# pvl_physicaliam

Determine the incidence angle modifier using the "physical" model.

## Contents

- Syntax
- Description
- Inputs
- Output
- Example
- References
- See also

## Syntax

- `IAM = pvl_physicaliam(K, L, n, theta)`

## Description

`pvl_physicaliam` calculates the incidence angle modifier using the physical model [1] which is based upon Snell's Law for transmission of light and and Bougher's Law for absorbtion within a cover. Required information includes incident angle, cover extinction coefficient, cover thickness

Note: Eqn. 14 in [1] is incorrect. The correct equation (implemented in this function) is:

.

## Inputs

- `K` - The glazing extinction coefficient in units of 1/meters. Reference [1] indicates that a value of 4 is reasonable for "water white" glass. `K` must be a numeric scalar or vector with all values >=0. If `K` is a vector, it must be the same size as all other input vectors.
- `L` - The glazing thickness in units of meters. Reference [1] indicates that 0.002 meters (2 mm) is reasonable for most glass-covered PV panels. `L` must be a numeric scalar or vector with all values >=0. If `L` is a vector, it must be the same size as all other input vectors.
- `n` - The index of refraction (unitless). Reference [1] indicates that a value of 1.526 is acceptable for glass. `n` must be a numeric scalar or vector with all values >=0. If `n` is a vector, it must be the same size as all other input vectors.
- `theta` - The angle of incidence between the module normal vector and the sun-beam vector in degrees. `theta` must be a numeric scalar or vector. For any values of `theta` where `abs(theta)>90`, `IAM` is set to 0. For any values of `theta` where `-90 < theta < 0`, `theta` is set to `abs(theta)` and evaluated.

## Output

- `IAM` - The incident angle modifier as specified in eqns. 14-16 of [1]. IAM is a column vector with the same number of elements as the largest input vector.

## Example

This example plots the IAM for glass over a range of incident angles.

    K=4;             %glazing extinction coefficient in units of 1/meters
    L=0.02;          %glazing thickness in units of meters
    n= 1.56;         %index of refraction
    theta = 0:90;    %incident angle in degrees
    IAM = pvl_physicaliam(K, L, n, theta);
    figure
    plot(theta,IAM)
    xlabel('Incident Angle (deg)')
    ylabel('IAM')
    title('Physical IAM Model Example')

## References

[1] De Soto, W., Klein, S. A., Beckman, W. A., 2006. Improvement and validation of a model for photovoltaic array performance, Solar Energy, vol 80, pp. 78-88.

[2] Duffie, John A. & Beckman, William A., 2006. Solar Engineering of Thermal Processes, third edition. Available from http://common.books24x7.com/toc.aspx?bookid=17160.

## See also

`pvl_getaoi` , `pvl_ephemeris` , `pvl_spa` , `pvl_ashraeiam` , `pvl_martinruiziam`

Copyright 2014 Sandia National Laboratories