5.1 Processus d’accélération
a. Le couple est calculé à l’aide de la puissance : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
La valeur moyenne approximative du couple, obtenue avec la caractéristique de couple de la figure 5.1 donne : MN = 1440rpm5500W⋅⋅602π =36,5Nm
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s=
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)=230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S = ⋅ ⋅ =
PV
518W 12A) 3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm → p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Jusqu’à la vitesse de synchronisme (qui est seulement atteinte approximativement) : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s=
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)=230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S = ⋅ ⋅ =
PV
518W 12A) 3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm → p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
En couplage étoile, le couple est réduit d’un facteur 3 : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s=
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)=230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S = ⋅ ⋅ =
PV
518W 12A) 3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm → p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Accélération jusqu’à 750 rpm :
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)=230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Avec un couplage triangle : 36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)=230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Caractéristique de couple et de courant avec les approximations graphiques des valeurs moyennes (Exercice 5.1).
42
Entraînements électriques – Entraînements électriques
c. jusqu’à 1250 rpm : MM,AVG,4 =MM,AVG,1 ≈ 1,6 · MN, ensuite : MM,AVG,5 =MM,AVG,3 ≈ 1,8 · MN
Pour un démarrage en étoile : 36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s=
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)=230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S = ⋅ ⋅ =
PV
518W 12A) 3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm → p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Pour un couplage en triangle : 36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)=230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S = ⋅ ⋅ =
PV
518W 12A) 3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm → p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Le total est la somme des deux modes de fonctionnement : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)=230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)=230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
5.2 Étoile-triangle
a. L’impédance d’une phase est exposée à différentes tensions, il s’en suit : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
La tension à la phase du moteur sera √−3 fois plus grande. Par conséquent, le courant sera aussi augmenté. Il y a donc un risque de surchauffe ! Le phénomène est encore accentué par la saturation de la machine.
b. RS = 0,4 Ω (Résistance d’une phase du moteur)
Pour un couplage en étoile, le courant nominal circule dans la machine : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = =
=
∆t nnS
s 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Pour un couplage triangle le courant est √−3 plus grand : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
c. Dans les conducteurs de ligne, le courant est une nouvelle fois augmenté d’un facteur
√−3 à cause du couplage triangle : 36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
5.3 ASM en couplage étoile
a. Pour un couplage en étoile, la tension aux bornes de la phase est √−3 plus petite que la tension à ses bornes (figure 5.2) :
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
b. Pour la puissance apparente, active et réactive : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
c. D’après les normes, une machine asynchrone IE3 de 2 ou 4 pôles d’une puissance d’environ 4 kW a un rendement d’environ 87 %:
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
43 Solutions
Z 400 V
Différence entre un couplage étoile et triangle (Exer-cice 5.2).
d. Pertes cuivres au stator:
2 2900 rad s
0,02kgm =
=
=
Ω J
→ s
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
5.4 Alimentation au réseau
a. On peut aisément déduire la vitesse de synchronisme à partir de la vitesse au point nominal :
2 2900 rad s
0,02kgm =
=
=
Ω J
→ s
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2 stator valent :
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Les pertes au rotor sont calculées à partir de la puissance d’entrefer.
36,5Nm 2π
1440rpm =
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
c. Avec le courant de 4,2 A, les pertes cuivre valent : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Lors de petites variations de charges proches de la zone linéaire, le glissement pour un quart du couple nominal est égal au quart du glissement nominal. En tenant compte de la vitesse de rotation synchrone ΩS on obtient :
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Et en fonction de la puissance d’entrefer, le rendement vaut : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
d. Comme uniquement la charge accouplée varie et que la vitesse de rotation n’est pas contrôlée, un convertisseur de fréquence ne va pas permettre la réduction des pertes.
Au contraire, de par son propre rendement, il va même péjorer le système global. (En fonctionnement avec un champ réduit à charge partielle une légère diminution des pertes serait possible.)
44
Entraînements électriques – Entraînements électriques
5.5 Alimentation U/f d’une ASM
a. Tout d’abord, le courant de phase à vide et au point de fonctionnement nominal est déterminé.
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
L’offset de tension (entre deux conducteurs) est déterminé par les résistances ohmiques à l’arrêt :
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
b. Offset de tension pour le point de fonctionnement nominal : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
c. La tension de sortie du convertisseur pour la vitesse de rotation nominale et la charge nominale représente le point nominal de la machine, ça signifie Un = 400 V.
d. Glissement nominal de la machine : 36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2 au point de fonctionnement nominal, la fréquence rotorique nominale vaut :
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Si l’on utilise l’approximation de couple pour des faibles glissements, il s’ensuit que le couple est proportionnel à la fréquence rotorique :
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
Il faut relever que dans cette équation le couple de décrochage est constant seulement si le rapport U/f et ainsi la magnétisation de la machine est constante. Ceci est valable uniquement dans la plage de réglage de la tension. Dès lors, la fréquence au stator doit être augmentée de la fréquence rotorique pour la charge nominale :
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
5.6 Alimentation U/f d’une SM
a. Les définitions des grandeurs et des angles sont représentés à la figure 5.3. Le courant est en phase avec la tension induite UP. Par conséquent, le facteur de puissance interne est cosφ = 1. Puisque la machine est connectée en étoile, le courant dans la machine est le même que le courant de ligne.
11,2kW 1 cos
3 , ,0 ,
45 Solutions
LS
Valeurs mesurées et diagramme des phaseurs d’une SM (Exercice 5.6).
b. La tension de la phase de la machine en étoile vaut :
2 2900 rad s
0,02kgm =
=
=
Ω J
→ s
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = =
=
∆t nnS
s 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
60
0= f p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
c. L’offset de tension à l’arrêt pour un couple nul est zéro puisqu’aucun courant n’est nécessaire. Offset de tension à l’arrêt pour un couple nominal : Dans ce cas, le courant nominal est fourni :
2π 1440rpm⋅
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2 rpm 4%
1500 rpm
60 =
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
d. En premier, la tension induite (tension à vide d’une phase de la machine) au point de fonctionnement nominale est calculée :
36,5Nm 2π
1440rpm 60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 = = 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
3= 750 =
∆t
117ms 24ms
3 93ms
2 = + =
∆t+
s 9230rpm 31
4=n = n
→ 135ms
s 9230rpm
rpm
4=1250 =
∆t
rpms 31163
3 4≈n =
n → 8ms
s 31163rpm
rpm
5= 250 =
∆t 143ms 8ms
5 135 max
, = A∆≈ = ⋅ =
A I
I
Z
(étoile)= 230V
IS ; (triangle) 400V 3 (étoile)
S
S I
I = Z = ⋅
173W (12A)
0,4Ω
3 2
,S= ⋅ ⋅ =
PV
518W 12A)
3
3 (triangle) (étoile)
(triangle)= ⋅ Str = ⋅ Str = ⋅ =
L I I
I
231V 3 400V
3= =
= N
S U
U
2,91kVAr
3,88kW 0,8
4850VA )
cos(
4,85kVA 7A
400V 3
3,38kW 87
, 0 3,88kW 87
12,1A A 7 3 230V 3
400V 3
(étoile)
(triangle)= = ⋅ = ⋅ Str = ⋅ =
Str I
Z I Z
rpm 1440
n= → ns=1500rpm→ p=2
3125W 0,96
3000W
1= =
Pδ ; 91,4%
6W 5 1 3125W
3000W 3000W
1 1 = (4,2A) 1,5Ω 3000 96 781W
773W
2
mech
P P η P
3,41A 3 5,9A 3
1,73A 3
2,60V 1,73A
0 1,5Ω
0
, =R I = ⋅ =
Uboost S
5,11V 3,41A
,N= S N=1,5Ω⋅ =
boost R I U
rpm 4,0%
1500
rpm 1440 rpm
1500 − =
rpm 1050 60/2 35Hz /
0= f 60 p= ⋅ =
n S
2,0Hz 4,0%
37Hz 2,0Hz Hz
10,7kW 15A
0,8 3 15A 432V 3
277V 3 480V/
,N = N 3= =
S U
U
20,8V 15A 0,8Ω
249V 3 432V/
0 3 ,
,N= N = =
P U
U
249V60Hz , , = 277V
3 480V
2 8,09Ω
/
8,09Ω 15A 121V
=
207V 0,833 60 249V
50
231V 3 400V
, = ⋅ =
3,55A 21,5mH 0Hz 5 2π
207V
231V =
−8,16A 0,021Ω
75Hz 2π
12,6A 8,16A
15A2 2
La tension induite est toujours proportionnelle à la vitesse : 36,5Nm
2π 1440rpm
60
5500W =
⋅
= ⋅ MN
58Nm 36,5Nm 1,6
0,02kgm 58Nm =
27700 rpm min
60 2 s 1 rad
2900 2
1= ⋅ ⋅ ⋅s =
n π
54ms s
27700 rpm rpm 1500
1 8080rpm 3
93ms rpms 8080
rpm
2=750 =
∆t
s 31163 rpm 1,6
1 1,8
3=n ⋅ =
n → 24ms
s 31163 rpm
rpm
rpm