Wind power technology - Wind Power Integration: Connection and System Operational Aspects - page 86

P S grid

V S ∠ d V R ∠0

X grid

Grid

ref
S gen

P

ref
S grid

P X grid
V S V R

δ

PWM

δ =

V R

V S (= V R )

ref
S gri Q

grid

ref
S grid

Q = 0

V S = V R +

V S

Figure 3.30 Load angle control of the grid-side converter

Note: The Betz Limit

Kinetic energy in the wind
Consider an airstream flowing at velocity V through an area A . If the air density is
r , the kinetic energy per unit volume is

1
2 r V 2
The wind power P over area A is the rate at which kinetic energy flows
through it

1
2 mV 2

E ¼ ¼

1
2 r AV 3
Taking r¼ 1.2 kg/m 3 , a wind speed of 10 m/s would appear to be able to
produce 600 W/m 2 . However, there is a theoretical limit.

P ¼ EAV ¼

Turbine air flow
From Figure 3.31, the mass flow rate is given by

m ¼ r AV ¼ r A 0 V 0

Turbine energy capture
A turbine will slow the upstream free air velocity V to V 0 downstream. The mass
flow rate through the turbine is

m ¼ r A V þ V 0
2