Optimization of Wind Farm Layout and Wind Turbine Geometry Using a Multi-Level Extended Pattern Search Algorithm That Accounts for Variation in Wind Shear Profile Shape

This paper presents a multi-level Extended Pattern Search algorithm (EPS) to optimize both the local positioning and geometry of wind turbines on a wind farm. Additionally, this work begins to draw attention to the effects of atmospheric stability on wind farm power development. The wind farm layout optimization problem involves optimizing the local position and size of wind turbines such that the aerodynamic effects of upstream turbines are reduced, thereby increasing the effective wind speed at each turbine, allowing it to develop more power. The extended pattern search, employed within a multi-agent system architecture, uses a deterministic approach with stochastic extensions to avoid local minima and converge on superior solutions compared to other algorithms. The EPS presented herein is used in an iterative, hierarchical scheme — an overarching pattern search determines individual turbine positioning, then a sub-level EPS determines the optimal hub height and rotor for each turbine, and the entire search is iterated. This work also explores the wind shear profile shape to better estimate the effects of changes in the atmosphere, specifically the changes in wind speed with respect to height on the total power development of the farm. This consideration shows how even slight changes in time of day, hub height, and farm location can impact the resulting power. The objective function used in this work is the maximization of profit. The farm installation cost is estimated using a data surface derived from the National Renewable Energy Laboratory (NREL) JEDI wind model. Two wind cases are considered: a test case utilizing constant wind speed and unidirectional wind, and a more realistic wind case that considers three discrete wind speeds and varying wind directions, each of which is represented by a fraction of occurrence. Resulting layouts indicate the effects of more accurate cost and power modeling, partial wake interaction, as well as the differences attributed to including and neglecting the effects of atmospheric stability on the wind shear profile shape.