ELECTRICAL ENGINEERING

Thit k iu khin cho cc b bin i in t cng sut

M hnh ha v thit k cc mch vng iu chnh

Trn Trng Minh 12/4/2013

Lecture notes on modelling and design of control system for power electronic converter

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Table of Contents 1 Thit k mch vng iu chnh cho Boost ConverterEquation Chapter (Next) Section 1 ........ 3

1.1 Hm truyn t cho Boost Converter ch dng lin tc (CCM) ............................... 3 1.2 Mch vng iu chnh in p .......................................................................................... 6 1.3 Thit k cc khu iu chnh trong mch vng in p .................................................... 7

1.3.1 Chn t u ra .............................................................................................................. 7 1.3.2 La chn in tr ca cun cm rL .............................................................................. 8 1.3.3 Tch bit tn s ca cp im cc v im zero bn phi trc o RHPzero................ 8 1.3.4 Tng cng d tr pha bng mch feedforward ..................................................... 9 1.3.5 Kho st tnh n nh ca thit k .............................................................................. 11

1.4 V d tnh ton................................................................................................................. 11 2 M HNH HA CC B BIN I DC-DC NG CT TN S

CAOEquation Chapter 2 Section 2 ............................................................................................................. 14 2.1 Cc phng php m hnh ha b bin i ng ct tn s cao ..................................... 14 2.2 Phng php trung bnh ha h phng trnh trng thi ................................................ 14

2.2.1 Xy dng phng trnh trng thi trung bnh cho Boost Converter .......................... 16 2.2.2 Phng trnh trng thi trung bnh cho Buck Converter ............................................ 17 2.2.3 Phng trnh trng thi trung bnh cho Buck-Boost Converter ................................. 19

2.3 Phng php trung bnh ha phn t ng ct ............................................................... 20 2.3.1 S tng ng bt bin ca phn t ng ct ..................................................... 21 2.3.2 M hnh tng ng trung bnh phn t ng ct cho Buck converter ................... 24

2.4 Phng php trung bnh ha mng ng ct ................................................................... 26 2.4.1 Trung bnh ha mng ng ct cho s Boost Converter ....................................... 26 2.4.2 Trung bnh ha mch ng ct cho Buck, Buck-Boost Converter ............................ 31 2.4.3 Hm truyn cho b bin i c tnh ti in tr cun cm rL v in tr rESR ca t 32 2.4.4 Hm truyn c tnh ti tn hao trn van bn dn v it ........................................... 34 2.4.5 M hnh trung bnh tnh ti tn hao do qu trnh ng ct ........................................ 36

3 M hnh cc b bin i trong ch dng gin onEquation Section (Next) .................... 38 3.1 M hnh trung bnh DCM buck converter ....................................................................... 38 3.2 M hnh tn hiu nh AC n gin cho ch DCM ..................................................... 42 3.3 M hnh tn hiu nh AC chnh xc hn cho buck converter ch DCM ................. 46

4 H thng iu khin theo dng in Equation Section (Next) ................................................ 50 4.1 S mt n nh khi D > 0,5 ............................................................................................. 51

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4.2 M hnh n gin bc nht .............................................................................................. 55 4.3 M hnh iu khin bng dng in chnh xc hn ........................................................ 60 4.4 Hm truyn cho cc b bin i c bn iu khin bng dng in trong ch dng

lin tc 66 4.4.1 Hm truyn cho buck converter ................................................................................. 66 4.4.2 Hm truyn cho boost converter ................................................................................ 68 4.4.3 Hm truyn cho buck-boost converter ....................................................................... 69

4.5 iu khin theo dng in trong ch dng gin on ................................................ 71 4.6 iu khin theo dng in bng b iu chnh dng c ngng .................................... 79

5 Chnh lu tch cc Equation Section (Next) ........................................................................... 83 5.1 S chnh lu l tng ................................................................................................. 83 5.2 Cc s chnh lu gn l tng ................................................................................... 84

5.2.1 Chnh lu gn l tng trn c s CCM boost converter .......................................... 84 5.2.2 Chnh lu gn l tng trn c s DCM flyback converter ...................................... 90

5.3 iu khin dng dng vo xoay chiu ............................................................................ 92 5.3.1 iu khin theo dng trung bnh ............................................................................... 92 5.3.2 iu khin theo dng in t trc .......................................................................... 96 5.3.3 iu khin bng b iu chnh dng c ngng v ch ti hn ........................... 98 5.3.4 M hnh ha s iu khin dng c ngng bng trung bnh ha mng ng ct

van PWM 101 5.4 B bin i mt pha vi s chnh lu gn l tng ................................................. 101

5.4.1 Khu tch tr nng lng ......................................................................................... 101 5.4.2 Mch vng in p ngoi vi bng thng hp ......................................................... 103

5.5 Chnh lu l tng ba pha ............................................................................................. 108 6 Ti liu tham kho................................................................................................................. 110

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1 Thit k mch vng iu chnh cho Boost Converter Ti liu tham kho [2] - Voltage Mode Boost Converter Small Signal Control Loop

Analysis Using the TPS61030; Application Report SLVA274AMay 2007Revised January 2009. 1.1 Hm truyn t cho Boost Converter ch dng lin tc (CCM)

Hnh H. 1-1 S Boost Converter.

Xt s boost converter cho trn hnh H.1, lm vic trong ch dng lin tc (Continuous Current Mode - CCM). Bng mt s phng php khc nhau nh trung bnh ha phng trnh trng thi, trung bnh ha mng kha ng ct, , c th thu c hm truyn tn hiu nh (AC) t u vo iu khin, l h s iu ch d, ti in p u ra vo cho boost converter nh sau:

1 er2

2

1 1

1z RHPz oo

dv do

o o

s svG G

s sd Q

(1.1)

Trong

2

21in o

doin

V VGVD

(1.2)

11

zCr C

(1.3)

221 L inRHPzero

o

D R r VRL L V

hay 2

2in

RHPzeroo

VRfL V

(1.4)

4

211 1L ino

o

r D R VR VL C L C

hay 1

2in

oo

VfVL C (1.5)

01L

C

Q rL C R r

(1.6)

Trong hm truyn (1.1) cha im zero z1 do in tr tng ng ni tip vi t lc u ra (tr ESR) v zero zRHPzero nm bn phi trc o, cp im cc do mch LC o. C th thy rng cp im cc o ph thuc vo t s truyn p gia u ra vi u vo Vin/Vo.

Hnh H. 1-2 th Bode ca khu cp im cc.

th Bode ca khu hm tryn ch c cp im cc o cho trn hnh H.2. T tn s cng hng fo th bin c nghing -40dB/dec. Cp im cc gy ra trn th gc pha thay i n -180.

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Hnh H. 1-3 th Bode ca khu c im zero bn phi trc o (im zero dng). Trn hnh H.3 th hin th Bode ca im zero dng (RHPzero). im zero dng

a n tng +20dB/dec trn c tnh bin v tr v pha n -90 trn c tnh pha. S thay i v pha bt u t tn s 0,1fRHPzero v t -90 ti tn s 10fRHPzero, nh th hin trn hnh H.3. tr v pha ny s nh hng n d tr n nh v pha trong mch vng in p, l yu t ta cn phi tnh n nh s ni n sau y.

Hnh H. 1-4 nh hng ca im zero dng n d tr n nh v pha.

Xt v d thy nh hng ca im zero dng. Tham s ca s H.1 cho nh sau:

6

10 ,100 ,3 ,3,6 ,2 1,8

o

in

o

o

L HC FV VV VI A R

Tnh ton tn s im cng hng ca cp im cc v tn s ca im zero dng theo (1.4), (1.5) nh sau:

2

6 61 3 203,62 10 10 100 10RHPzerof kHz

6 61 3 4, 23,62 10 10 100 10of kHz

Nh vy tn s fRHPzero cao hn nhiu so vi tn s fo, tuy nhin s gim gc pha bt u ti tn s 10 ln nh hn trc , t 2 kHz, nh hn fo = 4,2 kHz, nn nh hng n d tr n nh v pha ca mch vng iu chnh. iu ny c minh ha trn th hnh H.4. y l yu t gy mt n nh trong mch vng iu chnh theo in p, trong ch dng lin tc (CCM Continuous Current Mode). 1.2 Mch vng iu chnh in p

Cc khu trn mch vng iu chnh in p cho Boost Converter th hin trn hnh H.5, bao gm: hm truyn ca b bin i Gdv(s) ( phn tch mc I trn y); khu phn hi v mch feedforward GFB_ffc(s); b iu chnh Gerror(s).

Hnh H. 1-5 Mch vng iu chnh in p cho ch dng lin tc.

Theo hnh H.5 hm truyn ca h h s l:

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erdv FB ffc rorG s G s G s G s (1.7) 1.3 Thit k cc khu iu chnh trong mch vng in p

Qu trnh thit k cc khu trong mch vng iu chnh in p th hin trn hnh H.6. Phng php thit k bao gm cc la chn:

1. Tn s ca im zero bn phi trc o fRHPzero phi chn ln hn tn s ca cp im cc fo theo mt t l M ln (M s c gii thch qua v d sau y), iu ny trnh tr pha do fRHPzero nh hng n d tr n nh v pha.

2. Tn s xc nh bng thng ca mch vng fBW phi chn thp hn hoc ti tn s to nn sm pha ln nht do mch feedforward mang li im zero ti tn s fz. Cc bc thit k tin hnh theo cc mc sau y.

1.3.1 Chn t u ra

Hnh H. 1-6 Thit k b iu chnh. T lc C phi c gi tr minimum cn thit m bo p mch in p u ra hay

st gim in p xy ra khi ng ti vo nm trong phm vi cho php. p mch in p

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bao gm p mch do in tr ni tip t ESR sinh ra v do p mch do t lc cc xung in p t u ra b bin i, theo cc biu thc sau y:

, ,o ripple ESR oV I ESR (1.8)

. ,11o on o ino ripple C

o

I T I VVC C V f

(1.9)

min,, ,

11o inrippleo ripple C o

I VCV V f

(1.10)

Khi ti c bin ng itran, st p xy ra trong khong thi gian dt khi mch vng iu chnh cha kp tc ng. Nu cho php st p l Vo,dip th c th xc nh gi tr nh nht cn thit ca t t biu thc sau:

min,, ,

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tran trantran

o dip o dip BW

i iC dtV V f

(1.11)

Trong dt ly gn ng bng 1/fBW cho n gin. 1.3.2 La chn in tr ca cun cm rL

in tr rL ca cun cm L c nh hng mnh n ch lm vic ca mch vng iu chnh. RL c tc dng n nh d tr pha (lm pha chm tin n -180 hn). Tuy nhin rL cng lm tng tn tht trn cun cm. V vy chn rL c th trn c s cho php tn hao trn cun cm trong tn hao tng l bao nhiu, v d c 30 % trn tng tn hao,

,,max 2

30% total lossL

in

Pr

I (1.12)

Trong Ptotal,loss=Po(1-1/), l hiu sut do thit k mong mun. Thng thng c 80 90% trong cc ng dng cng sut nh. 1.3.3 Tch bit tn s ca cp im cc v im zero bn phi trc o RHPzero

Tch bit tn s fRHPzero v fo theo t s M (M = fRHPzero/fo) l bc quan trng nht m bo tnh n nh ca mch vng iu chnh. Theo kinh nghim nu dng t lc l loi tantalum (t cht lng cao, kch thc nh m gi tr ln) th ESR c t 20 m n 100 m, c th chn M = 10. Nu dng t gm ESR rt nh, c vi m th M phi ln hn, c 15 tr ln tch bit hai tn s ESR v tn s ca cp im cc.

zeroESR

o

f Mf

, (1.13)

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M= 10 nu dng t tantalum, M=15 nu dng t gm. T biu thc cc tn s fRHPzero v fo trong (1.4), (1.5), suy ra gi tr cn thit ca in cm nh sau:

2in

o

VRL CM V

(1.14)

Khi ti l ln nht, in tr ti R nh nht, v in p u vo nh nht hai tn s fRHPzero v fo gn nhau nht. V vy iu kin ny xc nh gi tr cun cm ln nht cho php l:

2,minmin

maxin

o

VRL CM V

(1.15)

1.3.4 Tng cng d tr pha bng mch feedforward

Hnh H. 1-7 Mch phn hi in p v feedforward.

Trn hnh H.7 th hin mch ly tn hiu phn hi in p qua phn p R1, R2. Mch feedforward qua RC Ci, Ri. y l mch vi phn c tc dng l mch phn hi mm t u ra v. Mch vi phn ch tc dng ln thnh phn p mch ca in p u ra v nhng thay i nu c v lm thay i gc pha ca tn hiu phn hi.

Hm truyn ca cc mch ny s l:

1 11 11 12 2i i

ii i

sC R RG s

R R RsC R RR R

(1.16)

1

2 1z i if

C R R (1.17)

11 2 2 12 1 2

pi i

i

f R R R R R RCR R

(1.18)

10

Hnh H. 1-8 V d v c tnh tn s ca mt mch phn hi v khu phn hi mm.

V d v c tnh tn s bin pha ca mt mch phn hi v khu feedforward cho trn hnh H.8. Trong v d ny cc tham s nh sau: R1=1,24 M, R2=200 k, Ci = 10 pF, Ri = 100 k. cc tnh ton cho thy fz = 11 kHz, fp = 58 kHz, v b pha ln nht khong 25 kHz.

Trong tnh ton n gin c th gi thit rng b pha do mch phn hi mm em li xy ra ti tn s 2fz. Nh vy bng thng ca mch vng iu chnh phi nh hn tn s ny:

W 2B zf f (1.19) Trong bng thng xc nh t tn s fo ca cp im cc n tn s fBW, ti c

tnh bin c nghing -40dB/dec ct vi trc honh (0 dB):

3010 oG

BW of f (1.20)

25. 2 5 220log 20log1 2 1 2oo do inR V RG dB G

R R V R R

(1.21)

Trong (1.20) tuy c tnh bin ca cp im cc c nghing -40dB/dec nhng ta ly gn ng bng -30dB/dec tnh n nh hng c lm mm ha bi ESR v ca in tr rL ca cun cm.

T cc phng trnh (1.19), (1.20), (1.21) c th suy ra gi tr cn di ca cun cm phi tha mn:

2301 1 10

2 2oG

in

o z

VLC V f

(1.22)

T phng trnh (1.5) li thy rng tn s fo, do fBW, s ln nht khi in p u vo Vin c gi tr maximum. Do Lmin phi c tnh ti Vin,max:

11

230,max

min1 1 10

2 2oG

in

o z

VL

C V f

(1.23)

T (1.15) v (1.23) l hai iu kin xc nh gi tr cn thit ca in cm L. Trong gi tr Lmax xc nh iu kin tch tn s ca im zero bn phi trc o ra xa tn s cng hng fo ca mch lc bc hai LC mt khong bng M ln (M = 10 15), gi tr Lmin xc nh iu kin bng thng fBW ca h thng nm gia hai tn s fo v fRHPzero. C th thy rng Lmax t l vi C, trong khi Lmin t l nghch vi C. V vy khi tnh ton nu Lmax khng ln hn Lmin, c ngha l khng m bo c cc iu kin v tn s, ta phi chn li gi tr C t mc 1.3.1ln hn Cmin, v d bng 3 5 Cmin. 1.3.5 Kho st tnh n nh ca thit k

Cc bc thit k t 1.3.1 n 1.3.4 trn y c kim tra li n nh sau khi tnh ton bng th Bode. Tuy nhin th Bode ch m bo tnh n nh i vi tn hiu nh m cha m bo cc c tnh qu mong mun. V vy phi kim tra li thit k theo cc c tnh qu , v d khi ti thay i t bin v khi in p vo c bc nhy t ngt. Nu in p ra ch n nh tr li sau 3, 4 ln dao ng chng t d tr v pha l thp, ta phi tin hnh chnh nh li thit k bng cch lp li cc bc t 1 n 4. 1.4 V d tnh ton

V d tnh ton c cho dng Matlab script sau y.

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13

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2 M HNH HA CC B BIN I DC-DC NG CT TN S CAO 2.1 Cc phng php m hnh ha b bin i ng ct tn s cao

Cc b bin i DC-DC thng s dng MOSFET l van bn dn, c iu khin ng ct vi tn s cao, t vi chc kHz n 1 MHz. Nh m cc phn t nh t in, in cm hay my bin p cch ly c kch thc rt nh, dn n kch thc ca c b bin i cng rt nh gn (t c mt cng sut trn mt n v th tch W/cm3 kh cao). Thng thng tn s ca mng mch dao ng t nhin trong b bin i thp hn nhiu ln so vi tn s ng ct v nhng gi thit nh p mch ca in p mt chiu, ca dng in mt chiu tng i nh, ty thuc vo yu cu t ra ca thit k. Chnh v vy cc phng php trung bnh ha m t b bin i t ra rt hiu qu, trong c hai phng php chnh l: phng php trung bnh ha h phng trnh trng thi v phng php trung bnh ha mch ng ct. Phng php trung bnh ha phn t ng ct l mt dng ca trung bnh ha mch ng ct cng c s dng ph bin. 2.2 Phng php trung bnh ha h phng trnh trng thi

Trong phng php trung bnh ha h phng trnh trng thi (state space SS) mch in ca b bin i ng vi mi trng thi ng ct ca van bn dn c m t bi mt h phng trnh tuyn tnh:

x = x+= x+

d A Budty C Du

(2.1)

Trong A, B, C, D l cc ma trn ca phng trnh trng thi, x l bin trng thi; u l bin u vo; y l bin u ra.

Cc b bin i DC-DC c bn nh DC-DC gim p, tng p, va tng va gim (Buck Converter, Boost Converter, Buck-Boost Converter) c hai trng thi cho php ca van. Trong mt chu k Ts, thng gi l chu k ng ct, chu k iu ch PWM, gm hai khong thi gian ng vi hai trng thi, dTs v (1-d)Ts (0 < d < Ts).

ng vi trng thi 1 h c phng trnh trng thi:

1 1

1 1

x = x+= x+

d A B udty C D u

(2.2)

ng vi trng thi 2 h c phng trnh trng thi:

2 2

2 2

x = x+= x+

d A B udty C D u

(2.3)

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Cc ma trn A1, B1, C1, D1 m t mch in tuyn tnh ca s trong khong thi gian dTs (0 < d

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1 2 1 2

1 2 1 2

d A t Bu t A A B B U d tdty t C t Du t C C D D U d t

x x Xx X

(2.9)

2.2.1 Xy dng phng trnh trng thi trung bnh cho Boost Converter S Boost Converter cho trn hnh 2-1. Mch in tng ng cho hai trng thi ca

s cho trn hnh 2-2 v 2-3. ng vi mi trng thi mch in l mt s tuyn tnh.

Hnh 2-1 S Boost Converter.

Hnh 2-2 Boost Converter trong trng thi 1. Hnh 2-3 Boost Converter trong trng thi 2.Phng trnh trng thi cho trng thi 1 c dng:

1

1 1

LL L in

CC

C

o C C LC

di r i Vdt Ldv vdt C R r

Rv v r iR r

(2.10)

1 1 1 1

0 1; ; ; 010 0 0 0

LC

C C

C

r Rr RL R r R rA B C DL

C R r

(2.11)

Phng trnh trng thi cho trng thi 2 c dng:

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1

1 1

CLL L L C in

C C

CL C

C C

o C C LC

Rrdi Ri r i v Vdt L R r R r

dv R i vdt C R r R r

Rv v r iR r

(2.12)

2 2 2 2

1 1; ; ; 01 0 0 0

CL C

C CC C

C C

Rr Rr Rr RL R r L R r

R r R rA B C DLR

C R r C R r

(2.13)

p dng (2.5) cho (2.11), (2.13) s thu c phng trnh trng thi trung bnh. 2.2.2 Phng trnh trng thi trung bnh cho Buck Converter

Hnh 2-4 S Buck Converter.

S Buck converter cho trn hnh 2-4. Hai trng thi ca s cho trn hnh 2-5, 2-6.

Hnh 2-5 Trng thi 1 ca Buck Converter.

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Hnh 2-6 Trng thi 2 ca Buck Converter. Phng trnh cho trng thi 1:

1

Lin L L o

o C L CC

CL C

C C

diV L r i vdt

Rv r i vR r

dv RC i vdt R r R r

(2.14)

Do :

1 1 1

1 1; ; ; 01 0 0 0

CL C

C CC C

C C

Rr Rr Rr RL R r L R r

R r R rA B C DLR

C R r C R r

(2.15)

Phng trnh cho trng thi 2:

0

1

LL L o

o C L CC

CL C

C C

diL r i vdtRv r i v

R rdv RC i vdt R r R r

(2.16)

Do :

2 2 2 2

10; ; ; 001 0 0

CL C

C CC C

C C

Rr Rr Rr RL R r L R r

R r R rA B C DR

C R r C R r

(2.17)

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Do i vi Buck Converter A1 = A2; C1 = C2; D1 = D2 = 0 nn phng trnh trng thi trung bnh s c cc ma trn l:

1 1; ; ; 01 0 0 0

CL C

C CC C

C C

Rr Rr Rr RL R r L R r D R r R rA B C DL

RC R r C R r

(2.18)

2.2.3 Phng trnh trng thi trung bnh cho Buck-Boost Converter

Hnh 2-7 Buck-Boost Converter.

Hnh 2-8 Mch in tng ng trong hai trng thi.

Phng trnh cho trng thi 1:

1

LL L in

o CC

CC

C

diL r i Vdt

Rv vR r

dvC vdt R r

(2.19)

Do :

20

1 1 1

0 1 0; ; ; 010 0 0 0

L

C

C

r RL R rA B C DL

C R r

(2.20)

Phng trnh cho trng thi 2:

1

LL L o

o C L CC

CL C

C C

diL r i vdt

Rv r i vR r

dv RC i vdt R r R r

(2.21)

Do :

2 2 2 2

10; ; ; 001 0 0

CL C

C CC C

C C

Rr Rr Rr RL R r L R r

R r R rA B C DR

C R r C R r

(2.22)

2.3 Phng php trung bnh ha phn t ng ct Phng php trung bnh phng trnh trng thi trn y c u im l c c s ton hc

r rng. Cc bc tnh ton ch da trn cc php bin i ma trn v c th t ng ha bng mt s cng c hu hiu nh Matlab, Mathcad, Tuy nhin vic s dng cng c ton hc thun ty lm tch ri ngha vt l, dn n nhng kh khn khi gii thch cc c tnh thu c v tin hnh hiu chnh trong qu trnh thit k.

Phng php trung bnh ha mng ng ct (switching network averaging) vi xut pht ban u t trung bnh ha phn t ng ct (switch averaging) l cch lm t u khi mun m hnh ha cc mch in t cng sut. Ngy nay phng php ny li gy c s quan tm v m hnh thu c gn vi m hnh vt l, c th m t c cc phn t gy tn tht nh in tr khi dn dng ca van, st p trn van, mt s mch in k sinh (v d nh m hnh t in tn s cao l mt mch RLC). Phng php cng c th c dng cho cc s cng hng, cho s mt pha, ba pha, cc loi b bin i DC-DC, DC-AC, AC-DC. Trung bnh ha phn t hay mng ng ct u dng thay th mt phn ca mch in bng mt mng hai ca vi cc bin l in p, dng in ca 1 v ca 2, v1(t), i1(t), v2(t), i2(t). Ty theo in p hay dng in c th coi l bin c lp (v d in p ngun vo, u vo iu khin, in p ra trn ti), cc bin ny c m t bi ngun p hay ngun dng c lp. Hai bin cn li s tr thnh cc ngun dng hay ngun p ph thuc, ty theo chc nng hot ng ca s . Nu phn t c thay th bng mt mng hai ca th c th t n vo bt c s no phn tch tip. Tuy

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nhin v tr trong s ca phn t khc nhau dn n m hnh c th phc tp khng cn thit. V vy phng php trung bnh mng ng ct t ra ph hp hn cho mc ch m hnh ha.

Phng php trung bnh ha da trn c s chnh l cc i lng cn quan tm c iu khin hay thay i vi tn s thp hn nhiu (t nht l 10 ln), so vi tn s ng ct ca s . Khi c th b qua p mch ca in p hay dng in v ch cn quan tm n gi tr trung bnh ca chng trong mt chu k ng ct Ts. Sau khi trung bnh ha ta s loi b c phn t ng ct v thu c m hnh phi tuyn cho tn hiu ln DC. Tip theo s tin hnh tuyn tnh ha quanh im lm vic cn bng bng cch a vo cc bin ng nh i vi cc bin, cui cng s thu c m hnh cho tn hiu ln DC v tn hiu nh AC. 2.3.1 S tng ng bt bin ca phn t ng ct

Hnh 2-9 Phn t ng ct trong s b bin i DC-DC. Mch in c cc phn t ng ct ca s Buck Converter gia cc im k hiu l a,

p, c, c v ring li nh trn hnh 2-9. ngha ca k hiu l a l cc ni vo phn t ng ct tch cc (Transistor hay MOSFET trong s b bin i DC-DC), p l cc ni vi phn t ng ct th ng (passive, l it trong s ), c l cc ni vi im chung ca transitor v it (trong s Buck Converter chnh l cc gc ca MOSFET Q1 v catot ca it CR1). Chin lc trung bnh ha l ta ly trung bnh dng sng dng vo cc a v trung bnh dng sng in p gia hai cc Vc-p trong mt chu k ng ct Ts. Thng thng cc dng sng dng in, in p hon ton bit c qua vic phn tch nguyn l hot ng ca s . Hn na dng sng thng n gin nn php ly gi tr trung bnh khng kh khn g.

Php ly trung bnh cho php a ra c s bt bin ca phn t ng ct cho tt c cc b bin i DC-DC gm hai phn t, mt transitor l phn t tch cc v mt it l phn t th ng. Khi nim bt bin c hiu l s thay th s khng ph thuc vo n c ng dng trong mch in no. Cc s kha trong cc mch b bin i th hin trn hnh 2-10. Trong s kha c th thy bao gi in p vap cng l in p mt chiu, trong khi vcp th no cng c dng xung, nh trn hnh 2-11 c, d. V dng in bao gi dng qua im chung ic cng l dng mt chiu, th hin l dng tng i qua cun cm b ng ct, cn dng ia l dng qua transistor, phn t tch cc, cng c dng xung, nh trn hnh 2-11, a, b. Cc dng in p, dng in ny l bt bin, theo ngha l s no ca b bin i DC-DC th n cng nh vy.

22

Hnh 2-10 S kha trong cc b bin i, t tri sang phi, t trn xung di: Buck, Boost, Buck-Boost,

Cuk converters.

Hnh 2-11 Dng dng in, in p ti cc cng ca mch in ca phn t ng ct.

C th kim tra li dng dng in, in p trn hnh 2-11 qua dng sng in p, dng in ca cc phn t trn s Buck Converter (hnh 2-4) cho trn hnh 2-12. Theo hnh 2-12 c th thy cc mi quan h sau:

: 00 :c s

as s

i t t dTi t

dT t dT

(2.23)

: 00 :ap s

cps s

v t t dTv t

dT t T

(2.24)

Trong ia(t), ic(t) l gi tr tc thi ca dng in i vo im a v i ra im c, vcp(t), vap(t) l cc gi tr tc thi ca in p gia c-p v gia a-p. Ly trung bnh cc gi tr trong biu thc (2.23), (2.24) ta c c quan h gia cc i lng trung bnh:

23

a c

cp ap

i d i

v d v

(2.25)

Hnh 2-12 Dng sng in p, dng in ca cc phn t trn s Buck Converter (hnh 2-4) trong ch

dng lin tc.

Cc i lng trong ngoc ch gi tr trung bnh. Phng trnh (2.25) l dng bt bin ca h phng trnh m t phn t ng ct gm mt transitor v mt it trong cc s b bin i DC-DC, trong ch dng lin tc. Phng trnh bt bin (2.25) l cho tn hiu ln v khng c gii hn no cho cc tn hiu lin quan v l phi tuyn v c cha tch ca bin iu khin d vi cc bin dng in v in p.

thu c phng trnh cho tn hiu nh, c th tuyn tnh ha (2.25) quanh im lm vic cn bng bng cch cho cc bin c cc bin ng nh. V d h s iu ch d c cho di dng h s c nh d = D ng vi ch xc lp v lng bin ng nh d t nh sau:

d t D d t (2.26) Khi cc i lng khc cng c nhng p ng tng ng:

a a c c c c c cI i t D d t I i t DI Di t I d t d t i t (2.27) cp cp ap ap ap ap ap apV v t D d t V v t DV Dv t V d t d t v t (2.28)

24

Trong (2.27), (2.28) b qua s hng cui cng trong tng th hin l tch ca hai bin ng nh, c gi tr nh hn nhiu so vi cc s hng cn li, v tch cc thnh phn ca ch xc lp ra, ta c c quan h ca cc bin thin nh:

a cI DI : thnh phn dng in xc lp DC; (2.29) a c ci t Di t I d t : thnh phn dng in bin ng nh AC; (2.30)

cp apV DV : thnh phn in p xc lp DC; (2.31) cp ap apv t Dv t V d t : thnh phn in p bin ng nh AC. (2.32) p dng 4 phng trnh trn vo mt mch in n gin c th nhn thy rng thnh

phn mt chiu DC (khng ph thuc tn s) c th c thay th bng mt my bin p l tng vi h s my bin p gia s cp v th cp l 1:D. Nu in p s cp l Vap th in p th cp l Vcp = DVap. Nu dng th cp (dng ra ti c) l Ic th dng pha s cp l Ia = DIc. Cc tn hiu nh c a vo s bi cc ngun ph thuc. Vi dng ia(t) gm hai thnh phn, th nht l cI d t m t bi ngun dng ni gia a vi p, cn thnh phn cDi t phn nh qua my bin p. Vi in p apcp ap ap ap Vv t Dv t V d t D v t d tD

, ngoi thnh phn

th nht apDv t phn nh qua my bin p cn c thm ngun p ph thuc apV d tD nh th hin trn hnh 2-13.

Hnh 2-13 Mch in tng ng tn hiu ln DC v tn hiu nh AC ca phn t ng ct.

2.3.2 M hnh tng ng trung bnh phn t ng ct cho Buck converter Sau khi c c m hnh tng ng cho kha bn dn cho c tn hiu ln DC v tn

hiu nh AC, lp vo s vi mng in cn li ta c c m hnh cho Buck Converter, nh biu din trn hnh 2-14.

25

Hnh 2-14 M hnh cho ch dng lin tc ca Buck Converter.

M hnh trn hnh 2-14 c s dng trong phn tch cc quan h DC v AC. Khi phn tch tn hiu DC ta nhn xt rng: cc cun cm c tr khng bng 0, ngha l tr nn ngn mch, cc t in c tr khng bng v cng, ngha l tr nn h mch, cc tn hiu nh cho bng 0. T s c th thy quan h in ap cp oV V DV DV . Bit in p u vo, u ra s tnh c h s iu ch D cn thit.

Khi phn tch tn hiu AC ta gi thit Vin = 0 v ch quan tm n p ng vi tn hiu xoay chiu AC. i vi my bin p ta c quan h:

cpap ap in

cpV V Vvd vD D Dd

(2.33)

Quan h t vcp n vo bng: o RC

cp RC L

ZvZ Zv

(2.34)

Trong 1

1C

RCC

R sr CZ

sC R r l tr khng song song gia mch t lc C v ti R;

L LZ r sL l tr khng mch in cm L. Nh vy hm truyn gia u vo iu khin d vi u ra in p vo s l:

2

11

o o cp Cin

Lcp CLC

L L L

sr CVv v v RD R rd v d R rRr Ls C r s LC

R r R r R r

(2.35)

Hm truyn (2.35) hon ton ging vi kt qu thu c t nhng phng php khc, v d nh t phng php trung bnh phng trnh trng thi.

tm hm truyn gia in p u vo vi in p ra, p dng nguyn l xp chng, coi in p u ra b tc ng ca iu khin v in p u vo:

26

o invd vgv s G s d s G s v s (2.36) Xt ring u vo c bin ng in p nh inv , cn bin ng iu khin 0d , ta c:

1in cpv v

D (2.37)

T (2.34), (2.37), kt hp vi (2.35), suy ra:

2

11

o C

in L CLC

L L L

sr Cv RDR rv R rRr Ls C r s LC

R r R r R r

(2.38)

Cch lm ny khng ch ng vi m hnh Buck Converter m ta cn c th p dng cho cc s khc. Trong cch m hnh ha kha bn dn c th thc hin tng t i vi s Boost v Buck-Boost Converter. Trong cc s c th thy cu trc ca mch kha bn dn u c mt u vo ni vi kha tch cc, mt u ni vi it, mt u l im chung, tc l ba im a, p, c nh a ra trn y. 2.4 Phng php trung bnh ha mng ng ct 2.4.1 Trung bnh ha mng ng ct cho s Boost Converter

Mc ch ca phng php l thay th phn mch c phn t ng ct bng mt mng hai ca. T c th thay th mng ng ct phi tuyn bng mt mng tuyn tnh qua php ly trung bnh. Trc ht ta gii thiu phng php trung bnh ha mch ng ct xy dng cho Boost Converter. Mng ng ct cho trn hnh 2-13 m t bi mt mng hai cng vi in p v dng in tng ng. Trn s Boost Converter mng ng ct gm van MOSFET v it nh trn hnh 2-14. V dng vo cng 1 i1(t) chnh l dng qua cun cm nn coi l bin c lp, in p u ra trn t vo(t) ch thay i do ti thay i nn cng coi l bin c lp. V vy in p v1(t) v dng i2(t) coi l bin ph thuc, dng sng ca chng cho trn hnh 2-15 theo phn tch s hot ng ca s .

Hnh 2-15 M hnh mng ng ct.

27

Hnh 2-16 Mng ng ct trong s Boost Converter.

Hnh 2-17 Dng in p v1(t) (trn MOSFET) v dng dng i2(t) (dng qua it). Ly trung bnh in p v1(t) v dng i2(t) trong mt chu k Ts, vi gi thit vo(t), i1(t) p

mch khng ng k hoc ch thay i gn tuyn tnh, nh (2.39), thu c m hnh trung bnh nh hnh 2-16.

1

2 1 1

1 '1 '

o ov t d t v t d t v t

i t d t i t d t i t

(2.39)

Hnh 2-18 M hnh trung bnh.

28

Tin hnh tuyn tnh ha m hnh trn hnh 2-16 bng cch a vo cc bin ng nh:

1

11 1

22 2

; ' 1 '

gg g

L L

oo o

v t V v t

i t I i t

v t V v t

v t V v t

i t I i t

d D d t d d D d t

Ngun p ph thuc cng vo 1 tr thnh:

2 2 21 2 2 2 2' ' 'v t d t v t D d t V v t D V v t V d t d t v t (2.40)

S hng cui cng th hin l tch ca hai bin ng nh, c th b qua. S hng u tin 22'D V v t th hin ph thuc vo in p u ra 22V v t theo t l D, c m t bi

ngun p ph thuc. S hng 2V d t l ngun p iu khin bi h s iu ch, tr thnh ngun p c lp ni tip trong mch, s hng 1I d t tr thnh ngun dng song song trong mch.

Ngun dng ph thuc cng 2 tr thnh:

1 1 12 1 1 1 1' ' 'i t d t i t D d t I i t D I i t I d t d t i t (2.41) S hng cui cng th hin l tch ca hai bin ng nh, c th b qua. S hng u tin 11'D I i t th hin ph thuc vo dng in u vo 11I i t theo t l D, c m t

bi ngun dng ph thuc. S hng 1I d t l ngun dng iu khin bi h s iu ch, tr thnh ngun dng c lp song song trong mch.

Ngun dng v ngun p ph thuc c m t bi my bin p l tng vi t s my bin p 1:D. Kt qu thu c m hnh nh trn hnh 2-17. Trn hnh 2-17 my bin p l tng c k hiu nt m gia hai cun dy, du ~ trn v du - di ch rng my bin p ny cho php bin i c lng xoay chiu v lng mt chiu.

29

Hnh 2-19 M hnh trung bnh mng ng ct cho Boost Converter.

Hnh 2-20 M hnh trung bnh cho Boost Converter.

Lp m hnh mng trung bnh vo s ta c m hnh trung bnh ca Boost Converter nh trn hnh 2-18. T m hnh ny c th tin hnh phn tch mch a ra cc c tnh mong mun, trong quan trng nht l cc hm truyn t t in p u vo n in p u ra, Gvg(s), v t iu khin (h s iu ch d) n in p u ra, Gvd(s).

H thng c hai u vo, in p v iu khin, vy in p u ra c biu din bi xp chng tc ng ca chng:

go vg vdv s G s v s G s d s (2.42) Cc hm truyn c th c xc nh l:

0 0; g

o ovg vdd s v s

g

v s v sG s G s

v s d s (2.43)

T mch in tng ng hnh 2-18 vit phng trnh cho mch vng dng in qua cun cm v nt in p trn t, b qua cc thnh phn DC c lp nh Vg, IL v Vo v ang xt cc bin ng tn hiu nh:

'

'o

L o g

oo LL

sLi s V d s D v s v s

v ssCv s I d s D i s

R

(2.44)

30

Rt ra iL(s) v gii i vi vo(s);

'

''

o

o

o gL

o goo L

V d s D v s v si s

sLV d s D v s v sv s

sCv s I d s DR sL

Biu din c ov s di dng:

2 2 2 2

' '' '

o Lo g

D V sI L Dv s d s v sL Ls LC s D s LC s DR R

(2.45)

Rt ra c cc hm truyn t:

20 22 2

0 22 2

'1' 1' '

1 1' 1' '

o

g

o Lvd v s

ovg d s

g

D V sI Lv sG s

LC LDd s s sD RD

v sG s

LC LDv s s sD RD

(2.46)

Chuyn v dng tiu chun:

0 2

0 0

0 2

0 0

1

1 1

11 1

zvd vd

vg vg

s

G s Gs s

Q

G s Gs s

Q

(2.47)

Trong 0 0 0'' 1; ' ; ; ;' 'o o

z vd vgL

D V VD LQ D R G GC I L D DLC

. z l im zero dng, bn phi trc o. Mu s trong hm truyn (2.47) th hin c im cc bi p.

31

2.4.2 Trung bnh ha mch ng ct cho Buck, Buck-Boost Converter Bng cch lm tng t hon ton c th xy dng m hnh trung bnh mch ng ct

cho Buck, Buck-Boost Converter v c c cc hm truyn cn quan tm. Kt qu cho trn hnh 2-19, 2-20. Cc thng s c bn ca hm truyn i vi 3 s b bin i DC-DC c bn cho trong bng 2-1. Dng ca hm truyn gia in p u vo n in p u ra, gia u vo iu khin n in p ra v ngha cc thng s ging nh trong (2.47).

Hnh 2-21 M hnh trung bnh ca Buck Converter.

Hnh 2-22 M hnh trung bnh ca Buck-Boost Converter. Bng 2-1 Cc thng s cho hm truyn ca cc b bin i DC-DC c bn.

S Gvg0 Gvd0 0 Q z Buck D oV

D 1

LC LR

C

Boost 1'D '

oVD

'DLC

' LD RC

2'D RL

Buck-Boost

'DD

2'oV

DD 'D

LC ' LD R

C

2'D RDL

Bng 2-1 cho thy c hai b bin i l Boost Converter v Buck-Boost Converter c

im zero dng bn phi trc o trong hm truyn t iu khin n in p ra. T tn s z tr i h s khuch i c tng +20 dB/dec trong khi gc pha li b gim i n -90. iu ny dn n kh nng mt n nh trong h thng iu chnh in p mch vng kn. Chnh v iu ny m mch hiu chnh sai lch in p khng th ch dng hai phn t (lead lag thng thng) nh i vi Buck Converter m phi dng n 4 phn t, hai zero v hai im cc, nh phng php thit k mch vng iu chnh cho Boost Converter cp n phn 1.

32

2.4.3 Hm truyn cho b bin i c tnh ti in tr cun cm rL v in tr rESR ca t Dng s trung bnh ha mch ng ct, lp vo s cn li c tnh ti gi tr in tr

thun ca cun cm v in tr ESR ca t, c th a ra hm truyn chnh xc hn. Cc phn t tnh ti tn hao trn van bn dn nh RDson v st p c nh trn it VD0 cng c th c a vo s tnh ton tn hao trong mch.

2I d

1V d

ggV v

11I i

22I i

22V v

Hnh 2-23 M hnh trung bnh cho Buck Converter c tnh ti in tr thun cun cm rL v in tr tn hao trn t (ESR) rC.

Trn hnh 2-21 th hin s Buck Converter c tnh ti cc gi tr in tr thun trong mch cun cm v ESR trong mch t. Khi c nhng yu t thc t ny trong mch hnh dng dng i2 v in p trn t vC s khng cn dng tuyn tnh nn khi ly trung bnh trong mt chu k Ts tnh ton s phc tp hn. Tuy nhin nu lu rng rL v rC c gi tr thc t rt nh th nhng gi thit v dng tuyn tnh ca i2 v vC vn c th p dng, do mch in trung bnh cho mng ng ct c th p dng m khng cn thay i g. T nhng yu t thc t ny s ch thay i dng ca hm truyn tn hiu, nh s ch ra sau y.

T s ta c: 2 1 1v Dv V d (2.48)

Trc ht ta xt hm truyn t tn hiu iu khin n in p u ra nn gi thit

2

1 10 vv Vd .

2

o RC

RC L

ZvZ Zv

, trong

11

CRC

C

R sr CZ

sC R r l tr khng song song gia mch t lc C

v ti R; L LZ r sL l tr khng mch in cm L. Nh vy hm truyn gia u vo iu khin d vi u ra in p vo s l:

2

12 2

11

o o C

L CLC

L L L

sr Cv v v RVR rd v d R rRr Ls C r s LC

R r R r R r

(2.49)

33

Nu xt hm truyn t u vo n in p u ra th 21

0 vd Dv

, do (2.49) tr thnh:

21 2 1 2

11

o o C

L CLC

L L L

sr Cv v v RDR rv v v R rRr Ls C r s LC

R r R r R r

(2.50)

(2.49), (2.50) cho thy hm truyn t u vo iu khin n u ra v t u vo n u ra u xut hin im zero m 1/ Cr C , gi l im zero ESR. H s khuch i DC (khi s = 0) cng thay i theo h s / LR R r . c bit l xem xt mu s ca hm truyn ta thy tn s dao ng t do 0 v h s cht lng mch ti Q s u thay i so vi cc gi tr trong bng 2-1.

ggV v

11I i

oI d

oV d

11V v

Hnh 2-24 M hnh Boost Converter vi cc in tr rL v rC.

Xt s Boost Converter vi cc thnh phn in tr thun ca cun cm v in tr ESR ca t in trn hnh 2-22.

Vit phng trnh cho nt dng in qua t C, ch xt vi cc thnh phn xoay chiu:

1

11'' 1

o Coo o

RC C

v s i s sC R rI d s i s D I d s v s

Z D sCR sr C

, (2.51)

Trong 11

1C

RC CC

R sr CZ r R

sC sC R r l tr khng mch ti.

Vit phng trnh cho mch vng dng in qua cun cm:

1 'g oL oi s r sL v s V d s D v s (2.52) Thay biu thc dng i1(s) vo:

34

1' '1

Co g oo L o

C

sC R rD I d s v s r sL v s V d s D v s

R sr C

(2.53)

Gom cc s hn c ov s sang v phi, ta c:

1 '' 1 ' 11 'C L o

o g o o LC o o L

sC R r r sL D I LD v s v s V D I r s d s

R sr C V D I r

(2.54)

T c th thy vi 0 0; g

o ovg vdd s v s

g

v s v sG s G s

v s d s s xc nh c:

2

11' 1

o Cvg

g L CLC

L L L

v s sr CRG sD R rv s R rRr Ls C r s LC

R r R r R r

(2.55)

2

'1 1''' 1

oC

o o o Lo o Lvd

L CLC

L L L

D I Ls sr C

V D I rv s V D I r RG sD R rd s R rRr Ls C r s LC

R r R r R r

(2.56) So snh (2.55), (2.56) vi (2.45) c th thy s tng ng gia cc hm truyn v s

khc nhau bi s xut hin im zero ESR cc hm truyn sau ny. (2.56) cng ch ra im zero bn phi trc o v s ph thuc ca n vo cc thng s ti ti im lm vic cn bng.

Vi s Buck-Boost Converter cng c th tin hnh tng t tm ra cc hm truyn cn quan tm. 2.4.4 Hm truyn c tnh ti tn hao trn van bn dn v it

C th tnh ti tn hao trn van bn dn, ngha l tn hao trn in tr khi dn Ron ca MOSFET, v trn it, ngha l tn hao do st trn it khi dn dng VD0, trong s trung bnh ha. Trc ht xt v d vi s Buck Converter.

Xt s Buck Converter vi mng mch ng ct trong vng ch nht nt t nh trn hnh 2-23. Gi s khi van dn dng in tr khi dn Ron khng i v khi it dn st p trn it VD0 cng khng i. Trng thi ca s cho trn hnh 2-24, a, b. Trong mng mch ng ct v in p v1(t) chnh bng in p u vo, gn nh khng i, v dng i2(t) l dng qua cun cm

35

c p mch nh nn ta chn l cc bin c lp. Cn biu din i1(t) v in p v2(t) qua cc bin c lp ny v tn hiu iu khin d(t).

Hnh 2-25 S Buck Converter vi mng mch ng ct.

D S

GVg

L

C R

iL

iC

ioRon

uo Vg

L

C R

iL

iC

io

D

Ron

uoVD0

(a) (b)

Hnh 2-26 Mch in Buck Converter; (a) Khi van bn dn thng; (b) Khi van khng thng, it D thng.

Dng sng in p v2 v dng in i1 cho trn hnh 2-25.

Hnh 2-27 Dng dng in i1(t), in p v2(t).

Tnh ton cc gi tr trung bnh, lu rng tt c cc gi tr trung bnh u tnh trong mt chu k Ts:

36

1 2

2 1 2 0 1 0 2' 'on D D oni t d i t

v t d V R i t d V dV d V R d i t

(2.57)

T (2.57) c m hnh trung bnh tn hiu ln cho Buck Convverter nh hnh 2-26.

0' Dd V 1i t

2i t 2v t 1v t

Hnh 2-28 M hnh trung bnh tn hiu ln ca Buck Converter tnh ti tn hao trn van v it khi dn dng.

2.4.5 M hnh trung bnh tnh ti tn hao do qu trnh ng ct M hnh trung bnh c th tnh ti tn hao do qu trnh ng ct. Ly v d Buck

Converter nh trn hnh 2-23. y ta b qua cc tn tht do dn dng v trn cc phn t khc nh cun cm, t in. Xt n qu trnh phc hi ca it khi kha li. Khi it kha li c mt dng in m xut hin di tn ht in tch Qr ra ngoi tip gip p-n ca it. Thi gian di tn ht tr s, gi l thi gian phc hi. Qr v tr l cc thng s ca it do nh sn xut cung cp. Hnh dng sng dng i1(t) v in p v2(t) cho trn hnh 2-27.

Hnh 2-29 Dng sng dng in, in p trn phn t khi c hin tng phc hi ca it trong Buck

Converter.

Trn hnh 2-27 gi s u chu k it D trc ang dn dng qua cun cm, bt u kha li v xut hin dng in ngc. MOSFET bt u m ra v dng qua van ln hn dng qua cun cm phn dng ngc ca it. Trong thi gian it phc hi tnh cht kha st p trn it coi l rt nh, ch sau thi gian tr it kha hn, in p v2 s bng Vg. Tnh ton cc gi tr trung bnh:

37

1 1 2 20

1 sT r rs s s

Q ti t i t dt i t d i tT T T

(2.58) Thi gian dTs l khong thi gian m MOSFET tr i thi gian tr, do :

2 1v t d v t (2.59) T (2.58), (2.59) ta c m hnh trung bnh tn hiu ln Buck Converter nh trn hnh 2-

28. Cc thnh phn c lp trong (2.58) m t bi cc ngun dng pha s cp my bin p DC l tng. T my bin p cc thnh phn l l tng, khng tn hao. V vy tn hao trn s tnh bng:

1 2r rlosss s

Q tP v t i tT T

(2.60)

r

s

QT

1i t 2i t 2v t 1v t

2r

s

t IT

Hnh 2-30 M hnh trung bnh Buck Converter tnh ti tn hao do van ng ct. Trong ch xc lp s cho php xc nh c cc mi quan h sau:

o gV DV (2.61) Cng sut u vo b bin i bng:

1r r

in g g o os s

Q tP V I V I DIT T

(2.62)

Cng sut u ra bng: o o o g oP V I DV I (2.63)

Hiu sut b bin i bng:

38

11

g oo

r rin r rg o o

o s ss s

DV IPQ tP Q tV I DI DI T DTT T

(2.64)

3 M hnh cc b bin i trong ch dng gin on Trong phn 2.3 tin hnh m hnh ha b bin i trong ch dng lin tc

(Continuous Current Mode CCM). Trong ch CCM cc b bin i u c quan h vo ra c dng M(D), tc l h s truyn in p t u vo n u ra ch ph thuc vo h s iu ch D, l t s gia thi gian iu khin m van vi chu k ng ct Ts, m khng ph thuc vo ti R. iu ny ngha l trong m hnh cc b bin i pha u ra coi l ngun in p. Trong cc m hnh trung bnh tn hiu ln DC v nh AC, c th xc nh hm truyn t gia u vo n u ra Gvg(s) v gia iu khin vi u ra Gvd(s). C hai hm truyn ny u c c trng l c cp im cc (double pole) tn s thp do mch LC quyt nh. Thng thng tn s cp im cc ny ch c 0,01 0,05 fs, trong fs l tn s ng ct ca b bin i (ngha l khong 1 kHz n 5 kHz nu fs = 100 kHz). Khi m t tnh ti tn hao trn cun cm (rL) v in tr ni tip hiu dng trn t (rC hay ESR effective series resistant) xut hin im zero m, gi l ESRzero, tn s cao, c 0,1 fs. im ESRzero lm gim d tr v pha trong mch vng iu chnh dn ti h mt n nh. i vi hm truyn t iu khin n in p u ra, hai loi b bin i c bn boost converter v buck-boost converter c xut hin im zero bn phi trc o. im zero dng cng lm gim d tr v pha trong mch vng iu chnh v lm cho boost v buck-boost converter tr nn cc h pha khng cc tiu. V vy b iu chnh cho boost v buck-boost converter phi c dng phc tp, t nht l bao gm 2 im cc v hai im zero, trong khi i vi buck converter b iu chnh c th ch bao gm 2 phn t, 1 im cc v 1 im zero.

Cc b bin i u c th ri vo ch lm vic dng gin on (Discontinuos Current mode DCM). Ch dng gin on c trng bi dng qua cun cm bt u t 0 v kt thc cng bng 0 trc khi kt thc chu k ng ct Ts. Do dng gin on quan h in p vo ra s ph thuc vo ti, M(D,K), trong K l mt h s ph thuc ti. Nh vy m hnh b bin i pha u ra s khng th coi l ngun p c na. Phng php trung bnh phn t ng ct vn c dng m hnh ha b bin i. T m hnh trung bnh thu c tin hnh tuyn tnh ha c c m hnh tn hiu nh AC. Hm truyn thu c s cho thy ch c mt im cc tn s thp v mt im cc tn s rt cao, gn vi tn s ng ct fs. Do trong ch DCM vic thit k mch vng iu chnh s n gin hn, so vi CCM. 3.1 M hnh trung bnh DCM buck converter

Xt s b bin i buck cho trn hnh 2-23. Ta s theo phng php nh phn 2.3.2 xy dng mch in trung bnh tng ng cho dng sng dng in, in p ti hai ca ca mng mch ng ct. Dng sng dng in, in p trong ch DCM cho trn hnh 3-1. Theo dng sng dng in, in p, ta cn xc nh cc gi tr trung bnh ca cc u vo, u ra ca

39

mng ng ct v1(t), i1(t), v2(t), i2(t), theo cc bin trng thi ca s l dng qua cun cm, in p trn t, bin u vo l in p ngun vg, v cc khong thi gian iu khin d1Ts, d2Ts.

0

0

dTs Tst

t

ipk

vL(t)

i1(t)

v1(t)

i2(t)

v2(t)

t

t

t

t

0

0

0

0

Vg

q1

q2

iL(t)

vL(t) Vg-Vo

-Vo

d1Ts d2Ts d3Ts

VgVo

0

Hnh 3-1 Dng sng dng in, in p ca buck converter trong ch DCM.

Cc gi tr trung bnh u c xc nh trong chu k ng ct Ts nn trong cc biu thc sau y ta b qua k hiu ny cho n gin. in p u vo ca mng v1(t) n gin chnh l in p ngun nn ta c:

1 gv t v t (3.1) in p u ra ca mng ng ct v2(t) l in p trn it, c gi tr trung bnh bng:

2 1 2 3 1 30g o g ov t d t v t d t d t v t d t v t d t v t (3.2) Dng in u vo mng i1(t) c gi tr trung bnh l din tch hnh tam gic q1 bi en

trn hnh 3-1.

40

11 10

1 sTs s

qi t i t dtT T

(3.3) Din tch hnh tam gic bng y nhn vi nh, trong nh ca dng in bng:

1 g opk s v t v ti d t T L (3.4)

1 112 s pkq d t T i (3.5)

2111 2 s g os d t Tqi t v t v tT L (3.6) Dng i2(t) trung bnh bng:

22 20

1 sTs s

qi t i t dtT T

(3.7)

2 1 212 s pkq d t d t T i (3.8)

1 1 222 2 s g osd t d t d t Tqi t v t v t

T L (3.9)

d1(t) v d2(t) c lin quan n nhau nu lu rng gi tr trung bnh ca in p trn cun cm 0Lv t .

1 0 2 3

02 1

3 1 2 1

0 0

1 1

L g o

g

o

g

o

v t d t v t v t d t v t d t

v t v td t d t

v t

v td t d t d t d t

v t

(3.10)

Vi (3.10) ta c th biu din gi tr trung bnh dng sng dng in, in p ti hai ca ca mng ng ct di dng n gin nh sau:

1 gv t v t (3.11)

41

2 ov t v t (3.12)

211 1 22 sd t Ti t v t v tL (3.13)

2 1 1 212

22s

v t v t v td t Ti t

L v t

(3.14)

M hnh trung bnh cho ch DCM c th xy dng t (3.11) n (3.14). Trc ht t (3.13) c th thy dng u vo t l vi hiu in p gia cng vo v cng ra ca mng, theo nh lut m:

1 21 1ev t v t

i tR d

(3.15)

Trong 1 212

es

LR dd t T

(3.16)

Coi Re(d1) l in tr o tng ng. Thc cht khng c in tr no trong b bin i v ta ang gi thit cc phn t u l l tng. Cng sut gi tng tiu th bi Re c chuyn ra ngoi qua cng ra ca mng. (3.16) cho thy trong ch dng gin on DCM b bin i c m t bi m hnh in tr khng tn hao (Loss-Free Resistance LFR). LFR l khi nim ta s cn gp li sau ny trong m hnh cc b chnh lu l tng.

T (3.14) c th thy rng:

1 22 2 1 1 11ev t v t

v t i t v t v t i tR d

(3.17)

Biu thc (3.17) v tri th hin l cng sut u vo ca mng bng cng sut a ra u ra. T (3.16) m hnh trung bnh c th hin bng s trn hnh 3-2 bi in tr o Re(t) v mt ngun cng sut ph thuc bng:

2

1 2

1e

v t v tp t

R d

(3.18)

42

p t

Hnh 3-2 M hnh trung bnh buck converter trong ch DCM.

T m hnh tng ng c th tin hnh phn tch ch tn hiu ln DC c c mi quan h gia in p vo ra v iu khin. Khi phn tch ch DC ta ngn mch cc cun cm v tn s bng 0 tr khng in cm bng 0. Tng t nh vy ta h mch cc t in v DC tr khng ca t bng v cng. T s trn hnh 3-2 ta c:

22

1 21

22 2 2

o

e

o

V VIR R

V VIR

VP I VR

21 1 1

g o g o gg

e e e

V V V V VP V I V

R R R

Cho P1 = P2 v ang xt s l tng, khng tn hao, rt ra c quan h in p vo ra nh sau:

21 1 4 /o g e

V VR R

(3.19)

Theo (3.19) quan h vo ra M = Vo/Vg ca buck converter trong ch DCM ph thuc vo h s iu ch D (thng qua 1 21

2e

s

LR dd t T

) v thng s ca ti R.

3.2 M hnh tn hiu nh AC n gin cho ch DCM C th tm tt m hnh trung bnh cho mng ng ct ca cc s van trong cc b bin

i tiu biu nh trn hnh 3-3.

43

p t 1v t

2i t

2v t

1i t

Hnh 3-3 M hnh trung bnh cho mng ng ct trong ch DCM.

Trn hnh 3-3 phn kha ng ct, hnh 3-3 a, c m t bi in tr o Re(d1), phn it c m t bi ngun cng sut ph thuc p(t), hnh 3-3 b. M hnh trn hnh 3-3 b l m hnh tn hiu ln DC. c c m hnh tn hiu nh ta cn cho cc bin in p, dng in trn cc ca vo, ra cc bin ng nh quanh im lm vic cn bng v tin hnh tuyn tnh ha.

11 1

11 1

22 2

22 2

d t D d t

v t V v t

i t I i t

v t V v t

i t I i t

(3.20)

Trong cc biu thc (3.13), (3.14) ta biu din c gi tr trung bnh ca dng in 1 2,i t i t qua bin iu khin d1(t) v cc in p trung bnh 1 2,v t v t . Khi tuyn tnh

ha ta s thy rng cc dng in ny c th biu din qua t hp tuyn tnh ca cc bin ng nh 1 1 2, ,d v v di dng sau:

11 21 1

1

22 12 2

2

vi j d g vr

vi j d g vr

(3.21)

Phng trnh (3.21) m t mt mng hai ca nh trn hnh 3-4.

44

r2

2j d12g v

2i

2vr1 1j d 21g v1v

+

-

+

-

1i

Hnh 3-4 S tng ng mng hai cng tn hiu nh.

Cc tham s r, j, g th hin l cc h s bc nht trong khai trin Taylor ca quan h hm s biu din 1 1 2, ,i t f v t v t d t , nh trong phng php tuyn tnh ha thng s dng. V d khai trin Taylor ca dng i1(t) quanh im lm vic cn bng c th biu din bi (3.22):

1 1

2 2

1 1 21 11 1 1 21

1 1 222

1 1 2

, ,, ,, ,

, , ...

v V

v V

d D

f v V DI i t f V V D v t

vf V v D

v tv

f V V dd t

d

(3.22)

i vi buck converter, thnh phn DC trong (3.22) bng:

1 21 eV VIR D (3.23)

Cc h s bc nht trong khai trin Taylor (3.22) bng:

1 11 1 21 1, ,1 1

v Ve

f v V Dr v R D

(3.24)

2 2

1 1 21

2

, , 1v V

e

f V v Dg

v R D (3.25)

1 1 2 1 21 21 2

, , 2ed D d D

e e

f V V d R D V VV Vjd R D d DR D

(3.26)

Nh vy trong m hnh tn hiu nh in tr cng vo r1 bng vi gi tr in tr o Re(D). g1 th hin nh hng ca in p trn it i vi dng u vo. i vi buck converter dng u vo t l nghch vi in p u ra cng thng qua in tr Re(D), du m trong (3.25)

45

th hin iu ny. Cui cng j1 th hin nh hng ca bin ng nh ca h s iu ch i vi dng u vo.

Bng cch lm tng t i vi dng i2(t), biu din bi (3.14), ta c th xc nh c cc h s r2, g2, j2.

1 1 22 2 1 2 21, , ev t v t v t

i t f v t v t d tR d v t

(3.27)

2 2

22 1 2 1

22 2 2

, ,1 1v V

e

f V v D Vr v R D V

(3.28)

1 1

2 1 2 1 22

1

, , 2v V

e

f v V D V Vgv R D

(3.29)

2 1 2 1 21 22 2

, , 2ed D d D

e e

f V V d R D V VV Vjd R D d DR D

(3.30)

S tn hiu nh lp rp vo m hnh buck converter, c dng nh trn hnh 3-5.

2j d12g v

2i

2v1j d 21g v1v

1i

ovgv

Hnh 3-5 M hnh trung bnh tn hiu nh ch DCM cho buck converter.

M hnh trn hnh 3-5 c th dng a ra cc hm truyn tn hiu cn thit. Trong m hnh ny ta b qua p mch ca dng qua cun cm, v vy m hnh c th cho bit cc quan h tn s thp (khi coi dng qua cun cm l phng hon ton), khng chnh xc lm. Nh vy vng tn s thp c th coi cun cm b ngn mch, hm truyn t u vo n u ra Gvg(s) c th thu c nu coi bin ng nh 0d :

00 1o g

vg dg

p

GvG s sv

(3.31)

46

Trong 0 2 2gG g R r (3.32)

21

p R r C (3.33)

Hm truyn t iu khin n u ra c c khi coi bin ng nh in p u vo bng khng:

00 1go d

vd v

p

GvG s sd

(3.34)

0 2 2dG j R r (3.35) Cc hm truyn (3.31), (3.34) cho thy vng tn s thp m hnh DCM ch c mt im

cc n, thay v im cc kp nh trong ch dng lin tc CCM. y ta s dng gi thit gn ng l dng v p u p mch rt nh, v vy m hnh khng cho bit nhng c im vng tn s cao hay l gn tn s ng ct fs. M hnh vng tn s cao s c xt n sau y. 3.3 M hnh tn hiu nh AC chnh xc hn cho buck converter ch

DCM Hm truyn (3.31), (3.35) th hin ch c mt im cc p tn s thp, cn im cc

v c th im zero tn s cao do c in cm L b y ra vng tn s cao, khng tnh n. L do l ta ch da vo quan h gi tr trung bnh ca in p trn in cm bng 0, nh (3.10), m b qua p mch ca dng iL(t). Nu tnh n p mch ca dng in iL ta c th thu c m hnh chnh xc hn vng tn s cao (khng dng n gi thit in p trung bnh trn cun cm bng 0, v gi thit ny ch ng cho ch xc lp). Mun vy ta cn tnh gi tr trung bnh ca dng qua cun cm theo hnh dng dng in hnh 3-1.

1 1 22 2 sL g od t d t d t Ti t i t v t v tL (3.36) T (3.36) biu din c quan h ph thuc khong thi gian d2Ts vo bin iu khin d

= d1(t) v dng qua cun cm nh sau:

1

2 11e Lg o

R d i td t d t

v t v t

(3.37)

47

1

3 1 2 11 1 e Lg o

R d i td t d t d t d t

v t v t (3.38)

Nh vy, cng vi (3.11), (3.12), (3.13), (3.14), (3.38) tr thnh m hnh tn hiu ln cho buck converter. M hnh ny m t h thng tn s thp v c tn s cao lin quan n nh hng ca cun cm L. Tuy nhin khi s phng trnh nhiu ln khng th tin hnh biu din cc gi tr dng in, in p ca s b bin i ch qua cc bin ca mng ng ct.

i vi buck converter trong s trn hnh 2-23 vi dng sng dng in, in p trn hnh 3-1, chn in p u ra ca mng ng ct v2(t) v dng u vo i1(t) l bin ph thuc. Vi lu (3.38), biu thc ca v2(t) trong (3.2) s c dng chnh xc hn, ph thuc vo dng trung bnh qua cun cm iL, in p trung bnh u vo, u ra, v bin iu khin nh sau:

1

2 1 11 e Lg og o

R d i tv t d t v t d t v t

v t v t

(3.39)

C th tin hnh tuyn tnh ha (3.39) theo khai trin Taylor tng t nh lm trn. Quan h hm by gi phc tp hn v ph thuc bn bin c lp, bao gm c dng qua cun cm

sL T

i t , c dng nh sau:

2 2 , , ,g o Lv t v t v t i t d t (3.40) 2 2 2g o Lg vv t v t k v k i r d f (3.41)

Trong cc h s ca m hnh tn hiu nh c tnh bng gi tr o hm ring ca 2 ti gi tr lm vic cn bng xc lp.

22

, , ,1g g

g o L e Lg v V

g g

v V I D R D Ik D

v V D

(3.42)

22

, , , 1 1o og o L e L

v v Vo g

V v I D R D I Dk

v V D

(3.43)

22

, , ,1L L

g o L ei I

L

V V i D R D Dr

i D

(3.44)

22

, , ,1

g o L e Ld D g

V V I d R D If V

d D

(3.45)

48

Thay (3.39) vo phng trnh tnh dng i1(t):

11 1 1

1 11 1 e Lg oe e g o

R d i ti t d t v t d t v t

R d R d v t v t

(3.46)

Quan h hm ca dng 1sT

i t cng ph thuc bn bin, nh biu din sau y:

1 1 , , ,g o Li t v t v t i t d t (3.47) Tin hnh tuyn tnh ha (3.47) bng khai trin Taylor nh sau:

1 1 1g o Lg vi t v t g v g i h d j (3.48)

1 , , , 1 1 1g g

g o L e Lg v V

g e

v V I D R D I Dg D

v R D D

(3.49)

12

, , , 1 1 1o og o L e L

v v Vo e g

V v I D R D I Dg

v R D V D

(3.50)

11

, , ,1L L

g o Li I

L

V V i D Dhi D

(3.51)

11

, , ,1

g o L g Ld D

e

V V I d V Ijd R D D

(3.52)

T (3.41) n (3.52) cho php th hin m hnh tn hiu nh ca buck converter nh trn hnh 3-6 (cha c hnh v). T m hnh c th c c hm truyn t iu khin n dng qua cun cm iL nh sau:

2 11

L

r

p

i s fsrd s

(3.53)

Trong 22 2p

prf

L l tn s ca im cc. Vi r2 xc nh t (3.44), in tr o

bng 2 22 2e ss

L LR D fD T D

, ta c:

49

22 2 1 1e sp

R D D frfL L D D D (3.54)

V 11 4D D khi 0 < D < 1 nn c th thy rng im cc b y ra tn s cao hn tn s ng ct ca s . Nh vy trong ch DCM im cc tn s cao thc s khng nh hng g nhiu n bng thng ca mch vng iu chnh. Do h thng iu chnh cho DCM s n gin hn.

50

4 H thng iu khin theo dng in H thng iu khin v cc m hnh ha b bin i trong phn 1, 2, 3 trn y cp

n phng php iu khin theo in p, trong bin u vo iu khin l h s iu ch d trong s iu ch rng xung PWM. in p u ra l bin c iu khin trc tip (c o v). Cc m hnh trung bnh c xy dng, cho ch dng lin tc (CCM) v dng gin on (DCM), tuyn tnh ha quanh im lm vic cn bng v a ra m hnh tn hiu nh AC, t c c hm truyn t iu khin (bin d) n in p u ra.

Hnh 4-1 S buck converter iu kin theo dng in. Mt phng php iu khin khc cng c ng dng rng ri l iu khin theo dng

in. Cc nh sn xut cng cho ra nhiu loi IC chuyn dng cho cc mch iu khin theo dng in. Theo phng php ny bin iu khin l dng in nh qua transistor is,pk(t), u vo iu khin l dng in t ic(t). Mch iu khin s ng ct transistor sao cho dng nh qua n bng dng in t. S mch tng t trn hnh 4-1 m t nguyn l hot ng ny. Trn s tn hiu xung nhp a vo u vo S ca tri-g s xc nh chu k ng ct Ts. Dng in qua transistor is(t) c o v so snh vi dng in t ic(t). u mi chu k Ts transistor Q1 c iu khin m. Khi dng qua Q1 bng dng t ic(t) tn hiu so snh a vo u reset R ca tri-g lt trng thi, a ra tn hiu kha Q1 li. Dng qua transistor s gim cho n khi gp chu k Ts mi.

51

Mch vng phn hi in p c xy dng nh mch vng ngoi. Sai lch gia in p mong mun vref v in p u ra vo(t) c x l qua b iu chnh in p, tr thnh lng t cho mch vng dng in ic(t). C th thy rng mi quan h nh hng ca s thay i ic(t) v in p vo vg(t) i vi in p u ra c dng n gin nn vic thit k b iu chnh in p khng gp kh khn g.

u im c bn ca phng php iu khin theo dng in l quan h hm truyn t gia dng t ti in p u ra

o

c

v si s

n gin hn quan h gia tn hiu iu ch ti in p ra

ov s

d s

v c t hn mt im cc. Hn na im cc ny li tn s cao, gn vi tn s ng ct

fs. Nh vy c th xy dng c mt mch vng n nh bn vng vi bng thng rng m khng cn ti mch b sm pha.

u im na ca iu khin theo dng in l kh nng bo v transistor v bt c khi no dng vt qu ic(t) transistor u b kha li. Khi lm vic vi cc s c bin p cch ly iu khin theo dng in cng trnh c hin tng bo ha mch t do in p c cha thnh phn mt chiu trong cc khong thi gian c bin ng. Khi c s mt cn bng in p t ln cun dy my bin p xut hin thnh phn t ha mt chiu dn n dng t ha tng ln. Khi iu khin theo dng in transistor s t b kha li sm hn, dn n dn dn in p s t cn bng li. Do kh nng t cn bng in p m trong cc mch cu khng cn dng t ni u ra b bin i vi my bin p nh iu khin theo in p yu cu.

Nhc im ca iu khin theo dng in l s nhy vi nhiu. Nu tn hiu o dng in transistor is(t) c xung nhiu s lm lt tri-g sai thi im, v d u chu k m khi it kha li, dng phc hi ngc ca it gy nn xung dng ln qua transistor. V vy mch o dng phi c mt mch lc gim tc ng ca dng ngc ny. Mt kh khn na l khi dng qua cun cm c p mch qu nh th mch so snh dng nh cng khng th chnh xc c.

Mt vn t ra na l iu khin theo dng in s mt n nh khi h s iu ch D ln hn 0,5. Tuy nhin iu ny c th khc phc bng cch a vo tn hiu ic(t) lng b dng rng ca theo chu k Ts, nh s ni n sau y. 4.1 S mt n nh khi D > 0,5

xt hiu ng mt n nh khi h s iu ch D > 0,5 trong phng php iu khin theo dng in, ta xt dng dng in qua cun cm iL khi c bin ng nh ca dng xc lp ti u mi chu k:

00 0LL Li I i (4.1)

52

Trong IL0 l gi tr dng in ti u mi chu k Ts trong ch xc lp. Qu trnh c minh ha trn hnh 4-2.

Hnh 4-2 S thay i rng xung m khi c bin ng nh dng in. Theo hnh 4-2 trong khong 0 < t < DTs dng qua cun L c tng m1, trong khong

DTs < t < Ts dng c gim m2. V d i vi ba loi DC-DC c bn m1, m2 c cc gi tr sau:

- Vi buck converter: 1 g ov v

mL ; 2 ovm L (4.2)

- Vi boost converter: 1 gv

mL

; 2 g ov v

mL (4.3)

- Vi buck-boost converter: 1 gv

mL

; 2 ovm L (4.4)

Bit cc gi tr tng, gim dng in, c th suy ra quan h gia cc gi tr iL(0), ic, i(Ts), v dTs.

Trong giai on u, dng in tng tuyn tnh n khi t n gi tr iL(dTs) = ic, do : 10L s c L si dT i i m dT (4.5)

Do : 1

0c Ls

i id

mT (4.6)

Trong giai on dng gim tuyn tnh:

2

1 2

'0 '

L s L s s

L s s

i T i dT m d T

i m dT m d T

(4.7)

Trong ch xc lp, iL(0) = iL(Ts), d = D, m1 = M1, m2 = M2. V vy ta c:

53

21 2

1' 0 's s

M DM DT M D TM D

(4.8)

T hnh 4-2 th hin s thay i nh ca dng in khi c bin ng nh 0Li , c th thy rng bin ng nh u chu k (0) v cui chu k (Ts) u xy ra trong khong bin ng nh sdT , do :

12

0 0 'L L Lsm Di T i im D

(4.9)

Vy n chu k tip theo, ta c:

22 0' 'L L Ls sD Di T i T iD D

(4.10)

Nh vy sau n chu k ta c:

1 0' 'n

L L Ls sD Di nT i n T iD D

(4.11)

T (4.11) cho thy rng nu 1'DD

th bin ng L si nT s tin n 0 v ngc li s tin n . V D = 1 D, iu kin ny c ngha l D < 0,5 l iu kin iu khin theo dng in c th n nh.

S mt n nh khi D > 0,5 xy ra i vi tt c cc b bin i DC-DC c bn iu khin theo dng in. C th m bo tnh n nh ca b iu chnh dng in bng cch to ra mt tn hiu rng ca tng tuyn tnh vi nghing ma, vi chu k Ts, cng vo vi tn hiu dng in o c. S thc hin thut ton ny th hin trn hnh 4-3. Nh vy khu so snh s kha transistor li khi:

a s L s ci dT i dT i (4.12) Xt tc ng ca tn hiu rng ca khi dng ti u chu k c bin ng nh

00 0LL Li I i . Hnh 4-4 cho thy bin ng u chu k v cui chu k v gi tr u xy ra trong khong bin ng ca thi gian sdT :

10L s ai dT m m (4.13) 2L s s ai T dT m m (4.14)

54

Hnh 4-3 S h thng iu khin vi tn hiu rng ca cng vo tn hiu dng o c.

Hnh 4-4 Tc ng ca tn hiu rng ca i vi bin ng dng in u v cui chu k Ts.

Loi d ra khi (4.13), (4.14) ta c:

21

0 aL Lsa

m mi T im m

(4.15)

Lp li tng t (4.15) cho ti n chu k, ta c:

55

21

0 0n

naL L Ls

a

m mi nT i im m

(4.16)

Vi 21

a

a

m mm m

(4.17)

Nh vy 1 l iu kin mch vng dng in n nh. Thng thng in p u ra c iu chnh gi n nh trong khi in p u vo c

th thay i. Do nghing m2 c th bit c chnh xc theo (4.2), (4.4) vi buck, buck-boost converter. Vi boost converter th m2 vn b nh hng ca in p u vo. Tuy nhin hon ton c th chn ma theo m2 m bo n nh. V d thng c th chn:

212am m (4.18)

Mt gi tr na c th chn l: 2am m (4.19)

Khi 0 i vi ton b di thay i D. Ni cch khc bin ng cui chu k L si T bao gi cng bng 0 min l bin ng u chu k 0Li nh, khng lm khu so

snh b bo ha. Khi b iu chnh gi l c thi gian xc lp hu hn, hay l b deadbeat. 4.2 M hnh n gin bc nht

Hnh 4-5 S khi chc nng ca h thng iu khin theo dng in.

56

Khi iu khin theo mode in p ta c c hm truyn t t iu khin l h s iu ch d n u ra in p Gvd(s). Khi iu khin theo dng in vn phi c mch vng in p bn ngoi m bo chc nng n nh in p ra khi in p vo thay i v khng b nh hng khi ti c bin ng ln. Nh vy ta thc s cn c mi quan h gia lng t l dng in ic(t) vi in p u ra vo(t) c th thit k c tham s cho cc b iu chnh. H thng iu khin theo dng in vi tn hiu iu khin l ic(t), u ra b iu chnh l h s iu ch d, xc nh thi gian m ca transistor. C th thy rng d khng ch ph thuc vo ic m cn ph thuc vo dng in, dng in li ph thuc vo in p vo v ra. Nh vy mch vng iu chnh dng in thc s bao gm nhiu mch vng trong n, nh minh ha trn hnh 4-5.

Hnh 4-6 Mng ng ct trn s buck converter. Nhc li s buck converter nh trn hnh 4-6. Ta tin hnh trung bnh ha mng ng

ct trong ch dng lin tc. in p u ra mng v dng u vo c gi tr trung bnh l:

2 1

1 2

v t d t v t

i t d t i t

(4.20)

Cc gi tr trung bnh u tnh theo chu k Ts nn n gin ta b qua k hiu ny trong cc gi tr tring bnh trong ngoc.

Gi s dng i2(t) c gi rt gn dng t ic(t), c th vit: 2 ci t i t (4.21)

T (4.20), (4.21) c th loi d(t) ra:

2

11

c c

v ti t d t i t i t

v t (4.22)

Vit li (4.22) di dng quan h cng sut nh sau: 1 1 2 ci t v t v t i t p t (4.23)

57

Phng trnh (4.23) m t mch in cho m hnh buck converter iu khin theo dng in. Mch in tng ng cho trn hnh 4-7.

Hnh 4-7 M hnh trung bnh cho buck converter trong ch dng lin tc. Cho cc tn hiu bin ng nh:

11 1

11 1

22 2

22 2

cc ci t I i t

v t V v t

i t I i t

v t V v t

i t I i t

(4.24)

1 1 21 1 2 ccV v t I i t V v t I i t (4.25) Thnh phn DC bng:

1 1 2 1c cV I V I I DI (4.26)

2 11 2 11 1 1

cc

IV Ii t i t v t v tV V V

(4.27)

Trong (4.27) thay th cc quan h DC V2 = DV1, I2 = V2/R, I1 = DI2, I2 = Ic, ta c:

21 2 1c D Di t Di t v t v tR R

(4.28)

T (4.28) ta c m hnh tn hiu nh cho buck converter, iu khin bng dng in nh th hin trn hnh 4-8. Hnh 4-8 cho thy cng ra mng ng ct th hin l ngun dng, c gi tr ci t . Dng in cng vo c phn lm ba thnh phn. Thnh phn lin quan n ci t th hin bng ngun dng c lp v lin quan n ov t th hin bng ngun dng ph thuc,

58

cn thnh phn lin quan n gv t th hin qua in tr o m V1/I1, th hin c tnh ca ngun thu cng sut u vo.

Hnh 4-8 M hnh tn hiu nh cho buck converter, thu c t tuyn tnh ha s hnh 3-7. Trong (4.28) thay th cc in p v1(t), v2(t) bi cc in p u vo v ra ca s , ta c

1 gv t v t , v2(t) bng in p trn cun cm L cng vi in p u ra vo(t): 2 o cv s v s sLi s (4.29)

Vit li (4.28) di dng ton t nh sau:

21 1 c o gL D Di s D s i s v s v sR R R

(4.30)

Hnh 4-9 Mch in n gin ha cho m hnh buck converter iu khin bng dng in. Hnh 4-9 th hin mch tng ng cho phng trnh (4.30). T mch tng ng c

th thy rng u ra mng ng ct l ngun dng ci s qua cun cm L ti ti. V l ngun dng nn cun cm khng th nh hng ti quan h gia iu khin ci ti in p u ra. Do hm truyn t iu khin n u ra c dng n gin sau:

01

g

ovc v

c

v sG s R

sCi s

(4.31)

59

Nh vy iu khin theo dng in bin buck converter thnh ngun dng. Hnh 3-9 cng ni ln rng hm truyn t in p vo n in p ra bng 0:

0 0co

vg ig

v sG s

v s (4.32)

Phng trnh (4.32) ni ln rng s thay i in p vo vg(t) khng nh hng n in p ra v dng qua cun cm L ch ph thuc vo iu khin ic(t). H thng iu khin s hiu chnh h s iu ch d gi dng qua cun cm khng i, khng ph thuc vo s thay i ca in p vg.

Tin hnh cc th tc tng t, c th a ra c m hnh trung bnh cho boost, buck-boost converter khi iu khin bng dng in, nh th hin trn hnh 4-10.

Hnh 4-10 M hnh trung bnh ca cc b bin i iu khin bng dng in; (a) Boost converter; (b) Buck-

boost converter.

Tin hnh tuyn tnh ha cho m hnh trung bnh hnh 4-10 (a) thu c m hnh tn hiu nh cho boost converter khi iu khin bng dng in nh trn hnh 4-11.

60

Hnh 4-11 M hnh tn hiu nh cho boost converter, iu khin bng dng in.

Theo hnh 4-11 u vo ca mng ng ct ca boost converter th hin bng ngun dng ci , trong khi ca ra th hin l ngun cng sut ph thuc, bng vi cng sut ly vo bi dng ci pha ca vo. Do ngun dng ni tip vi cun cm L nn trong cc hm truyn ca boost converter khng th xut hin im cc do c cun cm. Mng ca ra l ngun cng sut c in tr xoay chiu r2 = R. hm truyn t in p vo n in p ra Ggv(s) khng th bng 0 v gi tr ca ngun cng sut t l thun vi in p vo vg. Hm truyn t iu khin n p u ra Gvc(s) c cha im khng bn phi trc o, ging nh hm truyn khi iu khin bng in p.

T hnh 4-11 ta c in p u ra bng:

2 1' 1 ' ' 2g

o cv ssL Rv s i s D

D R D R sC

(4.33)

T tnh c hm truyn u vo n u ra v iu khin n u ra ca boost converter nh (4.34), (4.35).

2

0

' 12 '1 2

g

ovc v s

c

R sLDv s D RG s sCRi s

(4.34)

01

2 '1 2

c

ovg i s

g

v s DG s sCRv s

(4.35)

4.3 M hnh iu khin bng dng in chnh xc hn Trn hnh 4-5 ta m t s khi chc nng ca h thng iu khin theo dng in,

trong c nhc ti mch vng dng in thc cht cha nhiu mch bn trong lin quan n cc lng phn hi t in p u vo, u ra. Tuy nhin cch xy dng m hnh n gin mc 3.2 cha a ra c cc mi quan h ny v ta gi thit dng trung bnh qua cun cm ng bng dng iu khin ic(t). Di y ta cn tnh ti yu t p mch ca dng iL(t) v tc ng

61

ca tn hiu rng ca ia(t) i vi mch vng iu chnh. Cc yu t ny nh hng n gi tr trung bnh ca dng qua cun cm, nh dng sng th hin trn hnh 4-12.

Hnh 4-12 Xc nh quan h ca dng trung bnh qua cun cm Li t vo ic(t). T dng sng trn hnh 4-12 ta c:

1 2

2 21 2

''2 2'

2 2

s sL c a s

s sc a s

m dT m d Ti t i t m dT d d

m d T m d Ti t m dT

(4.36)

Tuyn tnh ha (4.36) quanh im lm vic cn bng vi vic a vo nhng bin ng nh:

11 1

22 2

LL L

cc c

i t I i t

i t I i t

d t D d t

m t M m t

m t M m t

(4.37)

Trong (4.37) ta phi cho cc nghing m1, m2 bin ng v nghing ph thuc vo bin ng ca ngun u vo v p u ra.

Vi buck converter:

1 2 ;g o ov v vm m

L L (4.38)

Vi boost converter:

62

1 2 ;g g ov v vm mL L

(4.39)

Vi buck-boost converter:

1 2 ;g ov vm mL L

(4.40)

nghing ca tn hiu rng ca coi nh khng thay i ma =Ma. Khi (4.36) tr thnh:

1 21

2 22

2

' '2

sL cL c a s

s

M m t TI i t I i t M T D d t D d t

M m t TD d t

(4.41)

M ngoc (4.41), cho cn bng cc lng tn hiu DC v AC, vi lu DM1 = DM2 ta thu c:

2 2

1 2'

2 2s s

L c a sD T D Ti t i t M T d t m t m t (4.42)

Gii ra (4.42) vi d t ta c:

2 2

1 2'1

2 2s s

c L

a s

D T D Td t i t i t m t m tM T

(4.43)

Quan h (4.43) th hin s ph thuc ca h s iu ch vo cc bin ng ca tn hiu iu khin, dng in, nghing m1, m2, ngha l vo in p nh trong (4.2), (4.3), (4.4), l quan h ta ang cn. Biu din (4.43) di dng:

c L g om g vd t F i t i t F v t F v t (4.44) Trong 1/m a sF M T . Nhng h s Fg, Fv cho ba loi b bin i c bn lit k trong

bng sau: Bng 4-1 Cc thng s ca m hnh b iu chnh dng in theo hnh 4-13.

S Fg Fv Buck 2

2sD T

L 1 22 s

D TL

63

Boost 2 12

sD TL

2'2

sD TL

Buck-boost 2

2sD T

L

2'2

sD TL

T (4.44) xy dng c cu trc ca b iu chnh dng in nh trn hnh 4-13. Cu

trc b iu chnh trn hnh 4-13 th hin u vo l tn hiu t dng in ic(t), tn hiu phn hi o dng qua cun cm iL(t), tn hiu phn hi o in p ra vo(t), tn hiu feedforward t c vg(t), u ra l tn hiu iu khin h s iu ch d. Nh vy nu ta kt hp b iu chnh hnh 4-13 vi cc s mch tng ng iu khin bng in p, ch dng lin tc CCM, xy dng mc 2, ta s c c m hnh h thng iu khin bng dng in chnh xc hn.

Nh mc 2 a ra c cc quan h in p u ra vi iu khin v in p vo qua cc hm truyn Gvd(s), Gvg(s), cng nh dng qua cun cm c th biu din qua hm truyn t iu khin n dng in Gid(s), t in p n dng in Gig(s).

Hnh 4-13 S cu trc ca b iu chnh dng in.

Biu din cc mi quan h nh sau:

o gvd vgv s G s d s G s v s (4.45) L gid igi s G s d s G s v s (4.46)

Vi (4.45), (4.46), kt hp vi cu trc ca b iu khin dng in trn hnh 4-13, s cu trc ca b bin i c th th hin trn hnh 4-14.

64

Hnh 4-14 Cu trc cc b bin i iu khin theo dng in. Kt hp m hnh b iu chnh dng in vi m hnh tng ng ca ba loi b bin

i c bn th hin trn hnh 4-15, 4-16, 4-17.

Hnh 4-15 Cu trc h thng iu khin theo dng in cho buck converter.

65

Hnh 4-16 Cu trc h thng iu khin theo dng in cho boost converter.

Hnh 4-17 Cu trc h thng iu khin theo dng in cho buck-boost converter. c c cc mi quan h theo tn hiu iu khin dng in ic(t), c th s dng cc

php bin i trn s cu trc hnh 4-15 hoc bng cc php bin i i s. Dng bin i i s ta thay (4.46) vo (4.44):

1 m c g oig g vm idFd i G F v F vF G

(4.47)

Thay (4.47) vo (4.45) c c cc quan h in p ra theo tn hiu iu khin dng in, ta c:

66

1 m vdo c g o gig g v vgm idF Gv i G F v F v G v

F G

(4.48)

Gii (4.48) theo in p ra, ta c:

1 1vg m g vd m vd id ig vdm vd

o c g

m id v vd m id v vd

G F F G F G G G GF Gv i vF G F G F G F G

(4.49)

T (4.49) ta c c cc hm truyn mong mun gia u ra vi tn hiu iu khin dng v gia u vo vi u ra:

0 1go m vd

vc vc m id v vd

v s F GG sF G F Gi s

(4.50)

0 1co vg m g vd m vd id ig vd

vg cpm i sg m id v vd

G F F G F G G G Gv sG s

F G F Gv s

(4.51)

Cc biu thc (4.50), (4.51) th hin l cc quan h hm truyn tng qut cho cc b bin i DC-DC c bn trong ch iu khin theo dng in. 4.4 Hm truyn cho cc b bin i c bn iu khin bng dng in

trong ch dng lin tc Trong phn 4.3 ta a ra c biu thc cho hm truyn tng qut i vi cc b bin

i. Kt hp vi cc hm truyn t iu khin theo d n u ra cho cc m hnh dng lin tc mc 2 ta c hm truyn cho tng b bin i khi iu khin theo dng in. y a ra cc kt qu c rt gn nh trong [1], chng 12. 4.4.1 Hm truyn cho buck converter

Hm truyn n gin tnh phn 4.3 c dng:

1

0

ovc

c

ovg

g

v s RG ssRCi s

v sG s

v s

(4.52)

tnh hm truyn chnh xc hn ta phi tnh cc hm truyn t m hnh CCM iu khin theo h s iu ch d nh phn 2.

67

1

1

ovd

vg

VG sD den s

G s Dden s

(4.53)

Trong biu thc mu s bng:

21 Lden s s s LCR

(4.54)

T mch in tng ng trn hnh 4-15, tnh c:

1

1

oid

ig

sRCVG sDR den s

sRCDG sR den s

(4.55)

Thay (4.53), (4.54), (4.55) vo hm truyn tng qut (4.50) v rt gn, ta c hm truyn iu khin theo dng in cho buck converter l:

0 21

cvc

c c c

GG ss s

Q

(4.56)

Trong :

01

o mc

m o m v o

V FG F V F F VDDR D

(4.57)

1 1 m o m v oc F V F F VDR DLC (4.58)

1

1

m o m v o

cm o

F V F F VL DR DQ R

RCF VCDL

(4.59)

Hm truyn t u vo n u ra khi iu khin bng dng in tm c theo (4.51), qua mt s php bin i v rt gn c dng:

68

0 21

gvg cpm

c c c

GG s

s sQ

(4.60)

Vi 2

20

11 21 1

m g o

ag

m o m v o m o m v o

MF F VMDG D DF V F F V F V F F V

DR D DR D

(4.61)

Qc v c ging nh (4.59), (4.58). 4.4.2 Hm truyn cho boost converter

Hm truyn n gin:

21' '2 1 21 1

2 ' 1 2

ovc

c

ovg

g

Lsv s D R D RG s RCi s s

v sG s RCDv s s

(4.62)

Cc hm truyn t m hnh iu khin theo d:

21 ''

1 1'

ovd

vg

LsV D RG sD den s

G sD den s

(4.63)

2

2

12 2'

11'

oid

ig

RCsVG s

D R den s

sRCG s

D R den s

(4.64)

Biu thc trong mu s bng:

22 21 ' 'L LCden s s s

D R D (4.65)

69

M hnh chnh xc hn:

20 21 '

1vc c

c c c

LsD RG s G

s sQ

(4.66)

Vi:

02

2' 1 ' 'o m

cm o m v o

V FG F V F F VDD R D

(4.67)

22' 1 ' '

m o m v oc

F V F F VDD R DLC

(4.68)

221 ' ''

1 '

m o m v o

cm o m v o

F V F F VL D R DQ D R

F V F F VC RCL D

(4.69)

0 21

1gz

vg cpm g

c c c

s

G s Gs s

Q

(4.70)

20

2

11 '2' 1 ' '

m om g o

gm o m v o

F VF F VD RG

F V F F VDD R D

(4.71)

im zero bng:

3 21' 'm o

m g o

gzm v o

F VF F VD R D R

L F F V

(4.72)

4.4.3 Hm truyn cho buck-boost converter Hm truyn n gin:

70

2

22

1' '1 1 1

11 1 1

ovc

c

ovg

g

DLsv s D R D RG sRCDi s s

D

v s DG sRCDv s s

D

(4.73)

Cc hm truyn t m hnh iu khin theo d:

21 ''

1'

ovd

vg

DLsV D RG sDD den sDG sD den s

(4.74)

2

2

11 1'1

'

oid

ig

RCsV D DG sDD R den s

sRCDG sD R den s

(4.75)

Biu thc trong mu s bng:

22 21 ' 'L LCden s s s

D R D (4.76)

M hnh chnh xc hn:

20 21 '

1vc c

c c c

DLsD RG s G

s sQ

(4.77)

Vi:

02

2' 1 ' 'o m

cm o m v o

V FG F V F F VDD R D

(4.78)

71

21' 1 ' '

m o m v oc

F V D F F VDDD R DDLC

(4.79)

211 ' ''

1 '

m o m v o

cm o m v o

F V D F F VL DD R DDQ D RC F V F F V

RCDL D

(4.80)

0 21

1gz

vg cpm g

c c c

s

G s Gs s

Q

(4.81)

0 2 21' 'm o m v o

g

F V F F VDGD D R D

(4.82)

im zero bng: 2

2 2' 1 '

m g om ogz

o m g

F F VF VDD RV LF F D R D

(4.83)

4.5 iu khin theo dng in trong ch dng gin on Trong mc 3 tin hnh m hnh ha b bin i iu khin theo in p trong ch

dng gin on DCM. Trong trung bnh ha mng mch ng ct hai ca cho thy trung bnh ha dng sng ca phn transitor cho mt mch in tun theo nh lut m vi in tr hu dng o Re, trung bnh ha dng sng ca phn it cho mt mch in vi ngun cng sut ph thuc. Di y s cho thy iu khin theo dng in trong ch dng gin on th phn transistor s tr thnh mt ph ti hp th cng sut, cn phn it s tr thnh mt ngun cng sut ph thuc. Tuyn tnh ha mch in ny s thu c m hnh tn hiu nh AC.

Xt s buck-boost converter cho trn hnh 4-18. Dng sng dng in, in p cho trn hnh 4-19.

72

Hnh 4-18 S buck-boost converter v mng mch ng ct.

Hnh 4-19 Dng sng dng in, in p cho s trn hnh 4-18.

73

T hnh 4-19 c th thy gi tr bin dng ipk lin quan n dng iu khin ic v cc thng s ca mch nh sau:

1

1 1

c pk a s

a s

i i m d T

m m d T

(4.84)

Do gii ra vi d1:

1 1c

a s

i td

m m T (4.85)

Gi tr trung bnh ca i1(t) bng din tch phn tam gic bi en q1 trn hnh 4-19 chia cho chu k Ts, do bng:

11 112 pksqi t i t dT

(4.86)

C th thy rng trong khong 0 < t < d1Ts dc ca dng in l m1 nn gi tr dng in nh bng:

1 1pk si m d T (4.87)

T (4.85), (4.86), (4.87) c th biu din gi tr trung bnh 1i t nh sau:

2

21 1 1 1 1

1

1 1 12 2 2

cpk s s

a s

i ti t i t d m T d m T

m m T

(4.88)

Nu rng 11 1gLs

v tdi Lmm v tdt L T

(4.89)

C th vit li (4.88), (4.89) di dng:

22

11 1 1 2

1

1

11 22 1

c sc

sa s s a

Li fi t Lmi t v t m T p tm m T T m

m

(4.90)

Nh vy (4.90) th hin quan h ly vo cng sut ca mt ca mng ng ct. C th gii thch ngha ca cng sut hp th ca vo mt cch khc. l ti thi gian d1Ts dng qua cun cm t gi tr ipk. Nng lng tch ly trong cun cm bng:

74

212 pkW Li (4.91)

Do cng sut trung bnh tch ly trong cun cm bng:

212s pk sp t Wf Li f (4.92) Xt tng t nh vy cng hai, ta thy dng trung bnh u ra bng din tch tam gic

q2 trn hnh 4-19 chia cho chu k Ts.

22 212 pksqi t i t dT

(4.93)

C th thy rng do gi tr trung bnh ca in p trn cun cm phi bng 0 trong ch xc lp nn:

1

2 12

v td t d t

v t (4.94)

Thay (4.94), (4.92) vo (4.93) ta c:

2 2p t

i tv t

(4.95)

Vy cng u ra th hin quan h sau:

2

2 2 2

1

121

c s

a

Li fi t v t p t

mm

(4.96)

Biu thc (4.96) ni ln rng u ra th hin l ngun cng sut, bng vi cng sut hp th pha u vo mng trong khong thi gian d1Ts. Nh vy m hnh CPM-DCM th hin trn hnh 4-20.

75

Hnh 4-20 M hnh CPM-DCM.

Bng l lun tng t c th thu c m hnh dng gin on iu khin theo dng in (iu khin thi im ng m van khi dng nh qua cun cm bng vi dng t ic(t)), ca buck v boost converter nh trn hnh 4-21, a v b. Trong cc m hnh ny phn transistor thay th bi ph ti hp th cng sut, phn it thay th bi ngun pht cng sut, gi tr cng sut biu din bi (4.90) hay (4.96) vi cc gi tr nghing ca dng in m1 tng ng cho mi loi s .

- Buck converter: 1 g ov t v tm L ,

- Boost converter: 1 gv tm L , - Buck-boost converter: 1 gv tm L .

Hnh 4-21 M hnh dng gin on, iu khin theo dng in; (a) Buck converter; (b) Boost converter.

76

Cc quan h trong ch xc lp, tn hiu DC, c th thu c t m hnh 4-20, 4-21 bng cch ngn mch cc cun cm v h mch t in. V d vi s hnh 4-20 cng sut trn ti bng:

2oVPR

(4.97)

Cng sut ny n t ngun cng sut c gi tr bng: 2

2

1

121

c s

a

LI fP

MM

(4.98)

Trong M1, Ma l cc gi tr xc lp ca nghing dng in v rng ca b vo tn hiu dng. Ic l gi tr xc lp ca dng in t.

Gii ra cho Vo ta c:

1

12

1

s

o c

a

RLfV PR I

MM

(4.99)

Tin hnh tuyn tnh ha m hnh trn cc hnh 4-20, 4-21, bng cch a vo cc bin ng nh, nh phng php lm mc 4.3, ta s thu c cc m hnh tn hiu nh. M hnh tn hiu nh th hin trn hnh 4-22.

77

Hnh 4-22 M hnh tn hiu nh CPM-DCM; (a) Buck; (b) Boost; (c) Buck-boost. Cc thng s ca m hnh tm tt li trong bng 4-1, 4-2 sau y. Bng 4-2 M hnh tn hiu nh CPM-DCM, cc thng s ca ca vo.

S g1 f1 r1 Buck

21

1

111 1

a

a

mmM

R M mm

12c

II

1

2

1

111

a

a

mmMR

M mm

Boost 11

MR M

12c

II

2 1

1

2 /21 1

a

a

R

m mMM mMm

78

Buck-boost 0 12c

II

1

2

1

1

1

a

a

mmR

M mm

Bng 4-3 M hnh tn hiu nh CPM-DCM, cc thng s ca ca ra.

S g2 f2 r2 Buck

1

1

211 1

a

a

m M MmM

R M mm

12c

II

1

1

1 1

1 2

a

a

mMm

RmMm

Boost 11

MR M

12c

II

1R MM

Buck-boost 1

1

21

a

a

mmM

R mm

12c

II

R

Cc m hnh tn hiu nh ca s iu khin theo dng in trong ch dng gin

on trn hnh 4-22 rt ging vi m hnh iu khin theo in p dng gin on, v d trn hnh 3-5, ch khc gi tr cc thng s theo bng 4-1, 4-2. C th thu c c hm truyn t th hin c tnh ca s tn s thp t cc m hnh trn hnh 4-22 mt cch gn ng nu coi cun cm b ngn mch. Trong ch dng gin on gi tr in cm L th hin tng i nh nn cc im cc v im zero bn phi trc o lin quan n L u tn s rt cao, gn hoc ln hn tn s ng ct fs, v vy nh hng ca chng n vng tn s thp c th b qua. Khi m hnh tng ng tn hiu nh ca c ba s c dng nh trn hnh 4-23.

Hnh 4-23 Mch in tng ng m hnh tn hiu nh CPM-DCM n gin ha do t L=0 cho cc m hnh

trn hnh 4-22. Theo m hnh trn hnh 4-23 hm truyn t iu khin n in p u ra c dng:

79

00 1go c

vc v sc

p

GvG s si

(4.100)

Trong :

0 2 2

2

1c

p

G f R r

R r C

Hm truyn t in p vo n in p ra c dng:

00 1co g

vc t sg

p

GvG s sv

(4.101)

Trong : 0 2 2gG g R r . Vi mi s c th thay cc thng s t bng 4-1, 4-4 vo (4.101), (4.100) ta s c

c cc hm truyn tng ng. Mt phng n chnh xc hn l xy dng hm truyn trc tip t m hnh trn hnh 4-22, khi s thy c nh hng ca in cm L. 4.6 iu khin theo dng in bng b iu chnh dng c ngng

iu khin theo dng in cn c phng php kh ph bin l dng b iu chnh l b so snh c ngng, trong c hai loi l CRM v b so snh c di ngng khng i. CRM l ch ti hn gia ch CCM v DCM, trong ngng trn ca dng in l nh dng in, bng hai ln dng t trung bnh, cn ngng di bao gi cng l 0.

Trong phn 4.3 ta c m hnh b iu chnh dng in nh th hin li trn hnh 4-24, trong Fm t l nghch vi nghing ca tn hiu rng ca cng vo lng t dng in,

1/m a sF M T . Fg, Fv cho trong bng 4-4. M hnh buck converter iu khin theo dng in th hin li trn hnh 4-25.

80

Hnh 4-24 B iu chnh dng in trong b bin i iu khin theo dng in.

Hnh 4-25 M hnh buck converter iu khin theo dng in. Bng 4-4 Cc thng s ca m hnh trn hnh 4-24.

S Fg Fv Buck 2

2sD T

L 1 22 s

D TL

Boost 2 1

2sD T

L

2'2

sD TL

Buck-boost 2

2sD T

L

2'2

sD TL

Khi lm vic ch ti hn CRM th dng sng dng in c dng nh trn hnh 4-

26. im khc bit y so vi m hnh a ra c phn 4.3 l tn s ng ct thay i, ngha Ts s thay i ty theo dng in tng n dng t ic(t) v gim v 0 cui chu k ng ct nh th no. Nh vy y l dng m hnh c tn s thay i. Mt im khc na l cu trc

81

iu khin theo ngng ny khng dng n tn hiu rng ca vi nghing ma b vo lng t m bo n nh khi h s iu ch D > 0,5 nh khi lm vic vi tn s khng i. Cch tip cn vn ging nh phn 4.3 vi lu cc iu kin ca ch dng ti hn nh trn hnh 4-26. Hnh 4-26 cho thy hon ton khng cn tn hiu rng ca ma na.

Hnh 4-26 Dng sng dng in trong ch CRM. Theo dng sng hnh 4-26, gi tr trung bnh ca dng in bng:

1 2

2 21 2

''2 2'

2 2

s sL c

s sc

m dt m d ti t i t d d

m d t m d ti t

(4.102)

C th thy rng (4.102) ging nh (4.36), ch khc khng cn s hng lin quan n ma v chu k ng ct k hiu bng ch nh ts, thay v ch in v by gi chu k khng cn c nh na. Tin hnh tuyn tnh ha (4.102) bng cch a vo cc bin ng nh:

11 1

22 2

LL L

cc c

s s s

i t I i t

i t I i t

d t D d t

t T t

m t M m t

m t M m t

(4.103)

Ta c:

1 21

2 22

2

' '2

s sL cL c

s s

M m t T tI i t I i t D d t

M m t T tD d t

(4.104)

82

M ngoc (4.104), cho cn bng cc lng tn hiu DC v AC, vi lu DM1 = DM2 ta thu c:

83

5 Chnh lu tch cc 5.1 S chnh lu l tng

Cc s chnh lu thng thng dng it hoc thyristor v my bin p tn s thp l nguyn nhn dn n mo sng hi bc cao THD trn dng xoay chiu u vo v h s cng sut thp. Sng hi bc cao gy nn tn tht pht nng trn cc thit b in t trong mng in, t bin p ngun n cc loi ng c v mt s thit b bn dn khc. Ngoi ra vic s dng my bin p tn s thp c kch thc v trng lng ln l mt tr ngi ln cho vic ng dng rng ri cc thit b in t.

Ngy nay cc b chnh lu tch cc c nghin cu v a vo s dng ang dn thay th hon ton cc chnh lu thng thng, c cc s mt pha v ba pha. Chnh lu tch cc xy dng trn c s cc b bin i DC-DC hay cc b nghch lu DC-AC iu ch PWM, v vy cn gi l chnh lu PWM. Trc khi gii thiu cc s chnh lu tch cc ta cn n khi nim v chnh lu l tng. Chnh lu l tng l s bin i AC-DC nhng i vi ngun xoay chiu n th hin nh mt ph ti thun tr, ngha l c dng u vo hnh sin, lp li dng in p ngun, hn na c h s cng sut bng mt.

Nh vy chnh lu l tng i vi in p xoay chiu th hin nh mt in tr Re, v dng xoay chiu bng:

acace

v ti t

R (5.1)

Tuy nhin in tr Re khng c ngha l c s ta nhit y, ton b cng sut ly vo t pha xoay chiu c chuyn ra u ra mt chiu. Qu trnh iu khin ph thuc vo vic iu chnh in tr Re thng qua tn hiu iu khin vcontrol. Nh vy cng sut trung bnh ly vo t pha xoay chiu bng:

2

rmsav