PVsyst Cell Temperature Model

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The PV performance modeling application, PVsyst, implements a cell temperature model based on the Faiman module temperature model. The form of the model is:

$T_{c} = T_{a}+E_{POA}\frac{\alpha \left ( 1-eta_{m} \right )}{U_{0}+U_{1}\times WS}$

where

$T_{c}$ is cell temperature (°C)
$T_{a}$ is ambient air temperature (°C)
$\alpha$ is the absorption coefficient of the module (PVsyst default value is 0.9)
$E_{POA}$ is the irradiance incident on the plane of the module or array ( $W/m^{2}$ )
$eta_{m}$ is the efficiency of the PV module (PVsyst default is 0.1)
$U_{0}$ is the constant heat transfer component ( $W/m^{2}K$ )
$U_{1}$ is the convective heat transfer component ( $W/m^{3}sK$ )
$WS$ is wind speed (m/s)

PVsyst says little about what values to use for $U_{0}$ and $U_{1}$ . Note that the current default values assume no dependance on wind speed ( $U_{1}=0$ )

For free-standing arrays the current default is : $U_{0}$ = 29 $W/m^{2}K$ ; $U_{1}$ = $0$ $W/m^{3}sK$
For fully insulated arrays (close roof mount) the current default is: $U_{0}$ = 15 $W/m^{2}K$ ; $U_{1}$ = $0$ $W/m^{3}sK$

PVsyst users can also enter a NOCT (Nominal Operating Collector Temperature) in place of $U$ values. The program then automatically calculates $U$ values based on $\alpha =0.9$ and $eta_{m} =0.1$ .

Values for $U_0$ and $U_1$ can be calculated which correspond to the reference parameters for the Sandia Cell Temperature Model. The PVsyst model can be approximated as

$T_{c} = T_{a}+E_{POA}\frac{\alpha \left ( 1-eta_{m} \right )}{U_{0}+U_{1}\times WS}$

$T_{c} = T_{a}+E_{POA}\frac{\alpha \left ( 1-eta_{m} \right )}{U_{0}} \frac{1}{1 + \frac{U_{1}}{U_{0}}\times WS}$

$T_{c} \approx T_{a}+E_{POA}\frac{\alpha \left ( 1-eta_{m} \right )}{U_{0}} \left(1 - \frac{U_{0}}{U_{1}}\times WS \right )$

$T_{c} \approx T_{a}+E_{POA} [\frac{\alpha \left ( 1-eta_{m} \right )}{U_{0}} - \frac{\alpha \left ( 1-eta_{m} \right ) U_{1}}{U_{0}^{2}}\times WS]$

Similarly the Sandia Cell Temperature Model can be approximated as

$T_{c} =T_{a}+\frac{E_{POA}}{E_0}\Delta T + E_{POA} \times e^{a+b\times WS}$

$T_{c} \approx T_{a}+ E_{POA} \left(\frac{\Delta T}{E_0} + e^{a} \left( 1 + b \times WS \right) \right)$

$T_{c} \approx T_{a}+ E_{POA} \left(\frac{\Delta T}{E_0} + e^{a} +e^{a}b \times WS\right )$

Equating terms gives the following equations that relate the PVsyst cell temperature model parameters $\alpha, eta_{m}, U_{0}, \rm \ and \ \it U_{1}}$ to the Sandia Cell Temperature Model parameters $a, b, \rm \ and \ \it \Delta T$ :

$\frac{\alpha \left(1 - eta_{m} \right )}{U_{0}} = \frac{\Delta T}{E_{0}} + e^{a} \Rightarrow U_{0} = \frac{\alpha \left(1 - eta_{m} \right )}{\frac{\Delta T}{E_{0}} + e^{a}}$

$-\frac{\alpha \left(1 - eta_{m} \right )}{U_{0}} \frac{U_{1}}{U_{0}}= e^{a}b$

$-\frac{\alpha \left(1 - eta_{m} \right )}{U_{0}} \frac{U_{1}}{U_{0}}= e^{a}b \Rightarrow U_{1} = -\frac{e^ab \alpha \left( 1 - eta_{m} \right)}{\frac{\Delta T}{E_{0}}+e^{a}}$