Stochastic day ahead load scheduling for aggregated distributed energy resources

This paper presents an optimal Day-Ahead Electricity Market (DAM) bidding strategy for an aggregator leveraging a pool of residential prosumers: residential customers with local photovoltaic (PV) production and plug-in electric vehicle (PEV) charging flexibility. The aggregator's point-of-view differs from the social planner angle that is taken in the majority of the existing literature, mainly the aggregator is considered to be a private entity (e.g. an electricity retailer). We propose a novel approach to tackling this optimization problem, by including risk management in the objective function and chance constraints on the aggregated PEV mobility constraints. In a first step, we model local system constraints and define a stochastic optimization scheme that exploits the problem structure to distribute the objective among prosumers via dual-splitting. Dual splitting is achieved with two consensus variables: a shadow price for energy and for PEV charging. In a second step, we propose a projected gradient ascent algorithm to solve the dual problem and we prove its corresponding rate of convergence (upper-bound). Finally, we implement a case study, with a model of 100 prosumers, to illustrate the convergence rate of our algorithm. We show that we reach an acceptable level of precision with less than 50 iterations.