An Extended Pattern Search Approach to Wind Farm Layout Optimization

An extended pattern search approach is presented for optimizing the placement of wind turbines on a wind farm. The algorithm will develop a two-dimensional layout for a given number of turbines, employing an objective function that minimizes costs while maximizing the total power production of the farm. The farm cost is developed using an established simplified model that is a function of the number of turbines. The power development of the farm is estimated using an established simplified wake model, which accounts for the aerodynamic effects of turbine blades on downstream wind speed, to which the power output is directly proportional. The interaction of the turbulent wakes developed by turbines in close proximity largely determines the power capability of the farm. As pattern search algorithms are deterministic, multiple extensions are presented to aid escaping local optima by infusing stochastic characteristics into the algorithm. This stochasticity improves the algorithm’s performance, yielding better results than purely deterministic search methods. Three test cases are presented: a) constant, unidirectional wind, b) constant, multidirectional wind, and c) varying, multidirectional wind. Resulting layouts developed by this extended pattern search algorithm develop more power than previously explored algorithms with the same evaluation models and objective functions. In addition, the algorithm’s layouts motivate a heuristic that yields the best layouts found to date.© 2010 ASME