Influienta energetica astrategiilor de comanda
Posibilitati de comanda a motorului de inductie
• U/f constant
• U/√f constant
• Fluxul statoric constant
• Fluxul rotoric constant
• Fluxul de magnetizare constant
• Frecventa rotorica constanta
Expresiile fluxurilor in functie de parametrii
( )
RSm
mmRRR
mmsss
III
IjXIjXsR
IjXIjXRU
+=
+
+=
++=
σ
σ
0
Ecuatiile fazoriale in ipoteza neglijarii pierderilor in fier
RS
m
RmR
SmS
XXX
XXXXXX
2
1−=
+=+=
σ
σ
σCu notatiile
Expresiile curentilor
22
22
++
+
+
=
RSR
SRSR
S
RR
S
XXsRRXR
sRX
XsR
UIσ
22
22
++
+
+
=
RSR
SRSR
S
RR
m
XXsRRXR
sRX
XsR
UIσ
σ
22
++
+
=
RSR
SRSR
S
mR
XXsRRXR
sRX
XUI
σ
Relatii dintre curenti
Rm
RR
S IX
sRjX
I+−
=
Rm
RR
m IX
sRjX
I+−
=σ
Rm
RR
S IX
sRX
I
22
+
=
Rm
RR
m IX
sRX
I
22
+
=σ
Expresiile fluxurilor
RmSSS ILIL +=ΨΨΨΨ
( )22
22
++
+
+
=
RSR
SRSR
S
RSRS
SS
XXsRRXR
sRX
sRXXX
U
σ
σ
ωψ
( )22
22
++
+
+
⋅=
RSR
SRSR
S
RR
mm
XXsRRXR
sRX
sRX
LUσ
ψσ
22
++
+
⋅=
RSR
SRSR
S
R
mR
XXsRRXR
sRX
sR
LU
σ
ψ
Expresiile cuplului
22
2
23
++
+
=
RSR
SRSR
S
Rm
S XXsRRXR
sRX
sRX
UpCσ
ω
( ) 222
22
RSRS
SSRk XRXX
XRRs+
+=σ
( )( )( ) 222222
22
23
mSSSRSRS
m
Sk
XRXRXRXXUXpC
+++=
σω
Indicatori de calitate energetica
Puterea aparenta relativa S / SN
Puterea activa relativa P / PN
Curentul relativ absorbit IS / IN
Factorul de putere cosϕ
Randamentul electric ηe
Puterea aparenta relativa
22
22
233
++
+
+
⋅=⋅⋅=
RSR
SRSR
S
RR
S
XXsRRXR
sRX
XsR
UIUSσ
22
22
23
++
+
+
⋅=
RSR
SRSR
S
RR
NNN XXsRRXR
sRX
XsR
IUU
SS
σ
Factorul de putere
22
2
RR
mRSe
XsRX
sRRR
+
+=
22
2
RR
rRR
mSe
XsR
XXsR
XXX+
+
+=σ
σ
Se exprima din schema echivalenta in T a masinii
22cos
ee
e
XRR+
=ϕ
Randamentul electric
ϕcos3 ⋅⋅⋅= SIUPPuterea activa
Randamentul electric
PIRIRP RRSS
e
22 33 ⋅⋅−⋅⋅−=η
Comanda cu U/f constant
Variatia sk si Ck cu si fara Rs in functie de frecventa
0 10 20 30 40 50 60 70 80 90 1000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
f
sk
CkCkN RS=0
Ck
sk
Caracteristici mecanice
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.50
10
20
30
40
50
60
70
80
CCN
p.n
Puterea aparenta relativa
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
3
3.5
SSN
CCN
Curentul raportat
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.50.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
ISIN
CCN
Puterea activa relativa
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
3
3.5
4
PPN
CCN
Factorul de putere
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
cosϕϕϕϕ
CCN
Randamentul electric
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CCN
ηηηηe
Fluxul de magnetizare
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
0.66
CCN
ψψψψm
Comanda prin mentinerea constanta a raportului U/√f
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 1 2 3 4 5 60
10
20
30
40
50
60
70
80
CCN
p.n
Puterea aparenta raportata
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 1 2 3 4 5 60
0.5
1
1.5
2
2.5
3
CCN
SSN
Puterea activa raportata
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3PPN
CCN
Curentul raportat
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.5 30.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
CCN
ISIN
Factorul de putere
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
CCN
cosϕϕϕϕ
Randamentul electric
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CCN
ηηηηe
Fluxul de magnetizare
--- 5 Hz
--- 10 Hz
--- 20 Hz
--- 35 Hz
--- 50 Hz
--- 75 Hz
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
CCN
ψψψψm
Comparatia celor doua metode
0 0.5 1 1.5 2 2.50
10
20
30
40
50
60
70
80
CCN
p.n
--- 5 Hz --- 10 Hz --- 20 Hz
--- 35 Hz --- 50 Hz --- 75 Hz
0 1 2 3 4 5 60
10
20
30
40
50
60
70
80
CCN
p.n
Variatia factorului de putere
0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
CCN
cosϕϕϕϕ
--- 5 Hz --- 10 Hz --- 20 Hz
--- 35 Hz --- 50 Hz --- 75 Hz
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9cosϕϕϕϕ
CCN
Variatia randamentului electric
--- 5 Hz --- 10 Hz --- 20 Hz
--- 35 Hz --- 50 Hz --- 75 Hz
0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CCN
ηηηηe
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CCN
ηηηηe
Variatia fluxului de magnetizare
--- 5 Hz --- 10 Hz --- 20 Hz
--- 35 Hz --- 50 Hz --- 75 Hz
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
CCN
ψψψψm
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
0.66
CCN
ψψψψm
Variatia curentului
--- 5 Hz --- 10 Hz --- 20 Hz
--- 35 Hz --- 50 Hz --- 75 Hz
0 0.5 1 1.5 2 2.5 30.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
CCN
ISIN
0 0.5 1 1.5 2 2.50.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
ISIN
CCN
Comanda dupa fluxul rotoric
0 0.05 0.1 0.15 0.2 0.250
0.5
1
1.5
2
2.5
3
s
UUN
5 Hz10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa fluxul rotoric
0 1 2 3 4 5 6 70
10
20
30
40
50
60
70
80
ωωωω
CCN5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
smax=0.25
Comanda dupa fluxul rotoric
5 Hz
10 Hz
0 1 2 3 4 5 6 70
2
4
6
8
10
12
SSN
CCN20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa fluxul rotoric
0 1 2 3 4 5 6 70
0.5
1
1.5
2
2.5
3
3.5
4
4.5
IIN
CCN
5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa fluxul rotoric
5 Hz
10 Hz
0 1 2 3 4 5 6 70
2
4
6
8
10
12PPN
20 Hz
35 Hz
50 Hz
75 Hz
CCN
Comanda dupa fluxul rotoric
0 1 2 3 4 5 6 70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9cosϕϕϕϕ
5 Hz
10 Hz 20 Hz35 Hz
50 Hz
75 Hz
CCN
Comanda dupa fluxul rotoric
0 1 2 3 4 5 6 70
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1ηηηη
5 Hz
10 Hz20 Hz 35 Hz 50 Hz
75 Hz
CCN
Comanda dupa fluxul statoric
0 0.05 0.1 0.15 0.2 0.250
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
CCN
UUN
Comanda dupa fluxul statoric
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
ωωωω
CCN5 Hz
10 Hz20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa fluxul statoric
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
CCN
ωωωω
Comanda dupa fluxul statoric
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3
3.5
4
4.5SSN
5 Hz
10 Hz20 Hz
35 Hz
50 Hz
75 Hz
CCN
Comanda dupa fluxul statoric
5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3
IIN
CCN
Comanda dupa fluxul statoric
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
PPN
5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
CCN
Comanda dupa fluxul statoric
0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9cosϕϕϕϕ
5 Hz
10 Hz 20 Hz 35 Hz
50 Hz
75 Hz
CCN
Comanda dupa fluxul statoric
0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
5 Hz
10 Hz 20 Hz 35 Hz
50 Hz
75 Hz
CCN
ηηηηe
Comanda dupa fluxul de magnetizare
0 0.02 0.04 0.06 0.08 0.1 0.12 0.140
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2UUN
s5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa fluxul de magnetizare
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
10
20
30
40
50
60
70
80
ωωωω
CCN
5 Hz 10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa fluxul de magnetizare
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
ωωωω
CCN5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa fluxul de magnetizare
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3
3.5
4
SSN
CCN
5 Hz10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa fluxul de magnetizare
0 0.5 1 1.5 2 2.5 30.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2IIN
CCN
5 Hz10 Hz
20 Hz35 Hz
50 Hz
75 Hz
Comanda dupa fluxul de magnetizare
0 0.5 1 1.5 2 2.5 30
1
2
3
4
5
6PPN
CCN
5 Hz
10 Hz20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa fluxul de magnetizare
0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9cosϕϕϕϕ
CCN
5 Hz
10 Hz
20 Hz35 Hz 50 Hz
75 Hz
Comanda dupa fluxul de magnetizare
ηηηηe
0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CCN
5 Hz
10 Hz20 Hz 35 Hz 50 Hz
75 Hz
Comanda dupa frecventa rotorica constanta
0 0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
CCN
UUN
5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa frecventa rotorica constanta
ωωωω
0 0.5 1 1.5 2 2.50
10
20
30
40
50
60
70
80
CCN5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa frecventa rotorica constanta
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
SSN
CCN
5 Hz10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa frecventa rotorica constanta
0 0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
1.2
1.4IIN
CCN
5 Hz
10 Hz
20 Hz35 Hz
50 Hz
75 Hz
Comanda dupa frecventa rotorica constanta
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5
3
3.5
4PPN
CCN
5 Hz10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa frecventa rotorica constanta
0 0.5 1 1.5 2 2.50.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
cosϕϕϕϕ
CCN
5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Comanda dupa frecventa rotorica constanta
0 0.5 1 1.5 2 2.5
0.4
0.5
0.6
0.7
0.8
0.9
1ηηηηe
CCN
5 Hz
10 Hz
20 Hz35 Hz
50 Hz75 Hz
Comanda dupa frecventa rotorica constantaVariatia randamentului cu frecventa la 4 valori ale cuplului
ηηηηe
-10 0 10 20 30 40 50 60 70 8000.10.20.30.40.50.60.70.80.9
f
C =0.5
ηηηηe
-10 0 10 20 30 40 50 60 70 8000.10.20.30.40.50.60.70.80.9
f
C =1
ηηηηe
f-10 0 10 20 30 40 50 60 70 800
0.10.20.30.40.50.60.70.80.9
C =2.5
ηηηηe
f-10 0 10 20 30 40 50 60 70 8000.10.20.30.40.50.60.70.80.9
C =1.5
Comanda dupa frecventa rotorica constanta
cosϕϕϕϕ
f-10 0 10 20 30 40 50 60 70 800.35
0.40.450.5
0.550.6
0.650.7
0.750.8
0.85
C =1
cosϕϕϕϕ
f-10 0 10 20 30 40 50 60 70 800.35
0.40.450.5
0.550.6
0.650.7
0.750.8
0.85
C =2,5
cosϕϕϕϕ
f-10 0 10 20 30 40 50 60 70 800.35
0.40.450.5
0.550.6
0.650.7
0.750.8
0.85
C =2
cosϕϕϕϕ
f-10 0 10 20 30 40 50 60 70 800.35
0.40.450.5
0.550.6
0.650.7
0.750.8
0.85
C =1,5
Caracteristicile mecanice comparate
0 0.5 1 1.5 2 2.5 30
10
20
30
40
50
60
70
80
5 Hz10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
CCN
ωωωω
ωωωω
0 0.5 1 1.5 2 2.50
10
20
30
40
50
60
70
80
CCN5 Hz
10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
10
20
30
40
50
60
70
80
ωωωω
CCN5 Hz 10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
0 1 2 3 4 5 6 70
10
20
30
40
50
60
70
80
ωωωω
CCN5 Hz
10 Hz20 Hz
35 Hz
50 Hz
75 Hz
ψψψψR
fR
ψψψψm
ψψψψS
Variatia tensiunii la bornenele motorului
0 0.05 0.1 0.15 0.2 0.250
0.5
1
1.5
2
2.5
3
s
UUN
5 Hz10 Hz
20 Hz35 Hz
50 Hz
75 Hz
ψψψψR
ψψψψS
ψψψψm
fR
0 0.05 0.1 0.15 0.2 0.2500.20.40.60.81
1.21.41.61.8
5 Hz
10 Hz20 Hz
35 Hz
50 Hz
75 Hz
s
UUN
0 0.5 1 1.5 2 2.500.20.40.60.81
1.21.41.61.82
CCN
UUN
5 Hz
10 Hz20 Hz
35 Hz
50 Hz
75 Hz
0 0.02 0.04 0.06 0.08 0.1 0.12 0.1400.20.40.60.81
1.21.41.61.82
UUN
s5 Hz10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Puterea aparenta necesara
ψψψψRψψψψS
ψψψψmfR
0 1 2 3 4 5 6 70
2
4
6
8
10
12SSN
CCN20 Hz
35 Hz
50 Hz
75 Hz
0 0.5 1 1.5 2 2.5 300.51
1.52
2.53
3.54
4.5SSN
5 Hz10 Hz
20 Hz
35 Hz
50 Hz75 Hz
CCN
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5SSN
CCN
5 Hz10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3
3.5
4
SSN
CCN
5 Hz10 Hz
20 Hz
35 Hz
50 Hz
75 Hz
Curentul statoric absorbit
ψψψψRψψψψS
ψψψψm fR
0 1 2 3 4 5 6 700.51
1.52
2.53
3.54
4.5IIN
CCN
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3IIN
CCN
0 0.5 1 1.5 2 2.5 30.20.40.60.81
1.21.41.61.82
2.2IIN
CCN
5 Hz10 Hz
20 Hz 35 Hz
50 Hz
75 Hz
0 0.5 1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
1.2
1.4IIN
CCN
5 Hz
10 Hz
20 Hz35 Hz
50 Hz
75 Hz
Factorul de putere
ψψψψR ψψψψS
ψψψψm fR
0 1 2 3 4 5 6 700.10.20.30.40.50.60.70.80.9
cosϕϕϕϕ5 Hz
10 Hz 20 Hz 35 Hz50 Hz
75 Hz
CCN
cosϕϕϕϕ
f-10 0 10 20 30 40 50 60 70 800.35
0.40.450.5
0.550.6
0.650.7
0.750.8
0.85
C =2,5
0 0.5 1 1.5 2 2.5 300.10.20.30.40.50.60.70.80.9
cosϕϕϕϕ
CCN
5 Hz
10 Hz20 Hz 35 Hz 50 Hz
75 Hz
0 0.5 1 1.5 2 2.5 300.10.20.30.40.50.60.70.80.9
cosϕϕϕϕ5 Hz
10 Hz 20 Hz 35 Hz50 Hz
75 Hz
CCN
Randamentul
ψψψψRψψψψS
ψψψψmfR
ηηηηe
f-10 0 10 20 30 40 50 60 70 8000.10.20.30.40.50.60.70.80.9
C =1.5
0 1 2 3 4 5 6 700.10.20.30.40.50.60.70.80.91ηηηηe
5 Hz
10 Hz 20 Hz 35 Hz 50 Hz
75 Hz
CCN
0 0.5 1 1.5 2 2.5 300.10.20.30.40.50.60.70.80.91
5 Hz10 Hz 20 Hz 35 Hz
50 Hz
75 Hz
CCN
ηηηηe
ηηηηe
0 0.5 1 1.5 2 2.5 300.10.20.30.40.50.60.70.80.91
CCN
5 Hz
10 Hz20 Hz 35 Hz 50 Hz
75 Hz