ANALY~]S A~i:i .DES]GN·OF

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ANALY~]S A~i:i .DES]GN·OF

^{DELTA PWM}

STA1'JCAC_'TO DC CONVERT ERS. . "

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Me m or ial^{cf; . .}

.Uni~mit~or~:~dland ~.,;~.. !.

^Science•

December 198 8

r.

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St.Johii's .-Newfound land Canada

~:'"

.

~erJlis81on ~

..ha"'been granted' to..tJre National'.Libra~y of Canada to:.icrofilm this theds and' 't o .lend or·s e ll -..e c p fee'of th~,film; "

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The"'--author (copyright owner) - ---11a s r e8e r v'ed 0t"h'e r pUblication.,.~ ~ 9h t.s, :a n d

neither the thesis nor

extensive ext;ra<;:'t8.:f r o m i t llIay'be printed'or otherwise 'r e p r od uce d .with o ut hi s/h e r .\.wr itte~'pc:rmiuion.

L' autorhation a 't6 accor'd6e .

~u laca:~~~iot::q~:i~~~t::f:~:

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'ce t t:e·,.t h l\s et·et de-prater ou

~il:~nd~~^d,es.exem~~~,i.rell ~~

L'aut:e~r',(~it:'ulai~~'du"'droi~'

~d' auteur) .sa r6serve :lea\

,llu!: re s:..,.r01t 8depbbl1c_a.tionr;~ .n i lat=, ·116 11-& ni. der.longs", ex t r a ee d e c e l l'e-c! ne

.ecivet"at,re .,'lllpr.iJa6a.OU'·

Ilutre ment reproduits's a ne,_o n' autorlellt'on6,crite•.' " ..'.

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Abstract

. • ~ -' . • . I: . " " ,

Inthis thesis, the modelling, analysis and implementa.tlonofthe_~!e1~amodulation

•"" , .D '1" _'

technique asusedin controlledac·t"o-dcconver ters are'presente d. The'proposed.~..

mod.~i9~ s~~e. £undam~ntally.

^differ:

fr~m CQn~nti~n~,

^PWM

t_~,~ni~.e~_:

by'virtue of'itsaelf-ca:riergenerati~g^{ability.;T hi sintrinsicfeatureprcvldeethe-:}

added

advant~~eB'~£e~ of'im~lemen;'aiio~; :~~ti~u~~s_ conver~~-v01ta~e~~nyof '; ' . ", .~

and

'~~re im~~t~tly

^•.a

.J!,rec~ .cont~~

^onthe.

~in~ h~rcinie~~~tent_~,:

^{.•:_.c _, " • ',;'.: :}

An~~ytic_~.~ode~_i?_~~elo.~~"Y'h~"chprovideskeyinrorm~ti~n^onthe~,ax:>_..., ^::;

imu~'.~o~~e1er:·~witchi~g . fre fl!l' .: 1~~fiOri~

of:

dO~\n~t,_~ar~om~-.~?_.~,he ·

^':'

,.-:-,~~

P'YM8~~tchinginst~~,o~~~m~~atio,~'~~^the,~elta,~o~utator^..par~~~~rll ~8, .· ':~+

also carried out

b"

^meansofpar~etric·v.ariation8.~naelngle-ph eseconverter.

The deltaPWM·technique~is im~lem'ent~dⁱⁿboth s"singIe-phn:;eWid"Uu,ce.:.

phasetr ansist m: bridge

conv~~,~r: :I~ ',e~ch

^case,

't.he"oretic~ ~armonie " imaiysfs'

of, the converterwavefo~----sare'i>~e8~nte"db~edon'*e'di8~eF~u~~l~r'~fQr~If'a~'"

·"~roach. T~e

^{pe; :inentconverterwaveforms}

rexl~cri?~d ~~' tf~ of"~ener""~i~~d

^.

ewitchiug~ionsand the harmonic components are evaluatedusing:anFFT_

",

.

algorithm"Attention hasbeengiventothe design ofjhe'poWe! andlogic drcuit,.

,confor~ing^{to the}d~ltamodul~tor8~itching spe~ifications.Theorerleelresult e, are'

~ubs~~tiated

^byexperimental"

resuits,~co~du~te~"onpr;tot'ype 'singl~p~as'c

andthree-phase...

tr~sjst,?r

converters. " ':'

f. . . "

Perform ance ofthe three-phase:deltamodulatedconverterwi,tb typicaln-L-tI,"' and. dynamicmotorloadsare also considered.Th,e,resultsindicatc~the enhanced

s ;

pe~oJmancc

^{of thedelta'}mo'dul a tcd

~nverter yieldi~g

^{impr oved}

~ctot;

'nci sinu90idal linecurr ents and minimum filteringrequirements,

\

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. .

•

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iii

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...

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¢;":.',.

.

'

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-Acknowledgements

Iwoul d like_/to exPress.

..

my

..

eineere

.

giatitude to Professors,

.

^{. '}

. M

^.

.A.~an

^.

. ·

^and

J.E.Qu akoefo~beirinw¥u~bieguida,s{~^andcon·9tant.BuPR~rttbrough~iI.'^the prep~8tionoftb~sthe:.is.. _ . .• . -', \" . ."

ISP.eci!U:th anks areduetothet~chnicalstafh.tthe Facultyoi Engineering

and .

.-

-A;p~ed ~i~ce £or

^their

~i8t~~

^in.the

e~perjme~t,al)i8.rt o;t~~

^thesis,.:

> .: - ...

""1..,'.

Th.~·hi!lP:

^{of others}

dir~'cily

^''or

i~dir~~tl! in~olv~~<

^withthte

Bt~~r i~.~~~4

acknowledged.

Fin~lly,I'oweitWIto~ydear Iem ily fortheir"patience,'encou ragement1Wd".

• • 'I,.

blessin gs.

.\

{

Contents

Abst r a ct . ,

..

^{~/ '.}

"

^"

Ack~owle~q~~,..

" " Of.FigU:eS

V '

ListofTables 1 Int ro d uctio n

1'.1~Review<!.rPWM Techniques. . 13'-Objcdive3'o{the Ilrese,ntWork

2 Delta·PW¥ Techniqu e' 2.1"Int~dudio~toDelta Moduiation'..

2.1.1'Types of DeltaM9dulat~~s

,ii

.,

10

. '2

12 14 2.1.2

~ ~urvey

^{of Delta}

Modulati~n Si~ategies

ⁱⁿ

Pow~Elettronics

^1'8

2.1.3"")Re~uirementsof DeltarWMConverter

".2.2 g~lta'Modula tionTechnique".' ..:.. . 2.2.·1 DeltaModblated Converter..•'. 2.2.2

,; ."

'Delt a

~odulator.ci;rcuit 'rmpl~entation .\

19 21/.

24 25

66 66,

, . . ' . '. 'I

2.3, OM,SystemModelling,.", .", ._•..••'; "

'.;j; . ". ." . ' ;,

~

'', "

2.3.i

·An~ytia.i 'Model

^.

.I. , . ..• , : :

^{0,''' ' ' ". 33}

2.3.~

^.

De.ternii,~.tion ~lsf't~ng pOint8'

^{" .','"}

~ . :':~

^{.: '",36}

-2.4 Condudin~~arb. .','....•.... .•.•_. 38

' \ . j

3 SinglePh~seDe~ta;P WM,,~onverter . ..:)9

:~.1^},,ualysis of Singlefhase"l~~vert~~

... ...,. .. .: i: .

~

.

,'.?J,, : '.40

~·f.'-,~.in&l~:h.~e~MC<tfv~tiwi~h'fl:SiB,t~ve~~.-'.','.• ','. ','.4&

,3,~,1 y."r.tion~n,,~~m,jCon't"" L ',. : "'.:',.,,.; ,. 411' 3.2.2 yarta tlonmReference Signal Amphtude.'.. ...,,~".'., fi5~ 3.3',

Co~~erter' Petjo~mance\\'. I

^..'.''.:..',"-" :.". •.. 3.4 Exp";;m,nt;UV<rifi"tion'olCo,,,';"t';Pcl6':;"an<a•'.) :"

. ' :, .'',I, : · , ' . ;'

3.4.1 .Implementation 0j'the~gi~Circuit~",',.'..'..._._"

3.4.2

Exp~rimentalRe~~lts

.' ,.'.,.",,••.•. 71--.' 3.4.3 ExperimentalP~orIIl;an~o£ Single Phase Converter .... 80,'. 3.5 Compara tiveEval,,\atio~

6 ( .

D¥ ConverterwithPhaseControlled

Co~verter'^{'. ... .}.,8~

'3.6 ConcludingRemarks•..\.,,/.

" !.. . .

Three PhaseDM convertet

.4.1"

An,"Y'i~

01 Thr".Phase

~M c'onva;'~

With Reeietive .Loed

4.2.:Theoret~c,a1Perfo~mance

, f

^Three~haseOM:Converter '4.3::Implementat ionl#Th'reefhaseOMCo~verter.. . .. . 4.3.1 Power CircuitTopology

4.3,2 B; idge

Selectio~

^"Logic

~

, i

'I

90 91 .:103

<,,' ...107 . ,..107.

....110

.v.:

l\

4.3.3 Lo~Circujt ..

4.4 Experimental

Results.

4.5 C.qncluding Remarks.

. ... .. .. . 1 ,1(.

·,116

·•112 Experh;"e nta l Perfo rm an ce ofDM'Converte~'

.. ...

^{with'R. Lnnd Me-}

torLoads 12 3

\

134

· .1 23 (f

142 .. . ...142 5.1 DM.Convert er with R-LLoad; ... . . •,.

5.1.1 PerfcemenceofConv er terwith R-L Lead .12.7

~.2·De1taModul~tedDCMbtorDrive .. .130

:b."l Sepe.ra.~e1Y~Exci~ed

^DC

¥ot.o~

^{. ... 131}

5.2.2 Basic Equationsor·the"Motor 131

5.3

Perf~nn'~~

^{Characteristicsof}

I?~ Mot'6~

^Drive

.

5.4' ConcludingRemarks . . .' 141

6.. CO~l~lusiOI1S 6.1 Summary ..\

. \'

\

\.

.Q.3 Recommendationsfor Future Wotk. . . .

6.2 Major;;Contributions .

... .. " ,"

^{· .,144.}

....'.145

... REF F;REN C ES

VAPP'ENDIX•,A: Oerivat ion of DMSWit~hingIn st an ces 151 .AP~ENDIX^-B: Co-mp ut e r Programs / 154 .n.i NumerieR\~olutionofDel~aPWM S"';itchingInst a nces•. ... . .154 B.2 SinglePhaSe DM Converter ... ....!'"1,58

/ " .B.2.1·InputCurrentHAtmonic.Analysis. ·.158

vii'

.:

.

' .-1

.-:. '-1',

..I. .... '

,/

.:' .B.2.2 9ut p u t

Vol~age H'an;Ot;U~ Ana1~il

^{:.".. •.. . . ",160}

B.3'I'hr ee Pheee DM Converter ••. .••..•..••" 162 B.3.1 Inp..~tCua:rentHarmonic An'a1ysi...:.:..":. ....:.1~2' B.3.2 OutputVoltageHarmonicAnalYsis. ..•...• •'.. • . •165"-

B.4 Subroutines: .., . . " '..•..167

. ,

^~

.

.DA.l SubrcdtineFFT ." . .• • •• .. .... ...•'.',••'.•167

/ .

.

D.4.2 Subrou tinePWMWAVE.•. ...'.•:.,•• •'.'...168 B.4.3 Su~utineCARRIE~WA'VE •.", .•.~".',~.",.~.•.'.-170 ..-' .B.4~4 SubroutineRECONSTRUcr•:.•:•,..:•.•"•'..•"I ii..,.

~PPi:ND;~ . ^c. Sfh'~i4 D;~gram. ^{: ' "} ·· .~ 1;2

' . . " I'

.APP ENDiX.D:Circ9itPeeemetere .1 7.~."'·

. / '

^/

.

, ',1 '

^f\

.\

./ /

/

' /

A..f'\

A ! '/ .

^I

^"

^,:

·.viii

. ' .

,..

List of- Figures

^I

1.1 PWM strategies (a) Natural Sampling(b ) UniformSampling

1.2 Adaptivecontrol PWM .. ,;.

2.1 Linear delta

m,odul~tors: (~)

^single

~tegrli.tor ~M

^(b).sigmaDM

-..rt'-

16 17

22

26

27 I

....

·28

,

^t-

34

\c) exponentialDM. _{" ','}."',,. 2.2'(~)Asyncb'ronous.DM(b) Adaptive DM .. . . .. . • . . . 2.3 Rectangular wavedelta modu lation:{a} schematic of encoder (b)

typical

wa~eforms of

^the

~~dulation pr~ess

^:

~.

^{'.-: ..}

2.4.Schematicdiagram ofthe modified delta modulatorwith esymmet-

....

~hyst~reliis '

^{/ .}

2.5 Graphical illustration'::'rthe DMtechn ique forconverters . . ..'i 2.6 ApracticalDMcircuit[0'pWd~iogsinglephase1t~hingsignals 2.7·Outp utof deltamodulator over'successives\Yitchin~interval e . . .

~h , Singl~

^{ph ase DM}

~onvert~r

(a) Bchemati; of converter (b) typical wavefo~~!ora teBiBtive lo~" ." " " ,',' /:-"\',.'. . .'. 41 3;2'Graphical illustra tiori'for defining converter waveformsin,terms'of

\ -

general switching functions 43

ix

,3,3 (A)Simulatedco~verter wa~eforms: V.=.5 pu: switchingfre- ',,' , quency=1kHz,(a)outpu t Voltage(b)input current ,,~" ,~.^'46

3,3'(B)Si~ulated converte~ w~veforms:~.^=.5pu, switching£requ~ncy

=1.5 kHz,(a) out put,voltage(~). in~utc~nt,, .'. :,'.:;'. .:47' 3.4 Simula tedi~putline curren tspectr umofsinglephaseDM

eon'·

v~rter,

^A,=:.5V','An

=

.5V,V_R=·2.5V(a)

paramet~r

^{r =,,2}

p~,,'

^.

(b) peremeterr

=

.1p~, ,... .^{t'•" '"•,,•• •,,. ...... ,} 3.4

continu~:

^(c)

p~ameter r

^=.075pu

(d)

'parameter.,.:

=.O.5~u ,

^"

3.5 (A)

Va.ri~tion

ⁱⁿ

ri~~le'frequeney with'param~ter"r ~ incl.epeid~nt

variable',. , .". , ,,. ,,',,,,' ,',_.,' , : , , , . ,3.5, ,(B)Inp~tcurr~htharmonle order asefunctionofparamet~r;.^'",:

3.6 Simula~edinputlinecurrentepe ct r urnof 'Single phaseDMccn-

verte r.

t:J., =

.5V,A~

=

.5V,'"='.2 pu(a)parameter

V

R=·lY(b) /.

parameterVR=2V 56

3.6 eontimied:.Jc)parameterV~⁼3V (d)parameterVR=3.~V 57

'v . . . . .

3.7 Ripplefrequencyas'afunctfonofreferencesignal amplitude. 58

, , " , '('

3.8 Nonpalized A settingsrequir ed tocontroloutput voltage .'61 3-.9 Number of

commlitation~ pe~

^eyeL:

~er~us. q.~e;'."ge. o~tput

^{volt age}

,.',,., '~,., 61 3.10In put power factor as

'a'fu~ctiol)

of

a~ernge OU:tp'u~

voljage

'~ith -r-

as

~

parameter (singlephase'DM

c~nvcrter)

^{.' ..., 62 ",.:'} 3,11Disto rtion Iactoraa a Iunction ofaverage out pu t~olt~ge·w\ih.,.M'

a parameter(singlephaseOM converter)

...

\

".

(0'

, r

.-.' 67

3.14

BI~~iagr~

^DClogie-cirC1;1it for

8i~gi; ph~LlM

^converter'.

6~

^•

3.15 Timingdiagr~'ofsi"ngle phaseOMlogic circuit-. .69

3.16 Expe rimental~i1iogr~~jlll;Jlftratiog^{keywaveformsof delremod-}

ulator

(bMef

^{en 60Hz.}

op;"'ati~n). ··~- .=

^1.5V

p~ak.

^tJ.p

⁼

^An'•.

=.5V. :.;.', : ".~ ~.: " :. 70

"I..3.17.

Ex'~e;imcntal

^oscillogram s'o(

~¥tgle ~h~

^{OMconverter:Output}

•j.'

voltngctuldou~~I;t curr~twaveCorm8 ·:

^{.."; . . ,", . 72'}

3.18Expctimentalosdllpgramsofsinglephase

OM

l:Oo vcrte r:Irput '•.

curr~~t "'(avero~ms~ .

^{'/ ..', :....•": •. .": ....'... 1S}

3,.19~~m~talosCillograJl!Sofsi~gle^phU;eDMconver te r:l0I!ut c:ur'renthermouiespectra'•:" :.:.. , " 78. 3.20&mparl!!On ofpower:actor

~.UB·a.":era~e

^output.,.voltage for phase.

controlledbridgeeonverter,andDMconverter'.';. B:i

'I. . ,... . . -

~.21Compl'lrisono~ displac~ent

fa;\or

~uso;er~e.~~put^vOltage . .forphasecontrolledbridge·eoh~er·M.d~Mconverter", ,.!•• 86 3.22Distort ion factoras'afunc.ti.on ofaverage"outputvoltageforph~

;;,

.<$ '

" .

•

3.12Di8plllCC.men~^{factor u a}~nction'^of_av~age^output~oltake^with'

T &8ap~ameter (.iiiglephase OM09overter).

3.13SingleP,hase tran sistor'OM converter...'.•. .

controlledand

DM

convertersy~~ems : •." ••• .,. 4.1' Gcrt'cralthreeph~bridg econv~rtcr'topology.

4.2.·,Typicalweve formaoftli~,phaSeDM converter (a)outputvoltage (b)inputcurre n.tofone phase

xi

"

64

87 92

93

,,;,.\.' ; '.

. .

^.

.4:3 Simulatedthree phaseOMco~ver~^waveConns~~lwitehi.ng·rri- -quen cy

=

^{1.8 kHz:}V.'=0.3pu;(a)outputvoltag e (b)inputcurren t 96 4.4 Simul ated threephaseOM

con~rter

waveforD1Jl

for~tching ~ "

q~ency^{=1.8kHt :V.'=O.Spu;(a)output}voltage (b)inputcurtcnt 07 4.5 Simula tedt~eephaseOMco.p.v6rterwavelonnl forlwit<:hingIre-

,quency

=

1.~kHz:l'.=0.7I'" ;(a) output voltage (b)inpu t curren t'98 4.6 Theoret.ic~^har910nic~Peetra^{ofthree phaseOM'converter}f~r

switchin gfrequ ency=1.8 kHz:,~

=

O.~pu;(a )ou tput_vo.l~age f

..

"

4.1,Theore tical harmonic spectraofthreephaseDMconverte rfor swit chingfreq ue ncy=1,8 .kHz:.Vo=

O .S

pu;(a)

ot.it~ut

^voltage

.(b)inp ut'current,, , . . ,., •.,,...,.". .',•.. ..,,'.100

, . . . ' ..

4.8 TheQreticalhar monic spectraofthreephaseDMconverte rfor switching frequency=.1.8kHz:

v.. "'"

^{0.7pUi(a)outpu t}volt~e

(b) inputcurrent ,•... ... .•,101

I 4.9 .Inputpowerfactor&I.a.function of average outp u tvoltage (thr«- r.

i

•

(b)i1w ut current,,,,•,, ,,: ' . , . ....•.. ..., 99

"

phaseDMconverter).:.,., .•.•... ,.. . .. 4.10DistortionfactorM

-

a function, of averageoutp u t voltage(three.

phaseDMconverter) -. ....•. .,. ,..•. . . . ... . 104

105, 4.11Displac ementfactor as afunctionof;v~rageou tputvoltage(three

phaseDMconverter)

! , , , . , ,

,.106

4,12Threeph aseOMtransistorbridgeconfiguration,

xii

, ,.:,lOS'

4.13- Selectionoftr.~js~rconductionintervals: (8.)Line to.neutra.,l referencevoltages(b)lineto line refer ence voltages(c)transistor switchingsequence (d)statesofthe three phases~!1rcevolt ages ..112 ,4.14 Timing diagramofthe Intermediate sign als:(a ) command eignala

(b)intermediate transistor signals 4.15Block diagramof threephase logiccircuit

113 ...115~

4.16(a )Exp erimcntalthree~hase delim~dUlatorsWitchi~.gwaveforms. . (b)Command signals to identify ates of the supply voltages ...117 4.16(c)Inter media te~atingsign~s'~ }PMtransistorbasedrivesign als118 4.17Exp~rlm·cntal·w8.~eformsofthree phase OM converter{orVI> "'"0.3

pu; (a).outputvolt age' (b ) input·line current. . . 119 4.18Ex.;eri·mentelwaveforms of

thr~ p~ke

DM conve rterfQiVI>',=0.7

pu; (a) output voltage (b).inputline~un·ent . 129c::

/4.19 Experimental input line currentharmonic spectrumof three phase

DM'converter.. .. . . .121

:).1 Threeph aseDM converterconJigure.tio~withfreewheelingdiode . 125 5.2 Typical outp utvoltage waveformof threephaseOMconver terwith

R-Lloa d .

5.3 Experimentaloscillograrnsof threephaseDM converterwithR-

C

Iced(a)'Outp u t current,we.~erorm^,(b)e~rrespondinghar~oni~_.

I spectrum . .128

5,4

Exp;rim~ntal os'cillogr~s

of three ph'aseDM converter;ith

R-L '

load (a)'inp uteurte~twavef~nn(b) correspondinglinehar~onic spectr um

.

~.

j

xiii

_ .

..129

\."

" . .\ .,:.:

^..

~

^{''': ..:.J}

. .

'

.

:-:~

'

..

tiC"'."';':< , '•.•.. --",..,""

v

5.5 Threeph~

DM m otor

drivelI;St em•

.r ,', . .',. .. . . .

132.:

~rques~ cb~aet~~tiCs^{of 1/4·Hp",}di:·~tor controll~d^{by ..: '.}

three phase DMconverter.. ..••..••~'.~•. • '.' ••.. •\35 ;.

5.7 Power"facto rasafunction of motorspeed{experimental':esults)",13G 5.8

Di5~rt.ion raC~

^asa.

fu~tn

^or

m?tor .~ (~inent~ result~)137

5.9 Displacement factoras a fundionpCmotorspeed (experimen t ll1 . . results) .' :',... •.,...• . • • . •: ~.'138

·5.1~

Experiment al

oscill~grams-~h~'ec

^{phase DMconver terwithmotor .}

.\load:(a)ermetcrecurre nt'wavefo'rm(b),.corr espondingharmoni~..:

spectrum .<:>: :., ~." "._~..139 5.10cont inued:(e)inpu tcurrentofone phase (d)coriPl Pon,ding Iinc",

har'm~ruc l~ctrUm^{.•" ', '''- ','} 140

I

~

xiv '0

0'·'

."(;.2

. .

-.t.

~

·' '.

.,

List of Tables J \ c

3.1 Experi mental frequencyepeereeandcalculated performancepa-

~amctCI"8o.~9.ingle pheeeDMcon'f'terf~rT=.2pu ,,,,,.',. 80 Ex,p~rimenta1frequency6pectr~and~!~ula.ted per~~~c~ .po.-. ramct~r6ofsingle'phase J;>M converterfor '"

=

.1 pu;'.. . .",.. •81

3.3.Experimentalfrequency spectr a andcalculated performancepe-.

ram~tersofeinglep~Me,:DMconverter ferT=.075pu. .''':...,82

.'

r

r---. /' v

',"

l. . hapter 1

ntroduction.

:.•low operating p'ower

fac.~~ .(eSpe~ia.lly at.lig'ht l~a)'

⁾

;•gener ationof loworder harmonics in theeclinecur rent

ana

'~-- output.

timum perfcrrneace

~~ievable

by f.<ilseWi,dt h

~oduiatio~ (P~M)

techni.q\lel;l .h revolutloni aedtheReIdofstati~)ac"todcconverters:,Implementatiqn of .

,~ e:s~ 'teclpliqU~"~been ltilitatei ~y

^{the adventof}

P(l~.~ tr~~i~t.or8 :'Oft'~,r-.

i J

^g

~~tstan:di~g'eh~e:Cte;isti~

^of

'hi~'po~~~

^{han dling}

capabilitie8.~fMt ^Bwnching

Jd

~oat

significantly,

~/1e

^'ab:enceof

c~mmutation'

^circuitryin

~nverter .io~l~.

I ' . " :

. giles.Come;uen~IY,,conv~nti~nal t~:tor.based.C9~xerter.s^are~adUnllY~cing Areplacedbysolid statePW. controlled transilltor-ecnvert era.

J

\Traditionalphaseangle contro lled

conver'ter6'pro~e,d

particularly

att'ra'c~.ivc d~e ~

^the

inher~t

ruggedness,simplicity,iow

mainten~ce'

^and;ease

~£. ~;Urol

I

aIfordedbythenaturalcommutatio~of thyristors ,Hcwevcr.theyhev,un1~.ir- able prop erties

and

i~pose^certaindisadvantagesonth~power ne t wor:The'two

~i~f

^demerits

~f

^{theseconvertefaare:}

y .

r.· .

'1

. F"""':'

\

.2

.Moreover.IStheoutpu tvoltage is decreased.theinput

~

^{factordeer• •}

necessit a t iD,!I;the^Besour cetosup plyreeetbepower.The harmon icsgenera ted

. , .

^{. "}

tendtopollutethepower network and cau.seinterference't~th~her~uiprnentin doseproximity.Inde drives, theripplecausesoverheating andageneral derati

ns

of themo

. .

tor. ~ .

To'compenset e~epoo rperf o rmanceand.en hancethecon~ionefficiency, variousmethod s havebeenprcpoeed.Principalschemes'(or powerfactorimprove- rncni include;

1.Re~ti~e cOmpen8Rtio~

.r..,2.MultiphlU!erec(iRcRtion

4.PW~tech nlquee

1.ReactiveCompen&ation:.~1.2J

B~kauy.

^this

m~hod

^isa

lil~n~'a~proacb, ~tilizinll shunt~nduetor'

ca.t>acitor' (LC) filten.1theacside~d:'a·smoothi~. ructorin~es.attheoutp utde stage,..T~e L~fil~erlOcated at th ehar.m0niclOu~ceis{un ed lo resonance,a t_lowI ordercharaeteri~tic h~moniCll.T~~filterserves asa,lowimpedancepath}o r the harmoni c current'toflow,'virtual ly eliminatingtheirpresence in the,acsyst em,. .

~lthol,1gh th~ sch~~c ~eSU1t8

ⁱⁿ

~. de~te improve~ent

^{in the';urre ntwaveform,}

./ it bes the'

f~Uo;ing di~ad~t~ges: ·

⁽¹⁾

~

^{se parate}

filt~r

isre qu iredforevery"m ajor .h~.oniccomponent,or~,tematiV~y,.continuouittun~gis css;ntialtoelimin~te trou~l~omebermcnic'ordere, (2)-duetothel ergemagnit u deofcurrentand low

... .. .. ,

~

.. .

".:: ^,.:/;:

" -:' , . : .. . ..

^'

.';!

. '. I

...

"'. .' .

----. . ^{.. '}

^".

^{". '}

hannQllie..omponen~a,~&.e.8izediJ:duclotsaridcap !lcitorJare.~uired,(3)~he . ;filtereausesVf!ltagefi~et~tiotul,end(4)it

resuila

ininae~d^loeee.

2.

M~lt.iph~e Re~tiftcatiol1;

^(2.3}

"Sincc"han:no mccurre"ntiareafunctionofcon verterpui~,improvementinpower

fact orcanbeobtafned by increasingthenumberofou tput

~ub-:'"

^In-.g:Uera1,

an

"n; 'ulse,cof:l.V:rter

ge~~a~

hJl"lloclc compo nents

o~

^ord;ra

n~ ^{% 1.,}

^{where.kia. .}

Myinteger. Asfor example.asixpulse converlercontainsharmonicsof~rderl ,

~jll.

^7CII,

l~th,

^13:\.:'"'andccrreepcndlnglr;,8.twelvepulse

,c~nver.te~

^is'

chnract~r-

ieed

by

^{n» ,}13'11,23111;25cll,.'••h'~monicorde rs.-.This procedu re,uhin g a higher! numberofphasesfo rlow'orderharmo niccancel'lation

i.

ref:rredto88

phll8~ mui .·

~ '

.

. \

. ' " .

-

::

\

•tiplic ation: Multiph ase rectificationiarestrlct e dtohig h~",:,erec todeconverte r?

l'uch88

iu

gh:voll11gede

~r~.nU~ion(HYDe)

ayetemawhere

th~ ~t

^of

~djtion~

.powerappu atutandcompl~ ~tryarejustified,

.

^,

3.Se quenti".l~ntrol:14,5) ,

Improvement

in

power factorisachie vedby~ng~wo conve~rbrid~eaand usi~gsequent.ial~~rol.Inthisp~,DoeI;>rid~e^ismaint~nedinfull·advance (re::tifying)orfllli

r~tard

(in verting) and the d,her"

brid&~·

^is

c.ootn:l1~.

^Since

oneconverter operat.es.88adiod ebrldge.fbecaaesde

conn~tion simul~tce

^asemi

.,co.nverterhi.lboththemotorin~^lISwellsstheregen.er atingmodell>~esultingⁱⁿ

an.i~p~vernentindiaplecement ang le.T~esequent i:ucont rolmethodiscorn-"

pliceted,expensiveandonly,p~~in1lyeffccti v e" andhcncei~hasfounlllimitt:ld

uses.

r ...

'.':-'

"

(~

^.

"-:.;..:.

4.PWMTec hnique s:

•Unitydispl"c~entfllctor

.. f

•Highop~ratrn~powerract~r

Theline'c:omm.utationmethod offenlittleflexibili tyillcontrollin~"t.hyristor switch-, ingduetothc'natural commutatioDof.thyristors bylineVoltages::and subsequent coodu dionofthyristorll ondiffen-ntphaseS.Hence,thephaseangle controltech·'

~quc^ismoreorl~-resirided^astheonly~tro)parame~ill^{thyristorecm-en} inlllant s.with_tum-off.dictatedbyconverteroper~tio~. ^Incont rast,theforced commutationpri nciple'all~s^thyristorcommuta tion~t^{anydesiredinstantby} proVi_·ding_. each't fayrillto r_' with

it~ own com~utation drcui~.

_,^{InotherWor ds,}_{. /}

~U~

We'offorced commuta.tionincr easesthe versatilityorthe convert erand permits 'a'dlrect

co~ol

^orthyr iljtorIlwi tch ingtoimprove'perfcemenee.^{I ' ,}

" '.' ". 'f ..... , «. :

'Initially,contro lschem~inCO£]l(?iatio!:rorCedeommutetlorawerebased on

,a'singlepulseappfoach~Ilynirnetricall y:trigg er'thyristorpeire'perfialfcycle.' Variou ssingle"pulsecontrol,8ch~'havebeen';por t ed

in

theliterat ure

I S-

"1}

~d; m~e~,

^when

~' in CODjun~t~

^wit.h

~e

^{aI+ entioned}

sc~..

^{- \}

resultedinageneralim proVement.inconverler.performari ce.Howeer,itwas

aoaD

~~z.cd'~~maximum powerfactoTand~uctionⁱⁿioworder

h r cs

^~d"

beachievedb)'lwin!:multiplepulsesperhal!cycle.This openedthe ave nuefor , "'\"..

.pw{l_{, •} teclmi'que'1!I, wherethyristorm_I tehingsare governed_" by

certai~modul~ioD

_{, \}

lawssuetthatthe'ecwaveformcloselyresemble sa sinusOid'

PWM

techn~~~

ha vPgainedconsiderable attt:llti'o;11':l

~'nt y~du~

^tothe, ."., optimumperforni~ceattainablewith,asimpleco~vertertopol~gy,:~lesaJ~enf features of"PWMcontrolledac/dcconverterarc: ! '

. l

i

1 ·

\ ..:

",

' . ~-,.:.' ,.'....\'.

"

•Control1abilit~,..

•Reduced filt er size Limitat.ionsoftheprocess are:

•Complex eocteolcircuiu.

.,.' . 'l I, ''''f

./•Auxiliiuycommutet.icncircu'its \

, ' I

.•Incre8.'led1os~csdueto,high. switchingfrequency

.

"" \ ,, ,

1:1 .R evie w of PWM-Thc hp.iq u es

V an,

ue

';"';'0£ PWM'ech~;,u'B'ex;.' L d

^eonbe

"l!g~,;,oo

^..'

1.N~turalSampling 2.U~orfnSampling 3.6pfi~aI

P W1.f

and 4.-Ad aptive control PW M

'/...

"

. '

•

1.Natu r alSam.pling:

Inthena.tural sampling~cltniqueas shownjnFig .1;1(8.),t~,e,ilwitching'point~

are determi nedbythecro~singsofthe modulatingwavefonn, typicallya sine wave. ead anis oscelestriangle carrier wa ve.Th isteehniqti~.^mostco~monly^{rererr ed} toasSi~usoiaa1'PWM[7 -

. 9r.

hasthemodulatedwavcform containi ng harmonlea / as afundion~fthe'freque ncyrati o . Thefrequenc y ratio or'modulationindexis

2;

Uniro~mSRlIlp ling:

..1

..

r

defined as thera t io~fthe carrierfrequen.cy

to

mod ulating frequency.Thehi~er thefrequencyratio, the more distant thedominantharmonics are fromth e £un- damcntal component.

A~other ver8r~n

^{of the}

carrie~

^modulatedrwttechnique described~bove.uses a tJjan gularwave and a..,onstant derefere nce waveform.

Inthis ease,'~8tionin the delevelcontrolsthepulsewidths.Similar tothe Sinu!!Oida:IPWM,~ethd~~the harmoiu'ccontentis afunctionofthetriangular wave frequency[10].:'Highcarrierfrequency caus esthe dominantharmonicsto

. . .

eppcarin the upperfrequency spectru:n./~

/

1;hisPW_M'technique

..

Isbaaed on

.

a.sampl;andhold

^.

principle,^/ withthe

^.

modulating^.~

"(ave'repr~n~ed.by piecewiseline~eegrn ents,TheuniformsaIn pling a p p roach as ehownIn Fig.1.1(b),is essentially aderiVativeof thenat,ur~sam pling precess,"

withthecontinuoussine'waver~placedbyanequivalentsteppedversion .Ithas .the~dvantage'th a tthesam pling pulse canbemedesymmet rical aboutthetrough'~

of thecarrier.This result s inasignificant.reduct ionoflow':equency harmonics andelim ina'tion ofsubh~onic8atnon-in teger frequencyratios.Thetechniqu.!!'"

is particularlysu it able for microprocessorimplemen tation .

3. Opti malPWM:·

r

OptimalPW¥strategies,fCb~d·onthem~nimizationofcer~aincrit e.ria[11;i 2.J;

for:~fUllple'iliminationorminimization ofp.art icular harmonics,.haimoni ccur- rent distortion,peak current..etc.Asopposedto thenatural or uniform sampling methods, optimalPWMtechniquesrequireth~PWMwaveform to bed~fineda priori inte rmsofthe desired switchinginstancesandfollowed by their determluc-.

+.

.

^',

(a )

(.

+ v

/

. . (

-v

'-'"

SA"".'O' CARRIERWAVE

.f\ WAVE

(b )

_{I -}

~' °1\ A

~

tr 1\/

~\ II

;

--:.::-.

Figu re1.1:yWMstra tegies (a)Natura lSAmpling(b)UniforlllSml;lplin p;.

, J

I

\

I,

,

"

O~L!L':"""_M-=2.-_--""""",,....>..:>;

...

t

. v

a -v

-

~

c-

~

.

^{L - L -.}

PWM SIGNAL

Figure1.2;Ada pt ivecon trol PWM

\

;....-1-,.

\

/ ,

--tion through numerical teehnlquea,OptimalPWM techniques are

.

-computational

.

in!ep.siveandreq uirededicatedmicroproc~s^forBuc~ulin{plcrilenta~ion. ^. 4.AdaptiveCont r o lPWM:

_ .~rlnciple, ad&ptiv~^PWMt~chniq~es^utilizea "bang. bang" hyatetcsiscontro l approach to'~inimize^{a desired}Bi~al^{(uBuallyan errorsignal)with ineertnin}

_. ,, ' . .- . f . .,

critical limits.Inthisappro~h.MshownFig. l.2~'the.switchingins~anecsare inttiosically det enn in ed

.

^{\- -} -

by

^theintersection of the err or

.

^" slgrialwiththe

uppc~

^{; /-""}

andlower hyeeereeie boundarie;" For a_8inu~ojdeJrefere nceeiguel,themodulated waveformhas afund amental'frequen cyco~~~nent"equalto thereferenceIre- 'luene;,and-the?oll\iuant1iarmo~ic~^appear~~.ib'~rip~lef/'t'<tuericie~:,T~Crcf~re.

by adj usting thehys t eresislim its,dominanthar moni cs tanbe laterallyshifted towa:9.Sthe higherend ,ot-thefrequency spedrum;·'PhebdaptivePWMtech.~~que has adual ad\-ant"age:(i)itallows ac1~l~pcontrol process, and(2) t;e' Il!?dulatio~pr0'iess inherentlyeli~i~ateslower-order harmonjee.

~

^{hepresentworkutili~~}an edeptfvetontrolPWMteehniqubto,genera te the rtching waveforms for ec to de converters. TIle~r.oP09ed.PWM technique, . refe"edtolIS deltarnodulet jonincom~unic~tion terminology~ ,ha.. 'bee nused extensivelyindigit~signaltransmis~ion.Recently, the modulation.tcch:~iq~e has been 9ueCEi"ssfully incorporated ininvert<;r and ec motordrive applications , "{1l,13- 19J.Howeve r , itsuse incont~011edrectifier applications'hM~notbeen eddrease d. This thesis is directedtowar~8.comprehensivestUdy ofthe delt a modulation technique as applied to ac to dc converters.

.

~

,~

"

10

, ~

1.2 < O b j e c t iv es of the Present Work'

The objectivesofthif> thesisIU"Cto:

1.Investigate the characteristics

.

of the deltamodulationtechniq ueand develop ano.nalyticalmod elt,oaccuratelydescribethemodulatio~process.

2. UndertakeIl.quantitative analysiswith theperspe ct iveof predictingthe perfo rman ce of delt aPWMsingl:-phaseend'tbree-ph ese ec to deconverters.

. ,I

3.Provideexperi ment alresultst~valida tethepredicted result s.

• ,. I' "

Chap~cr2 covers the,essentials .ofthemodulat iontechnique.Ananalytical model ispresentedelongwith'a methodology fordetermini ng theswitchi ngchar- .ucteristicsof the'modulator.

Chapte r3isdevoted'to the study oft~e single--phase~ltaModulated(DM) converter. The procedureforsimulatingthe convert eris explainedand theoretical r~9u~tsofthec.onvcrt:;:~rfonn,fllcewith a.resi~tiveload

are

presen ted .Impl e- men tationaspects ofthe converter are discussedand experimental resul ts are also included. Anequitablecomparison ofthe

pM

converterwith othernoted PWM co~verters,althou gh desirab le;lsbeyond the scopepfthisthesis.However, the lAtter par tofthischaptercomparestheperforman ce crthcDM converterwit h the conventionAl phase anglecontro lledconverter:

IIICh apter4, thethree-p hase DM converte ris stud ied"indetail. The analysis. procedur eforpredic ting converte r performan ceispresented ,Implementa tion~f the three phesel~giccircu itIUJ.d th epower converter topologyarc described, Experim ent alresul ts of theconvert erwithresistivelondsare provided.

11

~...^~..

. I .t

Perform enee ofthe three-ph-:OMconverte rwith pasaiveR·Landmotor .:

loadsis investip;a.tcdinChapter 6.The anal,..ispresentedisbasedoncontinu~

ecrrent paode of operation .Experimental.retlults of a1/4I'aP, 120 volt,demotor areprovided.

'Conclusions an..dsuggestionsfor future work^BUou~linedinChapter 6.

·.... ;...:-:.>'.

I

t

Chapter 2

~,'

Delta PWM Technique

This chapter isdev~tedto the study oft~edelta PWM technique asapplied to/l-Cto de converters,The principleof operetjon,methodof control end an anaJ,yticalmodel

de8cri~n~

the modulationprocess arepresented . At.the outset;

. the fSlpil)':.-oC delle. modulators is intro?uced,leading to the development of the rcct~gular ~~v~delta modulator.A practical circuit to realize the .m0clulatoris presented along with the control scheme usedtovarythe outputvoltage. The delta PWM system is,modelled and a~umericalapproach fordetennining)h~

switchingiost,anees'isprovided.Finally,'inherent features,of the PWM scheme

are

outlined.

·2.1 Intr~duction ^{to Delta} Mud'ulat. ion "

.

,

III cdrnmunication systems,f'b.:e most prominent digital encoding technique ttl. ' .- , continuoussignals is·pulse code modulation (PCM). Several'variant or alternate

·tecllDiqu~

(19,2014ave

b~

proposed, the mosti';llport nnt class

compri~ng

^del;a

modulatio nandallied differentialencodingmethods.

.ClassicalPCM

entail~

the sampling, quantization end coding of an analog .12

..

13

)

. ^.

signal to a series of pulses. Theprocess'is inltiatedby samplingthean.n1~gelgnnl followe~yquantization,in which each sample isrepresc.nt ed byRdiscrete value chosenfrom a fixed number of possible levels.!the quantizedsamples arc then convertedinto a series

of

binarydigitsf~rmjngthecode word. In contraSt"the basicprinciple of differentia!encodingis to quantizeand encode changes in the signal, rather than instantaneoussamplevalues.

In the case of deltamodulation,~singleblnery digitisIPsed todescriM the chang~from o,nesamplevaluetothenex t. Thisdi~itis derived~~ coinparing'~

signal'amplitudeatone samplinginstan t withthe velue obtainedby rcconstruc.t-

"",thesign al fromthepreviousdigits.Hence,deltam~dulationcan bevi~w~d ~, a:~i~pl~type of predictive,quantizingsystemend ia cssent iaily a.I-digit ,(2.1~v~l)

diff~rential.pul~e c~de

^modulationsylite; "

~~ativ~ t~

PCM, delta modulat;on'is

"thesimplestknown methodfor analog Codigitalend digitalto analog conversion.

Thesalient featur esof thedeltamodulationtechnique a;e summo.rizcd {20 - 221

~a highresolutionAIr)inte rface since quantizingaccuracydepends on n single welldefinedstep, not aseries of thresholdlevelsas ill conventional AIDcC?nverters,.

• lowcomplexity resultingin inexpensive implementat ion.

•robustnessto transmissionerrors, nnd

•simple filtering require,?cnts,

In

.

additiontothesefeatures,the modulation^{~ '} technique offcrBthe option of either^{, '\}

-

^,

.

adigit al or analogcircuitimplementation. Thesepromisinguttribu tr..'8ofthc

./ ...

delta modulati ontechnique make ita potenti al eandid t te forpowerelectronic applications.

2.1.1 Types of De lt aMo d ul a tor s

. ^,.

i- f'

I

I r _r

!

3.

~incethedi~co~!. ~Lg~ltamodulati on in' the early1950's ,variousmodifications tothesin~leintegrat or delt a modulat orhave evolved. The familyofdelta mod- ul ator s,fro~abroaderperspecti,ve,can becategorized.int othefollowing three classesas[23].

1.Lineardelta modulat or

2.Asynch ronous deljemodulat~r

\

3.Adap tivedeltamodula tor

1.Lin ear deltamQ~2datOl;

The chiefcomponents'~fa linear delta modularare aquanti zer orhard-limiter , sam ple andholdcircuitryand afilter.Dependingontheconfigur ationofthese clements andthe type of filter employed, various

,

modulatorshave been dcvel-. , oped.Figure 2.1{a) depicts

a:

singleintegra tor delt amodulator(24]inwhich the' filterconsist sof en 'idealintegratorplaced inthefeedbackpath. An alternat e configurationFig...2:1(b),·designated⁸⁸,'~igmadeltamodul::tor.r21,24]^USC9an idcnl.intcgrat or inth~fecdforwar dpathwithunity feedback-closelooparrange- ment. Inthecaseofth~ exponenti~deltamoduiator[23]88shown in Fig. 2.1(c), theideal integratori~replaced by an RC combin ation serving as a low-passfilter.

••Thoughthe

topo~~

^ofeach modulatoris unique;';h cirfutputsare characterized

o by pulses quantized bothin time and amplitude.Hence,from thepowerelectron ic

. ,

!'

viewpoiil~.^{thiselMSofmodulators}i~ad8pt~blefor micropro cessor~on~l.

15

I I

modula t

2. Asynchronousd~ltamodblator .

Asyrichron~:;us^delta'modul at !onschem~^[23]~echaracterizedby'their ou\put' . pulsesquantizedonly inamplitudeand~notintime.Consequently,no satnpli.t:lg proces~e6'^areinvo lved. Thi6clese of mc dulatc rederi vesitsname,~y,;iriueof thenonlinearcharacteristicsof the quentizer,Fig. 2.2(1l.)illustratesatypical

8S;;~n?Us.

^delta

niQ<1~a.tor ~orisi8ting ~r

^ahysteresis'

q~antiaer

^{.and an}

1id~td

integrator.The part icular corifigur a.;ionterin~^Il.9arectMgul~wave'd~'lta

mod-

'uletor{22]

a11~7l co~~i~UOU8

^eri'coding

o~ the

reference signal,

Sin~in ^this

^system',

.e" 'in Corm ation is.

~ntained

^inthevarying-pu lsewid ths ;o'nlY"the z"ero crossingsof the"pulses

~eed

be

tr~smitted. ,

AS,a'result;

88yri~r~no'us d~lta. modula~or8

are ideallysuit~for~a.l~~circuitimpl eme ntation.

3.Adaptivedeltamodulators>

Complexittof t edeltamoduleeorincorporat jng adapt ive schemes

is~fnr

^greater.

than thelinear_designedrasynchron ous_{tcf encode}modula tors._signals

.

Thisisdue to the factthat^.'the

^.

h~viJ;lg .widebandwidthch~acteri8tiC8 andhen improve rcsclurionof the encodedsignal. Various.edepeivceeberace e been proposed,J.l1~tcommonamong~arebased onanoptio'taleo~t~ol

strat~gy

^{such as}tile use of amult ilevel

qu~ntizer)t

multist agedelt a

~odulator

(23J:An adapt ivedelta

~o'd~lator

^us'ing

~ ~ultil~vel qu~ntizer

^{isshown in}

Fig~

112.2(h).The quantizerlevel isinheren~lyselected,by themodulatorand therefore, it can accommoda teab ru ptchangesin the slope of theinp'ut eignal.A multi-

)0•

'st~e en~der, ~nt~s

^a

num~cr

^of

del~8

^modulation

8tages.wher~~eacJ~

^delta

• t:

tit1 "It)

' .,

". :

QUANTIZER

;

. .

^."

.

^~'.

IG SAMPL ER

Q.

) .~ltl

+ ^{. ~}

'.«tr

m(l)

",.

'., ~

£ ,

Fig ure 2,1:LilleR!'(.Ieltl~uiodulato rs:(a)singleintegratorOM(b)slgmaDM(e)

expo nenti al OM g

. ,

.

^"~.,

.

^{.; :}

.. .

,

.. ..

,.

^{xft)'~ etl)}

ffi

^m(tl

+

:,

l..'l

;..

.

^HYSTERESIS

.9.

^{~UANTIZ ER}

J -;

~ .

^SAMPl£R.

x(tJ e(t1 ~s mill

f'

MUlTI·LEVEL.

.Q

a.UAN Tl ZE~

J

Figure2.2:(a)Asynchronous OM (b)Adaptive OM

") r

.~

.;

~~~

..

^..1'

18

mod ulator'e neo des the ba ndlimi tederrorsignalofthepreviou s'deltamod~lator.

Ofthewide~ray of~~eltamodulatorsaY¢lable, the mos tauifable onefor a powerc1ce<.tIon ic·ai;pU"cationisdetermined byfactors8u~hes the power c:onven i0!1 scheme,eitherecto"dc.(red ifier ) orde to ac (inverter)and, theimplementation and controlschemes(microprocessorcbese or analog-base].In invertera~pli­

cationll,the outpu tfre quen cy (eithe rfixed orvariable)alsodict a te s thechoi~

thedelta modulat ionscheme.

2.1 .2 Survey

or

Delt a ModulationStrategiesin PowerElec- ercnice .

Recentl y,th~delta modulationt~chniqu~h85 gained considera bleat~tion^{as a.....}

pot ent ialPW~^scheme~or't:ont~l^ofPower conver ters. Most of);heliter ature on thesubject pertain s tothe.implemenre tionorinvertersand'adjustablespeed acdc!vCll. Char~ctecisticofthese applicationsereout putparameterssuchas variable-vol tage.varlable ,frequency operatiolJorvariable- voltage,coneten r.

freqUency.~pcratiJ whichmust

he afforded

~~

the modulator. ' Ziogll8[131has impl emented a freerunningrectangularwave.delta modulator to controla\olt~gesourceinverter."RJiliman,etel[14,151havemadeuse ofthe in- hcre n tVIf(voltage/ frequenc!)charactecisti~sor the symmetricalhyste resisdelta modu lator tocontrolthe speed of inductionandpermanent-magnetsynchronous .motors.ManiRS,eta.l'11~1have~uggCllted^itsusein currentcontrolofasWit~

moderectifier (SMR),thoughprovisionforcontrol lingthe outputvoltage is not

~ccounted fo~

^{by themodulationcircui t.'Itsuseinun}fntecruptible power'supplies (l! PS).forcontrollingboth therectifierstage aswellasinver ter switchinghasalso been reported117).

--j

.

~ .

.

^/ Kheraluw~et a!J18] haveemployed theSi~adelta~odulatorfor a.reao- nant delinkinverter.The eempleddata nature of thedelt~modulationstrategy .baa been exploited t.')realize the ewitchi c ge atthe zero

cros8ing~~f

^thelink

v~lt

^•.

age.

An optimalcontrol~trategyincorpor ating amultist agedeltamodulat or has .beenrepor ted by~man,etal(p]~~improveth~ per£ormanc~of a.single phase,

inverter.The modulat ionsystem~nsist~of a rectangularw~ve,delta.module-' tor followJd by anacti~efilternetwork,the outp utofwhich~sfedtoan.other rectangu larwa~edelta modulato r.

Altho~ghtheSi~adelta modulatorbaa beenU8~~inreson~t Ii~kinverters, itsapplica tion'in motordrivesisrestrict eddue"to the absence ofaV

If

con'trol. strategy. High samplingfrequ~ncydcm~dedbythedigitalencodingprocess' results in substantial

trarisist~r

switchinglosses.

On

'the otherbend--eberect- angularwave delta modufiito.r, besidesprovidi,ng.the desiredV/f -characterist ic, offeVlgood currenttrackinpbitit y,.Itis, theref? re suited forapplicationssuchee inverters,drives~wellas non-linearcontrol-systems.

#-

2.1.3 Requiremerlts of.Del~a PW~Convert er For PWM control ofa rectifierby the delta modula tiontechnique,themodulator must be instrumentalinprovidingthe following featur es:

~~ontimiouscontrolofthe output~~IJageovertheentireoperatingr!,nge,

•reduceand/oreliminatelower orderharmonics

•minimizeoutputvol~llgeripple

\..

•ease of implementati on.•

•

^\

^."

To meetthe first criterion,itisnecessarytohaveanindir~tcon troloft~epulse widthsof themodulatedpulses such that theratioof "on" pulsesto "off" pulses determinestheout put voltage.'Clearly,the family ofLineardelt amodulators are unable to satisfythis requirem ent due to thefact that the pulsesare~f~etion

'of sampling frequencyanda preset step size.

.Oneap~ro~in'over coming-thlelimitationinLinear deltamodulators is

t o"

adopt adifferent'scheme ofeontr~llingthe;out~utvolta ge.,Rather than-havinga.'.. filter of presetcharaderi8ti~,thetimecQn~tantll.!!8C?-9ateawith'the"on" pulse,~

is

maintain~

^aifferentfrom that-of'the

" off". _pUIs~. CO~gequently,

^.control

of"

the~ut;rl^voltage,is,,-,ch ieved by con tin uously 'changingr6c.tw~ti~e con~tants^".

Needlessto say,

t~e

^{procedu re}

sU'bsta.nti~lY ~plicates th~cuit

implement a- tion ,

Rectan gular wavedelt a mcduletor has theinherentability toy-ackthe. refer-

~ncesiYl:al within awell defined boundary esta blishedbythe hyater osia_thr~hold levels.-Thc modulator can thereforebe usedforeith'~rvoltageor curr en tcontr ol dc~ending'onthe reference9i~al. Anothe;~;'tributeof^{th is}modu lator concern s titcswitch ing frequency.SWit~j~g'frequcncy^andh~nce^harmoniccon t.,:0lcan beechievedin tbreeuniqu eways; (1) byadjustin g the-integ:~torparameters, (2) by changing theam~li~~deofthe reference signal, and (3)bycontr olling the hyst eresis_thres~~ldlevels.

The use of adaptiveschemesforconver terapplication~ is'debat~bleconsider- ,/iug that the mO,dula torisresponsibl eforencodinga well

de~ned

J;linusold nlsign al

I

of constantfrequency.Again,for controlpurp oses, the ad5.ptive scheme must

. .

^'/"

either,mai nt ai nsorc~angesstatescausingthe outp utpulse to similarlymaintain

J , alte rnativepositiveand negativeslo~esof equel magnitudeA..Depen di ng on

(

\ 21

/ .

incorp orat e8hysteresiscompar ator ..l!ndoubted1y,.adaptive deltamcdulatora. providesuperiorperformanceb~tattheexpense

o t

a8ubst lft1.tiall ycom plexcir-

~uit.^The same qualityperfOtit'ance canbeobtainedb;a singlerectan gularwave.

deltamodulatorusing a simple filternetwork .

Inlight oftheargumentspresented,rectapgul~wave delta modul atoris capa;

ble of meeting thecontrolled,rectifier,criteria.The intri nsicfeat ure'b~the'asyn- chronous~odulatOr,is^{classifiedasanadaptivePWMtechniqueasmentioned}

e~lier.~

As 81,lch,.the

~odulator'ser~es

adu8J. puryt.,of

e~co~in~ a

^tyPicalainu-

"

BOid~'refer~ce 8!~

^asW.e.U'M

contr~iiing' th~ outpu~

^{,.roftage,:< '. .}

" ' .

. . .. ' .

2.2 D el t a M odula t ion Technique

Rectangu lar'wave deltamodulationis8.d~fferentialencodingtechnique..The modu la tedpulsesare producedby theinteractionof the-referen cesignal andar locallyreconstru cted signal: As applied in.signalprocessing, therectangulardelta mod ula tionprocess

c~

^be

i1lustr~ted

^withthe Il.;id ofFig.

p . 3

The inputsignal,x(t) ,is eomperedwith the recons tructe d signal"y(t).The differenceis examined by the'comparatorcirc~it.^{In this}system, the comparator consis isr"ofa hysteresisquantizerwithsymmetricalAuantization levels±~.The binarywaveform:,(t)at the outp utofthemodulato rconsis tsofPUI~8of~qual magni tu de±Y.butofvaryingwidths.The pulsesareintf'gTllted in thefeedb ac k pQ,th to establish the car,rierwavefor~,,(t),consistingoflinearsegmentshavin~

the polarityof the'error e(t)defin~dasIx(t)- I/(t)j,the hysteresiscompar8.to~

'\

c.

.

.

..

22

~ ^{' -y}

^{y(lJ' ('(tl}

1ff ^""

^'Zjll)

'I

\

J

^I

. . _Q.

^"

^.

<:

,y

' ~ .,,, ' J!41V ' . . ~ .

^{,tl , .}

· : : a t

Figure 2.3:'Rectangularwavedeltamodul~tio(J:(a)schematic of encoder(b) tYP\cn!wnveformsofflllti1J{Jduh\t ionprocess

,

"

~

-.

/

_{. 23.·}

/

~r

^{changepolarity.}The -closedlooparran gemen t

ens~res

that the carrier'

f~th­

fullytrll.~~^theinput signalandthe modu iat orin turngives au-t p ut informo.tion correspondingtothediffe~till.tionof~hex(D-signal:

.Mathem8.tic~y,t_he sam pled mod ulat edswitchi~gwaveform%;(t)

c an

^beex-

pressed as-\23}

,;(t)~v. L:1i. gn[x(kT. )- u(kT. )]

. ^{. .}

where :'

±L.\ quanpizaticn level

± v. .

^{level of8witch i.Il8}~ulBes

.(2.1)

,(kT.) u(kT.)

~odulll.tingsign al predictedeignalatkT.

sgn .indica~~thesignof[x(kT. } -y(kT. )]

T. samplingtime.

Theequal slopeapproxim ationas illustratedinFig,2.3{b) isimplement edin' anefficie'ntman n erwitha simpledifferentiat ionofthelinear segmentsresul ting inaposit iveor negative pulse ofequal"heigh tQutofvarying width andfrequency.

Thedeltamod ul ati on processisessenti~lIy.conti nuous! providing8.digital repro- sentatio n6fthei~put'signalaslong~theinpu t,signal doesnotchan"tc

n t

nlatc~

greaterthanthe maximumaver age siopeofthecarrier waveform .Ifthl s occurs, the carrierwaveillunabl e

~o

track the referencesignaland-t he modulationproceaa ' fails. :rhephenomenon termedas slope overlo ad(21-241istheiillJiting~IUIC^of th~.~elta m~ulatiQntechni que.Beeau ae themodu latorenco desinform ationcor-

~8pondingto thederivat ive.oft.'l~messagefuncti on,the over lendchnrn.ctc\,istic 8

.... .

1.'·

.'/

24 arc0.{unction of theeiguei slope instead ofthe amplitude. In the absence of an inputelgnal,8.condition commonlyreferredto as the idle channel condition, the modulator outputs aSqUMCwave~jgnflj-illdicntingtheosci11atorynature of the circuit.

The switching frequencyof themodulato~canhecontrolled in threediffer- ent ways: by changingthe amplitude ofth~ r~fetencesignal,by changing the slope of thetri8.ngul~carrier wave or bydinngingthe magnitude of the window widths(±6 quantization

t~~l~).

^Theflexibility offered by the rectangular delta modulationsystem has mEl., it veryo.ttr~.tivefor converterapplications.

2,.2. 1 DeltaMod ulat ed Converter

TheW1Yllchrono~op6-ation of therectallgul~DM circuityieldsthe moduluted.J

pulsesquantized in amplitudewith thepuls~widthstI<;te~inedbythe-positive and nega"tiveslopetransitions in the currier wave. Forrec~ifierimplementation ,itis'necessary to control the output dc voltage viathe modulatedpulses which govern the transistor'on--off'. switchingaction.With a constant frequency mod- ulntillgsignal,theinherent self-carri.er.genera featureof theD~Itechnique allowsII.simplecontrol processfor varying the drthe converter.

-r:hemodifjed.rectangular~ave'delt a modulator shown inFi~.2,4 permits the voltage to be controlledviaWIM-ymmetricnl hysteresis quantizer.Thequan tlzcr thrc~holdlevels (Fig:2.4)or alternately, thedelta window )ridths, designated.6., und.6."'.controlthe outputvoltage s.uchthnt,maintainingt:J., greater ,than t:J...

leeds to no :ncrenscinthe output de level.'Qo~vel'sclY,if6 ..~sgreater than 6, Ute out putvcltegodecreesesr

26

ThesimplecontrolprocessthroughtbeMym.me·~ricGIdellAcontrol(ADO) procedureisgraphically illustrated in Fig. 2.6. In'this case,the modulated switchingpulaeetlM{t)areobt ained bytheinteraction

o r

th~ re{er~ncesineweve vnO) and the.triangularcarrier wavevc(t)generatedinthefeedback path. T1).e carrier isalJow~tooscillatewithinthe'deltawindowdefined

by

^{6., and}

'A

n loca tedabout thereference sinusoid. Wheneverthe'magnit ude of thecarrier wavereachesthe

bo.u~dary

^{ofeitherA"oranitreversesits slopeandthe output}

switchingpulsesaccordinglychangepolarity. Sincethe referenceinput aigna!

"tothe

modulat~r

^{is'Rsinusoidalsignal}

of-fi.~ea

^{frequency,the'}PWM..8wi:ching

sign!;ll generated

at

theotitp~t^{ofthemodulatorhasa}sinusoldelly'~ing^average value.This characteristicfeatureof the modulator,in essence,isth?principle behind PWM~+iques(S.-:-101.which aim toattenuatethe 10;.'~derharmonic components.pr esentintheconverter waveforms.

2.2.2 DeltaModulator Circ u it Ir.np1em,en t ation

Aprac tical circuit whichreeliaeetheDMschemeis shownin Fig.2.6.Com- para torAIc~nfim.11"edasa Schmitttrigger serves as ahysteresis comparat or and outputs pulses of gnitud eproportional to itssr.tur efion;olta ges of+V.and -V•.The sinusriidalrferenceormodulatingwa+:VR(t)is'ppliedt.othe input of compar\~,(.orAIand the car riervc(t ) isgeneratedin thefollowingmanner; when- ever theout putvoltage of Aaexceeds the thresh oldlimitsofCOIlilP8.ratorAllit

, .1 ,'

reversesthej;Q~arityofVM(t)at theout pu t-ofA1. Thisreversesthe slope of vc(t ) attheoutputofA3 •Itforces the carrier wavevc(t) to oecillete around the reference waveformVR(t) at ripplefrequencyf•.

.' 2G

".'':'\

r

,

^{• VIl(I).}

Velt)

H~T ~ --J

,tfjgure2.4:Schelllllticdiagramofthe modifieddelt a modulator with~nctrical

)IYSlCre sis

- .

t

- i

f/

\ '\

! ^{. .} ,

\

/ v.ll)

29

The hysteresis comparator

.

threshoid limits or

. ,

ttltem at ivelytbe delte, window

~idth!ll'lXe'es tab lished by thearms ratio.RtlR~such that:

.~

(2.2)

."'-.

, • ".

~I - V.I,

^(2.3).

The frequency'of the

modulat~

waveform I"

d~te<min~

^{by theRTCT}

oom~in!

^'

t~o~of integrator':42 •The risingand fallingslopes of the carrier wayeare given by:

- '.

where:

·1 .

Mp'= RTCT1+V,1

Mp positiveslopeofvc(l ) M..i1egll.tiveslope ofvc(t) RTGT timeconstan t of integratorA2

(2.')

(2.5)

In the circuit,the ratioRIIR2is set at aconst an t valuegiving~pand.6."di- redly propdrtional to the comperatcr's saturation voltages,Thi,sal1'o~lI.thcADC scheme to beimplementedin an efficient manner bythepertinentpfl.l'nmcte~8

+v,

,

.

and -

v..

By independently controlling

+

V.end-yo,the converter'soutputvolt-

.

^/

age can be controlled over theentirerange of opera tion.Since theslopesof the

,

.

carrier waveformare diree;tlYproportional to the pulse~~gnitudc"(+V, or /'

V ,,;

_th e control schcZ£:issimilar to the dual

inte~~tion

^[251'control process..--

./

30

H~wever,^withtheADC schemee~panding^over't.hecontrol range,particular attentionmustbe giventoth~,elopeov~rloadlimitation of the modulator , In thi scase,slope overl oad occurswhenth~^{slopeofeither}tlie ;ositive or negative seg m ents ofvc(t)islessthanthema."xi~um^{slopeof tbeeeferenceairiusoid. For&.}

constantamplitude 'modula t ingsine wave;tIR(t)=VRi1in(lUt),themax im um slope

.~ '

.

. .

.

and therefor e slopeoverload occurs when'the instantaneous slopesofeitherM~

orM~'goc s below theminimumlimit of 211'"jVR:Methemat.ically,theoondition

Icrs~opeoverload is givenby

forrisi~g 81~peⁱⁿ

voW, }

forIcll 'ingslopeinvc(t)

(2.6)

This sets the limitation on~and M n andconseque~ly"onthetimecon stantof the integrat,orwith+Y.and-V.beingthe controlverieblee.

Anotherfactorwhich bas been taken intoconsiderationin designing thedelta

;.modulato{issynchronizing the carrierwave withthereferencesinusoidalsign al, Fora particulnr'6pandl}. ..setiin-g,^"8.situat ionmay arise wherethefu ndame ntal frequencyofihe carrier wave may deviate from that ofthe referencesinewave, To ensure."synchronization between these"twosignals,the capacitor CT is mo- mentarily snortedto ground'!'t each zero'crossing ofthe referencesign~.This per m its thccepecltort~"discharge, f~rCingthecarrier.wave to besynchroni~ed-/

with thesi.~uBOidalreference,signal. forall6, 8Dd 6" values)·The different,ial encodingprincipleof the delta modulatorresults-Inthe modulatedwaveformbe.

ing'dispiac~d

^{by 90}

degr,~s

with'resp ect io the sinusoidalinput,The

pro~l~m

^is'