Page 186 - Hybrid-Renewable Energy Systems in Microgrids

Sensitivity and transient stability analysis of fixed speed wind generator 167

Machine equations are represented with respect to synchronously rotating reference
frame. For both stator and rotor, negative sign indicates currents out of the generator.
The system parameters and initial conditions are given in the Appendix. Modeling of PW=12ρW.AW.V .Cpwλw,βw
3
individual components is discussed as follows.

2.1 Wind turbine modeling

The WT extracts the mechanical power from the wind that can be calculated as [19]:

1
3
.
.
,
P = ρ A VC ( λ β ) (9.1)
W
2 W . W pw w w
2
3
where ρ w is the air density (kg/m ), A w is the area of turbine blade (m ), V w is the wind
velocity (m/s), C pw is the power coefficient, λ w is the tip speed ratio, and β w is the pitch
angle (degree). The power coefficient C pw is given by:
)
2
,
C ( α β ) = 0.5 λ ( − 0.02 β − 5.6 exp [−0.17 λ] (9.2) 2
ρw w w w Cρwαw,βw=0.5λw−0.02β −
5.6exp−0.17λ
The tip speed ratio is defined as:
R ω .
λ = bw w
m (9.3) λm=Rbw.wwVw
V w
where, R is the blade radius (m), w is the rotational speed (rad/s). The turbine
w
bw
torque coefficient C is related with turbine power coefficient C by the equation:
tw
pw
ρw
C tw ( λ) = C λ (9.4) Ctwλ=Cρwλ

1
2
.
T = . ρ A RC ( λ) (9.5) Tmw=12.ρw.Aw.Rbw2.Ctwλ
.
.
mw
2 w w bw tw
In Eq. (9.5), T mw is the WT output torque (Nm). The turbine operates at rated speed
since fixed speed is considered (Fig. 9.2).
2.2 Drive train modeling
Fig. 9.3 shows detailed and simplified two-mass drive train model of the WT generator
system.
This study considers the simplified two-mass model, which is sufficient for dynamic
and transient analyses [20].
The two-mass model can be expressed by: