Maximum Power Point Tracking Control of Wind Energy Conversion Systems - Wind Turbine Control and Monitoring - page 57

i d ¼ i deq þ i dn

ð 3 : 25 Þ

p u

i L þ C

2E s c 1 e q 1 = p 1

i deq ¼ ð 3 : 26 Þ

1

E s

i dn þ T 1 i dn ¼ v

ð 3 : 27 Þ

v ¼ð k 1 þ g 1 Þ sgn ð s 1 Þ ð 3 : 28 Þ

Þ; T 1 [ 0 ; k 1 [ 0.

where g 1 ¼ max ð T 1 i dn

Proof Consider the following Lyapunov function:

V ¼ 1

2 s 1

ð 3 : 29 Þ

Differentiating V with respect to time gives:

V ¼ s 1 s 1

ð 3 : 30 Þ

Based on Eqs. ( 3.22 ) and ( 3.23 ), it can be obtained:

p u

s 1 ¼ 2

C E s i d þ 2

i L þ c 1 e q 1 = p 1

1

C

Substituting Eqs. ( 3.25 ) and ( 3.26 ) into the above equation gives:

s 1 ¼ 2

C E s i dn

Differentiating s 1 with respect to time, it can be obtained:

s 1 ¼ 2

C E s i dn

Substituting the above equation into Eq. ( 3.30 ) gives:

s 1 s 1 ¼ 2

C E s s 1 i dn

Substituting Eqs. ( 3.27 ) and ( 3.28 ) into the above equation gives: