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Electric Generators and their Control for Large Wind Turbines 225
The electromagnetic torque T e is
3 3
(
T e = pL s − L sc) i i = × ( 30 03428 0 001087 ) × 250 ×(910 86 ) = 340013 Nm
−
.
.
.
1
2 dq 2
The delivered active power P 1 is
1 ω 314
30 0512 250 +
2
,
P 1 = T e − 3 Ri s s = 34 013× −× . ( 2 910 86 ) = 342 MW
.
2
.
p 1 3
The reactive power Q s is
Q s =− ( Li s d + Li ) =− ×314 0 03428 250 2 +1 087 ⋅10 −3 × 910 86 ) =− 288 MVAR
. (
2
2 2
2
3ω
×
.
.
3
.
1 scq
This leads to a power factor cos φ 1 = 0.767, which corresponds to a 6-pole CRIG at 50 Hz, delivering 3.4
MW, while the rated MVA was stated at 3 MVA. The efficiency η ei is, if the iron and mechanical losses
are neglected,
η ei = P 1 2
d (
P + 3 s R i + ) + 3 r R L m q i
2
2
q i
1
2 2 r L
.
= 342 2
. (
0 0326
.
2
2
.
.
.
342 + 3 0 052 2550 + 910 86 ) + 3 0 04266 . 910 86
2 2 0 033
.
= 96 01.%
The efficiency is rather acceptable, but when adding the iron and mechanical losses, the efficiency can
drop down to around 95%. A copper cage could bring down the slip for the same power to around (less
than) 1%, and thus, the efficiency would increase. The leakage inductances have been considered rather
large, and they may be reduced to some extent by design. As no real design is behind this numerical
example, an optimal design may bring notable CRIG improvements in performance per cost.
9.3.3 CRIG Control
Scalar (V/f with stabilizing loops), FOC, and direct power control may be implemented for control-
ling a CRIG [1–4].
A rather straightforward FOC of CRIG may be implemented in the synchronous coordinates, as
in direct and indirect versions, based on the equation obtained from (9.19):
ψ = ( s V − R ) sc s ⋅ r L (9.21)
∫
s s idtL i−
r L m
The integral may be “translated” into a filter to allow safe operation down to 4–5 Hz, or a com-
bined voltage and current observer may be used [16]. For the indirect FOC, current decoupling
equations need to be used. They use the following expressions from (9.19) and (9.20):
r L r L
ψ 1+ p = Li S ω 1 ψ r = Li (9.22)
md ;
r
m q
r R r R
