European Journal of Scientific Research - EuroJournals

Robust Control of a Doubly Fed Asynchronous Machine of a Wind Turbine System 797
Figure 1: Wind turbine system representation
The system use the wind power to drag the double fed asynchronous machine who acts as a
generator, the output power produced must have the same high quality when it enters the electrical
network, i.e: 220 volts amplitude and 60 Hz frequency and the harmonics held to a low level in spite of
wind speed changes and electrical energy consumption in active or reactive power form. References
[5], [6], [7] describe detailed models of wind turbines for simulations, we use the model equipped with
the doubly fed induction generators (asynchronous machine) (for more details see [8]), the system
electrical equations are given in ( d, q)
frame orientation, then:
The stator voltage differential equations are:
d
Vds = Rs.
I ds + Φ ds − ws
⋅Φ
qs
(1)
dt
d
Vqs = Rs.
I qs + Φ qs + ws
⋅Φ
ds
(2)
dt
The rotor voltage differential equations are:
d
Vdr = Rr
. Idr
+ Φdr
− wr
⋅Φ
qr
(3)
dt
d
Vqr = Rr
. Iqr
+ Φ qr + wr
⋅Φ
dr
(4)
dt
The stator flux vectors equations are:
Φ ds = L s.
Ids
+ M.
Idr
(5)
Φ qs = L s.
I qs + M . I qr
The rotor flux vectors equations:
(6)
Φ dr = L r . I dr + M.
I ds
(7)
Φ qr = L r.
Iqr
+ M . Iqs
(8)
The electromagnetic couple flux equation :
M
Cem p.
( Φ ds.
I qr −Φ
qs . I dr )
L
= (9)
s
The electromagnetic couple mecanic equation:
dΩ
= C + J + f . Ω
dt
Cem r
(10)
Where:
V , : Statoric voltage vector components in ‘d’ and ‘q’ axes respectively.
ds Vqs
V dr , Vqr
: Rotoric voltage vector components in ‘d’ and ‘q’ axes respectively.
I ds , I qs : Statoric current vector components in ‘d’ and ‘q’ axes respectively.
I dr , I qr : Rotoric current vector components in ‘d’ and ‘q’ axes respectively.
Φ ds , Φ qs : Statoric flux vector components in ‘d’ and ‘q’ axes respectively.
Φ , : Rotoric flux vector components in ‘d’ and ‘q’ axes respectively.
dr qr Φ