## 2 Methods
### A Multisource Heat Pump System for a New School Building: Control Logic  
#### 2.2.1 The Space Heating System  
The most important element in the control system is the algorithm to determine the most suitable heat source at every time. The two absorption heat pumps of the heating section can use both the solar circuit and the ground circuit. For the best exploitation of the energy sources (i.e., from the exergetic point of view), the best choice is to use the solar collectors' loop to heat (or, at least, to preheat) the radiant floor circuit, if the temperature is high enough. As a matter of fact, if the energy collected by the solar panel is sufficient, the space heating can be obtained for free (except for the pumping energy).  
Downstream, if the solar loop temperature after the preheating of the floor circuit is higher than the ground temperature, the water from the solar system can be used on the secondary fluid side of the heat pump evaporator. Should the solar system be off, or the temperature of the solar loop be not high enough, the heat pumps use ground heat.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Rated Capacity (kW)** & **Rated Efficiency** \\ \hline HP1 + HP2 & 74 (B0W60) & 1.25 (GUE) \\ HP3 + HP4 & 76 (B0W40) & 1.40 (GUE) \\ Boiler & 114.4 & 1.02 (condensing) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Heating generators of the central HVAC plant.  
Following these considerations, the evaporation temperature is always kept at the highest possible level, thus leading to the highest average COP.  
The control of the solar system follows the strategy shown in Figures 3 and 4 explained as follows:  
1. Wintertime with space heating system on: * The solar circuit pump is active if the radiation (constantly monitored with a solar radiation probe) is higher than a threshold value \(I_{T}\) defined as: \[I_{T}=\frac{a_{1}(T_{m}-T_{oa})}{\eta_{0}-\eta_{\min}}\] \(I_{T}\) is the radiation that provides the minimum acceptable efficiency \(\eta_{\min}\) given the solar field characteristics in terms of \(\eta_{0}\) (zero-loss solar system efficiency), \(a_{1}\) (heat loss coefficient), the minimum average temperature desired \(T_{m}\), and the outdoor temperature \(T_{oa}\). The desired \(T_{m}\) was set at 5 \({}^{\circ}\)C and \(\eta_{\min}\) to 0.01. \(\eta_{0}\) and \(a_{1}\) can be calculated from the respective values referred to the single collector, i.e., 0.75 and 4.14 W/(m\({}^{2}\) K), multiplied by CF5 which is the series correction factor, equal to 0.881 (for 5 collectors in series). \(I_{T}\) can be set, for instance, at 200 W/m\({}^{2}\); * If the solar circuit outlet temperature exceeds 38 \({}^{\circ}\)C (i.e., the radiant floor supply temperature increased by 3 \({}^{\circ}\)C), the solar outlet goes into the plate heat exchanger to preheat the return flow from the radiant floor loop, otherwise the exchanger is bypassed; * If the solar radiation is higher than a given value (that can be set, for instance, at 800 W/m\({}^{2}\)), once the solar loop flow has left the exchanger, it returns to the collectors to optimize the thermal levels; * If the temperature of the solar loop flow leaving the exchanger is higher than 5 \({}^{\circ}\)C (exchanger outlet temperature or collector outlet temperature), the flow goes to the evaporator of the heat pumps that are currently facing the baseload; instead, if the temperature is lower, the flow returns to the collectors; * From the evaporator, the flow returns to the collectors. 2. Wintertime with space heating system off: * The solar circuit pump is active if the radiation is higher than the threshold value \(I_{T}\); * Since the space heating plant is off, the solar loop flow goes into the ground exchanger, from where it returns to the collectors. 3. Summertime: * The operation is identical to the previous case.