1. Introduction - Firenze University Press

The optical efficiency of the tube collectors was 0=76 %, the coefficients a1=1.53 W °C -1 m -2 and
a2=0.0003 W °C -2 m -2 [22], the inlet and the outlet temperatures of the solar collector media were 70
and 90 °C, and the area of the solar collectors was 150 m 2 .
The selected acceptable tolerance in this Case Study was 10 %. The optimal number of TSs,
obtained by the proposed MILP model, was 8. It was an important achievement, as the initial
number of time-intervals from the measurements was 56. The minimal inaccuracy at this number of
TSs was 9.4 %. The TS determined for the irradiation can be seen in Fig 10.
G [W/ 700 m2 ]
600
500
400
300
200
100
0
4 6 8 10 12 14 16 18 20 t [h]
Fig 10: TS boundaries for irradiation.
307
measured data
discretization
result of
optimisation
The results, obtained for TS for irradiation, suggested 8 TSs. However, capture of the heat was
impossible when determining the efficiency of the capture system in the first and last TSs, as the
irradiation was too low. For this reason the number of TSs with a constant load of supply was, in
this case, 6. Fig 11 presents the final approximated load-profile for the supply of solar thermalenergy,
and the TS boundaries.
G [W/ 700 m2 ]
600
500
400
300
200
100
5.3. Combining the TSs
0
5 7 9 11 13 15 17 19 t [h]
Fig 11: TSs and approximated loads for solar thermal energy
After obtaining TSs the (i) heat demand variations and (ii) solar thermal energy supply were joined.
In order to combine them, the time-boundaries from both TSs were listed and any duplicates (if
existing) were eliminated. As can be seen in Fig 12, in this case study there were 5 TSs (with 6 time
boundaries) from the heat demand and 6 (with 7 time boundaries) from the solar thermal energy
supply. Combining them resulted in 12 cTSs (with 13 time boundaries). This case study clearly
showed how important it is to reduce the number of TSs for solar thermal-energy supply.