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8/13/2019 Vector Control of Ac Drives
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Topic 13: Vector Control of AC Induction
Motors
Spring 2004
ECE 8830 - Electric ri!es
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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$"nce dri!es ,'ere oscill"tions in"ir g"p flu( lin)"ges "re intoler"%le e&g&
ro%otic "ctu"tors centrifuges ser!os etc&
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Introduction (contd)
.'# does !ector control pro!ide superiord#n"$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&
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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&
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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$$ut"tor "nd %rus'es& T'e %"sicstructure "nd field flu( "nd "r$"ture MM"re s'o,n %elo,:
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Torque Control of DC Motors (contd)
T'e field flu( f*f+ produced %# fieldcurrent Ifis ort'ogon"l to t'e "r$"ture
flu( "*"+ produced %# t'e "r$"ture
current I"& T'e de!eloped torue Tec"n %e,ritten "s:
ec"use t'e !ectors "re ort'ogon"l t'e#"re decoupled i&e& t'e field current onl#controls t'e field flu( "nd t'e "r$"ture
current onl# controls t'e "r$"ture flu(&
'
e t a f T K I I =
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Torque Control of DC Motors (contd)
C $otor-li)e perfor$"nce c"n %e"c'ie!ed ,it' "n induction $otor if t'e$otor control is considered in t'e
s#nc'ronousl# rot"ting reference fr"$e*de-e+ ,'ere t'e sinusoid"l !"ri"%les"ppe"r "s dc u"ntities in ste"d# st"te&
T,o control inputs ids"nd i0sc"n %e used
for " !ector controlled in!erter "s s'o,non t'e ne(t slide&
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Torque Control of DC Motors (contd)
.it' !ector control:
ids*induction $otor+ If*dc $otor+
i0s*induction $otor+ I"*dc $otor+T'us torue is gi!en %#:
,'ere is pe") !"lue of sinusoid"l
'e t qs t ds qsrT K i K i i= =
r r
=
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Torque Control of DC Motors (contd)
T'is dc $otor-li)e perfor$"nce is onl#possi%le if i0s
4onl# controls i0s"nd does not
"ffect t'e flu( i&e& i0s
"nd ids
"re
ort'ogon"l under "ll oper"ting conditionsof t'e !ector-controlled dri!e&
T'us !ector control s'ould ensure t'e
correct orient"tion "nd eu"lit# of t'eco$$"nd "nd "ctu"l currents&
r
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Equivalent Circuit of Induction Motor
T'e co$ple( de-eeui!"lent circuit of "ninduction $otor is s'o,n in t'e %elo, figure*neglecting rotor le")"ge induct"nce+&
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Equivalent Circuit of Induction
Motor (contd)
Since t'e rotor le")"ge induct"nce '"s%een neglected t'e rotor flu( 5 t'e "ir g"p flu(&
T'e st"tor current !ector Isis t'e su$ 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= +$
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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,:
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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
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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 /
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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"$&
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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
&
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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 %# $e"suring slip speed&
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Direct Vector Control
In direct !ector controlt'e field "ngle isc"lcul"ted %# using ter$in"l !olt"ges "ndcurrent or 6"ll sensors or flu( sense
,indings&
A %loc) di"gr"$ of " direct !ector control
$et'od using " .M !olt"ge-fed in!erteris s'o,n on t'e ne(t slide&
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Direct Vector Control (contd)
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Direct Vector Control (contd)
T'e princip"l !ector control p"r"$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&
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Direct Vector Control (contd)
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&
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Direct Vector Control (contd)
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Direct Vector Control (contd)
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 =
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Direct Vector Control (contd)
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 = +
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Direct Vector Control (contd)
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&
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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
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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&
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"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&
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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&
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Indirect Vector Control (contd)
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Indirect Vector Control (contd)
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
= +
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Indirect Vector Control (contd)
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&
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Indirect Vector Control (contd)
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Indirect Vector Control (contd)
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
+ + =
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Indirect Vector Control (contd)
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
=
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Indirect Vector Control (contd)
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 =
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Indirect Vector Control (contd)
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
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Indirect Vector Control (contd)
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 = +
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Indirect Vector Control (contd)
An i$ple$ent"tion of indirect !ector controlfor 4-u"dr"nt oper"tion is s'o,n %elo,:
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Indirect Vector Control (contd)
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&
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Indirect Vector Control (contd)
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 =
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Indirect Vector Control (contd)
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&
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Indirect Vector Control (contd)
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&
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Indirect Vector Control (contd)
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
=
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Indirect Vector Control (contd)
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+&
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Indirect Vector Control (contd)
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:
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Indirect Vector Control (contd)
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&
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Indirect Vector Control (contd)
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
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Indirect Vector Control (contd)
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
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Indirect Vector Control (contd)
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&
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Indirect Vector Control (contd)
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
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Indirect Vector Control (contd)
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Indirect Vector Control (contd)
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
= =
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Indirect Vector Control (contd)
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&
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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
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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
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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
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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
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Vector Control of C!cloconverter
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$"# %e set to
ero *"s s'o,n+&
V t C t l f C l t
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Vector Control of C!cloconverter
Drive (contd)
T'e unit !ector sign"ls "re o%t"ined fro$t'e follo,ing eu"tions:
,'ere "nd
"nd is t'e "$plitude of t'e line !olt"ge&
( )cos cos cos cos sin sinsl e r e r e r = = +
( )sin sin sin cos cos sinsl e r e r e r = =
cos
s
dse
s
v
V =
sin
s
qs
e
s
v
V =
sV
V t C t l f C l t
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Vector Control of C!cloconverter
Drive (contd)
To illustr"te 'o, t'e dri!e ,or)s consider" dri!e t'"t is "cceler"ting fro$ "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&