Incidence angle modifier#

Some fraction of the light incident on a PV module surface is reflected away or absorbed before it reaches the PV cell. This irradiance reduction depends on the angle at which the light strikes the module (the angle of incidence, AOI) and the optical properties of the module.

Some reduction occurs at all angles of incidence, even normal incidence. However, because PV modules are rated with irradiance at normal incidence, the reduction at normal incidence is implicit in the PV module’s power rating and does not need to be accounted for separately in a performance model. Therefore, only the extra reduction at non-normal incidence should be modeled.

This is done using incidence angle modififer (IAM) models. Conceptually, IAM is the fraction of incident light that is transmitted to the PV cell, normalized to the fraction transmitted at normal incidence:

\[IAM(\theta) = \frac{T(\theta)}{T(0)},\]

where \(T(\theta)\) represents the transmitted light fraction at AOI \(\theta\). IAM equals (by definition) 1.0 when AOI is zero and typically approaches zero as AOI approaches 90°. The shape of the IAM profile at intermediate AOI is nonlinear and depends on the module’s optical properties.

IAM may also depend on the wavelength of the light, the polarization of the light, and which side of the module the light comes from. However, IAM models usually neglect these minor effects.

IAM functions in pvlib take an input angle in degrees and return a unitless ratio in the range 0–1.

Types of models#

Because total in-plane irradiance is the combination of light from many directions, IAM values are computed for each component separately:

direct IAM: IAM computed for the AOI of direct irradiance
circumsolar IAM: typically approximated as equal to the direct IAM
diffuse IAM: IAM integrated across the ranges of AOI spanning the sky and/or ground surfaces

Because diffuse light can be thought of as a field of many small beams of direct light, diffuse IAM can then be understood as the IAM averaged across those individual beams. This averaging can be done explicitly or empirically.

In principle, IAM should be applied to all components of incident irradiance. In practice, IAM is sometimes applied only to the direct component of in-plane irradiance, as the direct component is often the largest contributor to total in-plane irradiance and has a highly variable AOI across the day and year.

The IAM models currently available in pvlib are summarized in the following table:

Model	Type	Notes
`ashrae()`	direct	Once common, now less used
`martin_ruiz()`	direct	Used in the IEC 61853 standard
`martin_ruiz_diffuse()`	diffuse	Used in the IEC 61853 standard
`physical()`	direct	Physics-based; optional AR coating
`sapm()`	direct	Can be non-monotonic and exceed 1.0
`schlick()`	direct	Does not take module-specific parameters
`schlick_diffuse()`	diffuse	Does not take module-specific parmaeters

In addition to the core models above, pvlib provides several other functions for IAM modeling:

interp(): interpolate between points on a measured IAM profile
marion_diffuse() and marion_integrate(): numerically integrate any IAM model across AOI to compute sky, horizon, and ground IAMs

Model parameters#

Some IAM model functions provide default values for their parameters. However, these generic values may not be suitable for all PV modules. It should be noted that using the default parameter values for each model generally leads to different IAM profiles.

Module-specific values can be obtained via testing. For example, IEC 61853-2 testing produces measured IAM values across the range of AOI and a corresponding parameter value for the Martin-Ruiz model. Parameter values for other models can be determined using pvlib.iam.fit(). Parameter values can also be approximately converted between models using pvlib.iam.convert().