Generalized Empirical Regret Bounds for Control of Renewable Energy Systems in Spatiotemporally Varying Environments

Abstract

This paper focuses on the empirical derivation of regret bounds for mobile systems that can optimize their locations in real time within a spatiotemporally varying renewable energy resource. The case studies in this paper focus specifically on an airborne wind energy system, where the replacement of towers with tethers and a lifting body allows the system to adjust its altitude continuously, with the goal of operating at the altitude that maximizes net power production. While prior publications have proposed control strategies for this problem, often with favorable results based on simulations that use real wind data, they lack any theoretical or statistical performance guarantees. In the present work, we make use of a very large synthetic data set, identified through parameters from real wind data, to derive probabilistic bounds on the difference between optimal and actual performance, termed regret. The results are presented for a variety of control strategies, including maximum probability of improvement, upper confidence bound, greedy, and constant altitude approaches. In addition, we use dimensional analysis to generalize the aforementioned results to other spatiotemporally varying environments, making the results applicable to a wider variety of renewably powered mobile systems. Finally, to deal with more general environmental mean models, we introduce a novel approach to modify calculable regret bounds to accommodate any mean model through what we term an "effective spatial domain."