Optimal economic layout of turbines on windfarms

A general discrete model is formulated for the expected (i) Net Present Value (NPV) of the profit and (ii) yield of the investment (Internal Rate of Return - IRR) derived from windfarms on flat ground or over water. It is assumed that the wind-turbines are identical and of equal height, and are spaced equally along the axes of a rectangle, but not nesessarily at the same equal distance along both axes. The model considers wind shadowing in the down-wind direction and the effect of wakes behind the turbines, the joint wind-direction wind-velocity probability distribution and various relevant cost and revenue factors. Using the model, the optimal layout that maximizes the expected NPV and/or IRR was derived numerically for a given data set. The calculation proceeded in stages, so determining the optimal number and separation of turbines by row and column. Sensitivity analysis has shown that minor changes in the parameters do not affect the selection of the optimal layout.