# Optimization of Heat Pump Systems in Buildings by Minimizing Costs and CO\({}_{2}\) Emissions
## 4 Results
### Optimal Heating Systems for Different Buildings  
The optimization model simulations enabled us to determine the optimal heating systems for each building in terms of the type, number, and capacity of heat pumps and electric heaters needed to meet the heat demand for SH and DHW preparation. The results of the optimization include the optimal number of HPs and auxiliary EHs as well as the operating mode for each technology in hours per month over a 10-year period for each case analyzed. By minimizing the objective function of the problem analyzed, the dual objectives of lowest total costs of the selected heating system and lowest CO\({}_{2}\) emissions were achieved. The total costs include the cost of the installed technologies of the heating system, emission costs (if applicable), and maintenance and operation costs over a 10-year period. The main results of the optimized heating systems for different buildings are presented in Table 2, which includes the optimal heating system components, their heating capacity in December, and the proportion of heat produced by HPs and EHs in the first year for each analyzed building. Figure 7: Forecasted trend of CO\({}_{2}\) emission prices in Lithuania for the period of 2022–2031. Table 2 shows that, in all cases analyzed, the optimal heat production and supply system included air-to-water HPs as one of its components. Furthermore, for schools and a supermarket (buildings no. 9, 10, and 11), these HPs were combined with hybrid HPs. Therefore, the results of the problem showed that the goal of making the heating system neutral in terms of CO2 emissions was achieved for eight of the eleven buildings analyzed. However, the buildings for which hybrid HPs were selected will still slightly contribute to environmental pollution due to the burning of gas. 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 is expected to result in the emission of approximately 73 tons of CO2, which corresponds to a cost of approximately 12k EUR. During the analyzed period, CO2 emissions were measured in both the renovated and unenrovated schools; the renovated school produced 24 tons of CO2 emissions, while the unenrovated school produced 39 tons. This indicates that while hybrid HPs may be a cost-effective heating solution, their use may have environmental implications in terms of GHG emissions. However, utilizing an HP system instead of relying on DH significantly reduces CO2 emissions, especially when the DH supply is based on fossil fuels. Additionally, EHs of various capacities are selected for all buildings to meet the peak heat demand. The capacity of these EHs depends on the building's energy efficiency and the building's actual heat demand. The percentage of heat produced by EHs indicates that they covered the largest share of the total heat demand in the unenrovated five-story apartment building (no. 2). In this building, EHs produced approximately 5% of the total heat demand for the first year. Electric heaters made up the smallest proportion of the total heat needs in the most energy-efficient buildings, the five-story renovated apartment building (no. 1), as well as in two other buildings with low heat needs: the unenrovated two-story apartment building (no. 5) and the renovated three-story apartment building (no. 6). The capacity of the heat production and supply system depends on the actual heat needs in the buildings. The supermarket (building no. 9) had the highest actual heat demand and, as a result, had the highest total capacity of 310.82 kW. The renovated three-story and unenrovated two-story apartment buildings (no. 6 and 5, respectively), which had the lowest actual heat demands, had the smallest heating system capacities of 27.47 kW and 22.97 kW, respectively. The optimal modes of operation for the selected heat production and supply systems were also determined for the entire analyzed period.