## 4 Results  
In this section, the results of the integrated optimal sizing and operation in terms of Equivalent Annual Cost are shown and discussed. As mentioned, the optimization has been performed for both the energy system configurations shown in Figure 1, i.e., the proposed configuration with a reversible heat pump as single thermal back-up unit, and the traditional configuration with a boiler and a non-reversible electric chiller as thermal back-up units. Table 3 summarizes the main results obtained from the optimizations. In the evaluation of the carbon dioxide emissions, the values of the carbon intensity of the electricity from the grid and the natural gas are 325.2 and 202.0 g\({}_{\text{CO2 eq}}\)/kWh, respectively [42]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** & **Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(a_{ICE}\) & 7789 [13] & \(b_{CT}\) & 1 [37] & \(a_{B}\) & 345.9 [38] & \(b_{WT}\) & 1 [39] \\ \(b_{ICE}\) & 0.6 [13] & \(a_{RHP}\) & 1036 [23] & \(b_{B}\) & 0.79 [38] & \(r\) & 7\% [13] \\ \(a_{AC}\) & 375 [40] & \(b_{RHP}\) & 0.74 [23] & \(a_{PV}\) & 1500 [39] & \(c_{F}\) & 0.052 \(\ell\) kWh [41] \\ \(b_{AC}\) & 0.65 [40] & \(a_{EC}\) & 609 [23] & \(b_{PV}\) & 1 [39] & \(c_{PE}\) & 0.166 \(\ell\)/kWh [41] \\ \(a_{CT}\) & 28.75 [40] & \(b_{EC}\) & 0.79 [23] & \(a_{WT}\) & 1570 [39] & \(c_{SE}\) & 0.040 \(\ell\)/kWh [13] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Price of energy carriers and investment cost parameters (used in Equations (13)–(15)). Figure 5: Hourly energy demand data of the case study. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Energy System Configuration** & **Novel Configuration with** & **Traditional Configuration with** \\  & **Reversible Heat Pump** & **Boiler and Non-Reversible** \\  & & **Electric Chiller** \\ \hline Internal Combustion Engine (Nominal Electric Power) & 165 kW & 250 kW \\ Absorption Chiller & 190 kW & 290 kW \\ (Cooling Capacity) & 795 kW/660 kW & \(\backslash\) \\ Reversible Heat Pump (Heating/Cooling Capacity) & \(\backslash\) & 615 kW \\  & Electric Chiller & \(\backslash\) & 575 kW \\  & & 505 kW & 410 kW \\  & Wind Turbine & 0 kW & 0 kW \\  & Annual Operating Cost & 175.6 kW & 203.3 k€ \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal Equivalent Annual Cost: sizing and operation—results. First and foremost, the proposed configuration with reversible heat pump achieves the lowest EAC, with a 7% saving compared to the traditional configuration. The discounted payback period, considering the initial extra investment and annual cost savings of the proposed configuration compared to the traditional one, is around 2.5 years. Moreover, the installed capacity of RES is 23% higher in the proposed configuration. This is due to the installation of the reversible heat pump; indeed, the larger share of cooling covered by the RHP compared to the non-reversible electric chiller allows a higher self-consumption of the electricity produced by RES. Both the optimal design solutions do not comprise the wind turbine, because of the low wind speed at the site. For this reason, all the installed RES capacity is represented exclusively by the PV system. Another significant effect of the integration of the reversible heat pump is the low value of the annual carbon dioxide emissions, which is around 11% lower than that of the traditional configuration. Indeed, the use of natural gas is reduced by 18% with the integration of the reversible heat pump, as a result of the elimination of the boiler and the 34% downsizing of the internal combustion engine. Moreover, according to the European Commission Decision establishing the guidelines for Member States on calculating renewable energy from heat pumps [43], part of the energy produced by the heat pump may be considered as renewable energy if the seasonal coefficient of performance (SCOP) is higher than 2.5. In the case study, the SCOP of the reversible heat pump is equal to 3.3.