To increase the penetration of photovoltaic renewable energy (PV RE) in the residential building sector energy mix, the mismatch between mid-day production and evening electrical energy demand must be bridged. The use of heat pumps for space heating of residential buildings creates an opportunity for energy flexible residential buildings that rely on low-cost thermal energy storage systems. This paper explores the 'building as battery' concept (BaB), i.e. the use of the structural thermal capacity as a heat storage medium in winter. In these systems the building internal mass is preheated during solar daytime hours (using a PV RE powered heat pump) and cooled by discharge into the room air after sunset, for space heating. This study presents measured and simulated performance of BaB systems used for thermal energy storage in living rooms of three different apartment buildings with variable thermal insulation levels, ranging from typical southern Europe 1980s construction to a insulated apartment (Passive House certified). To assist in interpreting the results and facilitate their integration in simplified simulation of BaB systems in smart grids the model parameters of a simplified Resistance Capacitance model were found by fitting the experimental results. The results show that, for apartments with high thermal mass, thermal insulation is the key driver of BaB system thermal efficiency, with the highly insulated apartment reaching BaB efficiencies of 60-80%. For existing apartments with a low thermal insulation, the BaB approach is only effective when space heating is required right after sunset (just when PV RE powered heat pump charging finishes).