## Materials and Methods
### Annual Energy and Economic Analysis  
The annual PER is reported in Figure 16, also considering the electricity consumption by the circulation pumps (PER*). The latter was not negligible at all, mainly due to the pressure drops of the ground circuit. For example, for the A3 case the annual pump electricity consumption was around 1650 kWh: this was 3% of the total thermal and cooling useful energy, and around 11% of the total no-renewable primary energy supplied to the plant. Such a percentage was consistent with data found in previous authors' work in similar multi-source heat pump plants [26,27].  
From the energy performance point of view, the best solution was A4 (PER = 2.12, PER* = 1.92), whereas A3 was in second place.  
A more comprehensive choice of the preferred alternative can be done by considering the economic point of view as well. A reasonable estimate of the absorption single effect machine investment cost, and the evacuated tube and flat plate solar collectors specific cost was 26,500 \(\upmu\), 545 \(\upmu\)m\({}^{-2}\), and 310 \(\upmu\)m\({}^{-2}\) respectively (literature and manufacturer's average values [29, 30, 31, 32, 33]). The total investment costs for the solar thermal plant reported in Table 8 were determined by further reasonable hypotheses about  
Figure 16: PER and electricity consumption by the circulation pumps (PER*) for the different alternatives.  
Figure 15: Energy demand percentage covering of different energy sources and the primary energy ratio (PER) (alternative A3).  
the cost of other equipment (pumps, tubes, boiler, valves, etc.), and considering a 30% discount on price catalogue values. The cost of the ground field was calculated considering 10,000 \(\upcels\) of fixed cost plus 25 \(\upcels\) per meter of ground heat exchanger. The same table also reports the value of the economic incentive (\"Conto Energia Termico 2.0\"), that is defined as 65% of the plant total investment cost for retrofitting of nZEB [34]. For public buildings like schools, such an incentive can be allocated once at the beginning of the intervention.  
Other parameters useful for the economic analysis are: NG cost fixed at 0.70 \(\upcels\) Nm\({}^{-3}\), electricity cost at 0.22 \(\upcels\) kWh\({}^{-1}\), real interest rate 0.565%, and the 20 year period of the economic analysis.  
Figure 17 reports the results of the economic analysis of the different solutions with respect to a \"reference solution\" A0, set up by three 25 kW NG condensing boilers with an efficiency of 100% and an air cooled electric vapor compression chiller. The investment cost of A0 was evaluated as 26,910 \(\upcels\). The only-ground HP plant (A1) allowed the shortest discounted payback period (DPB), around one year, whereas the most efficient multi-source solutions (A3, A4) performed worse (5 and 7 years respectively). However, the shortest DPB criterion was short sighted for a HVAC plant. Instead, in terms of differential (with respect to A0) discounted net present worth (NPW), the most profitable solution was a multi-source HP plant with 40 m\({}^{2}\) of evacuated tube and 300 m boreholes (A3), that allowed gains of around 40 k\(\upcels\) in 20 years.