Physical IAM Model

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The physical model for the incident angle modifier is based on Snell’s and Bougher’s laws, and was published by De Soto et al. (2006). Our presentation here includes correction to a few errors present in that paper. The first step is to calculate the angle of refraction ( $\theta _{r}$ ) using Snell’s law.

$\theta _{r}=\arcsin \left ( \frac{1}{n}\sin \left ( \theta \right ) \right )$ , where $n$ is the index of refraction of the cover glass and the 1 in the numerator is the index of refraction of the air.

The incident angle modifier at an angle, $\theta$ , is a ratio between the transmittance $\left ( \tau \theta \right )$ at that angle and the transmittance when normal to the sun $\tau \left ( 0 \right )$ :

$IAM_{B}=\frac{\tau \left ( \theta \right )}{\tau \left ( 0 \right )}$ .

A good approximation of the transmittance of the module cover is given by:

$\tau \left ( \theta \right )=e^{-\left (\frac{KL}{\cos \left ( \theta _{r} \right )} \right )}\left [ 1-\frac{1}{2}\left ( \frac{\sin ^{2}\left ( \theta _{r}-\theta \right )}{\sin ^{2}\left ( \theta _{r}+\theta \right )} +\frac{\tan ^{2}\left ( \theta _{r}-\theta \right )}{\tan ^{2}\left ( \theta _{r}+\theta \right )}\right ) \right ]$ ,

where $K$ is the glazing extinction coefficient (1/meters) and $L$ is the glazing thickness (meters).

$\tau \left ( 0 \right )$ can be determined by $\tau \left ( 0 \right ) = \lim_{\theta \rightarrow 0} \tau \left ( \theta \right ) = \exp\left ( -KL \right )\left [ 1-\left (\frac{1-n}{1+n} \right )^2 \right ]$ .

DeSoto et. al lists the following typical input parameters for PV modules:

$n=1.526$ for glass

$K=4\; \textrm{m}^{-1}$ and

$L=0.002 \: \textrm{m}$

The resulting IAM function is plotted below:

References

De Soto, W., S. A. Klein and W. A. Beckman (2006). “Improvement and validation of a model for photovoltaic array performance.” Solar Energy 80(1): 78-88.