pvpltools.iec61853.martin_ruiz

pvpltools.iec61853.martin_ruiz(aoi, a_r=0.16)

Determine the incidence angle modifier (IAM) using the Martin and Ruiz incident angle model.

Parameters:

• aoi (numeric, degrees) – The angle of incidence between the module normal vector and the sun-beam vector in degrees.

• a_r (numeric) – The angular losses coefficient described in equation 3 of [1]. This is an empirical dimensionless parameter. Values of a_r are generally on the order of 0.08 to 0.25 for flat-plate PV modules.

Returns:

iam – The incident angle modifier(s)

Return type:

numeric

Notes

martin_ruiz calculates the incidence angle modifier (IAM) as described in [1]. The information required is the incident angle (AOI) and the angular losses coefficient (a_r). Note that [1] has a corrigendum [2] which clarifies a mix-up of ‘alpha’s and ‘a’s in the former.

The incident angle modifier is defined as

\[IAM = \frac{1 - \exp(-\cos(\frac{aoi}{a_r}))} {1 - \exp(\frac{-1}{a_r}}\]

which is presented as \(AL(\alpha) = 1 - IAM\) in equation 4 of [1], with \(\alpha\) representing the angle of incidence AOI. Thus IAM = 1 at AOI = 0, and IAM = 0 at AOI = 90. This equation is only valid for -90 <= aoi <= 90, therefore iam is constrained to 0.0 outside this interval.

References

[1] (1,2,3,4)

N. Martin and J. M. Ruiz, “Calculation of the PV modules angular losses under field conditions by means of an analytical model”, Solar Energy Materials & Solar Cells, vol. 70, pp. 25-38, 2001.

[2]

N. Martin and J. M. Ruiz, “Corrigendum to ‘Calculation of the PV modules angular losses under field conditions by means of an analytical model’”, Solar Energy Materials & Solar Cells, vol. 110, pp. 154, 2013.

Author: Anton Driesse, PV Performance Labs