# Module temperature

The module temperature has a strong influence on the characteristic curve of the PV modules.

The modules heat up depending on the installation situation, the module capacity, the type of module installation and the irradiation.

At a simulation interval of one hour, the module temperature $T_\text{Modul}$ is calculated statically from the irradiation $E$, related to the irradiation at STC ($E_\text{STC} = 1000 ~\text{W/m}^2$), and a temperature offset depending on the installation type:

$$T_\text{Modul} = T_\text{amb} + DT \cdot \frac{E}{E_\text{STC}}$$

Table 1: Heating DT in relation to the outside temperature, e.g. at irradiation $E = 1000 ~\text{W/m}^2$

DT Installation situation
29 K roof-parallel, well ventilated
32 K roof-integrated – rear-ventilated
43 K roof-integrated – not ventilated
28 K mounted – roof
22 K mounted – free area
20 K mounted – Floating PV

Source: DGS-Leitfaden Photovoltaische Anlagen, 3. Auflage, also Marco Rosa-Clot, Giuseppe Marco Tina, ‘Floating PV plants’ Academic Press, 2020.

The static temperature model is unsuitable for a simulation in minute time steps with alternating irradiation, since it does not take the thermal inertia of the module into account. A dynamic temperature model is therefore used for a simulation interval of one minute. The module is represented by a capacity $C$ with the module temperature $T_\text{ Modul}$:

$$\frac{dQ}{dt} = C \cdot \frac{dT_\text{Modul}}{dt}$$

A specific heat capacity of $830\frac{\text{J}}{\text{kg K}}$ and a module mass according to the module data set is used to calculate the heat capacity $C$.

The module is heated by the irradiation. This is contrasted by heat losses:

$$\frac{dQ_\text{Verluste}}{dt} = UA \cdot \left( T_\text{Modul} - T_\text{Amb} \right)$$

The heat loss rate $UA$ is determined from the static temperature offset

$$UA = \frac{E_\text{STC}}{DT}$$