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The need for frequency regulation capacity increases as the fraction of renewable energy sources grows in the electricity market. An aggregator can provide frequency regulation by controlling its generation and demand. Here we investigate the participation of an aggregator controlling a fleet of electric vehicles (EVs) and an energy storage (ES) in day-ahead regulation and energy markets and determine the optimal size of the aggregator's bids. The problem is formulated as a stochastic mixed integer linear programming model, taking into account the uncertainties regarding energy and frequency regulation prices. The risks associated with the uncertainties are managed using the conditional value-at-risk method. Because most EVs are charged in residential distribution networks, load flow constraints are also taken into account. A linear formulation based on the rainflow cycle counting algorithm is proposed to include the ES degradation costs incurred from following the frequency regulation signals into the objective function. The problem is studied within the context of a medium-voltage distribution network adopting the market rules of the California Independent System Operator. The results of the numerical analysis show how joint optimization of EVs and ES can improve the aggregator's profit, and verify that the proposed degradation cost formulation can effectively minimize the degradation costs of the ES.
Vatandoust et al. (2018) studied this question.