# Optimization of Heat Pump Systems in Buildings by Minimizing Costs and CO\({}_{2}\) Emissions
## 4 Results
### Optimal Heating Systems for Different Buildings
After analyzing the optimal modes of operation for each month of the first year, it was found that HPs were used to meet most of the heat demand. Electric heaters were only used during peak demand hours when the capacity required to meet the demand exceeded the maximum capacity of the HP systems. Figure 8 illustrates the amount of heat produced by the selected EHs and HPs in the five-story and nine-story apartment buildings during the first year of the analyzed period. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Building No.**} & **Selected** & **Number of** & **Number of** & **Capacity of Heat** & **Capacity of** & **Total Capacity** & **Contibution to** & **Enticulation to** \\  & **Types of** & **Selected** & **Selected** & **Pumps in** & **Electric** & **of the Heating** & **Total Heat** & **Total Heat** \\  & **Heat Pumps** & **Heat Pumps** & **Electric Heaters** & **December, kW** & **Heaters, kW** & **System, kW** & **Production** & **Production** \\  & & & & & & & & **per Year, \%** & **per Year, \%** \\ \hline
1. & Air-to-water & 1 & 1 & 58.61 & 7.5 & 66.11 & 99.7 & 0.3 \\
2. & Air-to-water & 2 & 3 & 78.58 & 39 & 117.58 & 94.9 & 5.1 \\
3. & Air-to-water & 2 & 4 & 117.22 & 60 & 177.22 & 96.2 & 3.8 \\
4. & Air-to-water & 3 & 5 & 137.19 & 63 & 200.19 & 97.7 & 2.3 \\
5. & Air-to-water & 1 & 1 & 19.97 & 7.5 & 27.47 & 98.6 & 1.4 \\
6. & Air-to-water & 1 & 1 & 19.97 & 3 & 22.97 & 99.8 & 0.2 \\
7. & Air-to-water & 1 & 1 & 58.61 & 30 & 88.61 & 95.8 & 4.2 \\
8. & Air-to-water & 2 & 3 & 78.58 & 31.5 & 110.08 & 96.9 & 3.1 \\
9. & Air-to-water, & 1 & 4 & 96.91 & 46.5 & 143.41 & 95.1 & 4.9 \\  & hybrid & 1 & & & & & & \\
10. & Air-to-water, & 3 & 5 & 175.49 & 69 & 244.49 & 97.0 & 3.0 \\
11. & Air-to-water, & 2 & & & & & & \\  & hybrid & 2 & 9 & 193.82 & 117 & 310.82 & 96.2 & 3.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results for the optimal heating systems in different buildings. Figure 8 shows that in the analyzed apartment buildings, the highest heat demand occurred in December and January. During these months, EHs also contributed to heat production by covering peaks in heat demand. In contrast, during the warmer months of the year (May-October), HPs were sufficient to meet the heat demand, and EHs were not used. Furthermore, EHs produced the most heat in the unrenovated nine-story building in December (approx. 11.4%), when the heat demand in this building was also at its highest. EHs made a minor contribution to heat production in two-story and three-story apartment buildings, which had the lowest heat demand. After adjusting for the effect of building volume and comparing relative heat demand, the results of the analysis revealed some notable changes. Specifically, the buildings with the highest relative heat demands were the unrenovated five-story and two-story apartment buildings. Furthermore, in the unrenovated five-story building, EHs produced the most heat per m\({}^{3}\), they contributed to approximately 5% of the annual relative heat demand, and during January, they produced over 9% of the monthly heat demand. Additionally, it was found that during the first year of the analyzed period, the use of EHs in this apartment building accounted for the largest portion of electricity consumption. Specifically, the EHs accounted for 20% of the total electricity consumption per year. The most energy-efficient was the renovated five-story apartment building, with the lowest monthly relative heat consumption. Additionally, in this building, EHs relatively produced the least amount of heat energy compared to other buildings, and the amount of electricity consumed by EHs accounted for less than 1.5% of the total electricity consumption per year. The other efficient building was a renovated three-story apartment building where EHs were used minimally, and the electricity consumption attributable to the use of EHs constituted slightly less than one percent of the total annual electricity consumption for SH and DHW preparation.