtorque characteristics could be obtained with proposed modelthan conv entional model. Thus the proposed model can beused very effectively in analysis and design of the BLDCmotor system.

[Reference][ I ] J.R. Hendershot Jr. and T.J.E Miller Design ofBrushless Permanent-Magnet Motors , Oxford Univ.

Press, 1994[2] Pragasen Pillay and Ramu Krishnan , Modeling,Simulation, and Analysis of Permanent-Magnet MotorDrives, Part : The Brushless DC Motor Dribe , IEEETrans. on Industry Application, Vol 25 N o 2, PP.274-279,1989

[3] S.J Kang, J.S. Kim, S.K. SUI,D.K. Kim, Precise PositionControl with a Low Cost BLDC M D rive , TheTransactions of the Korean Institute of ElectricalEngineers ,V ol 44 No 4, PP. 447-452, 1995 (in Korean)[4] S.Y. Lee, B.H. Kang, Y.M. Chae, H.S. Mok, G.H. Choe,D.K. Kim, J.S. Ryu BLDC Motor Model with Non-Linear Back-EM F Wave , Power Electroni~cs AnnualConference, P P. 22-25, 1999 (in Korean)

[5] E.Oran Brigham, The Fast Fourier Transfomi, Prentice-Hall Inc., 1974[6] User's Manual of M otor Expert, KOMOTEK

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