Dynamic Response of a Wind Farm Consisting of Doubly-Fed Induction Generators to Network Disturbance - Simulation and Modeling Methodologies, Technologies and Application - page 126

Fig. 2. Generic model of a DFIG

2.1 Aerodynamic Torque Model

Aerodynamic model involves the extraction of useful mechanical power from the
available wind power. Available wind power is given by

1
2

P = ρπ R V

23

(1)

wind

, R and V are the available power in the wind, air density (kg/m 2 ),
radius of the turbine blade (m) and the wind speed (m/s) that reaches the rotor swept
area (m 2 ). The fraction of wind power that is converted to the turbine mechanical
power

where

P

,

ρ

wind

P is given by

1

( )

P = ρπ R C

2

λ β , V

3

(2)

m p

2

where C gives the fraction of available wind power that is converted to turbine
mechanical power, and are the tip speed ratio and the pitch angle respectively.

λ β

C , λ

The and β are related by equation (3) and (4) [10]

c

 c 

5

( )

2 λ

C λ β , = c − c β − c e + c λ (3)

 

i

p 1 3 4 6

λ

  i

1 1 0.035

= −

(4)

λ 10.08 + β β

2

+ 1

i

c = 0.5176, c = 116, c =0.4, c = 5, c = 21 and c = 0.0068 ,the relationship

Given

between is given in figure 3.

The tip speed ratio is given by (5)

C against λ

at various β

R

V ω

t

λ = (5)