Optimization of an Airborne Wind Energy system using constrained Gaussian Processes

Abstract

Wind resources tend to be significantly stronger and more consistent with increasing altitude. This effect creates a potential for power generation that can be reaped by an Airborne Wind Energy system positioned at elevations exceeding the height of conventional wind turbines. A frequent design for such a system includes a flying airfoil tethered to a ground station. The station can be equipped with a power generator or for the application considered here mounted to a sea vessel. We demonstrate a data based method that can maximize the towing force of such a system by optimizing a low level tracking controller at the presence of constraints. We utilise Gaussian Processes to learn the mapping from the set points of the controller to both the objective and the constraint function. We then formulate a chance - constrained optimization problem that takes into consideration uncertainty in the learned functions. The probabilistic objective function is transformed into a deterministic acquisition function which indicates set points with high probability of improving the current optimum and the constraint function is penalized in regions of high uncertainty to ensure feasibility. Simulation studies show that we can find optimal set points for the controller without the use of significant assumptions on model dynamics while respecting the unknown constraint function.