Soiling effects on Incident Angle Losses

Sandia Model

Sandia has suggested using a 5th order polynomial function to represent angular optical losses on short circuit current (Isc) [1].

$f2\left ( \theta \right )=b_0+b_1\theta +b_2\theta^2+b_3\theta^3+b_4\theta^4+b_5\theta^5$

where the coefficient vector, $b$ , is determined from fitting experimental data measured outdoors.

An example result of this model is shown in figure 1. Note that the use of a 5th order polynomial causes a slight concave-up shape at low angles of incidence. This functional form actually results in $f_{2}$ values slightly >1 for part of this range (10-45 degrees) and values >0 for 90 degrees. These non-physical features are downsides of this model.

Figure 1. Sandia model for incident angle modifier (on Isc)

References:

[1]. King, D. L., E. E. Boyson and J. A. Kratochvil (2004). Photovoltaic Array Performance Model. Albuquerque, NM, Sandia National Laboratories, SAND2004-3535.