Distributed control enforcing group sparsity in smart grids

In modern smart grids, charging of local energy storage devices is coordinated within the distribution grid to compensate the volatile aggregated power demand on the time interval of interest. However, this results in a perpetual usage of all batteries which in return reduces their lifetime. In this paper, 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 a tailored Alternating Direction Method of Multipliers algorithm is proposed. Furthermore, the algorithm is embedded in a Model Predictive Control framework. Numerical simulations show that the proposed scheme yields sparse control while achieving reasonable overall peak shaving.