In order to estimate the auxiliary energy supplied by the heat pump to maintain the water inside the reservoir above 43°C, several reservoir volumes and ST areas were tested. We modeled the water temperature inside of the reservoir in each yearly simulation hourly time step, Ti, by using the following expression:

EHP — heat pump energy (< 43°C); ECoolmg — released energy to cool the reservoir (>80°C); Esolar — thermal solar energy collected; Eheatmg — house heating energy; EMHW — energy to heat the water for the washing machines (laundry and dishwasher); EMHW — losses through the reservoir surface; Vr — reservoir volume; Cp — water specific heat capacity; p — water density; Ti — reservoir water temperature.

The energy used to heat DWH is given by:

Edhw = p’ Cp • Vw (TDHW — Tw) (2)

VW — DHW volume; Cp — water specific heat capacity; p — water density; TDHW — domestic hot water temperature; Tw — water temperature from the tap.

The heat pump turns on if T i< 43°C. The heat pump energy demand is given by: eup = p4 Cp — v,. (Triin — y;.) (3)

Vr — reservoir volume; Cp — water specific heat capacity; p — water density; Tmin — reservoir water minimum temperature; Tj — reservoir water temperature.

If the water in the reservoir goes above 80°C (T > 80°C), heat is released in order to reduce the water temperature.

E0oo, ing=pCp-Vr{Ti-Tt^) (4)

Vr — reservoir volume; Cp — water specific heat capacity; p — water density; Tmax — reservoir water maximum temperature; Ti — reservoir water temperature.

Table 3 shows the use of the solar thermal system for the different scenarios. The first five scenarios the house is heated with the heat pump, in the last five is heated with solar thermal (the same division is used in tables 3, 4, 6 and 7).