In modern smart grids, charging of local energy storage devices is coordinated on a residential level to compensate the volatile aggregated power demand on the time interval of interest. However, this results in a perpetual usage of all batteries which reduces their lifetime. We enforce group sparsity by using an ℓp,q-regularization on the control to counteract this phenomenon. This leads to a non-smooth convex optimization problem, for which we propose a tailored Alternating Direction Method of Multipliers algorithm. We elaborate further how to embed it in a Model Predictive Control framework. We show that the proposed scheme yields sparse control while achieving reasonable overall peak shaving by numerical simulations.
@article{arxiv.2002.03393,
title = {Distributed Control Enforcing Group Sparsity in Smart Grids},
author = {Philipp Sauerteig and Yuning Jiang and Boris Houska and Karl Worthmann},
journal= {arXiv preprint arXiv:2002.03393},
year = {2020}
}