In general the output of the solar cycle is calculated using the formula:

Q = Q u — CL — Q

out abs heat pipe

The solar irradiation absorbed by the collector is:

Qabs = Edir ‘ П ‘ Aaperture ‘ F dir (0) + Ediffuse ‘ П ‘ Aaperture ‘ F diffuse

The calculation of the direct irradiance EdlI and the diffuse irradiance Ediff on the collector is based on the relevant meteorological values on the horizontal plane. Shading of the horizon can also be considered in these calculations.

The angle of incidence on the collector is [2]:

0 = arccos(-sin^C cosys cos(aS — aC) + cosyC sinYS)

For vacuum tube collectors the angle of incidence 0 is divided into a longitudinal 0 and a transversal angle of incidence 0t referring to the collector axis According to [3] the following formulas can be used:

0 =|rC + arctan(tan(90°-ys) • cos(aS — aC)) and

arctan(cosfS • sin(aS — aC))
cos#

The incidence angle modifier for the direct irradiance IAMdir of the vacuum tube collector is now defined by a longitudinal share IAMdirl and a transversal share IAMdir, t :

IAMdh(0) = IAM„„(А,)• IAMdlJ01).

The angles aS and yS describe the position of the sun according to DIN 5034 (aS: 0°=N, 90°=E, 180°=S, 270°=W. yS: 0°=horizontal, 90°=vertical) and aC and yC the orientation of the collector axis (aC: 0°=S, 90°=W, 180°=N, 270°=E. yC: 0°=horizontal, 90°=vertical).

The collector heat losses are calculated with the following formula:

Q heat = П • Aaperture •(k! •AT + k2 •AT2 )

The pipe losses are defined using the mean collector temperature Sc and the ambient temperature Sa as follows:

a pip,=V-te — sa )+k2′( — 20 °c)

with

and

Typically the calculation is done for a whole year including also the night hours without heat input to the collectors. During these hours the whole system cools down and in the morning the whole system has to be heated up to design temperature. For this calculation the heat capacity of the pipes, the heat transfer fluid and the collectors are considered. Collector parameters are input values and stored in the collector database. They may be obtained from collector manufacturers or from [4].