How is evaluated the module temperature during simulation ?

[André Mermoud]

The thermal behaviour of the field - which strongly influences the electrical performances - is determined by an energy balance between cell's heating up due to incident irradiance and ambient temperature:

U · (Tcell - Tamb) = Alpha · Ginc · (1 - Effic)

where Alpha is the absorption coefficient of solar irradiation (or identically 1 - Reflexion), and Effic is the PV efficiency, i.e. represents the electrical energy removed from the module.

The usual value of the Absorption coefficient Alpha is 0.9. It is eventually modifiable in the PV module definition dialog.

When possible, the PV efficiency is calculated according to the operating conditions of the module. Otherwise it is taken as 10%.

The thermal behaviour is characterised by a thermal loss factor designed here by U-value (formerly called K-value), which can be split into a constant component Uc and a factor proportional to the wind velocity Uv :

U = Uc + Uv · v (U in [W/m²·k], v = wind velocity in [m/s]).

These factors depend on the mounting mode of the modules (sheds, roofing, facade, etc...).

As we don't have reliable coefficients for wind velocity (and the wind velocity is often not well assessed in hourly values), PVsyst proposes as default to take a fixed U-value (i.e. assuming a constant wind velocity).

For free circulation around the modules, our measurements show a value of 29 W/m²K.

This coefficient refers to both faces, i.e. twice the area of the module.

If the module is thermally insulated on the back, the second face doesn't contribute, and we have half this value, i.e. 15 W/m²K.

Intermediate cases with air circulation duct may have values from 18 to 25 W/m². We don't avail of assessed measurements.

NB: Some people use the NOCT concept. You can get an equivalence between U factor and NOCT values by inputting the NOCT conditions in the above thermal balance. But to my mind this is confusing and should not be used.

Measurement of Uc and Uv

The measurement of these parameters is possible by using long-term data recorded on-site (several weeks or months).

You should avail of measurements of the Module temperature, the ambient temperature, the irradiance on the PV plane, and eventually the wind velocity.

You can plot the (Tarray-Tamb) difference as a function of the irradiance (may be negative during night by clear conditions, due to IR deficit with sky)

Then you can extract the parameters from a bi-linear fit (with wind) or simple linear fit (without wind, Uv=0).

PV array temperature measurement:

According to our experience, the PV module (cell) temperature may be recorded using a temperature sensor (thermocouple or PT100) glued or fixed with thermal grease on the rear side of the PV module, with a 1 cm thick polystyrene cover of 7 x 7 cm2.

The size of the thermal insulation is a compromise between a good insulation of the sensor with respect to external (in order that the heat flux is negligible), and the local perturbation of the local PV module temperature due to this insulation. This mounting mode optimization results from a diploma at the University of Geneva, where we had a special module with a thermocouple on the cell, included in the encapsulation, so that we had a reference for performing differential measurements.

NB: Ensure a good mechanical "external" fixation of the polystyrene piece (a simple adhesive tape is usually not sufficient at medium or long term).

NB: Some people propose to add 3°C to the rear-side measured temperature for taking into account the temperature drop due to a heat flux from the Cell to the sensor.

This would be valid if the sensor is not recovered by an insulation. In this case we don't know what is really measured by the sensor: an intermediate temperature highly depending on the ratio between the heat resistance in the rear sheet, and the sensor with respect to the ambient. Moreover the difference between cell and sensor is obviously proportional to the heat flux, i.e. the (TArray-TAmb) temperature. Therefore I can't understand this fixed correction of 3°C.

Please see the help about this subject ("Project design > Array losses in PVsyst > Array Thermal losses").