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• A new energy system is developed and examined using dynamic modelling to meet the needs of a two-story structure. • To decrease the size of the plant, including the PVT size and fuel consumption, the PCM is incorporated into the building. • Fuel consumption and prices are reduced by 17.24% and 8.57%, respectively, using the suggested approach. • Exergy efficiency, unit product cost, and CO 2 emission of 64.3 %, 0.26 $/kWh, and 0.21 kg/kWh are obtained respectively at optimum point. The buildings energy sector is expected to account for 40% of total world energy consumption and 40% participation on total carbon dioxide emissions, according to the International Energy Agency reports. The present study proposes a novel integrated system to meet all loads of the house's energy requirements. The system employs a heat storage tank rather than pricey batteries, which helps to keep the total cost of the system as low as feasible. Also, the system is developed for an on-grid operation, being capable to sell surplus energy to the grid helping to reduce the payback time. Dynamic modeling is conducted to analyze the system performance to provide heating, cooling and power demands of a case study building, for which two scenarios of with and without Phase Change Material (PCM) incorporation is considered. The influence of critical design factors is investigated, after which a tri-objective optimization is carried out. It was found that, the integration of PCM energy storage would reduce the annual heating and cooling demands of the building by 25.6%. As a result, the exergy efficiency of the proposed system increases by 13 % and the product cost is reduced by 8.57%. Based on the obtained yearly average results, the proposed building energy system yields exergy efficiency, unit product cost, and CO 2 emission of 64.3 %, 0.26 $/kWh, and 0.21 kg/kWh, respectively. [ABSTRACT FROM AUTHOR]