A Novel Method for Commutation Torque Ripple Reduction of Four-Switch, Three-Phase Brushless DC Motor Drive

Transcription

1 A Novel Method for Commutatio Torque Ripple Redutio of Four-Swith, Three-Phase Brushless DC Motor Drive A. Halvaei-Niasar*, A. Vahedi** ad H. Moghbelli*** Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 Abstrat: This paper presets a origial study o the geerated torque ripples of phase ommutatio i the Four-Swith, Three-Phase Iverter (FSTPI) Brushless DC (BLDC) motor drive whih is suitable for low ost appliatios. Aalyti values of torque ripple ad ommutatio duratio are obtaied for differet operatio oditios. Moreover, limitatio o the speed rage operatio aused from splittig of the DC-lik voltage is show exatly. The a ovel urret otrol tehique is developed to miimize the ommutatio torque ripple for a wide speed rage. The tehique proposed here is based o a strategy that the urret slopes of the risig ad the deayig phases durig the ommutatio itervals a be equalized by proper duty-ratios at ommutatios. Fially, the validity of the proposed aalysis ad developed torque ripple redutio tehique are verified via simulatio. Keywords: Brushless DC Motor, Commutatio Torque Ripple, Four-Swith Iverter. Itrodutio Brushless DC motors with trapezoidal bak-emf have bee widely used due to their high effiiey, high torque desity, low maiteae ad ease of otrol []. BLDC motors are fed with retagular stator urret as show i Fig. ad therefore, the developed torque is theoretially ostat. However, i pratie torque ripple exists due to the stator idutae, oggig effet ad motor feedig [2, 3]. Carlso aoued relatio betwee the ommutatio torque ripple ad the speed of a six-swith iverter BLDC motor drive [4]. For low ost appliatio, the four-swith, three-phase iverter (FSTPI) employs oly four swithes, a pair of omplemetary swithes as show i Fig. 2. A ompariso betwee six ad four swith iverters for a three-phase BLDC motor drive have bee preseted i [5, 6]. Although i the four-swith iverter, geeratig of 2 o odutig urret profiles is iheretly diffiult. Therefore, i order to use the four-swith topology for three-phase BLDC motor, ew otrol Iraia Joural of Eletrial & Eletroi Egieerig, 27. * The Author is with the Departmet of Egieerig, Uiversity of Kasha, Kasha, Ira. He is urretly a Ph.D. studet at Departmet of Eletrial Egieerig, Ira Uiversity of Siee ad Tehology, Tehra, Ira. ahalvai@yahoo.om. ** The Author is a Assoiate Professor ad member of Ceter of Exellee for Power System Automatio ad Operatio at the Ira Uiversity of Siee ad Tehology. avahedi@iust.a.ir. *** The Author is with the Departmet of ECE, Isfaha Uiversity of Tehology, Isfaha, Ira. He is urretly a visitig Assistat Professor at the Departmet of Siee & Mathematis, Texas A&M Uiversity at Qatar, Doha, Qatar. hassa.moghbelli@qatar.tamu.edu. methods should be used. The reported methods due to asymmetrial voltage problem have paid to odutio iterval operatio ad so there are't ay osiderable works for ommutatio itervals. I this paper, a origial study of ommutatio for FSTPI topology is proposed ad its drawbaks are explored aalytially. The, the possibility of reduig the torque ripple due to ommutatio for a FSTPI brushless d motor drive is proposed. Fially, a ovel torque ripple redutio method is developed to ehae the drive performae it is demostrated via simulatio. 2 Aalysis of BLDC Motor Drive Usig FSTPI 2. Modelig of FSTPI-BLDC Motor Drive The overall blok diagram of a FSTPI-BLDC motor drive is show i Fig. 2. Motor is oeted to a, b legs of iverter ad mid poit of DC-Bus. Mathematial model of a three-phase BLDC motor is expressed as: va R ia Ls M i a ea d v = R i + L M i + e b b s b b dt v R i L M i e s ad, v = v + v v = v + v v = v + v a a o b b o o () (2) where, v xo, v o, v x, i x, ad e x, are the lie termial voltage ad motor star poit with respet to poit o, phase termial voltage, phase urret, phase bak-emf Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27 83

2 Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 voltage, ad R, L s ad M are the phase resistae, phase idutae ad mutual idutae respetively [7]. Geerally a BLDC motor has two operatio regio; odutio regio ad ommutatio regio. I the odutio regio, two phases always odut the urret. Commutatio regio is trasiet regio betwee two odutio modes ad therefore, three phases iludig risig, deayig, ad o-ommutatig phases are all odutig. 2.2 Curret Regulatio I a Four-swith BLDC motor drive, urret regulatio eeds more attetio rather tha six-swith drive. Aordig to Fig., i mode II ad V, phases a ad b are odutig the urret ad phase is silet. However, the bak EMF voltage of phase (e ) a ause additioal ad uexpeted urret, resultig i Fig. Ideal sigal waveforms of three-phase BLDC motor. urret distortio i the phases a, b. Therefore, if i a ad i b are otrolled idepedetly, ifluee of the voltage e a be bloked ad therefore, there is t ay urret distortio i phase a ad b. Fig. 2 shows the ofiguratio of a FSTPI-BLDC motor drive with employig the diret phase urret (DPC) otrol tehique that two urret sesors are used. I additio to odutio regios, it is possible to exted the DPC otrol tehique to ommutatio regios. For low speed oditios, this tehique a regulate the urrets well. Therefore, the urret ad torque do't otai ay ripple more tha hysteresis bad. However, it has bee show that DPC otrol tehique a ot redue ommutatio torque ripple at high speed oditios [8]. Therefore, the effetive otrol tehique should be developed. Fig. 2 Cofiguratio of FSTPI-BLDC motor drive system via diret phase urret otrol method. 84 Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27

3 3 Aalysis of Commutatio i FSTPI-BLDC Motor 3. Phase Curret Behaviors i Commutatios Phase ommutatios i all modes of a six-swith iverter BLDC motor drive are the same together whereas, i four-swith iverter, they are differet. Deped o the motor speed, three differet ases may be foud for eah mode as the followig: Case B: Deayig urret vaishes before that the risig urret reahes to its fial value as show i Fig. 3(b). Case C: Risig urret reahes to (+I) before that the deayig urret vaishes as show i Fig. 3(). Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 Case A: Deayig urret (i d ) vaishes at the same time that the risig urret (i r ) reahes to its fial value (+I) as show i Fig. 3(a). (a) Case A evolutio For the followig aalysis, the stator resistae is igored ad the phase bak-emf voltages is supposed to remai ostat durig ommutatio. These assumptios lead to aalyti equatios for developed torque ripple values, ommutatio duratios ad et. (b) Case B evolutio () Case C evolutio Fig. 3 Curret behaviors durig ommutatio. Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27 85

4 Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th Curret Commutatio I this setio, the urret ommutatios are aalyzed at positive urret level whih are orrespodig to three modes II, IV ad VI. Commutatio at egative level i modes I, III ad V a be explaied i the same maer. Mode II I mode II, i d, i r ad i (o-ommutated urret) are orrespodig to i, i a ad i b respetively ad ommutatio is from phase to phase a as show i Fig.. The urret is trasferred by swithig o S ad S 4. Nevertheless, the urret is ot trasferred diretly ad it is doe firstly by atio of the freewheelig diodes. The iruit before ommutatio is show i Fig. 4(a). Immediately after swithig o S, the iruit topology is show i Fig. 4(b). From this poit, three ases A, B or C may be foud. To aalyze of iruit i these ases, the urret derivatives are firstly obtaied as follow. For sequee of Fig. 4(b), the KVL equatios usig Eq. () are writte as: V di + = R i + L + e + V 2 dt V di = R i + L + e + V 2 dt di = R i + L + e + V dt a a a o b b b o o (3) where, L= L s M. Substitutig the phase bak-emf voltages with their magitude, results: V e + e + e E 3 3 a b = = o (4) With simplifiatios, urret derivatives are expressed as: dia = dt 6L dib 8E = dt 6L di = dt 6L (5) With the same maer, for sequee of Fig. 4(), urret derivatives are obtaied from: Aordig to the motor speed, three followig ases a be ourred: Case A: I this ase, i ad i a reah to their fial values simultaeously ad therefore, their slopes are equal. The oditio for ourrig ase A from Eq. (5) is give by: E 3 = (7) V 8 Takig the begiig of the ommutatio as the time origi ad usig Eq. (5), i a is obtaied from: i (t) = t a (8) 6L Therefore, the ommutatio time t a be alulated from: t 3LI = (9) 2E Case B: I this ase, the ommutatio is doe i two sequees I ad II. I the first sequee ( < t< t ), i vaishes at t = t. It is haraterized by the iruit of Fig. 4(b) ad from Eq. (5), i (t) is obtaied from: i (t) = I t () 6L The duratio of this step is obtaied from Eq. () as: 6LI t = () At the ed of this sequee, from Eq. (6) i a is give by: i (t ) = I (2) a For seod sequee (t < t< t ), two phases a ad b are odutig i series (i = i ), ad KVL is as: a b dia 3V+ = dt 6L dib 3V+ 8E = dt 6L di = dt 6L (6) di di di a b a V= L + e L e = 2L + 2E a b (3) dt dt dt Therefore, the urret i a is expressed by: V 2E i (t) = I+ t (4) a 2L 86 Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27

5 Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 At the ed of sequee II, i a reahes to +I. So, the duratio of this step ( ) is obtaied from: 3V+ 8E 2LI = V 2E (5) The total duratio of the ommutatio i ase B is alulated from Eq. () ad Eq. (5): LI t = t + = V 2E (6) The oditio to have the ase B a be obtaied from relatios i a (t ) < + I ad < t as: 3 E < <.5 (7) 8 V This equatio explores the high speed rage of FSTPI- BLDC motor i modes II ad V. I this ase, urret i b is ot diretly ivolved i the ommutatio, but does ot remai ostat beause the slopes of urrets i ad i a are differet. The poit E / V=.5 is the limit poit for otrollig the urret ad at higher speeds, the urret otrol is impossible. Case C: For this ase, the ommutatio is also made i two sequee I ad II as show i Fig. 3(). At the first sequee (< t< t ), urret i vaishes ad it is haraterized by the iruit of Fig. 4(b). At the ed of this sequee, i a (t) reahes to +I. Usig i a (t) from Eq. (5), duratio of sequee I is obtaied from: 6LI t = (8) Seod sequee (t < t< t ) orrespods to Fig. 4() ad at the ed of sequee II, i reahes to zero. Therefore, the duratio of this step ( ) is: 8E 6LI = (9) (a) Before ommutatio (b) Commutatio with two swithes () Commutatio with two diodes Fig. 4 Commutatio sequee i mode II. (d) After ommutatio Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27 87

6 Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 The total duratio of the ommutatio i ase C is the summatio of Eq. (8) ad Eq. (9) ad is obtaied from: t 3LI = t + = (2) 2E The oditio to have the ase C is give by i (t ) >, that results: E 3 < (2) V 8 This equatio explores the low speed rage of FSTPI- BLDC motor i modes II ad V. I this ase, urret i b does ot remai ostat beause the derivatives of urrets i ad i a are differet. Hee, i low speed rage o-ommutated urret i b has some swell as show i Fig. 3() ad therefore, the torque ireases. Mode IV I this operatio mode, i d, i r ad i are orrespodig to i a, i b ad i respetively as show i Fig.. Aordig to the slopes of the urrets i a ad i b, it a be proved that i this mode always i < i is valid ad therefore, oly b a ase B ours. The urret derivatives are obtaied from: dia 3V+ = dt 6L dib 3V = + dt 6L (22) With the same maer of ase B i mode II, the followig equatios are derived: 6LI t = 3V+ 8E 4LI = 3V+ V 2LI t = t + = V The oditio to have this ase is expressed as: (23) (24) (25) E.25 V < (26) Mode VI I this operatio mode, i d, i r ad i are orrespodig to i b, i ad i a respetively. Commutatio is from phase b to phase ad the urret is trasferred by swithig off S 3 ad the swith S 2 is held o. With the same maer as mode II, three followig ases a our: Case A: 6LI t = The oditio for this ase is: Case B: (27) E = (28) V 8 2LI t = t + = V (29) The oditio for ase B that results from i (t ) <+ I ad < t is obtaied from: E < <.25 (3) 8 V Similar to the modes II ad IV, poit E / V=.25 is the limit poit for otrollig the urret at mode VI ad at higher speed, the urret otrol is impossible. Case C: 6LI 4V t = t + = 2V 3V+ The oditio to have the ase C is: (3) E < (32) V 8 I this setio, the phase ommutatio i modes II, IV ad VI have bee aalyzed. Developed equatios show that the urret ommutatios of six modes are differet together ad also are differet to the ommutatio of six-swith iverter BLDC motor drive [4]. 88 Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27

7 4. Torque Ripple at Commutatios Geeral expressio of torque for eah operatio mode is give by: Case C: By substitutig t from Eq. (8) ito Eq. (34), the torque at the ed of the first step is obtaied from: 2EI T= = T ω (33) 2EI 8E T(t ) = + ω 3V (4) Also, the torque betwee ommutatios is give by: Therefore, the relative torque ripple is give by: Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 T = (edid+ erir + ei ) ω (34) Supposig the bak-emf voltages are ostat i the ommutatio result i: 2E i T = (E i + E i E i ) = d r ω ω (35) To alulate the torque ripple durig ommutatio, the urret value of the o-ommutated phase should be obtaied at the ed of the orrespodig ase. Mode II Aordig to Fig. 4(b) ad usig Eq. (5) the urret of the o-ommutated phase is expressed as: 8E i (t) = i (t) = I t b (36) 6L Case A: I this ase, i b (t) is ostat i ommutatio ad the, torque remais ostat ad is equal to T. Therefore, T= (pu) (37) = = T T(t ) T 8E (pu) T (4) With the same maer for mode IV ad mode VI, the results are as the followig: Mode IV T Mode VI Case A: Case B: Case C: T(t ) T 8E (pu) T 3V+ = = T = = (42) T= (pu) (43) T(t ) T V 8E (pu) T V+ = = T T(t ) T V 8E (pu) T 2V (44) (45) Case B: By substitutig t from Eq. () ito Eq. (34), the torque at the ed of the first step is obtaied from: 2EI 8E T(t ) = + ω (38) With some alulatios ad dividig by T, the relative torque ripple i per uit is give by: T T(t ) T 8E (pu) T = = (39) The same explaatios a be preseted for modes I, III ad V that the same results for ommutatio torque ripple are obtaied. Equatios (37), (39) ad (4)-(45) are oly valid if the urret a be otrolled. It meas they must ot exeed their orrespodig limit poits. For a typial BLDC motor, the ommutatio duratio ad the relative torque ripple alulated as equatios (36)-(45) are show i Fig. 5 ad Fig. 6 respetively. For six-swith iverter topology, ommutatio duratio has a optimum value at poit V= ad also the urret limit poit is V= 2E. However, i the four swith topology, ommutatio duratio for all modes is ireasig whe the speed ireases ad has ot ay optimum value. Moreover, the urret limit poit redues to poit V=. This is the mai drawbak of four-swith topology. It meas that for E / V> / 4 regio, the urret otrol is impossible ad atually the Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27 89

8 Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 drive operatio rage is limited to E / V< / 4 oditios ad half of the omial speed rage of BLDC motor drive is aessible. O the other had, the torque ripple equatios show that for a ostat voltage of DC-Bus, the relative torque ripple due to ommutatio is idepedet of the urret, but it depeds o the bak-emf voltage (i.e. speed). Beause of asymmetrial stator phase voltages, the torque ripple are differet at eah operatio mode as show i Fig. 6. The relative torque ripple reahes to 5% ad % at low speed i differet modes ad it redues to -5% at V=. I the ext setio, for ommutatio torque ripple redutio at E / V< / 4 regio, a ovel otrol tehique is preseted. [se] 2 x Modes 3,6 Fig. 5 Commutatio duratio i differet modes. Commutatio duratio /8 /4 3/8 /2 E/V Modes,4 Torque ripple 5 Commutatio Torque Ripple Redutio Commutatio aalysis of four-swith iverter shows that the ommutatio ripple always our ad torque ripple redutio is eessary. Usig the diret phase urret (DPC) otrol tehique at ommutatio duratio a elimiate the ommutatio torque ripple i low speed rage (ase C) i a FSTPI-BLDC motor drive. However, for high speed rage (ase B) it has bee show that DPC otrol method a ot elimiate the ommutatio torque ripple [8]. Therefore, a ovel otrol tehique based o the urret slope equalizatio of two ommutated urrets is developed. This tehique elimiates the torque ripple at wide rage lower tha urret limit poit V=. Proposed tehique is developed for modes II, IV ad VI ad for other modes, the developed relatios are the same. 6 Swith Iverter Modes 2, Swithed Iverter Modes 2,5 [pu] Modes,4 Modes 3,6 Fig. 6 Relative torque ripple amplitude i differet modes. -.5 /8 /4 3/8 /2 E/V 9 Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27

9 Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th Torque Ripple Redutio i Mode II Case B: I this ase the urret limit poit is E / V=.5 ad so for iterval 3/ 8< E / V<.5, the urret otrol or torque ripple redutio a be used. However the regio 3/8< E / V<.5 is above of the urret limit poit for modes I, III, IV, VI that is V=. It meas the urret otrol i this ase of two modes II ad V is useless. Case C: I this ase, it is lear that i < i, as show i Fig. a 7(a) ad from Eq. (6). To math the slopes of the urrets, swithig o S 4 dereases the slope of i a ad slope equalizatio a be obtaied. Solid lie shows the modulated waveform of the urret i a. Fig. 7(b) shows the iruit topology whe S is off. KVL equatios durig ommutatio itervals a be writte as: V di S = R i + L + e + V 2 dt V di = R i + L + e + V 2 dt di = R i + L + e + V o dt a a a o b b b o ad the voltage of the motor star poit is give by: (46) V E V = (S ) o (47) 6 3 that, S=+ refers to S is o durig the swithig ad S= refers to S is off. The averaged slopes of ommutated urrets are obtaied as the followig: dia = 4D V V dt 6L [ ] di = + dt 6L [ 2D.V 2V ] Equalizig slopes of urrets i a ad i leads to: D 2,Low _ (48) = + (49) 2 V From Eq. (2), < E / V< 3/ 8. But, D will be 2,Low betwee ad if / 8< E / V< 3/ 8. Moreover, it a be show that for iterval < E / V< / 8, by swithig o S 4, slope mathig betwee urrets i a ad i is aessible. Therefore, i this ase the duty yle is obtaied from: D 2,Low _ 2 3 2E = + (5) 4 V Torque Ripple Redutio i Mode IV Setio 3.2 stated that i mode IV oly ase B ours. Equatio (22) shows i < i. Mathig of these urret b a slopes a be obtaied either by dereasig the slope of i a via swithig of S. Fig. 8 shows the iruit topology ad urret behavior i this ase. With the same maer, the averaged slopes of ommutated urrets are obtaied: dia = 4D.V 3V dt 6L [ ] dib = + dt 6L [ 2D.V 3V ] Equalizig the slopes of the urrets i a ad i b results: D 4,High (5) = (52) V Equatio (26) presets that the urret otrol limit poit i modes I ad IV is E / V=.25. Therefore, the developed duty yle D is valid. 4,High Torque Ripple Redutio i Mode VI Case B: From Eq. (3), the urret otrol for iterval /8< E / V<.25 is possible. Fig. 9 shows the iruit topology ad urret behavior i this ase ad it a be show that i < i. I order to math the urret b slopes, swithig o S 3 dereases the slope of i b. Usig the same explaatio, duty yle is obtaied from: D 6,High = (53) V 2 From Eq. (3), / 8< E / V<.25 ad therefore, the developed duty yle is valid. Case C: I this ase, it a be show that i < i. To math of b these urret slopes, swithig o S 2 dereases the slope of i ad therefore, the slopes beome equal. Fig. shows the iruit topology ad urret behavior i this ase. With the same maer, duty yle is obtaied from: D 6,Low 3 2E = + (54) 4 V From Eq. (3), E / V< / 8 ad therefore, developed duty yle is valid. Fig. shows the developed duty yles of ew torque ripple redutio tehique for all operatio modes. Moreover, the used swithes at eah mode have bee idiated. As log as the speed ireases the duty yle of the orrespodig swithes ireases. Atually the duty yles are valid at lower tha poit V=. Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27 9

10 Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 (a) Curret behavior Fig. 7 Curret behavior ad iruit topology i ase C (low speed) of mode II. (a) Curret behavior Fig. 8 Curret behavior ad iruit topology i mode IV. (b) Ciruit topology whe S is o (b) Ciruit topology whe S is o (a) Curret behavior (b) Ciruit topology whe S 3 is o Fig. 9 Curret behavior ad iruit topology i ase B (high speed) of mode VI. (a) Curret behavior Fig. Curret behavior ad iruit topology i ase C (low speed) of mode VI. (b) Ciruit topology whe S 2 is off 92 Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27

11 Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 6 Simulatio This setio verifies the developed torque ripple redutio tehique via simulatio. Fig. 2 shows the blok diagram of the implemeted four-swith brushless DC motor drive system i Simulik. Speed otrol blok reates the urret referee. I urret otrol blok usig diret phase urret (DPC) otrol method, the phase urrets are regulated ad duty yles (D a ad D b ) of the power swithes are developed. I torque ripple redutio blok, developed duty yles, for ommutatio itervals are modified usig the ew proposed duty yles i this paper whih are show i Fig.. I power iverter blok, proper phase voltages are geerated ad applied to BLDC motor. I BLDC motor blok, phase urrets are alulated from Eq. (). The rated parameters of BLDC motor are give i the table. The performae of the system is simulated at speed 2 rpm. Fig. 3 shows the urret waveforms i both ases with ad without applyig the proposed torque ripple redutio tehique. Curret ripple reahes to 2.5 [A] (about 4%) that is high. Usig the developed tehique it redues to lower tha 7%. Fig. 4 shows the eletromageti torque without ad with applyig the proposed tehique. I simulatio, DC-lik voltage of the iverter has set to 6 [V] ad at speed ω=2 rpm, bak-emf voltage beomes 22.4 [V] ad so, E/V ratio is betwee /8 ad 3/8. Fig. 5 shows the urret ommutatio i mode II (IV) without usig the developed torque ripple redutio method. It is obvious that there is ot ay ommutatio torque ripple. It is beause of that, ω=2 rpm is loated at low speed rage of mode II ad as stated earlier, DPC otrol method a elimiate ommutatio torque ripple i ase C. However, for modes IV (I) ad VI (III) as stated i Eq. (26) ad Eq. (3), operatio poit ω=2 rpm is loated at high speed rage (ase B) of these modes ad it is prospeted that ommutatio torque ripple ours. Fig. 6 shows the ommutatio ripple redutio i mode IV. Usig developed tehique sigifiatly redues the urret ripple ad urret slopes beome equal together. Fig. 7 shows the swithig ommad to swith S that is set to 56%. DPC otroller ommads swith S to be zero, but developed torque ripple redutio method, durig ommutatio modifies it to 56%. Fig. 8 shows the urret waveforms i mode VI. Applyig the proposed tehique redues the urret ripple sigifiatly. Table Rated Parameters of BLDC Motor. P rated [hp] ω rated 35 [RPM] R.75 [Ω] L s -M 3.5 [mh] K t.2 [N.m/A] K e.7 [V/(rad/se)] I rated [A] V DC-Bus 6 [V] Z p 2 J 8.2e-5 [Kgm 2 ] Fig. 2 Blok diagram of the FSTPI-BLDC motor drive with ew ommutatio torque ripple redutio tehique. Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27 93

12 6 i b i i a 3 [A] Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 [A] time (se) (a) Without applyig the torque ripple redutio 6 i b i i a time (Se) (b) With applyig the torque ripple redutio Fig. 3 Phase urret waveforms of the BLDC motor with/without torque ripple redutio Without torque ripple redutio.5 [N.M] With torque ripple redutio.5 [N.M] time (Se) Fig. 4 Developed eletromageti torque i differet modes. 94 Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27

13 [A] i Phase Currets i b i a Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th time (se) Fig. 5 Curret ommutatio i mode II without usig torque ripple redutio. [A] [A] 5-5 i Fig. 6 Curret ommutatio i mode IV. 5 i a i a -5 i time (Se) Without torque ripple redutio i b i b With torque ripple redutio.5 Fig. 7 Applied swithig ommad to S i mode IV time (Se) Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27 95

14 i [A] Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 [A] i a i b Fig. 8 Curret ommutatio i mode VI. i i a i - b time (Se) 7 Colusio This paper presets a aalytial study o ommutatio torque ripple i a four-swith brushless DC motor drive. The aalyti equatios of ommutatio itervals ad ommutatio torque ripple are obtaied for eah mode. Developed results show that phase ommutatio harateristis are differet for eah operatio modes. It shows also the limit poit of urret otrol redued to half of its orrespodig poit i a six-swith iverter. It meas the aessible speed rage that the phase urrets a be regulated as retagular is limited to half of omial speed. The, a ew torque ripple redutio tehique has bee developed that is apable to elimiate the torque i etire speed rage lower tha urret otrol limit poit V=. Atually it is based o the slope equalizatio of the deayig ad risig urret i ommutatio iterval. The validity of the developed method has bee demostrated via simulatio. The proposed method ehaes the performae of the FSTPI-BLDC motor drive ad a be used for low ost appliatios. Referees [] R. Krisha; Eletri Motor Drives: Modelig, Aalysis ad Cotrol, Pretie-Hall of Idia, New Delhi, 23. [2] Jahs T. M., Soog W. L., Pulsatig Torque Miimizatio Tehiques for Permaet Maget AC Motor Drives---A Review, IEEE Trasatios o Idustrial Eletrois, Vol. 43, No. 2, April 996, pp [3] Joog-Ho Sog, Ik Choy, Commutatio Torque Ripple Redutio i Brushless DC Motor Drives Usig a Sigle DC Curret Sesor, IEEE Trasatios o Power Eletrois, Vol. 9, No. 2, Marh 24, pp [4] Carlso R., Maze M. L., Dos J. C., Fagudes S., Aalysis of torque ripple due to phase ommutatio i brushless DC mahies, IEEE Trasatios o Idustry Appliatios, Vol. 28, No. 3, May/Jue 992, pp [5] Lee B. K., Kim T. H., Ehsai M., O the feasibility of four-swith three-phase BLDC motor drives for low ost ommerial appliatios: topology ad otrol, IEEE Trasatios o Power Eletrois, Vol. 8, No., pp , Jauary 23. [6] Lee J. H., Cha AHN S., Hyu D. S., A BLDCM drive with trapezoidal bak EMF usig four-swith three phase iverter, IEEE Idustry Appliatios Coferee, pp , 2. [7] Halvaei Niasar A., Moghbeli H., Vahedi A., Modelig ad Simulatio Methods for Brushless DC Motor Drives, Iteratioal Coferee o Modelig, Simulatio ad Applied Optimizatio, ICMSAO, pp.5-96/5-6, 25, UAE. [8] Kim G. H., Kag S. J., Wo J. S., Aalysis of the ommutatio torque ripple effet for BLDCM fed by HCRPWM-VSI, IEEE Applied Power Eletrois Coferee ad Expositio, pp , Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27

15 Dowloaded from ijeee.iust.a.ir at :28 IRST o Friday Jauary 25th 29 Abolfazl Halvaei-Niasar, Ph.D. Studet, Departmet of Eletrial Egieerig, Ira Uiversity of Siee & Tehology, Narmak, Tehra, Ira. Tel: , Fax: , EML: ahalvai@yahoo.om He was bor i Kasha, Ira i 974. He reeived his B.S. ad M.S. i 998 ad 2 from Isfaha Uiversity of Tehology (IUT) ad Uiversity of Tehra (UT) both i eletrial egieerig respetively. He is ow studyig i Ira Uiversity of Siee & Tehology (IUST) for Ph.D. His researh iterests are maily the otrol systems & istrumetatio, DSP based otrol systems, eletri drives, PM Brushless DC motor drives, sesorless drives. He is a studet member of IEEE. Abolfazl Vahedi, Assoiate Professor, Departmet of Eletrial Egieerig, Ira Uiversity of Siee & Tehology, Narmak, Tehra, Ira, Postal ode: , Tel: , Fax: , EML: avahedi@iust.a.ir He was bor i Tehra, Ira i 966. He reeived his B.S., M.S. ad Ph.D. i 989, 992 ad 996 from Ferdowsi Mashhad Uiversity, Istitut Natioale Polytehique de Lorraie (INPL-FRANCE) ad INPL all i eletrial egieerig respetively. He has direted several projets i the area of ovetioal ad speial eletri mahies ad drives. His researh iterests are maily desig, implemetatio ad optimizatio of eletri mahies iludig tratio motors ad drives. He is a member of Ceter of exellee for power system automatio ad operatio at Ira Uiversity of Siee ad Tehology (IUST). He is also member of IEE ad SEE. Hassa Moghbeli, Visitig Assistat Professor at Qatar Departmet of Siee ad Mathematis, Texas A&M Uiversity, Po. Box 23874, Eduatio City, Doha, Qatar, , ad also Departmet of Eletrial & Computer Egieerig, Isfaha Uiversity of Tehology, Isfaha, Ira. Tel: , EML: hassa.moghbelli@qatar.tamu.edu He was bor i Isfaha, Ira i 95. He reeived his B.S., M.S. ad Ph.D. i 973, 978 ad 989 from Ira Uiversity of Siee ad Tehology (IUST), Oklahoma State Uiversity ad Uiversity of Missouri-Columbia (UMC) all i eletrial egieerig respetively. He has direted several projets i the area of eletri drives, power systems, eletri vehiles, hybrid eletri ad fuel ell vehiles ad railway eletrifiatio. His researh iterests are eletri drives, power eletrois, ad desig of eletri ad hybrid eletri vehile. He is a member of IEEE, ASME, ad SAE. Iraia Joural of Eletrial & Eletroi Egieerig, Vol. 3, Nos. 3 & 4, July 27 97