Cell Temperature
Cell temperature is generally defined by incident irradiance, wind speed and module properties. Wind speed dependence is not included in all models, and in any case is sometimes removed by adjusting model parameters appropriately; determining wind speed to an acceptable degree of accuracy at a PV plant is challenging. The cell temperature model available in SolarFarmer is the PVsyst model, which is described below. In addition, the Sandia cell temperature model is also described to provide a glance into other literature models.
PVsyst Cell Temperature Model (Release 1)
The PVsyst cell temperature model can be found documented here:
Using this model, the temperature of a cell in module \(j\) at time \(t\) is given by:
$$T_\text{c} \left(j, t \right) = T_\text{a} \left( t \right) + \frac{\alpha G_\text{poa,soil} \left(j, t \right) \left(1 - \eta_\text{m} \right)}{U_\text{c} + U_\text{v} \ WS \left( t \right)}$$
Where:
\(T_\text{a}\left(t\right) \) is Ambient air temperature
\(\alpha\) is Absorption coefficient of module (default is 0.9)
\(\eta_\text{m}\) is nominal module efficiency (default is 0.1)
\(U_\text{c}\) is constant heat transfer component (W/m²/K)
\(U_\text{v}\) convective heat transfer component (W/m²/K/(m/s²))
\(WS\left(t\right)\) is wind speed (m/s)
Standard values for \(U_\text{c}\) and \(U_\text{v}\) within DNV from [8]:
| Mounting | \(U_\text{c}\) [W/m²/K] | \(U_\text{v}\) [W/m²/K/(m/s)] |
|---|---|---|
| Car port canopies | 25 | 1.5 |
| Open rack in rows | 25 | 1.2 |
| Wind deflector on all rows | 20 | 1.0 |
| Wind Deflector Shields on Some Modules/Rows | 23 | 1.0 |
| Flush-mount systems | 18 | 0.7 |
The role of \(\alpha\) in this formula is to allow for effects like the \(\IAM\) effect described in Incidence Angle Modifier Effect and Incidence Angle Modifier. Hence an alternative version of this cell temperature model can be used, where the \(\alpha\) is dropped and \(G_\text{iam}\) is used in place of \(G_\text{poa,soil}\):
$$T_\text{c}\left(j, t\right) = T_\text{a}\left(t\right) + \frac{G_\text{iam} \left(j,t\right) \left(1 - \eta_\text{m}\right)}{U_\text{c} + U_\text{v} \ WS\left(t\right)}$$
\(G_\text{iam}\) is defined in Incidence Angle Modifier Effect of this document. The user may prefer the version including \(\alpha\) for comparison with PVsyst results.
Sandia Cell Temperature Model
The Sandia Cell Temperature Model is not used in SolarFarmer, but it is documented here anyway.
$$T_\text{c}\left(j,t\right) = T_\text{m}\left(t\right) + \frac{G_\text{iam}\left(j,t\right)} {G_\text{ref}} \Delta T$$
Where:
\(\Delta T\) is the temperature difference parameter between back-of-module and cell temperature under an irradiance of 1000 W/m². This is the temperature difference. Sandia use \(\Delta T\) of 2 for polymer backed modules, glass on glass uses \(\Delta T\) of 3.
\(T_\text{m}\left(t\right)\) is the Sandia back-of-module temperature. See: https://pvpmc.sandia.gov/modeling-steps/2-dc-module-iv/module-temperature/sandia-module-temperature-model/
$$T_\text{m}\left( t \right) = \ G_\text{iam}\left( j,t \right) \left( e^{a + b \ WS} \right) + T_\text{a}\left(t\right)$$
The parameters \(a\) and \(b\) depend on the module construction and mounting, with typical values (supplied by Sandia) as follows:
| Module type | Mount | a | b |
|---|---|---|---|
| Glass/cell/glass | Open rack | -3.47 | -0.0594 |
| Glass/cell/glass | Close roof mount | -2.98 | -0.0471 |
| Glass/cell/polymer sheet | Open rack | -3.56 | -0.0750 |
| Glass/cell/polymer sheet | Insulated back | -2.81 | -0.0455 |
| Polymer/thin-film/steel | Open rack | -3.58 | -0.113 |
| 22X Linear Concentrator | Tracker | -3.23 | -0.130 |