Optimal Power Smoothing of Airborne Wind Energy Systems via Pseudo-Spectral Methods and Multi-objective Analysis

The problem of optimizing the power output of a class of Airborne Wind Energy Systems (AWES), named fly-gen, is considered. Fly-gen AWES, called windplanes in this paper, harvest wind power by means of an autonomous tethered aircraft that carries out periodic trajectories roughly perpendicular to the wind flow (crosswind conditions), using onboard turbines and converters and an electric tether to transfer power to the ground. The amount of generated power and its variability strongly depend on the flown trajectory, whose optimization is a highly nonlinear and non-convex problem. Differently from most of the existing literature on the topic, this problem is here addressed from a multi-objective perspective, where both the average power and its variability are considered. Through a recently-proposed pseudo-spectral decomposition of the states and inputs, a rather small-scale nonlinear program is derived to obtain a periodic orbit that maximizes the average power under a constraint on its variability. Then, a series of such programs is formulated and solved to approximate the Pareto front of the problem. Finally, the latter is exploited to analyze the possible trade-offs. The main finding of this work is that, contrary to what postulated so far in the scientific community, it is possible to operate the windplane with minimal power fluctuations (10% of the average) with a very small reduction of mean power, of the order of 5% with respect to the maximum achievable. Additional considerations regarding the sensitivity of the optimal trajectories to various factors are presented, too. These results pave the way for a completely novel way of optimizing and controlling windplanes.