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The increasing share of renewable energies in the electricity sector promotes a more decentralized energy supply and the introduction of new flexibility options. These flexibility options provide degrees of freedom that should be used optimally. Therefore, in this paper, a model predictive control-based multi-objective optimizing energy management concept for a hybrid energy storage system, consisting of a photovoltaics (PV) plant, a battery, and a combined heat pump/heat storage device is presented. The concept’s objectives are minimal operation costs and reducing the power exchanged with the electrical grid while ensuring user comfort. In order to prove the concept to be viable and its objectives being fulfilled, investigations based on simulations of one year of operation have been carried out. Comparisons to a simple rule-based strategy and the same model predictive control scheme with ideal forecasts prove the concept’s viability while showing improvement potential in the treatment of nonlinear system behavior, caused by nonlinear battery losses, and of forecast uncertainties.

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