Page 108 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

Offshore Wind Chapter | 4 101

The previous equation gives the values of the PDF at the centre of the bins.
It is usually not possible to find a perfect PDF that matches all these values.
However, using a curve fitting approach (e.g. trial and error), we can find the best
shape parameter (k) that can fit these values. The bottom plot in Fig. 4.15 shows
the Weibull distribution for two shape parameters: 2.2 and 3. Based on this plot,
k = 2.2 is a better fit. Note that once k is specified, the scaling parameter (c)
will be determined by the average wind speed and k (Eq. 4.15).

Calculation of Power Output and Capacity Factor
So far, the frequency distribution of the hourly wind speed has been determined
for this site. This distribution can be represented by a relative frequency
histogram or the Weibull distribution. By combining the power curve for
the wind turbines and wind probability distribution, the power output can be
estimated.
Consider a typical year that has 365 days or 8760 h. Based on our calcula-
tions, we can predict how many hours the wind blows with a certain speed, and
compute the power using the power curve. Then, we can do calculations for all
wind speeds and add the total power. Fig. 4.8 shows the power curve of a 6 MW
turbine representing (approximately) the Haliade-150 wind turbine.
Table 4.1 summarizes the details of the calculations for the electricity
production during a year for this project. Based on this table, the capacity factor
of the wind farm is 47.5%, and the annual production of electricity is about
125 GWh, if we directly use the histogram and relative frequencies. If we use
the PDF, the capacity factor and annual energy production will be 49.5% and
130 GW, respectively. The calculation steps are explained as follows:
1. Evaluate the power for each wind speed interval/bin based on the power
curve (Columns I and II)
2. Estimate the percentage of time (probability) that the wind blows for
each wind speed in bins (Columns III and IV). This probability can be
estimated based on the Weibull distribution (method 1; Column III) or
relative frequency (method 2; Column IV).
3. Determine how many hours in a year the wind blows for each wind speed.
This is calculated by multiplying the probabilities and the number of hours
in a year (8760): Columns V and VI.
4. Calculate energy for each bin by multiplying the number of hours that wind
blows with that speed (Column V or VI) and corresponding power (Column
II).
5. Sum all energy productions to calculate energy for a year.
6. Consider a reduction due to operation and maintenance. We assumed that
10% of the time the turbines are not available and reduced the energy
production by 10%, on average.
7. Multiply the energy production by number of turbines. According to
the table, the total energy production using method 1 (the Weibull