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We introduce and study various models for satisfying electrical energy demands of prosumers in a microgrid, while optimizing their costs. Each prosumer has individual demands of electrical energy, which can vary day-by-day, and which they can satisfy by either generating electrical energy through a self-operated mini power plant like a solar panel, through buying from an external energy provider, such as the main grid or by trading with other prosumers. Our models take into account two key aspects motivated by real-life scenarios: first, we consider a daily volatility of prices for buying and selling the energy, and second, the possibility to store the self-generated energy in a battery of finite capacity to be either self-consumed or sold to other prosumers in the future. We provide a thorough complexity analysis, as well as efficient algorithms, so that prosumers can minimize their overall cost over the entire time horizon. As a byproduct, we also solve a new, generalized version of the KNAPSACK problem which may be of independent interest. We complement our theoretical findings by extensive experimental evaluations on realistic data sets.
Codazzi et al. (Fri,) studied this question.