Wind power technology - Wind Power Integration: Connection and System Operational Aspects - page 75

Electrical
output

P s

Mechanical
input

P air gap

P m

P r

Stator
Cu + iron
losses

Rotor Cu
loss

Power through
the slip rings

Figure 3.20 DFIG power relationships

From (3.17) and (3.18), the stator power P s is expressed by

P s ¼ P m P r ð 3 : 19 Þ

Equation (3.19) can be written in terms of the generator torque, T ,as

T w s ¼ T w r P r ð 3 : 20 Þ

where P s ¼ T w s and P m ¼ T w r . Rearranging terms in (3.20),

P r ¼ T ðw s w r Þ ð 3 : 21 Þ

The stator and rotor powers can then be related through the slip s as

P r ¼ sT w s ¼ sP s ð 3 : 22 Þ

where s is given in terms of w s and w r as

s ¼ ð w s w r Þ
w s

ð 3 : 23 Þ

Combining (3.19) and (3.22) the mechanical power, P m , can be expressed as

P m ¼ P s þ P r
¼ P s sP s
¼ð 1 s Þ P s

ð 3 : 24 Þ

The total power delivered to the grid, P g , is then given by
P g ¼ P s þ P r

ð 3 : 25 Þ

The controllable range of s determines the size of the converters for the DFIG.
Mechanical and other restrictions limit the maximum slip and a practical speed
range may be between 0.7 and 1.1 pu.