UC San Diego

Many design optimization problems, including the optimal layout of wind turbines within a wind farm, enforce constraints to prevent the design from crossing the boundary of the feasible space. When applying gradient-based optimization to such problems, the models must provide an accurate representation of the feasible space and be continuous, smooth, amenable to differentiation, and fast-to-evaluate. This thesis presents the work from two intertwined topics involved in modeling geometric non-interference constraints and wind farm optimization. First, we formulate a new method that uses B-splines to generate an efficient-to-evaluate level set function that approximates the signed distance function for boundary constraint enforcement. Adapting ideas from the field of surface reconstruction, we formulate an energy minimization problem to calculate the B-spline control point values. Unlike previous constraint formulations, the new method requires an initial setup, but results in a more efficient and scalable representation of the geometric non-interference constraint. We present the results of accuracy and scaling studies performed on our formulation. Second, we perform optimization studies to the design of a wind farm. Utilizing the aforementioned constraint method, we perform a layout, yaw misalignment, and hub height optimizations to improve the annual energy production of a wind farm. These models used are verified and compared to industry-leading frameworks that conduct similar optimization studies. Overall, the new constraint method provides an effective way to conduct optimization studies, such as the one conducted in this thesis, with high computational efficiency, and shows promise as a tool for many more design optimization problems.