Prformanc Analysis of BLDC Motor for Sinusoidal and Trapzoidal Back-Emf using MATLAB/SIMULINK Environmnt Pramod Pal Dpartmnt of Elctrical Enginring Maulana AzadNational Institut of Tchnology Bhopal, India T M Shubhum Dpartmnt of Elctrical Enginring Maulana Azad National Institut of Tchnology Bhopal,India Abstract: Th Brushlss DC Motor find varity of applications in domstic and industrial applications. BLDC Motor has som important charactristics lik low and high powr dnsity and as of spd control. This papr prsnts a thr phas invrtr fd Brushlss DC motor. Th procss considring th dvlopmnt of BLDC Motor Modl in MATLAB/SIMULINK nvironmnt with sinusoidal and trapzoidal back-emf wavform and also includs a comparison study for th harmonic analysis for sinusoidal and trapzoidal back-emf modls. trapzoidal back-emf wavforms. Wrf SPEED CONTROL CURRENT CONTROL POWER INVERTER BLDC MOTOR Ky Words: BLDC Motor, Simulink Modl, back-emf I.INTRODUCTION Brushlss DC Motor has th charactristics of DC motor but liminats th nd of commutator and brushs this rducs th losss in th machin and also improv th fficincy but incrass th cost. Thrfor BLDC Motor rplacs th convntional DC Machin in high fficincy applications. Th main rason for motor spd control is to account a signal for dmandd spd and to driv th motor for that spd [1]. BLDC Motor uss DC voltag sourcs but th commutation is don lctronically. BLDC Motor coms in varity of powr ratings from low rang to high rang. It has som advantags ovr convntional DC motors lik noislss oprations, highr fficincy, bttr spd and torqu charactristics and longr lif []. Th slction of right BLDC motor for various applications is vry important. Th back-emf is th most important factor which affcts th torqu producd in th BLDC Motor. Normally BLDC motor has trapzoidal back-emf with rctangular wavform of stator currnt. It causs constant valu torqu but practically torqu rippl xists du to currnt rippl, phas currnt commutations and non uniform back-emf wavforms thrfor always a diffrnc xists btwn actual valu and simulation rsults. Th papr attmpts to compar BLDC Motor prformanc for both sinusoidal and Vdc Tload Fig.1 BLOCK DIAGRAM OF BLDC MOTOR CONTROL SYSTEM Fig.1 shows block diagram of BLDC motor control systm. Hr hystrsis or PWM control is to b usd for maintaining th actual currnt flowing into th motor as clos as possibl to th rctangular rfrnc valus [3]. Th major disadvantag of BLDC Motor is its highr cost and high dgr of complxity introducd by th six stp invrtr [4], [5]. II MATHEMATICAL MODELLING Modling of BLDC Motor can b don by considring it as a convntional thr phas synchronous motor. It has thr phas stator and prmannt magnt rotor. Th currnt inducd in th rotor can b minimizd by th high rsistivity of both th magnt and stainlss stl laminations. Th BLDC Motor can b modld in both d-q axis modl and also abc phas modl analysis. Th important quations in modling of BLDC Motor ar as follows: Vab = R ia ib + L d dt Vbc = R ib ic + L d dt ia ib + a b [1] ib ic + b c [] Vca = R ic ia + L d dt ic ia + c a [3] 541
R= Pr Phas Stator Rsistanc L=Pr Phas Stator Inductanc i a,i b,i c =Instantanous Stator Phas currnt V ab,v bc,v ca = Instantanous Stator Lin voltags ab, bc, ca =Instantanous phas back-emf Th Phas currnts can also b writtn as: ia + ib + ic = 0 Thus th quation can b writtn as: θ = Wm J=Momnt of Inrtia in Kg/m K f =friction constant in NM/Rad/Sc. T L =Load Torqu in NM III. SIMULINK MODEL ic = (ia + ib) Thus th lin voltag givn by quations [1] and [] can b writtn as: Vab = R ia ib + L d dt Vbc = R ia + ib + L d dt ia ib + a b [4] ia + ib + b c [5] Th flux of th prmannt magnt rotor and spd of th rotor will influnc th back-emf as xplaind as follows: a = b = K ωm K ωm F(θ) [5] F[θ Π 3 ] [6] c = Kωm F[θ 4Π ] [7] 3 Thus th lctromagntic torqu is givn by: T = K K F θ ia + F θ Π 3 [8] Whr θ = P θ m Elctrical Angl,dgr Wm=Rotor Spd in Rad/Sc. K=back-Emf constan in volt/rad./sc. ib + K F θ 4Π 3 Th dynamics of th motor and load as follows: To = KfWm + J d dt To TL = KfWm + J d dt Wm + TL [9] Wm [10] ic Fig. SIMULINK MODEL FOR PWM CONTROL OF BLDC MOTOR Th simulink modl of BLDC Motor is as shown in th figur. In BLDC Motor th commutation is don lctronically and th stator winding will b nrgizd in a squnc and this maks rotor position information critical for succssful commutation. Th stator winding will b nrgizd in propr squnc according to th information providd from th rotor snsors mbddd into th stator. Normally Hall Effct snsors ar usd for snsing th position of rotor. In th prsntd modl thr hall snsors ar usd and this is th main disadvantag of th prsnt modl th snsors can also b minimizd by using a diffrnt tchniqu for PWM control of BLDC Motor [6]. If North Pol is passs through th hall snsor it will giv activ high signal and if South Pol passs through hall snsor it will giv activ low and thus this squnc will giv commutation logic. PWM gnration block will uss following quations for signal gnration J d dt Wm = To TL KfWm [11] Va = T1 Vd (T4) Vd [13] Wm = Kf Wm + 1 (To TL) [1] J J Vb = T3 Vd (T6) Vd Vc = T5 Vd T Vd [14] [15] Thus as xplaind by th abov quations for vry 60ᶿ lctrical rotations th hall snsor will chang its stat and 54
six stps will b takn to complt on lctrical dgr of rotation. It is not ncssary that on lctrical dgr of rotation is qual to on mchanical dgr of rotation. Th lctrical and mchanical dgr of rotation will b rlatd as follows: θ = P θm [16] θ =Angl of rotation in lctrical dgr θ m =Angl of rotation in mchanical dgr IV. SIMULATION RESULTS TABLE 1 BLDC MOTOR SPECIFICATION PARAMETER VALUE UNIT Vd 16.966V Volts Stator Phas 4.8750 Ω Rsistanc R Stator Phas 6.5-3 H Inductanc L No. of Pols 4 Inrtia 15.17 10-6 Kgm Kw 56.3 10-3 VradS- 1 SIMULATION RESULT FOR SINUSOIDAL WAVEFORM: Fig.4 Back Emf Fig. 4 Torqu FFT ANALYSIS FOR SINUSOIDAL WAVEFORM Fig.3 Spd Fig.5 FFT Analysis for Spd Currnt Fig.6 FFT Analysis for Back-Emf 543
Fig.7 FFT Analysis for Currnt Fig. 11Currnt Fig.8 FFT Analysis for Torqu SIMULATION RESULT FOR TRAPEZOIDAL WAVEFORM: Fig. 1 Torqu FFT ANALYSIS FOR TRAPEZOIDAL WAVEFORM Fig.9 Spd Fig. 13 FFT Analysis for Spd Fig.10Back-Emf Fig.14 FFT Analysis for back-emf 544
Comparison of Sinusoidal and Trapzoidal wavform for stator currnt Typ of wavform Currnt Rippl Pak Valu THD Ia Ib Ic Sinusoidal 0 7.6 7.6 7.5 46.34 Trapzoidal 0 7.4 7.4 7.5 50.71 \Comparison of Sinusoidal and Trapzoidal wavform for Back-Emf Fig.15FFT Analysis for Currnt Typ of wavform Back-Emf Rippl Pak Valu THD Ea Eb Ec Sinusoidal 0 55.8 55.8 55.8.57 Trapzoidal 0 47.5 47.5 47.5 36.48 Fig. 16 FFT Analysis for Torqu Comparison of Sinusoidal and Trapzoidal wavform for spd and torqu Typ of Spd Torqu wavform Rippl Pak valu TH D Rippl PEAK VALU TH D E Sinusoidal 0. 93.5 5. 0 13.6. 5 Trapzoid al 0.05 9.5 60.5 0 1.8 9.4 0 IV. REFERENCE [1] Application charactristics of prmannt magnt synchronous and brushlss dc motors for srvo drivs, prsntd at th IEEE IAS Annual Mting, Atlanta, 1987. []M. Lajoi-Maznc, C. Villanuva, and J. Hctor, Study and implmntation of a hystrsis controlld invrtr on a prmannt. [3] T. M. Jahns, Torqu production in prmannt magnt synchronous motor drivs with rctangular currnt xcitation, IEEE Trans. Ind. Appl., vol. IA-0, no. 4, pp. 803-813, July/Aug. 1984. [4] A. A. Aboulnaga, P. C. Dsai, F. Rodriguz, T. R. Cook, and A. Emadi, A novl low-cost high-prformanc singl-phas adjustablspd motor driv using PM brushlss DC machins: IIT s dsign for 003 futur nrgy challng, in Proc. 19th Annu. IEEE Applid Powr Elctron. Conf., Anahim, CA, Fb. 004, pp. 1595 1603. [5] C. W. Lu, Torqu controllr for brushlss DC motors, IEEE Trans. Ind. Elctron., vol. 46, no., pp. 471 473, Apr. 1999. [6] S. Anand, M. Nikola, J.Young and K. Mahsh An FPGA Basd Novl Digital PWM Control Schm for BLDC Motor Drivs IEEE Trans. On Ind. Elctron., Vol. 56, No.8, Aug. 009. 545