# Optimization of Heat Pump Systems in Buildings by Minimizing Costs and CO\({}_{2}\) Emissions
## 3 Case Study  
### Analysis of Heat Consumption  
In order to select the optimal heating system, the first step is to perform a detailed analysis of hourly heat consumption data, taking into account heat demand of the analyzed buildings, consumption trends, efficiency, and heat consumption peaks. Hourly heat consumption data of different buildings and hourly outdoor air temperatures were used for the statistical analysis. The analysis covered the period from 2021 to 2022 (hourly data for one full year). In total, data from 11 different buildings were analyzed, including renovated and unrenovated apartment buildings, schools, kindergartens, and a supermarket, to cover a wide spectrum of typical buildings. The general information of the selected buildings for the analysis is presented in Table 1.  
Among the constraints of the analyzed optimization problem is the requirement to meet the actual heat demands of each month during the analyzed period. To achieve this, the total monthly heat demand for SH and DHW preparation for the analyzed buildings were calculated from the hourly values. In addition, monthly values were summed to determine the total annual heat demand for each building, which is shown in Table 1. The actual heat consumption depends heavily on the area, volume, and whether the analyzed building is renovated or not. In order to eliminate the influence of building volume on heat consumption, the hourly relative heat demand (kWh/m\({}^{3}\)) was further analyzed. The highest heat demand for both renovated and unrenovated buildings was observed in December 2021, during which the average outdoor air temperature was the lowest (\(-3\)\({}^{\circ}\)C). The differences in relative heat consumption between renovated and unrenovated apartment buildings are presented in Figure 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Building No.** & **Building Type** & **Number** & **Renovation** & **Area, m\({}^{2}\)** & **Volume, m\({}^{3}\)** & **Annual Heat** & **Maximum Heat** & **Demand per** \\  & & **of Stories** & & & & & **Hou, kWh** \\ \hline
1. & Apartment building & 5 & Renovated & 2452 & 7357 & 221.16 & 65.03 \\
2. & Apartment building & 5 & Unrenovated & 2510 & 7530 & 397.28 & 123.03 \\
3. & Apartment building & 5 & Renovated & 4520 & 13,561 & 551.27 & 185.25 \\
4. & Apartment building & 9 & Unrenovated & 5866 & 17,598 & 658.96 & 199.23 \\
5. & Apartment building & 2 & Unrenovated & 460 & 1381 & 85.73 & 26.00 \\
6. & Apartment building & 3 & Renovated & 531 & 1594 & 59.21 & 20.58 \\
7. & Kindergarten & 2 & Renovated & 2146 & 6438 & 197.28 & 86.75 \\
8. & Kindergarten & 2 & Unrenovated & 2189 & 6567 & 255.49 & 109.00 \\
9. & School & 3 & Renovated & 6288 & 18,864 & 276.00 & 147.40 \\
10. & School & 2 & Unrenovated & 8495 & 25,485 & 644.17 & 243.00 \\
11. & Supermarket & 1 & Renovated & 7405 & 29,619 & 569.05 & 309.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main information of the analyzed buildings. Figure 2: Comparison of relative heat consumption in renovated and unrenovated apartment buildings. The presented data demonstrate that the consumption of renovated residential apartment buildings is, on average, 30% lower than that of unrenovated buildings. It was also observed that the relative heat consumption in unrenovated apartment buildings also depends on the number of stories; consumption was the highest in an unrenovated two-story building and the lowest in an unrenovated nine-story building (Figure 2). Heat consumption is not only dependent on whether the building is renovated or not but also on the type and purpose of the building and user habits. In commercial buildings and public institutions, heat consumption can be affected by the working hours in these buildings. When making technical decisions to update the heating system, it is crucial to take into account the energy needs of a specific building, which is why public institutions (e.g., schools and kindergartens) and a supermarket were included in the analysis.