Array Thermal losses

Thermal Model

The parameters of the Thermal behaviour of the field are defined in the "Array Losses" dialog (see also Array Losses definition).

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

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

i.e. Tcell = Tamb + 1 / U · ( Alpha · Ginc · (1 - Effic) )

where:

-	Tamb is the ambient temperature, acc. to the meteo data,

-	Ginc is the irradiance on the module or PV array (the simulation uses GlobEff, effective irradiance taking soiling and shades into account).

-	Alpha is the absorption coefficient of solar irradiation, i.e. (1 - reflexion). The usual value of the Absorption coefficient Alpha is 0.9. It is eventually modifiable in the PV module definition dialog.

-	Effic is the PV efficiency (related to the module area), i.e. the energy removed from the module. When possible, the PV efficiency is calculated according to the operating conditions of the module. Otherwise it is taken as 10%.

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

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

NB: This U-value is quite equivalent to the Heat transfer factor [W/m²·k], used for example in building physics for the characterization of walls or windows.

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

For free circulation, this coefficient refers to both faces, i.e. twice the area of the module. If the back of the modules is more or less thermally insulated, this should be lowered, theoretically up to half the value (i.e the back side doesn't participate anymore to thermal convection and radiation transfer).

Determination of the U-parameters

The determination of the parameters Uc and Uv is indeed a big question. We have some reliable measured data for free mounted arrays, but there is a severe lack of information when the modules are integrated. What value should be chosen according to the air duct sizes under the modules, and the length of the air path ?

It should be noticed that the heat capacity of the air is very low. Even with large air vents, the flowing air under the modules may quickly attain the equilibrium with the modules temperature at the end of the duct, leading to no heat exchange at all. Therefore for the top of the array the back-U value may be the fully insulated U-value; you can have big differences between the regions of the array near the air inlet, and at the outlet. PVsyst doesn't take this inhomogeneity of the array temperature into account.

On the other hand, the use of the wind dependency Uv is very difficult. Reliable knowing of the wind velocity is extremely seldom (some programs construct synthetic hourly values from monthly data, but on which basis and with which models ?). And the "meteo quality" wind velocity (measured at 10 meter height in free environment) is not representative of the velocity at the array level (there may be a factor of 1.5 between them). In this respect the Uv value is obviously not the same for these two definitions of the wind velocity.

Default and proposed values

In the absence of reliable measured data, PVsyst proposes default values without wind dependency (i.e. assuming an average wind velocity):

-	For free-standing systems (with air circulation all around the collectors), according to our measurements on several installations:

Uc = 29 W/m²·k, Uv = 0 W/m²·k / m/s

-	Therefore for fully insulated backside (no heat exchange at the backside, only one side contribution to the convecting heat exchange), the U value should be divided by 2:

Uc = 15 W/m²·k, Uv = 0 W/m²·k / m/s

-	For intermediary cases (semi-integration, air duct below the collectors), the value should be taken between these 2 limits, but preferably lower than 22 W/m²·k as the air heat removing is often not very efficient. The default value proposed by PVsyst for any new project is

Uc = 20 W/m²·k, Uv = 0 W/m²·k / m/s

We have chosen this value, as we consider that it is more representative of usual rooftop systems, managed by "less professional" people who will not necessarily modify the PVsyst default. For big systems, we suppose that trained engineers will indeed adjust this parameter (for example at 29 W/m² for row-like big power plants).

Now if reliable wind velocity data are present in the data, we don't have much reliable measured data.

According to their own measurements, some users proposed, when using standard meteo values such those in the US TMY2 data (usually around 4-5 m/sec on an average in continental - not-coast places), and free-standing system, the following U-values:

Uc = 25 W/m²·k, Uv = 1.2 W/m²·k / m/s

With an average wind velocity of 3 m/s, this corresponds to U = 28.6 W/m²·k, close to the PVsyst standard value.

NOCT Values

Some practicians - and most of PV module's catalogues - usually specify the NOCT coefficient ("Nominal Operating Cell Temperature"), which you are advised to completely forget... Please have a look at this topic !