Gradient Descent Algorithm with Greedy Repositioning Using Power Deficit Aggregation of Wakes to Accelerate the Offshore Wind Farm Layout Optimization Problem in Irregular Concession Areas

Abstract

Wind farm layout optimization is essential to maximize the energy production of renewable energy systems. A new layout optimization method for offshore wind farms is proposed to minimize power deficits due to the wake effect without limitation on the number of turbines, the shape, or the extension of the concession area. The main engine of the algorithm is a gradient-descent method in which throughout the optimization process, new turbines are progressively and randomly included within the concession area and quickly expand outward, looking for areas with less perturbation, in turn, pushing the previous ones. When the optimization process ends, to avoid local maxima, it enters into a process of suppression of the set of locations that cause the greatest potential (power deficit). Then, a map of potential for the entire area is created, and a greedy algorithm places new turbines to complete the layout with the final number of turbines. The overall process is completed in 25 s. To drastically speed up the search process and the creation of the potential map, a simplification has been validated and added: for turbines affected by multiple wakes, the resulting power has been calculated by using a linear aggregation of power deficits, instead of the usual linear (or quadratic) aggregation of speed deficits. Owing to this type of aggregation, an analogy is established between power deficit and repulsive non-isotropic electrostatic potential energy, which allows using the properties of conservative fields. Thanks to this, the process is 20 times faster than any other layout optimization algorithm found in the revised literature. Irregular concession areas are easily treated using Stokes’ theorem to detect outer points.