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This paper presents an energy management system (EMS) for a smart home, which is equipped with a fuel cell used for heat and power cogeneration, a PV system, an electric car, a battery and a storage unit for thermal energy. The EMS is computed using dynamic programming and considers the financial consequences of energy demand and generation and the availability of the electric car according to the driver's preferences and habits. We evaluate the performance of the proposed EMS with numerical simulations and compare it to a simpler management system that aims to generate as much electrical energy as possible within the household. The results show that the presented approach enables the response of demand and generation in the household to the supply conditions of electricity. Additionally, we describe and discuss a way to decrease the computation time of the EMS by approximating the influence of random variables.