Page 232 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

Electric Generators and their Control for Large Wind Turbines 219

V , V , V , V , ψ , ψ , ψ , ψ , L , L , L , R , R , J, T , T mech , p are stator voltages, rotor voltages, sta-
q
qr
dr
d
e
m
s
s
r
d
q
r
dr
qr
1
tor and rotor flux linkages, inductances, resistances, inertia, electromagnetic and mechanical torque,
and pole pairs.
Aligning the system of coordinates to the stator flux ψ is beneficial because the latter varies less,
s
except in the case for faults. Consequently,
d
ψ = ψ s = ψ d , ψ q = , ψ q = 0 (9.14)
0
s dt
 dψ d 
 = 0 and zero resistance (R = 0),

s
 dt 
V d ≈ 0, V q ≈ −ωψ d , ψ q = =0 L i + L i s q (9.15)
mqr
1
Consequently, the stator active and reactive powers P , Q become
s
s
3
P s = ( V i d + V i q) = 3 V i q = 3 1 ωψ L m
2 d q 2 q 2 d L s i qr (9.16)
3
3
Q s = ( Vi d − Vi q) = 3 V q i d =− ω ψ d (ψ d − Li dr)
i
2 q d 2 2 1 L s m
It becomes clear that active and reactive stator power control can be accomplished through the
rotor currents i , i . The rotor voltages for steady state are from (9.13) and (9.16):
qr
dr
V dr =− Ri rdr + LS i qr1
sc ω
*
  (9.17)
V qr =− Ri rqr − Sω 1  L m ψ d + Li
*
scdr 
 L s 
The current controllers in rotor coordinates for i and i have to be accompanied by the compen-
qr
dr
sation of back-emfs (the second terms in [9.17]). Figure 9.8 shows how field-oriented control (FOC)
of the rotor-side PWM converter is accomplished.
As shown in Figure 9.9, a similar FOC aligned to the grid voltages vector (or to their virtual flux)
can be used for the grid-side PWM converter.
A digital simulation code is used to study the transients of a 2 MW DFIG, when a three-phase
short circuit occurs and the dq currents in the stator are limited to 50% I s rated (I ) and 150% I s rated (I ),
q
d
respectively, with the results as shown in Figure 9.10 [4].
The machine data are P = 2 MW, V = 690 V, 2p = 4, f = 50 Hz, l = 3.658 pu, l = 0.0634 pu,
1n
1
snl
n
sl
m
l = 0.08466 pu, r = 4.694 × 10 pu, r = 4.86 × 10 pu, and h (inertia) = 3.611 s.
−3
−3
r
rl
s
It is evident that the machine may stand the fault, and it also retains control. The speed increases
during transients, because the active power cannot be transmitted to the grid during the short-circuit
condition. With the current demanding grid standards for wind generators, DFIGs should remain
online even during asymmetric dip voltage sags, while providing reactive current to be ready to
participate in the voltage restoring right after the fault.
All these aspects require special treatment and additional measures of protection of the machine-
side converter [2].
The DFIG has proved to be a cost-effective 3G transmission wind generator and is used up to
4.5 MW, despite the brush–copper ring power transfer to the rotor. There are ways to obtain 10 MW
with 1G transmission system (down to 50 rpm) [12].