A series of papers by Martin and Ruiz (2001; 2002; 2004) describe the optical reflectance loss for PV modules and model the effect of these losses on annual energy.

Martin and Ruiz (2001) establish that the angular losses (AL) of a PV modules are a function of the solar incident angle ($\theta_A_O_I$).

$AL(\theta_{AOI})&space;=1-\frac{\overline{T}(\theta_{AOI}&space;)}{\overline{T}(0)}=1-\left&space;[&space;\frac{1-exp(-\cos&space;(\theta_{AOI})/a_r)}{1-exp(-1/a_r)}&space;\right&space;]\cong&space;1-\frac{1-\overline{R}(\theta_{AOI})}{1-\overline{R}(0)}$

where T(x) is the weighted transmittance at incident angle x, R(x) is the weighted reflectance at incident angle x, and $a_r$ is the angular losses coefficient, an empirical dimensionless parameter to fit in each case.

An angular factor, $f_{I\alpha}$ , is defined by the ratio of the PV module’s short circuit current, $I_{sc}$, at incident angle α to the $I_{sc}$ at normal incidence:

$f_{I\alpha}=\frac{I_{sc}(\theta_{AOI})}{I_{sc}(0)&space;\cos(\theta_{AOI}))}\cong&space;\frac{1-\overline{R}(\theta_{AOI})}{1-\overline{R}(0)}$

This angular factor is the incident angle modifier.

The angular factor can be experimentally determined for a finite number of incidence angles, α, and the data may be used to fit an appropriate angular losses coefficient, $a_r$, to determine the angular factor for any incident angle.

It should be noted that when experimentally determining $f_{I\alpha}$, the light source must be collimated (beam irradiance).

Sample results of the Martin & Ruiz model for varying a_r

## References

[1] Martin, N., Ruiz, J. M. Calculation of the PV modules angular losses under field conditions by means of an analytical model. Solar Energy Materials & Solar Cells 70, pp. 25-38.

[2] Martin, N., Ruiz, J. M. A New Model for PV Modules Angular Losses Under Field Conditions. International Journal of Solar Energy, 2002, Vol. 22(1), pp. 19-31

[3] Martin, N., Ruiz, J. M. Annual Angular Reflection Losses in PV Modules. Progress in Photovoltaics: Research and Applications. 2005; 13:75-84