acionamentos elétricos elementos r, c, l e m
TRANSCRIPT
Elementos R, C, L e M
Elementos Resistivos
0
1
0 0
1
0
0 0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
qd s
abcs abcs abcs
qd s s s s qd s
r
s
s s s qd s s
s
qs s qs
qd s qd s qd s ds s ds
s s s
r
r
r
v r i
v r i
v r i
v r i
v K r K i
K r K r
v r i
Elementos Indutivos
10
0
101
0 0
abcsabcs
qd s s
qd s s
s qd s
s qq s d s sd
d
dt
d
dt
d d
dt dt
λv
λ Kv K
K λKv λ K
010 0
1
1
2 2cos cos cos
sin cos 03 3
2 2 2 2 2sin sin sin sin cos 0
3 3 3 3 3
1 1 1 2sin c
2 2 2 3
qd s
qd s qd s
s
s ss
ss
dd
dt
d
dt
dt
λK KK
KK
λK
v
1
2os 0
3
0 1 0
1 0 0
0 0 0
ss
d
dt
KK
PRt
0
0
1
0
0
0
01
0
0
0
0 1 0
1 0 0
0 0 0
1 0 0
0 1 0
0 0 1
qd s
qd s
qsqs ds
dsqd s ds qs
ss
s
s qd s
qs
ds
qd s
s s
qs
ss
ds
d
dt
dv
dtd
vd
d
dtd
dtd
dt
t
d
t
td
v
d
d
λK Kλ
v
KKv
v
2 60
Elementos Capacitivos
abcsabcs
d
dtq
i
1
0
0
1
1 0
00
s qd s
qd s s
s qd s
s qd sqd s s
d
dt
d d
dt dt
i
K qi K
K qK q K
0
1
1 0
0 0
00
00
qs
dqs ds
s
d
s qd s
qd s s qd s s s
qd sqds
q
q
q
qsqs ds
dsds qs
s
s
q
s
d d
dt dtd
dt
dqi q
dtdq
i qdt
dqi
dt
q
K qi K q K K
iq
q
1 0 1 0
1 0 0
0 0 0
ss
d
dt
KK
Enrolamento trifásico comindutâncias mútuas
0 0
0 0
0 0 0
s
s s
s
s s
s
as asR asL
asbc bs bsR bsL
cs csR csL
r
r
L M M
L M L M
M M L
v v v
v v v v
v v v
r sr
sL
sr
sL
sr
sL
csi
bsi
asi
M M
M
asv
bsv
csv
0
0
00
10 0
2
0 0 0 0 0 0
s qs
s ds
s s
qsqs ds
dsqd s ds qs
ss
qd s s s s qd s
L M iL M i
qsqs qsR qsL s qs ds
dsds dsR dsL s ds qs
L M i
s sR sL s s
dv
dtd
vdt
dv
dt
dv v v r i
dtd
v v v r idt
v v v r i
v
λ K L K i
qsv
qsi
ds
sL M
sr
dsv
srqs
sL M
dsi
0sv
sr
2sL M
dsi
1
0 0
0 0
0 0 2
s
s s s s
s
L M
L M
L M
K L K
Exercício
Encontre , , e . Considere , , e .
sr
sL
sr
sL
sr
sL
csi
bsi
asi
M M
M
asv
bsv
csv
qsv
qsi
ds
sL M
sr
dsv
srqs
sL M
dsi
0sv
sr
2sL M
dsi
Próxmia Aula
Motores de Indução no Sistema qd0
0 0
0 0
0 0
1 1
2 21 1
2 21 1
2 2
s
abcs s
s
ls ms ms ms
abcs ms ls ms ms
ms ms ls ms
r
r
r
L L L L
L L L L
L L L L
r
Lsr
sL
sr
sL
sr
sL
csi
bsi
asi
M M
M
asv
bsv
csv
A
A’
C’
C
B B’
0
1
1
0
1 1
2 21 1
2 21 1
2 2
30 0
23
0 02
0 0
abcs s abcs
dq s dq s
ls ms ms ms
s ms ls ms ms
ms ms ls ms
s s s
s
ls ms
ls ms
ls
s s
L L L L
L L L L
L L L L
L L
L L
L
K L K
K L
λ
K
λ L i
i
L
indutância de dispersão
indutância de magnetizaçãols
ms
L
L
Matriz indutância válida para motores trifásicos no sistema
Matriz indutância válida para motores trifásicos no sistema
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
-1.5
-1
-0.5
0
0.5
1
1.5
B C A
A
A’
C’
C
B B’
Indutância Mútua em MITs
• Porque é ?
00 0
00 0
qsqs s qs ds
dsds s ds ds
ss s s
qrqr r qr r dr
drdr r dr r qr
rr r r
v r i
v r i
v r i
v r i
v r
d
dtd
i
v
dtd
dtd
dtd
dtd
rd
it
0 0
0 0
qs ls qs M qs qr
ds ls ds M ds dr
s ls s
qr lr qr M qs qr
dr lr dr M ds dr
r lr r
L i
L i
L i i
L i i
L i i
L i
L i
L i
L
L i i
i
1 0 00 0 0
0 00 0 0
0 00 0 0
0 0 0 0
20 0 0 0
r L L LL L L s ls M Mi ls M MqsL L r LL L L ls M s Mi ls M Mds
L r L LL L Li r M r r lr r MM lr MqrL L L L LM lr Mi r M r lrdr
Jr P
...
0
3 30 0 0
4 410 0 0
0 0 0
0 0 0... 0
0 0 0 02
0 0 0 0
iqs
idsiqr
L r ir M drP PL i L i rM dr M qr
L L Lls M M v
qsL L Lls M M v
dsL L LM lr M
L L LM lr M
TJ LP
0 00 0 0
0 00 0 0
0 00 0 0
0 0 00 0
0 0 0 0 3 32 0 0 04 4
r L L Ls ls M Mi S Mqs
L L r Lls M s MS Mi
dsL r L LM Ri r M r r lr r Mqr M R
L L L ri r M r lr r MPdrP PJ L i L ir M dr M qr
0 0 0
0 0 0
0 0 00
0 0 00
0 0 0 02
i vS Mqs qsS Mi vds dsM Ri
qr M Ri Pdr
TJ Lr
iqs Sr M
sidsiqr
id
S L L M Lls
r
M r M
r
0 0 00
0 0 0
0 0 00
0 0 00
0 0 0 02
S L M L LM r lr r M i
i vS Mqs qsrr S M v
dsM Riqr M R
PTJ Lr
i Sr i S L L M L i Mqs s qs ls M r M
ds
r
ds
id
r i S L M L L i S vr qr M r lr r M dr qs
M lr
M lr M ls lr ls
M
M lr M ls lr ls
M ls
M lr M ls lr ls
L LS
L L L L L L
LM
L L L L L L
L LR
L L L L L L
i Sr i S L L M L i Mr i S L M L L i S vqs s qs ls M r M ds r qr M r lr r M dr qs
Ls
0
M
0
0
0
S
0
M
0
M
0
R
0
0
0
M
0
R
0
0
0
0
0
J2P
R
M2
R S
0
M
M2
R S
0
0
0
R
M2
R S
0
M
M2
R S
0
M
M2
R S
0
S
M2
R S
0
0
0
M
M2
R S
0
S
M2
R S
0
0
0
0
0
1
J2P
Motor de indução no referencial rotórico
2
1 m
s r
L
L L
Torque
• Torque eletromagnético
• Torque mecânico
• Equação de estado
'
2m dr qs
e PPr
mpp qs ds
r
L i LT N N i i
LL
rm n r d
dT J B
dt
1 10
0 01 0
er
dr
nr
r
B TJ JJ
1 1 1 1 1x = A x +B u
• Fluxo Magnético
• Ângulo do Rotor
rm ds
r
rm
rds
r
r
L dL i
R dt
RLL
IsR
L
01 q
s mer d
idt
i
6
Iabc
5
wr
4
Phidr
3
Te
2
Ids
1
Iqs
sin
seno
dq0
sin_cos
abc
dq02abc
cos
cos
1/J
s+B/J
Transfer Fcn5
Lm*Rr/Lr
s+Rr/Lr
Transfer Fcn4
1
0.013311s+1.25
Transfer Fcn(with initial outputs)
1
d*Le.s+Re
Transfer Fcn
Product
1s
Integrator
[Ids]
Goto1
[Iqs]
Goto
ws*Le*d
Gain2
ws*Le*d
Gain1
Np*Lm*Lm/Lr
Gain
[Ids]
From6
[Iqs]
From5
[Ids]
From4
[Ids]
From3
[Iqs]
From2
[Ids]
From1 [Iqs]
From
Divide1
Divide
0.0
Constant2
Lr/Rr
Constant1
2
Vds
1
Vqs
Corrente de eixo em quadratura (A)
Corrente de eixo direto (A)
Tensão q
Tensão d
Densidade de f luxo magnético mútuo
Torque Eletromagnético
Rotação do Rotor (rd/s)
Rotação do Rotor (rd/s)
Correntes abc
Correntes dq0
Escorregamento(rd/s)
Rotação doCampo Girante
(rd/s)
Angulo (rd)
eT
Modelo do MIT
wm
Te
Scope4
Scope2
Scope1
SaturationRampProduct
Phidr
PIDPID
PIDPID
MITdq0
Vds
Vqs
Iqs
Ids
Te
Phi_dr
wr
MIT - dq
Iqs
Ids
[Vqs]
[Vds]
[Iabc]
[Te]
[wm]
[PHIdr]
[Rampa]
[Ids]
[Iqs]
[Ids]
[Iqs]
[wm]
[wm]
[PHIdr]
[PHIdr]
[Iabc]
[Iqs]
[wm]
[Rampa]
[Te]
[Te]
[Ids]
[wm]2*pi*60/3
Constant3
0.7
Constant1
Controle externo do MIT
Parâmetros do motor a simularParâmetro Valor nominal
2 2cos cos cos
cos sin 13 32 2 2 2 2
sin sin sin cos sin 13 3 3 3 3
1 1 1 2 2cos sin 1
2 2 2 3 3
L M MsM L Ms sM M Ls
L
2 2 2 2 2 2cos cos cos cos cos cos cos cos cos
3 3 3 3 3 3
2 2 2 2 2sin sin sin in sin sin s
3 3 3 3 3
L M M M L M M M L
L M M M L M Ms
S S S
s S
L
cos sin 1
2 2 2 2in sin sin cos sin 1
3 3 3 3
1 11 1 1 1 2 2cos sin
1 1 1
2 2 2 21
2 2 2 3 3
cos cos co
2
3
2 2
S
S S S
S
M L
L M M M L M M M L
L
s
SM L
L
2 2 2 2s cos cos cos
cos sin 13 3 3 3
2 2 2sin sin sin sin sin sin cos sin
3 3 3 3 3
1 1 1
2 2 2
M M L
L M L M M L
L M L M L
S
s S S
S S S M
21
3
2 2cos sin 1
3 3
2 2 2 2 2 2cos cos cos cos s2 2 2 s in cos sin cos cos
3 3 3 3in
3 3
2
3
L M L M L M L M L M L MS S S S S S L MS
s
L
2 2cos cos
3 3
2 2 2 2 2 2 2cos sin cos sin cos sin sin sin sin sin sin
3 3 3 3 3 3 32 2 2sin
S S
S S S S
L M L M
S S SL M L M L M L M L M L M L SM L LS M M
2
3
1 1 2 1 2 1 1 2 1 2 3cos cos cos sin sin sin 3
2 2 3 2 3 2 2
3
23
3 2 3
02
2
0 0
20
33
0 0
L M L M L M L M L M L M L M
L M
L
S S S S S S S
S
S Ms
L
32
0 0
0
0 2
0
0
L M
L M
L MsL M
S
S
S
S
L
Dedução da matriz indutâcia de MITs para o sistema
2
1
1dr ds dss
qr qs q
ds dss
qs qsm m
dr ds
r mqr
ds
qs
dr ds
r mqr qs
dr ds
sm
ds
qs
s rr
qr m m
m
m
qs
iL L
i
iL
i iLi i
LiLi i
iL L
L
LL
L L
L
L
i
i
L
2dr m
qr
qs
ds dsm s r
qs qsr r
i
iL L L LiL L
1
0 1
1 0
0 1
1 0
0
0
ds dss
qs qsm m
r
ds ds dsdss
qs qs qsqs
dr dr drdr
i
r slqr qr qrqr
dr
rqr
LiL L
v iR
v i
v iR
v i
iR
i
2
2
0 1
1 0
0
0
dr ds dsm s rr
qr qs qsm m
dr ds mr
qr qsm
dr
qr
i
d
L L LLiL L
L LL
L
rdsr
qrqs
ds dsr s r
qs qsm m
iR L RiL L
2 2
0 1
1 0
0
0
dr dsm m s r dsdrm m s r
qr qsr r
d
qsq
ss r
q
r
s
r
m
r
dr
rqr
dsr s
iL
iL
dsr
qsm m
ds
qs
iL L L L iL L L LiL L i
r
q
L
sm
L
iR L RiL
L
LL
22 2
2 0 1
1 0
0
0dr ds dsdrr r m s r r m r m s r
qr
dsm s r
qsm
dsm s r
qsm
dr
rqr
dss r
qsq ms qsqrr m r m r m r
i iR R L L iL RiL
iL L LiL
iL L LiL
L L L L L L Li iL L L L L L L
2 22
2
0 1
1 0
0 1
1 0
dr
rqr
ds drdsdr r m s r m s rsl
qs qrqsqr m r
r m s r
m r
r m s r
m
d
m r
sdr
qsqr
i iL L L L L LR L L L
L
Li iL L L
i
i
L
R L L L
L L
0
0drsl
qrsl
2 20 1
1 0dr dr ds dsds r m r m s r m s r
slqr qr qs qsqs r r r r
i iR L R L L L L L Ri iL L L L
Modelo do Motor Referenciado no Fluxo Rotórico
Estator
Total Rotors ls mL L
ds sdr ds
m m
ds m ls ds m
L
drL L i L i
Li i
L L
Estator
Total Rotors ls mL L
qs sqr qs
qs m
m m
l qs
L
s m qr
i
L L i L i
Li
L L
Total
2
dr r m ds
dr r m ds
m sdr
dr
ds s
m
ds dsm m
m
rr
L L i
L
i
L
L LL i
L L LLi
L L
2
qs sq
qr r qr m qs
qr r qs m qs
m sqr qs qs
sm m
m
r
m
r
L i L i
L L ii
L L LLi
L
Li
L
L
L
rr
r
L
R
2
1 m
s r
L
L L
2rr m s
dr ds dsm m
L L LLi
L L
2
2
1m s m
sds dsds r s r s r s r
drqs qsqs PP r m sm s
ss rr s r s
v
vN
L R Lii L L L L L
ii L LL RL LL L L
Estator Rotor
qsqs s qs ds
dsds s ds ds
dv R i
dtd
v R idt
0
0
qrr qr r dr
drr dr r qr
d
dtd
t
i
d
R
R i
qs ls qs M qs qr
ds ls ds M ds dr
L i i
L i i
L i
L i
qr lr qr M qs qr
dr lr dr M ds dr
L i
L
L i i
L ii i
ds sdr ds
m m
Li i
L L
2 2cos cos cos
cos sin 13 32 2 2 2 2
sin sin sin cos sin 13 3 3 3 3
1 1 1 2 2cos sin 1
2 2 2 3 3
L M MsM L Ms sM M Ls
L
2 2 2 2 2 2cos cos cos cos cos cos cos cos cos
3 3 3 3 3 3
2 2 2 2 2sin sin sin sin sin sin
3 3 3 3 3
L M M M L M M M L
L M M
S S S
M L Ms S Ms
L
cos sin 1
2 2 2 2sin sin sin cos sin 1
3 3 3 3
1 1 1 2 2cos
1 1 1 1 1 1
2 2 2sin 1
2 2 2 3 3
cos cos c
2
3
2 2 2
M L
L M M M L M M M L
L M L
s
S
S S S
S S
L
2 2 2 2os cos cos cos
cos sin 13 3 3 3
2 2 2sin sin sin sin sin sin cos sin
3 3 3 3 3
1 1 1
2 2 2
M M LS
s S S
S S S
L M L M M L
L M L M L M
21
3
2 2cos sin 1
3 3
2 2 2 2 2 2cos cos c2 2 2 sinos cos sin cos sin cos cos
3 3 3 3 3 3
2
3
L M L M L M L M LS S S S S S SM L M L M
s
L
2 2cos cos
3 3
2 2 2 2 2 2 2cos sin cos sin cos sin sin sin sin sin sin
3 3 3 3 3 32s
32 2in
L M L M
L M L M L M L M L M L M L M L M L M
S S
S S S S S S S S S
2
3
1 1 2 1 2 1 1 2 1 2 3cos cos cos sin sin sin 3
2 2 3 2 3 2 2 3 2 3 2
03
23
02
0
20
3
0 0
S S S S S S SL M L M L M L M L M L M L M
L M
Ls
S
S M
L
33
2
0 0
0
0 2
0
0
S
S
L M
L M
L MSMS
sL
L
0 0 0
0 0 0
0 0 0
0
L L LM lr ML L L L L L L L L L L LM lr M ls lr ls M lr M ls lr ls
L L Li M lr MqsL L L L L L L L L L L LM lr M ls lr ls M lr M ls lr lsids
L LL M lsMiqrL L L L L L L L L L L LM lr M ls lr ls M lr M ls lr lsidr LM
r
0 0
0 0
0 0
0 0
3 30 0 0 0 04 4
0 0 0 02
r L L Ls ls M ML L r Lls M s M
L r L Lr M r r lr r M
L L L rr M r lr r ML L P PM ls
L i L iM dr M qrL L L L L L L L L L L LM lr M ls lr ls M lr M ls lr lsP
J
0 0 0
0 0 0
0
L L LM lr ML L L L L L L L L L L LM lr M ls lr ls M lr M ls lr ls
L L Li M lr MqsL L L L L L L L L L L LM lr M ls lr ls M lr M ls lr lsids
L LL M lsi MqrL L L L L L L LM lr M ls lr ls M lridr
r
0 0 0
0
0 0 0
0 0 0 02
vqs
vds
L L L LM ls lr lsL LL TM lsM L
L L L L L L L L L L L LM lr M ls lr ls M lr M ls lr lsP
J