## 3 Results and Discussion  
### Key Performance Indicators (KPIs)  
In this Section, the standard key performance indicators (KPIs) [31] adopted to assess the energy and environmental performance of the four configurations of the HVAC system modeled in TRNSYS are described. First, the energy performance achievable by the system can be calculated on a monthly basis by means of the indicators reported in the following equations:  
\[COP_{n,i}=Q_{h,i}/\left(E_{el,compr,i}\right) \tag{1}\]  
\[COP_{i}=Q_{h,i}/\left(E_{el,compr,i}+E_{el,pump,i}\right) \tag{2}\]  
\[EER_{n,i}=Q_{c,i}/\left(E_{el,compr,i}+E_{el,pump,i}\right) \tag{3}\]  
\[EER_{i}=Q_{c,i}/\left(E_{el,compr,i}+E_{el,pump,i}\right) \tag{4}\]  
where \(COP_{n,i}\) and \(EER_{n,i}\) are the net energy performance coefficients of the heat pump only during the \(i\)-th month, \(COP_{i}\) and \(EER_{i}\) are the overall energy performance coefficients of the generating subsystem during the \(i\)-th month, which take into account both the heat pump and circulating pump's performance, \(Q_{h,i}\) and \(Q_{c,i}\) are the thermal energy supplied by the heat pump in heating and cooling mode during the \(i\)-th month, respectively, and \(E_{el,compr,i}\) and \(E_{el,pump,i}\) are the electric energy absorbed by the heat pump compressor and by the circulating pumps coupled to the generator during the \(i\)-th month, respectively. As pointed out before, the electric energy need of a single pump is calculated for configurations based on the air-source heat pump, whereas when the ground-source unit is considered, the contribution of two circulators (i.e., borefield side and load side of the heat pump) is taken into account. Finally, it is important to mention that the electric energy consumption of the external heat-exchanger fans for the air-source heat pump is already included in the COP and EER values provided by the manufacturer. Figure 5: Heating (**a**) and cooling (**b**) capacity, COP (**c**) and EER (**d**) of the ASHP at the minimum and maximum frequency for R-410A and R-454B. Similarly, it is possible to evaluate the net seasonal energy efficiency of the heat pump (\(SCOP_{n}\) and \(SEER_{n}\)) and of the whole HVAC system (\(SCOP\) and \(SEER\)) by means of Equations (5)-(8), where the summations of thermal and electric energy are performed over the entire duration of the heating and cooling periods. More in detail, the heating season ranges from 15 October to 15 April (182 days), while the cooling one ranges from 10 May to 10 September (123 days). \[SCOP_{n}=\sum_{i,heat}Q_{h,i}/\sum_{i,heat}E_{el,compr,i} \tag{5}\]  
\[SCOP=\sum_{i,heat}Q_{h,i}/\sum_{i,heat}\left(E_{el,compr,i}+E_{el,pump,i}\right) \tag{6}\]  
\[SEER_{n}=\sum_{i,cool}Q_{c,i}/\sum_{i,cool}E_{el,compr,i} \tag{7}\]  
\[SEER=\sum_{i,cool}Q_{c,i}/\sum_{i,cool}\left(E_{el,compr,i}+E_{el,pump,i}\right) \tag{8}\]  
Finally, the overall energy efficiency over the entire year can be assessed through the annual performance factor, calculated by Equations (9)-(10) for the heat pump (\(APF_{n}\)) and the entire HVAC system (\(APF\)):  
\[APF_{n}=\left(Q_{h}+Q_{c}\right)/\left(E_{el,compr,heat}+E_{el,compr,cool}\right) \tag{9}\]  
\[COP_{i}=Q_{h,i}/\left(E_{el,compr,i}+E_{el,pump,i}\right) \tag{2}\]0  
where \(Q_{h}\) and \(Q_{c}\) are the thermal energy supplied by the heat pump along the entire heating and cooling season, respectively, and \(E_{el,compr,heat}\), \(E_{el,pump,heat}\), \(E_{el,compr,cool}\) and \(E_{el,pump,cool}\) are the electric energy absorbed by the heat pump compressor and by the circulating pumps during the heating and cooling season, respectively. In addition, the TEWI (total equivalent warming impact) index has been selected to study the environmental performance of the studied system configurations.