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52

Bouhadouza Boubekeur et al.: Application of STATCOM to increase transient stability of wind farm

Pwt = C p Pv = C p (λ , β ).

ρAwt vw3

(1)

2

Where C is the power coefficient of wind turbine (C is
the function of the blade pitch angle and the tip-speed
is the swept area; is the
ratio); is the air density;
wind speed. The tip-speed ratio .is defined as:

λ=

wwt .R
v

(2)

Where w is mechanical angular velocity of wind turbine blades; R is radius of wind turbine blades. The numerical method of C is in Ref .
,

!!&quot;

0.5176

#\$

*+,

% 0.4β % 5( e -\$ . 0.0068

(3)

The IG space vector model is generally composed of
three sets of equations: voltage equations, flux linkage
equations, and motion equation. The voltage equations for
the stator and rotor of the generator in the arbitrary reference frame are given by :

1

vds = R s i ds − ϕ qs + w

s

1
v = R s i qs + ϕ +
ds
 qs
ws

d
ϕ ds
dt
d
ϕ qs
dt

1 d

vdr = R r i dr − s.ϕ qr + w dt ϕ dr = 0

s

1
d
v = R r i qr + s.ϕ +
ϕ qr = 0
qr
dr

ws dt

(6)

(7)

Where
01

2

3

045.567

%

5.589 ;3
78 43

:

(4)

There is always an optimum tip speed ratio λ= corresponding to the maximum power coefficient of wind turbine
C &gt;?@ for any pitch angleβ. The β 0 without considering
wind turbine status at extreme wind speed.
The output torque of wind turbine is :
AB

(5)

CDE

The electrical torque is given by this equation after several converted steps:

Te = L m (i dr .i qs + i qr .i ds )
dwr Tm − Te
=
dt
J

(8)
(9)

The power flow studies in the IG are represented in
Fig .4 .

The relation betweenC , β and λ is shown in Fig .3.
0.6
B=0°
B=5°
B=10°
B=15°
B=20°

X: 8.1
Y: 0.48

0.5

Cp

0.4

Figure 4. Power flow and losses in an IG.

0.3

3. Statcom

0.2

0.1

0
0

1

2

3

4

5

6

7
8
lamda

9

10

Figure 3. Aerodynamic power coefficient variation
ratio and pitch angle .

11

12

13

14

15

against tip speed

0.48) is achieved
The maximum value of C (
8.1.
for
degree
and
for
0
F
To extract the maximum power generated, we must fix
the advance report F
is the maximum power
cient
.
2.2.2.Generator Model
In real wind power market, three types of wind power
system for large WTs exist. The first type is fixed-speed
wind power (SCIG), directly connected to the grid. The
second one is a variable speed wind system using a DFIG
or SCIG. The third type is also a variable speed WT, PMSG
.

A STATCOM is a controlled reactive-power source. It
provides the desired reactive-power generation and absorption entirely by means of electronic processing of the voltage and current waveforms in a voltage source converter
(VSC). This function is identical to the synchronous condenser with rotating mass, but its response time is extremely faster than of the synchronous condenser. This rapidity is
very effective to increase transient stability, to enhance
voltage support, and to damp low frequency oscillation for
the transmission system .
The schematic representation of the STATCOM and its
equivalent circuit are shown in Fig 5.

Figure 5. STATCOM, VSC connected to the AC network via a shunt
transformer.

The STATCOM has the ability to either generate or ab-