The exploitation of renewable energy sources in the building sector is a challenging aspect of achieving sustainability. The incorporation of a proper storage unit is a vital issue for managing properly renewable electricity production and so to avoid the use of grid electricity. The present investigation examines a zero-energy residential building that uses photovoltaics for covering all its energy needs (heating, cooling, domestic hot water, and appliances-lighting needs). The building uses a reversible heat pump and an electrical heater, so there is not any need for fuel. The novel aspect of the present analysis lies in the utilization of hydrogen as the storage technology in a power-to-hydrogen-to-power design. The residual electricity production from the photovoltaics feeds an electrolyzer for hydrogen production which is stored in the proper tank under high pressure. When there is a need for electricity, and the photovoltaics are not enough, the hydrogen is used in a fuel cell for producing the needed electricity. The present work examines a building of 400 m2 floor area in Athens with total yearly electrical demand of 23,656 kWh. It was found that the use of 203 m2 of photovoltaics with a hydrogen storage capacity of 34 m3 can make the building autonomous for the year period.