The energy payback time can be determined by comparing the primary energy embodied in the system (PEAin) with the amount of primary energy that will be saved by the thermal solar system during its estimated lifetime (PEAsub) according to equation 1.

PEA, (t) = PEASub (t) (1)

As can be seen from equation 2, the primary energy embodied in the system (PEAin) comprises the cumulative energy demand for the production (KEAp), for the operation (KEAo) and for the maintenance (KEAm).

PEA, (t) = KEAp + KEAo • t + KEAm • t (2)

The cumulative energy demand for production (KEAp) also includes transport, assembly and installation of the thermal solar system. It has to be taken into consideration that the cumulative energy demand for the operation and the maintenance are dependent on the lifetime of the thermal solar system.

The amount of primary energy saved by the thermal solar system (PEAsub) is determined by the difference of Qconv, tot and the auxiliary energy (Qaux, tot). Qconv, tot represents the total primary energy requirement of a conventional system that is necessary to meet the hot water and in case of a comibsystem also the space heating demand.

PEAsub (t) _ (Qconv, tot Qaux, tot) • t

The energy payback time AZ is calculated according to equation 4.