# Module temperature

The module temperature has a strong influence on the characteristic curve of the PV modules. Figure 3: Typical course of module efficiency at different module temperatures.

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

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