Hot water energy balance takes into account the output of the
heat storage tanks, unmet hot water and load, Eq. (14). The heating
energy balance equation at the collection node, which is indicated
in Fig. 1, is guaranteed by Eq. (15). The hot water level in the tank at
the end of period t þ 1 is equal to the inventory level at previous
time period plus the amount of hot water generated by the solar
collectors, heat pump, biomass boiler and NG boiler during time
period t minus the quantity of hot water consumed by the building
during the same period, Eq. (16)