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Zero Energy Buildings (ZEBs) are considered as one of the key elements to meet the Energy Strategy of the European Union. This paper investigates cost-optimal solutions for the energy system design in a ZEB and the subsequent grid impact. We use a Mixed Integer Linear (MILP) optimisation model that simultaneously optimises the building’s energy system design and the hourly operation. As a ZEB have onsite energy generation to compensate for the energy consumption, it is both importing and exporting electricity. The hourly time resolution identifies the factors that influence this import/export situation, also known as the building’s grid impact. An extensive case study of a multi-family house in Germany is performed. The findings show that the energy system design and the grid impact greatly depend on the ZEB definition, the existing policy instruments and on the current energy market conditions. The results indicate that due to the feed-in-tariff for PV, the cost-optimal energy design is fossil fuelled CHP combined with a large PV capacity, which causes large grid impacts. Further, we find that heat pumps are not a cost-optimal choice, even with lower electricity prices or with increased renewables in the electric power system. [ABSTRACT FROM AUTHOR]