Calculation of the power generated by a wind turbine:
A wind turbine power curve is represented in a simplified manner by:
Cp is the conversion rate of the turbine:
ρ=1.225 kg.m-3
a. Calculate the swept area (A) of the turbine such as the power is a continuous function at v=12 m.s-1.
When v= 12 m.s-1, the power delivered by the turbine is equal to 1.5 MW and is also defined by a constant conversion rate Cp=0.37.
b. What is the radius of the turbine?
c. If the tip speed ratio is equal to 6, what is the rotation speed for v=12 m.s-1?
d. This turbine is installed at a site where the average wind speed is equal to at the elevation of the turbine hub. Draw on the same graph the power curve of the turbine and the Rayleigh's function providing the PDF of the wind speed of the site.
e. Show the average wind speed, the most probable wind speed and the most contributing wind speed.
Most probable wind speed equals 0.8 average speed: 6.4 m/s
Most contributing wind speed equals 1.6 average speed: 12.8 m/s
f. What is the probability for the turbine not to producing (v<4 m.s-1 or v> 25 m.s-1)?
Hint:
Probability for vo is
g. What is the probability for the wind speed being between 12 m.s-1and 25 m.s-1?
h. What is the annual energy produced when the turbine is at its maximum power (1.5 MW)?
By definition of a PDF:
Therefore when (which is when 12
i. What is the annual energy produced by the turbine when its conversion rate is constant (Cp=0.37)?
Similarly to h, we can calculate the average power generated when the conversion rate of the turbine is constant (4
j. What is the energy generated by the turbine over a year?
From h and I the energy generated by the turbine over the year is:
Energy= 2,238 + 2,806=5,044 MWh
k. What is the capacity factor of the turbine at this site?
By definition:
l. Is this turbine well adapted to the site?
Yes, this turbine is well adapted to the site since it has a capacity factor between 0.35 and 0.40. It combines larger capacity factor which allows a better return on investment and a good average conversion rate which provides a larger amount of energy.