Page 230 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

Electric Generators and their Control for Large Wind Turbines 217

( R s + ω 1 I + jω 1 L m ψ = − V s
j L sc)
s
L r r
(9.10)
 
− R r L m I + R r + jSωψ =− V r
s 

1
L r  L r  r
with V and R given, and stator power factor assigned a value cos φ , the stator current I is
s
s
s
s
I s = P s (9.11)
3cos ϕ s ( )
V s
I = ( cos ϕ s ( ) − jsin ϕ s ( )) (9.12)
s I s
Now from (9.10), φ is first calculated and then V is obtained for a given slip frequency Sω and
s
1
r
stator frequency ω . It is feasible to absorb some reactive power through the stator from the power
1
grid and magnetize the machine partially from the rotor via a PWM converter or to operate the
stator at unity power factor and thus fully magnetize the machine from the rotor when |ψ | > | ψ |
s
r
and |I | > |I |.
r
s
An example follows.
Example 9.1
Consider a DFIG with the following data:
P sn = 3 MW, cos φ sn = 1, V snl = 3.2 kV/Y line voltage rms, at S max = −0.25, turns ratio a rs = 4/1,
r s = r r = 0.01 pu, r 1m = ∞, l sl = l rl = 0.06 pu, l 1m = 3 pu, f 1n = 50 Hz, 2p = 6 poles. Calculate

a. Parameters R s , R r , X sl , X rl , and X 1m , in Ω
b. For S = −0.25 and maximum power P max , at cos φ sn = 1, calculate the rotor current, rotor volt-
age, and its angle δ v with respect to V s (in stator coordinates), rotor active and reactive power
P r , Q r , and total electric power P e = P s + P r .
c. Calculate the rotor-side converter kVA and the corresponding phasor diagram.

Solution

a. The stator current from (9.11) is simply
×
I s ( ) = P s = 310 6 = 541 9 A
.
s=−025. 3 V sn cos ϕ n ( ) 3 ×3200 ×1

The nominal (base) reactance X n is

X n = V snl /3 = 3200 = 3 413 Ω
.
.
I n 3 × 541 9
Thus,

×
.
.
.
R 1 = R r = rX n = 0013 4134 = 0 034134 Ω
s
×
.
.
.
X rl = X ls = lX n = 0063 4134 = 0 2048 Ω
sl
=
.
.
X m = l X n = ×33 4134 10 24 Ω
m