Question

A wind turbine with cut-in velocity of 8m/s and cut-out velocity of 30 m/s is installed at a
site with Weibull shape factor 2.4 and scale factor of 9.8 m/s. for how many hours in a day,
will the turbine generate power, estimate the probability of wind velocity to exceed 30 m/s.

Answer 1

GIVEN DATA:

Cut in Velocity, (V₁) = 8 m/s, Cut out velocity, (V₂) = 30 m/s, Weibull shape factor, K = 2.4 and scale factor, c = 9.8 m/s

TO FIND:

No of power genrating hours of wind turbine in a day ?

SOLUTION:

The cumulative distribution function of the velocity, V is given by, F(V) =

Probability of wind velocity between V₁ and V₂ is given by, P(V1<V<V2) = F(V₂) - F(V₁)

i.e., P(V₁<V<V₂) =

P(V₈<V<V₃₀) = = 0.5409 - 4.29 = 0.540899

the turbine will generate power in a day = 0.54089924 = 12.98 hrs

The Probability of wind exceeding 30 m/s is given by P(V>V₃₀) = 1 - (1) =

= 4.29 = 0.000000429