Dynamic Simulation of Brushless DC Motor DrivesConsidering Phase Commutation for Automotive

ApplicationsWonbok Hong#l, Wootaik Lee#2 ,Byoung-Kuk Lee*3

#l Dept. ofControl and Instrumentation Engineering, Changwon National UniversitySarimdong 9#, Changwon, GyeongNam, 641-773, South Korea,

1idhistory@changwon. ac .kr2wootaik@sarim. changwon. ac .kr

School ofInformation and Communication Engineering, Sungkyunkwan University300 Cheoncheon-dong, Suwon,Gyeonggi-do, 440-746, Korea

Address Including Country Namebkleeskku@skku.edu

Abstract This paper proposes the advanced model of brushless BLDC motor drives are indispensable for the rapid predictiondc motor drives considered behaviour of commutation and of the motor drive system during the evaluation of differentwaveform of back-EMF for dynamic simulation of automotive BLDC motors and designing control algorithms early in theapplication under Matlab/Simulink environment. We need a design process. It makes possible to vary and optimizemodel of BLDC motor drives that control algorithm and BLDC components and subsystems designs and to predictmotor drive system can be designed and simulated as a point of performance of the system for given goals and constraints [2].system level. The model has to consider commutation Several simulation models have been proposed for thephenomenon. A waveform of back-EMF of BLDC motor can be . .modified to depend on BLDC motor type. To satisfy above analysis ofuBLDGnmotoruries.rTese mod are bas onfactors need a co-simulation technique with other circuit level state-space equations, Fourier series, and the d-q axis modelsimulation tools. However, there are severe constraints, i.e. [3-5]. Even though the previous works made a greatsimulation speed and interface with tools. The advanced model contribution to simulate the BLDC motor drives, no modelsproposed in this paper considers behaviour of commutation and are appropriate for development and analysis of controlwaveform of back-EMF for comprehensive analysis and algorithm of BLDC motor drives under Matlab/Simulinkprediction of dynamic characteristics ofBLDC motor drives. The environment, which is a de facto standard tool in control andcommutation phenomenon is implemented by functional system engineering. One of the models, in [6], the authorsbehaviour description and back-EMF is modelled by pattern of proposed model by means of the switching function conceptwaveform. The developed model is split into few parts withobject-oriented manner for reusability and scalability. It is easily alo wit thep iertr. Howvrthe moelomenotintegrated with other models of automotive application, properly reflect the electronically commutation phenomenon

and a waveform of back-EMF is trapezoidal. A torque rippleI. INTRODUCTION of BLDC motor is mainly influenced by the electronically

Electric motors have played a crucial role in the evolution commutation and back-EMF. Hence it is needed toof the automotive industry. Existing trends in more compensate the existing model's precise commutationelectrification of automobiles indicate a further increase in phenomenon and back-EMF [4] [8].deployment of electromechanical energy devices in coming The advanced model proposed in this paper takes intoyears. Due to historical, technical, and economical incentives account the commutation phenomenon which is implementeddc-brushed machines have been the favourite choice for functional behaviour and waveform of back-EMF which isnumerous automotive applications ranging from starters to given pattern of back-EMF. Therefore, it can be expected thatauxiliary devices. Ease of control, capital investment, and the developed model can be an easy-to-design tool for therelatively low cost of manufacturing compared to other energy design and analysis of BLDC motor drives as well as controlmachines, as advanced motor drive technologies emerge [1]. algorithms.On the other hand, due to the brushes, dc motors suffer form a II. MODELLING OF BLDC MOTOR DRIVE SYSTEMlower reliability, since the brushed wear down by operation

The delLINGoF BLD moTOR DI SYS teMand need-time to time maintenance or replacement. This dc The developed model was modelled by object-orientedmotor's drawback can be eliminated by using a BLD motor. manner for reusability and scalability according to typicalThat's why BLDG motor drives are becoming widely used in system partitioning and all behaviour of components isindustrial areas. implemented by basic block of Matlab/Simulink. Fig. 1 shows

Replacement of a DG motor by a BLDG motor places the overall Simulink block diagram of developed model forhigher demands on a control algorithm. Simulation models Of BLDG motor drive system. As shown fig. 1, the proposed

1-4244-0743-5/07/$20.OO ©2007 IEEE 1377

model largely consists of four components: 120-degree P (eaia +ebib + ecic) (2)conduction signal generator, Voltage Source Inverter, m 2Electrical part of BLDC, and Mechanical part of BLDC. The m

folloingasumpton i fo ipentio. where P iS the number of pole and coin1S angular velocity offollowing assumption iS for implementation.mThe motor is not saturated. rotor. The equation comes from point of energy betweenIron losses are negligible mechanical energy and electrical energy.Stator resistances of all the windings are equal, and self- The mechanical part ofBLDC motor can be modelled asand mutual inductances are constant. Jm6 + Bmi = Tm - (3)Power semiconductor devices in the inverter are ideal where Jm is inertia and Bm is damping ratio.

BLOC

Moor_- B. Voltage Source InverterUdc* Udc theta

U6 Ucon GateABCtBC ClUan bcS The fig. 3 shows an equivalent circuit of the 3-phasestheta Uabcn 6al thneta Te onm3a_mit BLDC motor drive. The inverter operation can be divided intoJabcn TE- Iomea_m six sectors according to the current conduction states as shown

ED ~theta FreeABC _ h labc T heta h t 4

Eabc onmega Ea be EE Ib onmega gFm-< megI Infg.14.SquareWave PWM Inverter BLDC BLDCIR

A. Fig. 1 Simulink diagram of BLDC Motor Drive System T 7= rUOl ;4Uc|U;

BLDG motor model is composed of two parts. One is an > I ;electrical part which calculates electromagnetic torque andcurrent of motor. The other is a mechanical part which Fig. 3 BLDC Motor and Inverter Equivalent Circuitgenerates revolution ofrotor. Under the above assumption, the sector 1 2 3 4 5 6electrical part ofBLDG motor can be represented as

[~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Ua[O_YO[1(Uab lb[ 0 0a 1 M dt [ ^ [ b U U

where ea, eb, and ec areback-EMF. .___

L is self inductance, M is mutual inductance, and R is phaseresistance.1

GCDFig. ISimComega ri-e- -,i F ig.4 6 Sector of BLDC 12O °On-Mode drive

Gainl8 Dot Product6 1 J|||theta Commutation Normal

rl I-K I interval rinterval

Gain2A Dot Product8 I

Fig. 2 Simulink diagram of back-EMF A I

There are two types of stator windings variants: trapezoidal \1and sinusoidal motors. The model proposed in this paper has /sinusoidal waveform of back-EMF. But as modifying in theS1tr-fdotted rectangular, the model also has trapezoidal waveform S3 turn-onof back-EMF. Especially waveform of real back-EMF can beused using look-up table. It iS very important property becauseFi.5Tpcluretwvfmofdincmuaindistortion is occurred in the back-EMF when motor revolves A sector is divided into two parts, commutation and normalin high speed. interval. The commutation interval is the initial freewheeling

The electromagnetic torque is expressed as interval, just after switching, when both mesh current are non-

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zero. During commutation interval, all three lines are In a similar way, the commutation phenomenon of otherconducting. The subsequent period when only phase B and sectors is analysed. The model was developed using Simulinkphase A are conducting is called normal interval. Normal basic block with functional behaviour description as shown ininterval begins when freewheeling mesh current extinguishes. fig. 8. The inverter takes DC bus voltage, back-EMF, and gateDuring commutation interval, ia is decaying and ib is signal and then calculates each phase voltage.increasing. Ideally dib/dt =-di,jdt so that i, remains constant. [ l

~~~0It is shown in fig. 5 which is typical current waveform of

Uola °

during commutation. Each line-line voltage is calculated la ETbdepending on the interval. The detailed switching states and be E13- n

conduction sequence are described in fig. 6. C E 4)For example, the sector is changing from 6 to 1. In the T ,

normal phase of sector 6 the top switch of phase A and bottom [ _switch of phase B are on state. There is then only one meshfor current to flow, i.e., the loop through phases A and B asshown in Fig. 6-(a). In this context the phase voltages (a) Normal phase current flow of the sectorrepresent as

diaIuao = UO = Ria + L a+ ea + Uo (4) 1dt lajI _ _ _

Ubo =-uO= Rib+ L dt + eb +uno (5) ' b IC

uco= ec +uno (when, ic=0) (6) T 6JO91I

Un, =-(-ea-eb) (7) [ T___2

Uan U0 -Uno Ria + L dia +e (8) (b) Commutation phase current flow of sector 6 to sector Ian ono a dt a

ubn =uo -uno = Rib+ L dt + eb (9)~~~~~~~~~~~~~~~~~~~~~~~~~~~(10)

Corresponding rotor position sector is changing from 6 to 1. bIClT3-

The bottom switch of phase B turn-off and the bottom switch lc z -

of phase C simultaneous turn-on. Ideally the current in line B 6

should remain constant, while the line A current falls to zeroand the line C current builds up to the set-point value. There L Iare two meshes for current to flow as shown in fig. 6-(b). Thephase voltages represent as (c) Normal phase current flow of the sector 1

diaUao =u0 Ria+ L dta + e + U () Fig. 6 A sequence of Commutation in the wye connection

dib C. PWM 120-degree conduction signal generatorUb0 Ri ++(2dt 120-degree conduction signal generator model is

di implemented as shown fig. 7, and this model can generateuco =-u0 =Ric+CL C+e +nUo (13) exact square wave switching patterns. In order to simulate

1 dt detailed this switching signal, this block is used. When youuo =(u -E), (14)develop control algorithms and implement Simulink block, the

3 block put in front of this block. The frequency of carrier signalwhere, E = ea + eb + ec is 16KHz.

uan = -uno =Ria +L da +ea (15)dt

Ubn =0~UnOu =Rib +L dt+deib (16)

Ubn =-uo-uno =Rib +L d+e (17)dt

Fig. 7 Simulink diagram of square wave PWMUtri

theta [-K: ~~~~~~~~~~~~~~~GateAthetaPhase Va (u2-[]

GateBt

(u[2]>u[1]) GateBb G

[4 ~~~~~~~~~~~GateABCPhase_Vb ([iu])GateCt

GateCb

Uc Phase Vc~- *| ~~~~~~~~~~~~~~~~~~FreeABC

Uco 1/(0 5*UdcNom

Ucon

Udc

GateABO [Eb] Ubn)

[Uno]

[Eb] ~LIIzIV*KComm

Eabc I [thet] U

[sector] theta ++ [sector][ector

[Uo]~~~~~~~~~~n

Fig. 8 Simulink diagram of Inverter for BLDC Motor

Numberofpole p 4 EAIII. SIMULATION RESULTS AND DISCUSSION

Table 1 shows the BLDG motor specification to examine First step is to examine implementation of functions whichthe performance of the proposed model. Simulation was are commutation phenomenon and waveform of back-EMF.performed two steps. Fig. 9 show results of first step simulation that 80V dc bus

voltage and 0.2Nm load torque are applied to the system.Table 1. Motor specification Modulation index is 80%. The voltage which is applied to

Description |Symbol Value Unit BLDG motor depends on the modulation Index. If modulationPhase resistance Rs 988.9 mQ index is high, applied voltage should be high. Fig. 9-(a), (b)Phase inductance L 2.7236 mH are a simulation result that commutation phenomenon is addedMagnitude of flux v 56.235e- 3 Wb to the BLDG motor drive and o.nly (a)'s back-EMF waveform

linkage miS trapezoidal and (b) iS sinusoidal. Fig. 9-(c) iS theFriction coefficient Bm le-3 Nm /(rad Is) experimental result that the BLDG motor has sinusoidal

waveform of back-EMF. To know effects of commutation andertiaeofmoment e15.p17e-6 NmFmwaveform of back-EMF compares with each current of phase.

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The current has gradient because of effects of inductance. If Current [A]back-EMF is trapezoidal, the gradient is fixed. However, if 2back-EMF is sinusoidal, the gradient is not fixed as shown in 1.5fig. (a) and (b). Current is made by subtracting back-EMF '1_xfrom applied voltage. Therefore, current distortion, which is 1dotted circle in fig. 9-(b), is occurred in the normal interval, 0.5 If Tv1when BLDC motor has sinusoidal waveform of back-EMF.The line circle regions mean commutation interval. On the 0 = -=commutation interval sparks of the current of phase A is V

-0 .5represented. Two figures, (a) and (b), show that the developedmodel well reflects commutation phenomenon, even though -1the interval of commutation of both figures is a little different,experimental about 0.2msec and simulation about 0.15msec.As shown in fig 9-(b), (c), the shape is same. However, the 2 _ __ _ _speed of developed model is a little faster than experiment. 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09The reasons are that components are ideal and losses areignored. Finally of the first step simulation current ripple ofphase A is compared. The developed model and experiment Current [A]were just compared to know how much the model well reflect F F 7 F 7real phenomenon. A torque ripple is inferred from the current 1.5 Xripple because current ripple directly affects torque ripple.Table 2 shows a result of comparison of simulation andexperiment. It is enough to analyze torque ripple considering 0.5

-- --=

-0.5-0.5 -

-2 -l LliL0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09

time[s]

(b) Commutation with sinusoidal

Current [A]ll

1.5

.5

0

-0.5 -

-2 lL L L0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09time[s]

(c) Experiment

Fig. 9 Result of simulation and experiment

measurement error. As shown in figure 10, simply a ripplefactor was defined the following as

R.F.= PPx1OO (18)Rave

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where, R is relative difference between maximum value The speed of the Motor [rpm]400077 7

and minimum value of current ripple and Rave is average valueof current ripple.

3000 X -

Table 2. Comparison of ripple factorSimulation Experiment

Load torque: 0.2 Nm 70.030o 67.75°o 2000

Second step is validation of dynamic characteristic of 1000BLDC motor drive. Fig. 11 shows the results of second stepsimulation that 80V DC bus voltage and 0.2Nm of loadtorque are applied to the system with open-loop control. 0Modulation index is 80%. Transient state is examined through 0 0.02 0.04 0.06 0.08 0.1this simulation. Fig. l1 -(a) shows the speed of the motor. Fig. time[s]1 1-(b) is electromagnetic torque and (c) is current of phase A. (a) Speed of the motorRipple of the current exactly due to the commutation as shown Electromagnetic Torque [Nm]in Fig. l l-(c). The current ripple directly affects the 2.5 l7electromagnetic torque. In addition to back-EMF waveform is 2sinusoidal thus a distortion of current is occurred.

25 1.5 -X + _

2 0.51.5 t t; f 0

1 --R-0.

0.5 RLave AX X0 0.02 0.04 tm[]0.06 0.08 0.

°c 'l*ll ,j len (b) Electromagnetic torque of the motorCurrent [A]

-0.5 e + +12

1001502002503003504004505005506000.10 +

Fig. 10 Definition of ripple factor,

IV. CONCLUSIONS 6._

This paper presented an improved model of BLDC motordrives considered behaviour of commutation in case of 4dynamic simulation. The feasibility and performance of the 2_model is examined by simulation. Comprehensive analysis of fX>l ul lH u:l . Al lM gll uthe BLDC motor drives is allowed and dynamic characteristic 0can be effectively monitored and predicted. This model was -2implemented under Simulink environment with modular 0 0.02 0.04 0.06 0.08 0.1manner. Thus the proposed model can be used very effectively time[s]in analysis and design of control algorithms of the BLDC (c)Currentoeofthe motor

motordri m. Fig. 11 simulation result from the model

What has been presented in this paper is only the first step REFERENCES

inthis paerelopmente an impovemodel of BLDC motorDrv

in the development of the model of BLDC Motor Drive ~~~~~~~[1] A. Emadi, "Handbook of Automotive Power Electronics And MotorSystem. It is suitable to analyze tendency of dynamic Drives" CRC Press, 2005.behaviours of BLDC Motor Drive System. In the future, we [2] W.T. Lee and J.P. Hong, "Object oriented modelling of an Interiorwill be trying to increase accuracy of the model for quantity Permanent Magnet Synchronous Motor Drives for Dynamic Simulationanalysis through the analyzing the primary factors of error. of Vehicular Propulsion"[3] P. Pillay and R. Krishnan, "Modeling, simulation, and analysis of

permanent-magnet motor drives, part II: the brushless DC motordrive," IEEE Trans. on Industry Applications, vol. 25, no. 2, pp. 274-279, March/April 1989.

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[4] R. Carlson, M. Lajoie-Mazenc, and C. dos S. Fagundes, "Analysis oftorque ripple due to phase commutation in brushless DC machines,"IEEE Trans. on Industry Applications, vol. 28, no. 3, pp. 632-638,May/June 1992.

[5] P. D. Evans and D. Brown, "Simulation of brushless DC drives," Proc.of the IEE, vol. 137, no. 5, pp. 299-308, September 1990..

[6] B.K. Lee and M. Ehsani, "Advanced Simulation Model for BrushlessDC Motor Drives", EMP 31(9) #6709, Electric Power Components andSystem, 31:000-000, 2003.

[7] J.R. Hendershot Jr and The Miller, "Design of Brushless Permanent-Magnet Motors" Oxford Univ. Press, 1944.

[8] Y.S.vJeon, H.S. Mok, G.H. Choe, D.K. Kim, and J.S. Ryu,"A newsimulation model of BLDC motor with real back EMF waveform",IEEE CNF. On Computers in Power Electronics, 2000. COMPEL 2000.pp.217 - 220, July 2000.

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