PV Performance Modeling Collaborative | Sandia PV Array Performance Model

Functions:

$f_{1}$ is a 4th order polynomial function of absolute air mass, $AM_{a}$ , and is called the air mass modifier. It is defined as:

$f_{1}\left ( AM_{a} \right )=a_{0}+a_{1}AM_{a}+a_{2}\left ( AM_{a} \right )^{2}+a_{3}\left ( AM_{a} \right )^{3}+a_{4}\left ( AM_{a} \right )^{4}$

where $a$ is the vector of coefficients that are determined from module testing.

$f_{2}$ is a 5th order polynomial function of angle of incidence, $AOI$ , and is called the angle of incidence modifier. it is defined as:

$f_{2}\left ( AOI \right )=b_{0}+b_{1}AOI+b_{2}\left ( AOI \right )^{2}+b_{3}\left ( AOI \right )^{3}+b_{4}\left ( AOI \right )^{4}+b_{5}\left ( AOI \right )^{5}$

where $b$ is the vector of coefficients that are determined from module testing.

$E_{e}$ is the “effective irradiance”. It is defined as:

$E_{e}=\frac{I_{sc}}{I_{sc0}\left \{ 1+\alpha _{Isc}\left ( T_{c}-T_{0} \right ) \right \}}$ , where:

$I_{sc0}$ is the short circuit current at reference conditions.

$I_{sc}$ can be calculated from (eq. 1) above.

$\delta$ is a function of $T_{c}$ defined as: $\delta =\frac{n\times k\left ( T_{c}+273.15 \right )}{q}$ , where:

$n$ is an empirically determined ‘diode factor’,

$k$ is Boltzmann’s constant ( $1.38066\times 10^{-23}J/K$ ),

$q$ is the elementary charge constant ( $1.60218\times 10^{-19}coulomb$ )

$\beta _{Voc}$ is a function of effective irradiance, $E_{e}$ , defined as: $\beta _{Voc}=\beta _{Voc0}+m_{\beta Voc}\left ( 1-E_{e} \right )$ , where:

$\beta _{Voc0}$ is the temperature coefficient for module open circuit voltage at irradiance conditions of $1000 W/m^{2}$ .

$m_{\beta Voc}$ is a coefficient describing the irradiance dependence for the open circuit voltage temperature coefficient (typically equals zero)

Parameters:

$E_{b}$ is beam irradiance on the plane of array

$E_{d}$ is the diffuse irradiance on the plane of array

$E_{0}$ is reference solar irradiance ( $1000 W/m^{2}$ )

$T_{c}$ is cell temperature ( $^{\circ}C$ )

$T_{0}$ is reference cell temperature ( $25^{\circ}C$ )

$f_{d}$ is the fraction of the diffuse light that is used by the module. For typical flat plate modules $f_{d}$ is usually assumed to be equal to 1. For concentrators the value can be smaller than 1.