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Efficient energy production and consumption are fundamental points for reducing carbon emissions that influence climate change. Alternative resources, such as renewable energy sources (RESs), used in electricity grids, could reduce the environmental impact. Since RESs are inherently unreliable, during the last decades the scientific community addressed research efforts to their integration with the main grid by means of properly designed energy storage systems (ESSs). In order to highlight the best performance from these hybrid systems, proper design and operations are essential. The purpose of this paper is to present a so-called model predictive controller (MPC) for the optimal operations of grid-connected wind farms with hydrogen-based ESSs and local loads. Such MPC has been designed to take into account the operating and economical costs of the ESS, the local load demand and the participation to the electricity market, and further it enforces the fulfillment of the physical and the system's dynamics constraints. The dynamics of the hydrogen-based ESS have been modeled by means of the mixed-logic dynamic (MLD) framework in order to capture different behaviors according to the possible operating modes. The purpose is to provide a controller able to cope both with all the main physical and operating constraints of a hydrogen-based storage system, including the switching among different modes such as ON, OFF, STAND-BY and, at the same time, reduce the management costs and increase the equipment lifesaving. The case study for this paper is a plant under development in the north Norway. Numerical analysis on the related plant data shows the effectiveness of the proposed strategy, which manages the plant and commits the equipment so as to preserve the given constraints and save them from unnecessary commutation cycles. • A hydrogen-based ESS model includes several degradation costs of the electrolyzer and fuel cell. • Degradation costs concern working cycles and life spans of the electrolyzer and fuel cell. • Features, like warm and cold start, are considered through continuous and logical states combined. • An MPC controller minimizes the logical state switching between different operating modes. • The controller meets local load demand and maximizes revenue in the electricity market. [ABSTRACT FROM AUTHOR]