Capacity factors for wind turbines

Capacity factors in Finland for six wind turbine models, Vestas V90-3.0 MW, V90-2.0 MW, V112-3.3 MW, V126-3.3 MW, V117-3.45 MW and V136-3.45 MW at four turbine hub heights 75, 100, 125, 150 m. Wind speed data are from Finnish Wind Atlas [1, 2], from which the Weibull distribution shape and scale parameters (labeled ‘Weibull all data k’ and ‘Weibull all data A’, respectively) and the frequencies of the wind sectors (‘Frequency all data’) were used.

To simulate a wind farm where each turbine experiences a slightly different wind speed, we used a normal distribution with variance \(\sigma^2(v) = 0.2v + 0.6\,\mathrm{m/s}\), (where v is wind speed) to smooth (convolute) the original power curves [3, 4].

The calculation of capacity factor cf at wind atlas grid point k is described by the formula
\(\mathit{CF}_k = \mathop{\mathbb{E}}_{i, s} g(v_i) \approx \sum_{s=1}^{12} f_{k,s} \sum_{i=1}^N p_{k,s}(v_i) g(v_i) \Delta v\),
where g(v) is the power curve function for current wind turbine model, vi the mean wind speed of bin i, fk,s the frequency of occurrence of wind direction s at point k, N the number of wind speed bins, pk,s(v) the Weibull probability density function for sector s at point k at the hub height and Δv the width of the wind speed bin.

References

1. Finnish Meteorological Institute, “Finnish Wind Atlas,” 2008. [Online]. Available: http://www.windatlas.fi. [Accessed: 28-Jun-2016]
2. B. Tammelin, T. Vihma, E. Atlaskin, J. Badger, C. Fortelius, H. Gregow, M. Horttanainen, R. Hyvönen, J. Kilpinen, J. Latikka, K. Ljungberg, N. G. Mortensen, S. Niemelä, K. Ruosteenoja, K. Salonen, I. Suomi, and A. Venäläinen, “Production of the Finnish Wind Atlas,” Wind Energy, vol. 16, no. 1, pp. 19–35, Jan. 2013.
3. Staffell, Iain, and Richard Green. 2014. “How Does Wind Farm Performance Decline with Age?” Renewable Energy 66. Elsevier Ltd: 775–86. doi:10.1016/j.renene.2013.10.041.
4. Staffell, Iain, and Stefan Pfenninger. 2016. “Using Bias-Corrected Reanalysis to Simulate Current and Future Wind Power Output.” Energy 114 (November): 1224–39. doi:10.1016/j.energy.2016.08.068.