Vector Control of Ac Drives

8/13/2019 Vector Control of Ac Drives

1/61

Topic 13: Vector Control of AC Induction

Motors

Spring 2004

ECE 8830 - Electric ri!es


2/61

Introduction

Sc"l"r controlof "c dri!es produces goodste"d# st"te perfor$"nce %ut poor d#n"$icresponse& T'is $"nifests itself in t'e de!i"tion

of "ir g"p flu( lin)"ges fro$ t'eir set !"lues&T'is !"ri"tion occurs in %ot' $"gnitude "ndp'"se&

Vector control*or field oriented control+ offers$ore precise control of "c $otors co$p"redto sc"l"r control& T'e# "re t'erefore used in'ig' perfor$"nce dri!es ,'ere oscill"tions in"ir g"p flu( lin)"ges "re intoler"%le e&g&

ro%otic "ctu"tors centrifuges ser!os etc&


3/61

Introduction (contd)

.'# does !ector control pro!ide superiord#n"$ic perfor$"nce of "c $otorsco$p"red to sc"l"r control /

In sc"l"r control t'ere is "n in'erentcoupling effect %ec"use %ot' torue "ndflu( "re functions of !olt"ge or current

"nd freuenc#& T'is results in sluggis'response "nd is prone to inst"%ilit#%ec"use of t'order '"r$onics& Vectorcontrol decouples t'ese effects&


4/61

Torque Control of DC Motors

T'ere is " close p"r"llel %et,een toruecontrol of " dc $otor "nd !ector control

of "n "c $otor& It is t'erefore useful tore!ie, torue control of " dc $otor%efore stud#ing !ector control of "n "c$otor&


5/61

Torque Control of DC Motors (contd)

A dc $otor '"s " st"tion"r# field structure*,indings or per$"nent $"gnets+ "nd "rot"ting "r$"ture ,inding supplied %# "

co$$ut"tor "nd %rus'es& T'e %"sicstructure "nd field flu( "nd "r$"ture MM"re s'o,n %elo,:


6/61


T'e field flu( f*f+ produced %# fieldcurrent Ifis ort'ogon"l to t'e "r$"ture

flu( "*"+ produced %# t'e "r$"ture

current I"& T'e de!eloped torue Tec"n %e,ritten "s:

ec"use t'e !ectors "re ort'ogon"l t'e#"re decoupled i&e& t'e field current onl#controls t'e field flu( "nd t'e "r$"ture

current onl# controls t'e "r$"ture flu(&

'

e t a f T K I I =


7/61


C $otor-li)e perfor$"nce c"n %e"c'ie!ed ,it' "n induction $otor if t'e$otor control is considered in t'e

s#nc'ronousl# rot"ting reference fr"$e*de-e+ ,'ere t'e sinusoid"l !"ri"%les"ppe"r "s dc u"ntities in ste"d# st"te&

T,o control inputs ids"nd i0sc"n %e used

for " !ector controlled in!erter "s s'o,non t'e ne(t slide&


8/61


.it' !ector control:

ids*induction $otor+ If*dc $otor+

i0s*induction $otor+ I"*dc $otor+T'us torue is gi!en %#:

,'ere is pe") !"lue of sinusoid"l

'e t qs t ds qsrT K i K i i= =

r r

=


9/61


T'is dc $otor-li)e perfor$"nce is onl#possi%le if i0s

4onl# controls i0s"nd does not

"ffect t'e flu( i&e& i0s

"nd ids

"re

ort'ogon"l under "ll oper"ting conditionsof t'e !ector-controlled dri!e&

T'us !ector control s'ould ensure t'e

correct orient"tion "nd eu"lit# of t'eco$$"nd "nd "ctu"l currents&

r


10/61

Equivalent Circuit of Induction Motor

T'e co$ple( de-eeui!"lent circuit of "ninduction $otor is s'o,n in t'e %elo, figure*neglecting rotor le")"ge induct"nce+&


11/61

Equivalent Circuit of Induction

Motor (contd)

Since t'e rotor le")"ge induct"nce '"s%een neglected t'e rotor flu( 5 t'e "ir g"p flu(&

T'e st"tor current !ector Isis t'e su$ of

t'e ids"nd i0s!ectors& T'us t'e st"tor

current $"gnitude is rel"ted to ids"nd

i0s%#:

r

m

sI$

2 2s ds qsI i i= +$


12/61

Phasor Diagrams for Induction Motor

T'e ste"d# st"te p'"sor *or !ector+di"gr"$s for "n induction $otor in t'e de-

e*s#nc'ronousl# rot"ting+ reference fr"$e

"re s'o,n %elo,:


13/61

Phasor Diagrams for Induction Motor

(contd)

T'e rotor flu( !ector is "ligned,it' t'e de"(is "nd t'e "ir g"p !olt"ge

is "ligned ,it' t'e e"(is& T'e ter$in"l

!olt"ge Vsslig'tl# le"ds t'e "ir g"p !olt"ge

%ec"use of t'e !olt"ge drop "cross t'est"tor i$ped"nce& i0scontri%utes re"l po,er

"cross t'e "ir g"p %ut ids

onl# contri%utes

re"cti!e po,er"cross t'e "ir g"p&

( )r m =

mV


14/61

Phasor Diagrams for Induction

Motor (contd)

T'e first figure s'o,s "n incre"se in t'etorue co$ponent of current i0s"nd t'e

second figure s'o,s "n incre"se in t'e flu(

co$ponent of current ids& ec"use of t'eort'ogon"l orient"tion of t'ese co$ponentst'e torue "nd flu( c"n %e controlledindependentl#& 6o,e!er it is necess"r# to

$"int"in t'ese !ector orient"tions under "lloper"ting conditions&

6o, c"n ,e control t'e i0s"nd idsco$ponents

of t'e st"tor current Isindependentl# ,it' t'e

desired orient"tion /


15/61

Principles of Vector Control

T'e %"sic conceptu"l i$ple$ent"tion of!ector control is illustr"ted in t'e %elo,%loc) di"gr"$:

7ote: T'e in!erter is o$itted fro$ t'is di"gr"$&


16/61

Principles of Vector Control (contd)

T'e $otor p'"se currents i" i%"nd ic"re

con!erted to idss"nd i0s

s in t'e st"tion"r#

reference fr"$e& T'ese "re t'en

con!erted to t'e s#nc'ronousl# rot"tingreference fr"$e d- currents ids"nd i0s&

In t'e controller t,o in!erse tr"nsfor$s

"re perfor$ed: 1+ ro$ t'e s#nc'ronous d- to t'e

st"tion"r# d- reference fr"$e

2+ ro$ d4

-4

to "4

%4

c4

&


17/61

Principles of Vector Control (contd)

T'ere "re t,o "ppro"c'es to !ector control:

1+ irect field oriented current control

- 'ere t'e rot"tion "ngle of t'e i0s

e!ector

,it' respect to t'e st"tor flu( 0r9sis %eingdirectl# deter$ined *e&g& %# $e"suring "irg"p flu(+

2+ Indirectfield oriented current control

- 'ere t'e rotor "ngle is %eing $e"suredindirectl# suc' "s %# $e"suring slip speed&


18/61

Direct Vector Control

In direct !ector controlt'e field "ngle isc"lcul"ted %# using ter$in"l !olt"ges "ndcurrent or 6"ll sensors or flu( sense

,indings&

A %loc) di"gr"$ of " direct !ector control

$et'od using " .M !olt"ge-fed in!erteris s'o,n on t'e ne(t slide&


19/61

Direct Vector Control (contd)


20/61


T'e princip"l !ector control p"r"$eters ids4

"nd i0s4 ,'ic' "re dc !"lues in t'e

s#nc'ronousl# rot"ting reference fr"$e

"re con!erted to t'e st"tion"r# referencefr"$e *using t'e !ector rot"tion *V;+%loc)+ %# using t'e unit !ector cose"nd

sine& T'ese st"tion"r# reference fr"$econtrol p"r"$eters idss4"nd i0ss4"re t'enc'"nged to t'e p'"se current co$$"ndsign"ls i"

4 i%4 "nd ic

4,'ic' "re fed to t'e

.M in!erter&


21/61


A flu( control loop is used to precisel#control t'e flu(& Torue control is "c'ie!edt'roug' t'e current i0s

4,'ic' is gener"ted

fro$ t'e speed control loop *,'ic' includes" %ipol"r li$iter t'"t is not s'o,n+& T'etorue c"n %e neg"ti!e ,'ic' ,ill result in "neg"ti!e p'"se orient"tion for i0sin t'e

p'"sor di"gr"$&

6o, do ,e $"int"in ids"nd i0sort'ogon"lit#/

T'is is e(pl"ined in t'e ne(t slide&


22/61



23/61


6ere t'e de-efr"$e is rot"ting "ts#nc'ronous speed e,it' respect to t'est"tion"r# reference fr"$e ds-s "nd "t

"n# point in ti$e t'e "ngul"r position oft'e de"(is ,it' respect to t'e ds"(is is e*5et+&

ro$ t'is p'"sor di"gr"$ ,e c"n ,rite:

"nd cossdr er =

sinsqr er =


24/61


T'us

"nd

T'e cose"nd sinesign"ls in correct

p'"se position "re s'o,n %elo,:

cos

s

dre

r

=

sin

s

qr

e

r

= ( ) ( )

2 2s s

dr qr r = +


25/61


T'ese unit !ector sign"ls ,'en used in t'e!ector rot"tion %loc) c"use idsto $"int"in

orient"tion "long t'e de-"(is "nd t'e i0sorient"tion "long t'e e-"(is&


26/61

ummar! of alient "eatures of

Vector Control

A fe, of t'e s"lient fe"tures of !ectorcontrol "re:

T'e freuenc# eof t'e dri!e is not

controlled *"s in sc"l"r control+& T'e$otor is


27/61

Vector Control (contd)

Tr"nsient response ,ill %e f"st %ec"usetorue control %# i0sdoes not "ffect

flu(&

Vector control "llo,s for speed controlin "ll four u"dr"nts *,it'out"ddition"l control ele$ents+ since

neg"ti!e torue is directl# t")en c"reof in !ector control&


28/61

"lu# Vector Estimation

T'e "ir g"p flu( c"n %e directl# $e"sured in" $"c'ine using speci"ll# fitted se"rc' coilsor 6"ll effect sensors& 6o,e!er t'e drift int'e integr"tor ,it' " se"rc' coil ispro%le$"tic "t !er# lo, freuencies& 6"lleffect sensors tend to %e te$per"ture-

sensiti!e "nd fr"gile&

An "ltern"ti!e "ppro"c' is to $e"sure t'eter$in"l !olt"ge "nd p'"se currents of t'e$"c'ine "nd use t'ese to esti$"te t'e flu(&T'ese tec'niues "re discussed on pp& 3>3-

3>8 of t'e ose te(t&


29/61

Indirect Vector Control

Indirect !ector control is si$il"r to direct!ector control e(cept t'e unit !ectorsign"ls *cose"nd sine+ "re gener"ted in" feedfor,"rd $"nner&

T'e p'"sor di"gr"$ on t'e ne(t slide c"n

%e used to e(pl"in t'e %"sic concept ofindirect !ector control&


30/61

Indirect Vector Control (contd)


31/61


T'e ds-s"(es "re fi(ed on t'e st"tor "ndt'e dr-r"(es "re fi(ed on t'e rotor& T'ede-e"(es "re rot"ting "t s#nc'ronous

speed "nd so t'ere is " slip difference%et,een t'e rotor speed "nd t'es#nc'ronous speed gi!en %#:

Since ,e c"n ,rite:

e r sl

= +e edt =

e r sl

= +


32/61


In order to ensure decoupling %et,een t'est"tor flu( "nd t'e torue t'e torueco$ponent of t'e current i0s s'ould %e

"ligned ,it' t'e e"(is "nd t'e st"tor flu(co$ponent of current ids s'ould %e "ligned

,it' t'e de"(is&

.e c"n use t'e de-"(is "nd e-"(iseui!"lent circuits of t'e $otor *s'o,n ont'e ne(t slide+ to deri!e controle(pressions&


33/61



34/61


T'e rotor circuit eu"tions $"# %e ,ritten "s:

( ) 0dr r dr e r qr d

R i

dt

+ =

( ) 0qr

r qr e r dr

dR i

dt

+ + =


35/61


T'e rotor flu( lin)"ge eu"tions $"# %e,ritten "s:

T'ese eu"tions $"# %e re,ritten "s:

dr r dr m dsL i L i = +

qr r qr m qsL i L i = +

1 mdr dr ds

r r

Li iL L

=

1 mqr qr qs

r r

Li i

L L

=


36/61


Co$%ining t'ese ,it' t'e e"rlier eu"tions"llo,s us to eli$in"te t'e rotor currents,'ic' c"nnot %e directl# o%t"ined& T'e

resulting eu"tions "re:

,'ere &

0dr mr dr r ds sl qr r r

d LRR i

dt L L

+ =

0qr mr

qr r qs sl dr

r r

d LRR i

dt L L

+ + =

sl e r =


37/61


or decoupling control t'e tot"l rotor flu(needs to %e "ligned ,it' t'e de-"(is "nd so,e ,"nt: 0r50 5? d0r@dt 50

If ,e no, su%stitute into t'e pre!iouseu"tions ,e get:

"nd

,'ere '"s %een su%stituted for &

r

r r

m dsr

r

dLL i

R dt

+ =

m r

sl qs

rr

L Ri

L

=

r


38/61


or i$ple$enting t'e indirect !ector controlstr"teg# ,e need to t")e t'ese eu"tionsinto consider"tion "s ,ell "s t'e eu"tion:

7ote:

A const"nt rotor flu( results in t'e eu"tion:

so t'"t t'e rotor flu( is directl# proportion"l

to idsin ste"d# st"te&

m dsr

L i =

e r sl = +


39/61


An i$ple$ent"tion of indirect !ector controlfor 4-u"dr"nt oper"tion is s'o,n %elo,:


40/61


e"tures of t'is i$ple$ent"tion:

iode rectifier front-end ,it' " .Min!erter ,it' " d#n"$ic %r")e in t'e dc

lin)& 6#steresis-%"nd current control&

Speed control loop gener"tes t'e torueco$ponent of current i0s

4&

Const"nt rotor flu( is $"int"ined %# usingt'e desired ids

4&

T'e slip freuenc# sl4is gener"ted fro$

t'e desired i0s4&


41/61


Slip g"in sis gi!en %#:

e"nd e"re gi!en %#:

"nd

T'e incre$ent"l encoder is necess"r#for indirect !ector control %ec"use t'eslip sign"l loc"tes t'e rotor poleposition ,it' respect to t'e dr"(is in "

feedfor,"rd $"nner&

*

*

sl m rs

qs r r

L RK

i L

= =

*

e sl r = + edt =


42/61


If i0s4B0 for neg"ti!e torue p'"sor i0sis

re!ersed "nd sl*"nd sl+ ,ill %e neg"ti!e& T'e speed control r"nge c"n %e e(tended

into t'e field ,e")ening region %#incorpor"ting t'e dotted line p"rt of t'ei$ple$ent"tion *see figure %elo,+& 7ote:Closed loop flu( control is no, reuired&


43/61


6"r$onic content of '#steresis-%"ndcurrent control is not opti$u$& Also"t 'ig'er speeds t'e current controller

,ill s"tur"te in p"rt of t'e c#cle%ec"use of t'e 'ig' %"c) e$f&

S#nc'ronous current controlc"n %e

used to o!erco$e t'ese pro%le$s& Seeose te(t pp& 32-34 for det"ils&


44/61


A dc $otor-li)e electro$ec'"nic"l $odelc"n %e deri!ed for "n ide"l !ector-controlled dri!e using t'e follo,ing

eu"tions:

32 2

me qsr

r

LPT iL

=

r r

m dsr

r

dLL i

R dt

+ =

2 re L

dT T J

P dt

=


45/61


A tr"nsfer function %loc) di"gr"$ iss'o,n %elo,:

7ote: T'e torue Teresponds inst"ntl#

%ut t'e flu( '"s first order del"# *,it'

ti$e const"nt 5Dr@;r+&


46/61


T'e p'#sic"l principle of !ector control c"n%e e(pl"ined $ore cle"rl# ,it' t'e 'elp oft'e %elo, de-eeui!"lent circuits:


47/61


Since ids"nd i0s"re %eing controlled ,e c"n

ide"ll# ignore t'e st"tor-side p"r"$eters&.it' 0r50 under "ll conditions t'e e$fsource on t'e rotor side de-circuitsl0r50&T'is $e"ns t'"t in ste"d# st"te idsflo,s onl#

t'roug' t'e $"gnetiing induct"nce D$ %ut

in t'e tr"nsient c"se is s'"red %# t'e rotorcircuit ,'ose ti$e const"nt 5 Dlr@;r&


48/61


In t'e e-circuit,'en torue is controlled %#i0st'e e$f sldrc'"nges inst"nt"neousl#*%ec"use +& Since 0r50 t'is

e$f c"uses " current *D$@Dr+i0sto flo, t'roug't'e rotor resistor ;r& If Dlris neglected "nd

flu( is const"nt idsis seen to onl# flo,

t'roug' D$"nd i0sonl# flo,s t'roug' t'e rotorside "s desired&

/sl dr m r qs rL R i L =

r


49/61


A serious issue ,it' respect to indirect!ector control is t'"t of slip g"indetuning& T'is is due pri$"ril# to!"ri"tion in rotor resist"nce& T'is effect isillustr"ted %elo, ,'ere ;r5"ctu"l rotor

resist"nce "nd

5 esti$"ted rotor resist"nce&

rR


50/61


Continuous on-line tuning of sis !er#

co$ple( "nd co$put"tion"ll# intensi!e&6o,e!er t,o $et'ods one %"sed on

e(tended "l$"n filtering*E+ forp"r"$eter esti$"tion "nd " second one%"sed on " $odel referencing "d"pti!econtroller*M;AC+ "ppro"c' "re good

options& T'e E $et'od ,ill %econsidered l"ter ,'en stud#ingsensorless !ector control %ut t'e M;AC$et'od is descri%ed ne(t&


51/61


In t'e M;AC "ppro"c' " reference $odeloutput sign"l F4t'"t s"tisfies t'e tuned!ector control condition is usu"ll# "

function of ids4"nd i0s4 $otor induct"nces"nd oper"ting freuenc#& T'e "d"pti!e$odel F is esti$"ted %"sed on $otorfeed%"c) !olt"ges "nd currents "s s'o,n

in t'e ne(t slide& F is co$p"red to F4"nt'e resulting error used to esti$"te t'eslip g"in t'roug' " -I co$pens"tor&Slip g"in tuning is "c'ie!ed ,'en F5F4&

sK


52/61



53/61


Suppose ,e decide to use torue "s t'e$odel p"r"$eter F& T'us

Su%stituting D$ids4for gi!es:

T'e "ctu"l torue c"n %e esti$"ted fro$ t'est"tor fr"$e !"ri"%les using t'e eu"tion:

* * *3

2 2

me qsr

r

LPX T i

L

= =

r

2* * * *3

2 2

me ds qs

r

LPX T i i

L

= =

( )

3

2 2

s s s s

e ds qs qs ds

P

X T i i

= =


54/61


7ote: D$"nd Drp"r"$eter !"ri"tions

"ffect t'e esti$"tion "ccur"c# of F4

"nd "t lo, speeds t'e st"torresist"nce ;s"ffects t'e esti$"tion

"ccur"c# of F&


55/61

tator "lu#$%riented Vector Control

Gntil no, ,e '"!e onl# consideredrotor flu(-oriented !ector control&Airg"p flu( or st"tor flu(-oriented

!ector control is "lso possi%le %ut "t "cost of " coupling effect t'"t reuiresdecoupling co$pens"tion& See osete(t pp& 381-384 for det"ils&

Vector Control of Current "ed


56/61

Vector Control of Current$"ed

Inverter Drive

Vector control c"n "lso %e e(tended tocurrent-fed dri!es "s illustr"ted %elo,:

Vector Control of Current "ed


57/61

Vector Control of Current$"ed

Inverter Drive (contd)

ri!e oper"tes ,it' regul"ted rotor flu( "ndt'e speed control loop is t'e outer loop&T'e speed loop gener"tes t'e torue

co$$"nd Te4

,'ic' is t'en di!ided %# togener"te i0s

4& T'e flu( loop gener"tes ids4&

is used to control t'e firing "ngle of t'ep'"se controlled rectifier t'roug' "

feed%"c) loop& T'e in!erter freuenc# iscontrolled %# " p'"se-loc)ed loop *DD+ sot'"t t'e st"tor current is $"int"ined "tt'e desired torue "ngle ,it' respect to t'erotor flu(&

r

sI$

sI$

V t C t l f C l t


58/61

Vector Control of C!cloconverter

Drive

Vector control c"n "lso %e used ,it' "Sc'er%ius dri!e ,it' c#clocon!erter "s s'o,n:

V t C t l f C l t


59/61


Drive (contd)

;ec"ll in t'e Sc'er%ius dri!e Hsgis sent to

t'e line in su%s#nc'ronous $otoring "nd-sgis sent to t'e line in supers#nc'ronous

$otoring ,'ere sgis t'e slip energ#&

Currents Ip"nd II"re t'e in-p'"se "nd

u"dr"ture current co$ponents ,it'

respect to t'e slip !olt"ge Vr& T'e errorfro$ t'e speed control loop gener"tes t'edesired current Ip

49 "nd II4$"# %e set to

ero *"s s'o,n+&

V t C t l f C l t


60/61


Drive (contd)

T'e unit !ector sign"ls "re o%t"ined fro$t'e follo,ing eu"tions:

,'ere "nd

"nd is t'e "$plitude of t'e line !olt"ge&

( )cos cos cos cos sin sinsl e r e r e r = = +

( )sin sin sin cos cos sinsl e r e r e r = =

cos

s

dse

s

v

V =

sin

s

qs

e

s

v

V =

sV

V t C t l f C l t


61/61


Drive (contd)

To illustr"te 'o, t'e dri!e ,or)s consider" dri!e t'"t is "cceler"ting fro$ "su%s#nc'ronous speed ,it' " co$$"nd

supers#nc'ronous speed&At su%s#nc'ronous speed:

I:?0 sl?0 "nd sg?0&

At s#nc'ronous speed sl50 "nd I:is dc&At supers#nc'ronous speed:

I:B0 5? slB0 "nd sgB0&

Vector Control of Ac Drives

Documents

Transcript of Vector Control of Ac Drives