## 2 Methods
### A PVT Multisource Heat Pump System for a Retrofitted Gym: Design Phase  
The second case study concerns the retrofitting of a part of an old (completed in 1960) high school building of Feltre (Northern Italy) that will be started in 2021. The climate is rather severe in wintertime (3100 degree days). A large gym (33 \(\times\) 25 \(\times\) 8.40 m) expanding on two levels and other rooms (changing rooms, bathrooms with toilet and showers, and technical rooms on the ground floor; an office, a small gym and a bar on the first floor; six laboratories on the second floor) will be refurbished with the aim of realizing a NZEB, with a total floor area of 2435 m\({}^{2}\), and an enclosed gross heated volume of 11,060 m\({}^{3}\). Figure 5: Flow diagram for ventilation recovery control system. Figure 6: The ventilation plant operating with ground exchangers (**left**) and in ventilation recovery mode (**right**). The design phase was based on Trnys(r) dynamic simulation, defining 20 thermal zones, each with a suitable scheduling of the presence of people, lighting, and other internal gains, humidity, and air temperature set points. The HVAC system provides ventilation by two AHU, space heating and cooling, and DHW production. It is set up by a solar section composed of glazed PVT and plain PV that drive a heat pump which satisfies all the loads. The thermal energy produced by the PVT provides DHW heating or at least preheating; moreover, it can act as a cold source of the heat pump. The various components are connected via suitable storage tanks as depicted in Figure 7.  
The large gym is heated by a radiant floor system, and it is cooled by an all-air system providing the ventilation service (6600 m\({}^{3}\) h\({}^{-1}\)). Another AHU (7000 m\({}^{3}\) h\({}^{-1}\)) provides ventilation for the laboratories that are heated and cooled by fan coils. The other rooms (small gym, bar, and offices) are equipped with fan coils as well, whereas toilets are heated only (by radiators). The glazed PVT collector was modeled by the type 50c (based on the type 1 modeling the solar thermal collector based on Hottel-Whillier equation). The main features refer to a real glazed PVT module available on the market [20]. The mass flow rate entering the PVT field depends on the series/parallel configuration. In this case, this is set up in two equal groups where the collectors are in parallel with a group in series with the other, as in the parametric study the solar field varies between 20 and 60 m\({}^{2}\) (Table 2). Such a configuration allows one single value for the mass flow rate; that is, a single circuit connecting the solar section with the ground. An operation threshold of the solar radiation intensity (\(S\)) between 50 and 100 W m\({}^{-2}\) and a comparison between the tanks set points and the temperatures in the different circuits (Figure 7) is the base of the control logic of the plant. The ground field is composed by \(n\times 100\) m in a row of vertical tube U heat exchangers, distance 6 m, \(n=3\)-4-5 as a function of the solar field area as described in Table 2. It is modeled by type 557a. The tanks, whose sizes for each alternative considered in this study  
Figure 7: Simplified functional diagram of the HVAC plant. are reported in Table 2, are modeled by type 60d (pre-DHW tank, DHW tank) and type 4a (hot tank, cold tank, heat source tank). In case the temperature in the upper part of the hot tank and the DHW tank is below the set point (50 and 45 \({}^{\circ}\)C, respectively, with a dead band of 3 \({}^{\circ}\)C) and the main generators (PVT and heat pump) are not available, a 3-kW auxiliary electric resistance supplies the heating and DHW load, respectively. Type 927 models the water-water heat pump. The performance is simulated on the basis of nominal data from a manufacturer at the operating temperatures of the heat source and sink varying in useful ranges (respectively, T source tank \(\leq\) 25 \({}^{\circ}\)C and hot tank or heat source tank max 52 \({}^{\circ}\)C).