Analytical modelling of wind speed deficit in large offshore wind farms.pdf

Analytical Modelling of Wind Speed Deficit in Large Offshore Wind Farms Sten Frandsen*, Rebecca Barthelmie, Sara Pryor, Ole Rathmann, S?ren Larsen and J?rgen H?jstrup, Ris? National Laboratory, DK-4000 Roskilde, Denmark Morten Th?gersen, EMD, Aalborg, Denmark The proposed model for the wind speed deficit in wind farms is analytical and encompasses both small wind farms and wind farms extending over large areas. As is often the need for offshore wind farms, the model handles a regular array geometry with straight rows of wind turbines and equidistant spacing between units in each row and equidistant spacing between rows. Firstly, the case with the flow direction being parallel to rows in a rectangu- lar geometry is considered by defining three flow regimes. Secondly, when the flow is not in line with the main rows, solutions are suggested for the patterns of wind turbine units cor- responding to each wind direction. The presentation is an outline of a model complex that will be adjusted and calibrated with measurements in the near future. Copyright ? 2006 John Wiley Sons, Ltd. Received 22 November 2004; Revised 8 November 2005; Accepted 10 November 2005 WIND ENERGY Wind Energ. 2006; 9:39–53 Published online 11 January 2006 in Wiley Interscience () DOI: 10.1002/we.189 Copyright ? 2006 John Wiley Sons, Ltd. Research Article * Correspondence to: S. Frandsen, Ris? National Laboratory, DK-4000 Roskilde, Denmark. E-mail: sten.frandsen@risoe.dk Contract/grant sponsor: Danish Public Service Obligation (PSO) Introduction The engineering models presently applied for calculating production losses due to wake effects from neigh- bouring wind turbines are based on local ‘unit-by-unit’ momentum equations, disregarding the two-way inter- action with the atmosphere. Other models, which did not reach engineering relevance or maturity, predict the array efficiency of infinitely large wind farms by viewing the wind turbines as roughness elements. A third option is to apply CFD sche