# Optimization of Heat Pump Systems in Buildings by Minimizing Costs and CO\({}_{2}\) Emissions
## 6 Conclusions  
In this paper, a methodology for selecting the optimal heat production and supply systems for various building types, considering technical, economic, environmental, and social factors was presented. The methodology enables us to minimize total costs and reduce CO2 emissions of the heating system consisting of various HPs and EHs over a 10-year period, taking into account changes in technical and economic parameters over that time frame. The optimization problem was addressed through a multi-objective approach and solved using MINLP, resulting in the optimal number of components and their optimal operating hours each month. The model was applied to various types of renovated and unrenovated buildings, including schools, kindergartens, apartment buildings, and supermarkets. The results provide a comparison of the heating system's dependence on building type, heat demand, and efficiency. Furthermore, the model can be easily expanded to include additional technologies of HPs or EHs and adapted to any specific building, making it a highly applicable tool. The results of the performed case study demonstrated that the capacity of the optimal heat production and supply system is dependent on the building's heat demand and efficiency. The supermarket required the largest heating system with a capacity of 310.8 kW, with an annual heat demand of 569 MWh. On the other hand, the lowest capacity of heating system was required for the renovated three-story apartment building, with a capacity of 22.97 kW and an annual heat demand of 59.21 MWh. The results of the analysis of various heating technologies, including air-to-water, ground source, hybrid HPs, and EHs, revealed that the optimal solution was a combination of air-to-water HPs and EHs. For the specific case of an unrenovated school and a supermarket, the combination of these technologies with hybrid HPs proved to be the most effective solution to meet their heat demand. This study emphasizes the importance of taking building characteristics, such as renovation status, into consideration when selecting heating technologies to ensure energy efficiency and cost-effectiveness. Based on the results of CO2 emissions, the highest CO2 emissions during the analyzed period were in the supermarket, for which two hybrid HPs were selected. Over a 10-year period, the use of hybrid HPs in the analyzed supermarket was expected to result in the emission of approximately 73 tons of CO2, which corresponds to a cost of approximately 12k EUR. Additionally, CO2 emissions were measured in both the renovated and unrenovated schools, which produced 24 and 39 tons of CO2 emissions, respectively. For the remaining analyzed buildings, the goal of making the heating system neutral in terms of CO2 emissions was achieved. The economic viability of various heating systems for buildings was assessed using financial indicators. The results showed that low production costs and high demand lead to high profits and positive financial performance. The heating systems in renovated five-story and unrenovated nine-story apartment buildings had the most favorable economic outcomes, with an LCOH of 0.0831 EUR/kWh, short payback periods of 8.55 and 8.89 years, a high IRR of 8% and 7%, and a high NPV of 10.7k EUR and 9.8k EUR, respectively. Conversely, the worst-case scenario featured high production costs and low demand, resulting in low profits and negative financial performance. The heating systems in renovated three-story apartment buildings and renovated schools had unfavorable outcomes, with an LCOH of 0.0956 EUR/kWh and 0.0961 EUR/kWh, long payback periods of 21.73 years and 17.86 years, a negative IRR of \(-\)5% and \(-\)2%, and a negative NPV of \(-\)6.5k EUR and \(-\)19.6k EUR, respectively. The study suggests that while some heating systems may not be economically feasible, others offer promising investment opportunities. Therefore, it is crucial to account for both scenarios when making business decisions and reducing risks. **Author Contributions:** Conceptualization, R.U., R.B., L.M.