Offshore Wind
“The UK is a world leader in producing offshore wind energy”
“Offshore wind farms benefit from higher and more consistent wind speeds”
“Offshore wind farms are usually larger than onshore – as there is more space – so they can produce more energy”
EDF Renewables
Wind Resource Assessment
In order to calculate the total power output of the wind turbines, it is needed to evaluate real wind data from the proposed location. The data for this analysis was obtained from NASA’s website [1], which is also the database of HomerPro. The dataset consisted of daily wind speeds from 2011 up to 2020.
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Wind speed measurements were taken 10 meters above sea level, while the hub height of each turbine is 100 meters above the sea level. So, the first step was to adjust the wind speeds at rotors’ height, which resulted in higher values than the ones at lower height. For this purpose, power-law was applied and given by:
α=0.11 [2]
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As the wind data was transposed, the statistical analysis can be held. A common statistical analysis for daily and average wind speeds at a specific location, is the Weibull distribution. Its probability density function is given by:
where v is the wind speed, k is the dimensionless shape parameter and c is the scale parameter, which has the same units as the wind speed [3].
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The shape parameter (k) reflects the width of data distribution, and the larger the shape parameter is, the narrower the distribution will be. The scale parameter controls the scale of a plot of data distribution [3].The width of the data distribution is reflected by the shape parameter (k), and the greater the shape parameter, the narrower the distribution would be. The scale parameter determines the scale of the data distributed.
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Parameters k and c were calculated using MATLAB software and found k=2.5457 and c=9.3811.
Figure 1: Weibull distribution (k=2.5457, c=9.3811)(made with SPSS)
Wind Turbine- Power Output
The theoretical energy can be harvested by a wind turbine is given by:
where ρ is the density of the air at the hub height, u is the mean wind speed at hub height as well, and A is the swept area of the wind turbine [4].
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The power coefficient Cp (overall efficiency of turbine) is the defined as the ratio of the generated electrical power (Pe) to the available theoretical wind power (Pt):
The power coefficient depends on various characteristics of the wind turbine, such as aerodynamic, electrical and mechanical efficiency. The maximum theoretical power coefficient of a horizontal axis wind turbine is 59% (or Cp=16/27), a value calculated by a German scientist, which is called Betz limit.
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The efficiency (power coefficient) of a wind turbine is not constant; it varies with the wind speed and this variation is depicted in the power curve (Figure 2).
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Wind turbine power output is given by the equation:
Figure 2: Power curve of Vestas V164 7MW
The wind turbine is not able to produce electricity at very low wind speeds (< 4 m/s), due to a lack of torque to overcome friction, or at very high speeds (>25 m/s), otherwise it will be damaged. As the wind reaches the cut-in speed, the power output increases. Around certain speeds (12 – 24 m/s), though, the power output reaches a maximum level (limit), which is called rated power output, and this is the highest level at which the electrical generator can continue to operate. When the wind speed exceeds the rated output wind speed (>25 m/s), a mechanism is used to keep the power almost steady, such as changing the blade angles (pitch system).
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In our case we have chosen a Vestas V164 wind turbine of rated power of 7 MW with the specifications shown in Table 1.
Table 1: Wind turbine specifications
References
[1] https://power.larc.nasa.gov/data-access-viewer/
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[2] "Wind profile power law | Wikiwand", Wikiwand, 2021. [Online]. Available: https://www.wikiwand.com/en/Wind_profile_power_law. [Accessed: 12- May- 2021].
[3] T. Chang, F. Liu, H. Ko, S. Cheng, L. Sun and S. Kuo, "Comparative analysis on power curve models of wind turbine generator in estimating capacity factor", Energy, vol. 73, pp. 88-95, 2014. Available: 10.1016/j.energy.2014.05.091 [Accessed 12 May 2021].
[4] S. Neill and M. Hashemi, "Offshore Wind", Fundamentals of Ocean Renewable Energy, pp. 83-106, 2018. Available: 10.1016/b978-0-12-810448-4.00004-5 [Accessed 12 May 2021].