Chapter 6 CHOPPER-CONTROLLED DC BRUSH MOTOR DRIVES
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- Eleanore Robbins
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1 Chpr 6 CHOPPE-CONTOLLED DC BUSH MOTO DIVES 6.. INTODUCTION Th DC hoppr DC o DC powr lr vrr (PEC) wh ford ommu. I ud for rmur vol rol n DC bruh moor drv. DC our o upply DC hoppr r br or dod rfr wh oupu flr o ypl for urbn lr rnpor ym or o low powr DC bruh moor drv. Thyror, bpolr powr rnor, MOSFET or IGBT r ud n DC hoppr. Th b fur r hown n Tbl 6. nd hy orrpd o nl, wo- or four-qudrn opr. Tbl 6.. Snl-ph hoppr fur for h DC bruh moor Typ Choppr fur -I hrr Fr-qudrn (p-down) hoppr + Vo o S D + V L Fun V = V for S V = for S off nd D - - Sd qudrn, rnr (p-up) hoppr o + Vo - D2 S2 L + V - V = for S2 V = V for S2 off nd D2 Two qudrn hoppr + Vo S D2 L = for S or D2 = for S2 or D > for S or D < for S2 or D2 S2 D Two qudrn hoppr - + S2 D2 V = +V for S & S2 V = V for S & S2 off nd D & D2 Vo L D S - 9
2 2 Choppr-rolld d.. bruh moor drv Four qudrn hoppr + S Vo S2 - D D2 L S3 S4 D3 D4 S4 & S3 off S & S2 oprd V> - rvrbl S2 & S off S3 & S4 oprd V< - rvrbl Th fr-qudrn hoppr (Fur 6.) oprd by urnn h PES for h nrvl, whn h upply vol nd o h lod. Durn h nrvl off, whn h mn wh off, h lod urrn flow hrouh h frwhln dod D. Th oupu vol hown n Fur 6.. Th vr vol V v Fur 6.. Fr-qudrn hoppr opr. ) nuou mod; b.) dnuou mod Vv V T (6.) Th, p-down hoppr. Cn frquny (n T) rol prfrrd n ordr o mprov h npu flr opr nd rdu h pobly of dnuou urrn mod (Fur 6.b) opr. Th vol qu for n pd V L d K p n for d ; (6.2) L d ; ;, d T for duou mod (6.3) For nuou urrn mod = T nd (T) = () for dy. For h DC bruh r moor
3 ELECTIC DIVES 2 K n Krm n (6.4) In (6.4) K rm rfr o h rmnn flux whl h mnz urv of h mhn drd lnr. Th vr oupu vol for h dnuou mod my b drmnd non h h moor vol hn zro V V T v ; T T T (6.5) Th oupu urrn xpr r obnd from (6.2)-(6.3) V L A ; for (6.6) T for L nuou urrn ' A' ; for T for dnuou urrn (6.7) Th nuy d ( ) = ( ) (6.8) Th vr oupu urrn v v d ' d T (6.9) For h d-qudrn hoppr (Tbl 6.b) h DC moor.m.f. wh S 2 produ urrn r n ndun L L d ; for ; d (6.) Whn S 2 urnd off, h nry ord n h nduor n bk o h our l V > V wh h olu V ' L d ' ; T d (6.) L B (6.2)
4 22 Choppr-rolld d.. bruh moor drv V ' Th boundry d r B ' L (6.3) ( ) '( ), () nd '(T) (6.4) I hu pobl wh <V o rrv h nry bk from h DC bruh moor by un h nduor L n nry nk (Fur 6.2). Fur 6.2. Sd-qudrn hoppr opr Th wo-qudrn hoppr (Tbl 6.,d) ombn of fr nd d-qudrn hoppr. Fnlly wo-qudrn hoppr r ombnd o obn four-qudrn hoppr. A h hoppr n -off wh, h our urrn hoppd (Fur 6.3). Th mk h pk npu powr dmnd hh. Alo, h upply urrn (Fur 6.3) h hrm whh produ vol fluu, nl nrfrn,.
5 ELECTIC DIVES 23 Fur 6.3. Sour urrn wvform.) fr-qudrn opr, b.) d-qudrn opr. An LC npu flr (Fur 6.4) wll provd ph for h rppl urrn uh h ly (pproxmly) h vr urrn drwn from h upply. Th n h hrm urrn n n h upply (Fur 6.4b) n X / n nx X n I I n L C / nf / f h n r 2 (6.5) Fur 6.4. Fr-qudrn hoppr wh LC npu flr.) b ru, b.) quvln ru for nh hrm whr f h h hoppn frquny (f h = / T) nd f r h rn frquny of h flr f r / 2 LC. To vod rn f h 2 3f r. Gvn h vry of fur n Tbl 6. w wll prod drly wh
6 24 Choppr-rolld d.. bruh moor drv numrl xmpl n prlll wh horl dvlopmn o fl quk ml of knowld THE FIST-QUADANT (STEP-DOWN) CHOPPE A DC bruh moor wh prmnn mn x wh h d =, K p =.55 Wb / rpm, fd hrouh fr-qudrn hoppr (Tbl 6.) from 2 VDC upply n (dl) rmur urrn of A. Drmn:. h rn of duy yl from zro o mxmum pd; b. h rn of pd. Solu:. Th vr oupu vol V A ndll n = nd hu V V 2 (6.6) V V V n Thu mn V 2 2 (6.7) For mxmum pd, h vol 2V ( = ). Cqunly, vr from /2 o. b. Th vol qu for mxmum pd V mx I K p n mx (6.8) 2 n mx rpm (6.9) Th pd rn hu from zro o 2 rpm.. For h DC bruh moor nd hoppr bov nd =.3, lul h ul rmur urrn wvform, vr vlu, nd vol vr vlu n = 6 rpm, for h hoppn frquny f h = 5Hz. Drmn h hoppn frquny for whh h lm bwn dnuou nd nuou urrn rhd m bov. Solu: W now pply h rmur urrn xpr (6.6)-(6.7) fr for f h = 5Hz. Th urn- m nrvl T 2. 2 wh f h 5 m fh 5 m (6.2)
7 ELECTIC DIVES 25 A A ' A' Aumn dnuou urrn mod Alo A'. 36 Th urrn bom zro = ; A = A' 3 ' ; A' ; T 2 m (6.2) (6.22) (6.23) (6.24) Fur 6.5. Dnuou urrn Thu ndd h urrn dnuou. Th vr urrn v : T d v v d A ' d 88 d (6.25) Th hoppn frquny for h lm bwn h dnuou nd nuou urrn obnd for 3 T ; fh' T In h bom Hz (6.26) T (6.27)
8 26 Choppr-rolld d.. bruh moor drv A h urrn dnuou h vr vol from (6.5) V v V T T T V (6.28) 6.3. THE SECOND-QUADANT (STEP-UP) CHOPPE FO GENEATO BAKING A DC bruh moor wh PM x fd hrouh d-qudrn hoppr for rnrv brkn (Tbl 6.b). Th moor d r = ; L = 2mH; = 8V (vn pd). Th upply vol V 2VDC nd = Drmn:. Th wvform of moor urrn for zro nl urrn b. Th wvform of our urrn. Th mxmum vr powr nrd Solu:. Th urrn wvform r hown n Fur 6.2 nd 6.3 wh =. L B ; (6.29) b. ' V ' L ; B T (6.3) Fur 6.6. Th p-up d-qudrn hoppr. Th boundry d r ; ' ; ' T Th unknown r B, B nd T. Cqunly, (6.3)
9 ELECTIC DIVES B B'; B'= (6.32) (6.33) T ; T hu T (6.34) No h h our urrn our durn h S urn-off nd nv, provn h rnrv opr. Th vr our urrn v T L v ' ' d T ' T T B T L ; v ' A (6.35) Th vr powr rnrd P v P v v ' V W (6.36) 6.4. THE TWO-QUADANT CHOPPE Cdr wo-qudrn hoppr (Fur 6.7) upplyn DC bruh moor wh pr x. Th lod urrn vr bwn I mx > nd I mn <. Fur 6.7. Two-qudrn hoppr upplyn prly xd DC bruh moor Drmn:. Th vol nd urrn wvform for h lod urrn vryn bwn n I mx > nd I mn < wh I mx > I mn.
10 28 Choppr-rolld d.. bruh moor drv b. Drv h xpr of h dun m d2 nd d of h dod D nd D 2 for. Solu:. L u fr drw h lod urrn whh vr from pov mxmum o nv mnmum (Fur 6.8). Th du nrvl for h of h four wh T, D 2, D, T 2 r T for d2 < < ; T 2 for d < < T; (6.37) D for < < d ; D 2 for < < d2 b. Th qu for h urrn r: V L d ; for d L d ; for T d wh h olu: (6.38) (6.39) V L A ; (6.4) ' ' L ; A T wh h boundry d () = mn, (T) = mn nd ( ) = ( ). (6.4) Fur 6.8. Vol nd urrn wvform of wo-qudrn hoppr-fd DC moor Th unknown A, A nd r obnd from
11 ELECTIC DIVES 29 A I mn A' I mx (6.42) (6.43) L T A ln ' / A (6.44) Cdr DC bruh moor who d r = 2V, =, L = 5mH, = 8V, I mx = 5A, I mn = 2A nd hoppn frquny f h =.5kHz. For h wo-qudrn hoppr bov lul:. Th / T = ro. b. Th dun nrvl of h 4 wh. Solu:. Th n A, A, xpr dvlopd bov ((6.42)-(6.44)) yld A I mn A (6.45) A' Imx A (6.46) T 2. 2 f h 5 m (6.47) 5 T 3 2 ln85 / L 3 ln A'.56 3 / A.884 b. Th dun nrvl of D 2, d2, orrpd o = 3 3 (6.48) d2 L V d 2 L A 3 V ln ln A 42 Thu h mn wh T du for m nrvl 3 (6.49)
12 3 Choppr-rolld d.. bruh moor drv d2 (6.5) To lul h dun m of h dod D w pply h d ( d ) = d L A ' (6.5) d L ln A ' ln (6.52) Cqunly, h dod D du for.33 m. Fnlly, h wh T 2 du for h m nrvl T d (6.53) No: A n bov, h wo-qudrn opr of h hoppr rd n h vr of / T h mn wh ommnd nl l nd, rpvly, T nrvl houh hy du l m hn h, llown h dod D 2 nd D o du. Th wo-qudrn hoppr h h dvn of nurl (nuou) rn from moor o nror THE FOU-QUADANT CHOPPE A DC bruh moor wh pr x fd hrouh fourqudrn hoppr (Tbl 6.). Show h wvform of vol nd urrn n h hrd nd fourh qudrn. Solu: Th b ru of four-qudrn hoppr hown n Fur 6.9. Fur 6.9. DC bruh moor fd hrouh four-qudrn hoppr If T 4 ll h m, T -D nd T2-D2 provd fr- nd (rpvly) d-qudrn opr hown n prvou prrph. Wh T 2 ll h m nd T 3 -D 3 nd, rpvly, T 4 -D 4 h hrd- nd fourh-qudrn opr obnd (Fur 6.). So, n f, w hv 2 wo-qudrn hoppr n n urn.
13 ELECTIC DIVES 3 Howvr, ly 2 ou of 4 mn wh r urnd nd off wh h frquny f h whl h hrd mn wh kp ll h m nd h fourh off ll h m. Fur 6.. Four-qudrn hoppr upplyn DC bruh moor.) Thrd qudrn: v<, Vv<; b.) Fourh qudrn: v>, Vv<. Four-qudrn opr rqurd for f rp rvrbl vrbl pd drv. A xpd, dnuou urrn mod lo pobl bu hould b vodd by nrn h whn frquny f h or ddn n ndun n r wh h moor. L u um h: A DC bruh moor, fd hrouh four-qudrn hoppr, work moor n h hrd qudrn (rvr mo). Th mn d r V = 2V, =.5, L = 2.5mH, rd urrn I n = 2A; rd pd n n = 3 rpm; pr x.. Clul h rd.m.f.,, nd rd lromn orqu, T. b. For n = 2 rpm nd rd vr urrn ( v = I n ) drmn h vr vol V v, / T =, nd mxmum nd mnmum vlu of moor urrn I mx nd I mn for khz whn frquny. Solu:. Th moor vol qu for dy : V v for rd vlu V v = V = 2V, = n = 2A, hu (6.54) n K p n n V v V (6.55)
14 32 Choppr-rolld d.. bruh moor drv K n p n 5 b. Th moor qu n h hrd qudrn V v n Wb (6.56) h dun m for T 3 (Fur 6.) Vv T V T f h 3 V, (6.57) (6.58) (6.59) Form ((6.4)-(6.4)) h moor urrn vr (Fur 6.) drbd by V ' L A ; (6.6) ' ' L ; A T Th urrn nuy d ( ( ) = ( )) provd (6.6) L A V ' ln ' / A (6.62) Th d d obnd from h vr urrn xpr T V ' T v d ' d T L L T From (6.62) nd (6.63) w obn: A A' T L (6.63)
15 ELECTIC DIVES 33 A V ' L ' / A ; V' V; K pn V.. A' / A { AA' 25. } 5. Now w my lul I mn = () I A V ' mn Alo I mx = ( ) (6.64) (6.65) A 525. A ' (6.66). 43A 525. A' (6.67) A' 24.94A (6.68) A 37.62; A' 3.92 (6.69) A (6.7) I A mx ' A (6.7) 6.6. THE INPUT FILTE A fr-qudrn hoppr wh n L-C npu flr uppl DC bruh moor wh PM x undr n urrn r-up.. Dmr h mxmum rm rppl urrn n h hoppr urrn h our duy yl =.5. b. For f h = 4 Hz, I = A, h rm fundmnl (AC) urrn llowd n h upply % of DC upply urrn. Cpor of mf whh n k 5 A rm rppl urrn r vlbl. Drmn L f nd C f of h flr for f h > 2f r.. For b. lul h DC, fr nd hrd hrm of h upply urrn. Solu:
16 34 Choppr-rolld d.. bruh moor drv. Th hoppr fur (Fur 6.) provd qur urrn pul for of wdh. Fur 6.. Fr-qudrn hoppr wh LfCf flr.) b ru, b.) hoppr npu urrn Thu, h DC, I d, rm I rm nd rppl I rppl ompn of hoppr urrn r: I d I (6.72) 2 I I d I rm (6.73) I I I I rppl (6.74) di rppl Th mxmum rppl urrn obnd for d whh ld o = / 2. Th flr dn wll b prformd for h wor. b. To dn h flr w nd fr h hoppr urrn hrm n whh, for =.5, 4 I I d n n 3 n5 2n (6.75) wh I d rm 3 rm I 5 2 A (6.76) A (6.77) 5. 5 A (6.78)
17 ELECTIC DIVES rm 25 2 A (6.79) Th npu (our) AC urrn no o urp % of DC npu urrn, h I I d 5 5 A. Aordn o Equ (6.5) for n = w obn I xc x x L C I Alo, h fundmnl por urrn I C xc ; 5 45 or x L xc xl xc (6.8) x L xc I C I 45 5 xl xc xc xc A (6.8) A h mf por n k 5A, uh por n prlll r ndd nd hu C f = mf. On h ohr hnd, h rn x L xl xc (6.82) x L 398. Lf H (6.83) Th flr rn frquny f r fr 27 LC f f Hz (6.84) Th ro bwn h hoppr whn frquny f h nd h flr rn frquny f r fh / fr 4 / Th m AC urrn ompn (6.5) (fr flrn) r I 45 I fh fr 35 /. A (6.85) I I I 3f / f h I r 5f / f h r A (6.86) A (6.87) A nod h L f C f flr produ dr rdu of our-urrn hrm.
18 36 Choppr-rolld d.. bruh moor drv 6.7. DIGITAL SIMULATION THOUGH MATLAB/SIMULINK Smul rul of DC moor drv wh four-qudrn hoppr r prnd. Th moor modl w nrd n blok (DC bruh moor n Fur 6.2). Chnn of moor prmr d by lkn hr blok. A dlou box ppr nd you n hn hm by modfyn hr dful vlu. Th moor modl blok nlud h pobly of ddn n xr ndun n h moor ru (L dd ). Th drv ym of PI pd rollr (K =, T =.), PI orqu rollr (K = 5, T =.5) nd moor blok. Th udy xmn h ym bhvor durn rn, lod prurb (.2) nd pd rvrl wh no lod (.5 ) nd nohr lod prurb (.6 ). Th nr p ( ) n b modfd from h Smulnk Smul / Prmr. Th hoppr frquny 2 khz nd h blok npu h / T ro. To fnd ou h ruur of h blok prnd bov, unmk (Op/Unmk). Eh mkd blok n brf drp of h blok (npu / oupu / prmr). Th blok drm of h lr drv ym prnd n Fur 6.2.
19 ELECTIC DIVES 37 Fur 6.2. DC bruh moor drv blok drm Th moor ud for h mul h h follown prmr: V d = 2V, I n = 2A, n n = 3rpm, =.5, L =.25H, J =.km 2, K p = 2.2Wb. Th Fur ( ) rprn h pd (Fur 6.3), orqu (Fur 6.4) rp nd urrn (Fur 6.5) nd vol (Fur 6.6) wvform, for h rn pro nd lod orqu (8Nm) ppld.2, nd rvrl wh no lod.5 nd lod orqu ppld.6.
20 38 Choppr-rolld d.. bruh moor drv n [rpm] Tm [] Fur 6.3. Spd rnn rp Torqu [Nm] Tm [] Fur 6.4. Torqu rp I [A] Tm [] Fur 6.5. Currn wvform (). V [V] Tm [] Fur 6.6. Vol wvform (V). F rp wh rhr low urrn rppl obnd du o h rhr hh (2 khz) whn frquny for 5 m lrl m n DC bruh PM moor four-qudrn drv.
21 ELECTIC DIVES SUMMAY In h hpr, nl, wo- or four-qudrn hoppr b fur n nr wh h DC bruh moor (for n pd) hv bn nrodud. In ll fur h PES hv bn drd dl - wh nnnou hrd ommu (whn). n DC-DC vrr hv no bn rd. Th nrd rdr nvd o udy h lrur []. Choppr, rfr, f h m problm of nuoudnuou urrn mod whn. Undr dnuou urrn mod, for low vol low ndun moor nd low whn frquny (hyror), h dpndn of oupu vol h /off m ro of PES rndr h rol luh. Inrn h whn frquny or nludn r ndun olv h problm. Th npu urrn h hrm nd hu n npu flr rqurd o rdu hm o pbl lm. A h urrn n h moor pul, r mu lo b xrd n n h rmur oppr lo nd h vnul drn of h moor for rn ppl whn hoppr-fd. Th nr bwn h hoppr nd h moor n pd dud n h hpr hould b nud wh lod-loop rol o produ vrbl pd drv. Th wll b d n h nx hpr, houh h Mlb mul prrph 6.7 np POBLEMS 6.. A p-down (buk) fr-qudrn hoppr hown n Fur 6.7. Fur 6.7. Sp down (BUCK) hoppr. Expln h prnpl nd drw h ndun vol nd urrn wvform for nuou urrn mod. b. Clul h oupu vol nd urrn for rv lod fun of duy ro drn dl whn nd zro lo.
22 4 Choppr-rolld d.. bruh moor drv 6.2. For problm 6. fnd for h lm bwn nuou nd dnuou urrn mod nd h vr oupu vol for dnuou urrn mod. Plo h vr oupu vol vru vr oupu urrn boh for nuou nd dnuou mod A p-up (boo) fr-qudrn hoppr hown n Fur 6.8. Cdrn dl lmn drmn:. Th vol nd urrn wvform for nuou urrn mod. b. Th boundry bwn nuou nd dnuou urrn mod.. Th oupu vol rppl for nuou urrn opr. Fur 6.8. Sp-up (boo) hoppr 6.4. A four-qudrn hoppr upplyn DC bruh moor wh PM x rolld hrouh PWM wh bpolr vol whn, Fur 6.9, whr (T A+, T B- ) nd (T A-, T B+ ) r rolld mulnouly. Drmn:. Th vol nd urrn wvform for pov rol vol V rol. b. Th vol nd urrn wvform for nv rol V. Fur 6.9. Four-qudrn hoppr wh DC bruh moor 6.5. A DC r bruh moor h h d: L = 2 mh, =, rd vol V n = 2 V, rd urrn I n = A, rd pd n n = 8 rpm. Th rmnn flux ndud vol rd pd rm = 5V. Whn fd from fr-qudrn p-down hoppr, 2 Vd wh =.3, f h = 5 Hz rd pd, lul h rmur wvform, vr urrn nd vr vol Solv problm 6.5. wh Mlb/Smulnk or PSp mul prorm.
23 ELECTIC DIVES SELECTED EFEENCES. N. Mohn, T.M. Undlnd, W.P. obbn, Powr lr, Sd d, Chpr 7, Wly, 995.
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