Nearly zero-emission buildings (nZEBs) are increasingly being constructed in Europe. There are also incentives to refurbish older buildings and transform them into nZEBs. However, permission is not always granted for their connection to the grid to infuse surplus photovoltaic electricity due to the grid being overloaded with a large number of renewables. In this study, the case of a refurbished school building in Central Greece is examined. After refurbishing it, a significant amount of photovoltaic electricity surplus is observed during the summer and neutral months, which cannot be exported to the grid. The absence of an adequate battery storage capacity resulted in the rejection of an application for exporting the school’s surplus to the network and the photovoltaic installation staying idle. An alternative approach is proposed in this work, involving a shift in the export of the photovoltaic electricity surplus to the evening hours, in order for the school to be granted permission to export it to the network. To this end, an optimal battery storage size is sought by employing a building energy system simulation. The mode of operation of the battery designed for this application is set to discharge daily, in order to export the electricity surplus in the afternoon hours to the evening hours, when it is favorable for the network. Additionally, the optimal size of the thermal energy storage of the heating system is studied to further improve its energy efficiency. Our battery and storage tank size optimization study shows that a significant battery capacity is required, with 12 kWh/kWp photovoltaic panels being recommended for installation. The ever-decreasing cost of battery installations results in the net present value (NPV) of the additional investment for the battery installation becoming positive. The solution proposed forms an alternative path to further increase the penetration of renewables in saturated networks in Greece by optimizing battery storage capacity.