## 4 Results
### Energy Analysis  
In addition to the embedded and control efficiency, the overall energy consumption should also be evaluated. Concerning the supply water temperature control modality, the climatic control has the undeniable advantage of reducing its seasonal mean value of about 4 \({}^{\circ}\)C in non-insulated buildings, 2.5 \({}^{\circ}\)C in insulated buildings, and 2 \({}^{\circ}\)C in well-insulated buildings (Figure 8). The ceiling systems need higher water temperatures than floor systems because of the lower convective heat transfer coefficient and of the smaller active surface; for this reason the ceiling systems show the greatest temperature reductions among the three kinds of radiant systems when going from the fixed temperature to variable supply temperature related to outside air (climatic control strategy). As regards the operation time, the climatic control obviously shows an increase, which is equal to 58%, 46% and 41% for the non-insulated, insulated and well-insulated buildings respectively. A simplified evaluation of the energy consumption of the entire heating system was done considering a water-to-water heat pump as generator, a primary loop, and a secondary loop with their pumps (Figure 9). Figure 8: Hours of operation of the radiant systems and mean value of the supply water temperature in the different cases. Figure 9: Simplified layout of the considered heating system. The electric energy consumption of the heat pump was estimated considering a heat source constantly at 12 \({}^{\circ}\)C and a temperature difference at the evaporator of 5 \({}^{\circ}\)C (water source temperature from 12 \({}^{\circ}\)C to 7 \({}^{\circ}\)C). The nominal conditions in Table 9 from a commercial datasheet were considered to evaluate the coefficient of performance (COP). For evaluating the COP of the heat pump the ideal coefficient of performance of a Carnot cycle has been used:  
\[COP_{id}=\frac{T_{cond}}{T_{cond}-T_{evap}} \tag{7}\]  
where the condensing and evaporating temperatures of the cycle have been evaluated as follows:  
\[T_{cond}=\frac{T_{w,in,cond}+T_{w,out,cond}}{2}+5 \tag{8}\]  
\[T_{evap}=\frac{T_{w,in,evap}+T_{w,out,evap}}{2}-5 \tag{9}\]  
By using Equations (3)-(5), in nominal condition the ideal Carnot cycle gives \(COP_{id,nom}\) = 9.41. At each time step of the simulations the ideal coefficient of performance \(COP_{id}\) was calculated considering the mean value of the water temperature in the condenser equal to the supply water temperature \(T_{w,in}\) of the radiant panels. The COP of the heat pump was then estimated as follows:  
\[COP=COP_{id}\frac{COP_{nom}}{COP_{id,nom}} \tag{10}\]  
At each timestep the electric energy consumption of the heat pump \(E_{hp}\) can be calculated as:  
\[E_{hp}=\frac{Q_{w}}{COP} \tag{11}\]  
From the seasonal thermal energy and the corresponding electric consumption, the mean value of the COP can be calculated. This is called seasonal performance factor, SPF, and its value can be seen in Figure 10 (right axis) together with the electric energy require by the heat pump (left axis). The higher SPF which can be achieved with the climatic control of the supply water temperature makes the heat pump electric consumption lower, but also the electric consumption of the auxiliaries should be evaluated. As already seen in Figure 8, the number of hours of operation of the pump of the secondary loop is much higher in the case of climatic control instead of constant supply water temperature. The pressure drops of each combination of radiant system and building type were calculated and the electric power of the pump was then evaluated from the chart of a common high efficiency pump for domestic use. For the primary loop the number of hours of operation of the pump was calculated from the seasonal thermal energy need and the nominal thermal power of the heat pump.