SAPM_EFF_IRRAD

This function converts plane-of-array direct and diffuse irradiance into the effective irradiance actually absorbed by module cells under the Sandia model. It applies both a spectral adjustment based on absolute airmass and an incidence-angle modifier based on angle of incidence.

The SAPM effective irradiance relationship is:

E_e = f_1(AM_a) \left(E_b f_2(AOI) + f_d E_d\right)

Here f_1 is the spectral response polynomial, f_2 is the angle-of-incidence modifier, and f_d is the diffuse fraction coefficient. Supply the required coefficients as a 2D list of key-value pairs such as [["A0", 1.0], ["B0", 1.0], ["FD", 1.0]].

Excel Usage

=SAPM_EFF_IRRAD(poa_direct, poa_diffuse, airmass_absolute, aoi, module_params)
  • poa_direct (float, required): Direct irradiance on the plane of array (W/m^2).
  • poa_diffuse (float, required): Diffuse irradiance on the plane of array (W/m^2).
  • airmass_absolute (float, required): Absolute airmass (unitless).
  • aoi (float, required): Angle of incidence (degrees).
  • module_params (list[list], required): 2D list of SAPM coefficients [[‘key’, value], …].

Returns (float): Effective irradiance (W/m^2), or an error string.

Example 1: Standard Effective Irradiance

Inputs:

poa_direct poa_diffuse airmass_absolute aoi module_params
800 100 1.5 30 A0 1
A1 0
A2 0
A3 0
A4 0
B0 1
B1 0
B2 0
B3 0
B4 0
B5 0
FD 1

Excel formula:

=SAPM_EFF_IRRAD(800, 100, 1.5, 30, {"A0",1;"A1",0;"A2",0;"A3",0;"A4",0;"B0",1;"B1",0;"B2",0;"B3",0;"B4",0;"B5",0;"FD",1})

Expected output:

900

Example 2: Diffuse-only irradiance case

Inputs:

poa_direct poa_diffuse airmass_absolute aoi module_params
0 200 1.5 30 A0 1
A1 0
A2 0
A3 0
A4 0
B0 1
B1 0
B2 0
B3 0
B4 0
B5 0
FD 1

Excel formula:

=SAPM_EFF_IRRAD(0, 200, 1.5, 30, {"A0",1;"A1",0;"A2",0;"A3",0;"A4",0;"B0",1;"B1",0;"B2",0;"B3",0;"B4",0;"B5",0;"FD",1})

Expected output:

200

Example 3: Reduced diffuse fraction coefficient

Inputs:

poa_direct poa_diffuse airmass_absolute aoi module_params
700 100 1.5 30 A0 1
A1 0
A2 0
A3 0
A4 0
B0 1
B1 0
B2 0
B3 0
B4 0
B5 0
FD 0.8

Excel formula:

=SAPM_EFF_IRRAD(700, 100, 1.5, 30, {"A0",1;"A1",0;"A2",0;"A3",0;"A4",0;"B0",1;"B1",0;"B2",0;"B3",0;"B4",0;"B5",0;"FD",0.8})

Expected output:

780

Example 4: Spectral scaling below unity

Inputs:

poa_direct poa_diffuse airmass_absolute aoi module_params
800 100 1.5 30 A0 0.95
A1 0
A2 0
A3 0
A4 0
B0 1
B1 0
B2 0
B3 0
B4 0
B5 0
FD 1

Excel formula:

=SAPM_EFF_IRRAD(800, 100, 1.5, 30, {"A0",0.95;"A1",0;"A2",0;"A3",0;"A4",0;"B0",1;"B1",0;"B2",0;"B3",0;"B4",0;"B5",0;"FD",1})

Expected output:

855

Python Code

Show Code 
from pvlib.pvsystem import sapm_effective_irradiance as result_func

def sapm_eff_irrad(poa_direct, poa_diffuse, airmass_absolute, aoi, module_params):
    """
    Calculate SAPM effective irradiance accounting for spectral and incidence losses.

    See: https://pvlib-python.readthedocs.io/en/stable/reference/generated/pvlib.pvsystem.sapm_effective_irradiance.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        poa_direct (float): Direct irradiance on the plane of array (W/m^2).
        poa_diffuse (float): Diffuse irradiance on the plane of array (W/m^2).
        airmass_absolute (float): Absolute airmass (unitless).
        aoi (float): Angle of incidence (degrees).
        module_params (list[list]): 2D list of SAPM coefficients [['key', value], ...].

    Returns:
        float: Effective irradiance (W/m^2), or an error string.
    """
    try:
      def to2d(x):
        return [[x]] if not isinstance(x, list) else x

      eb = float(poa_direct)
      ed = float(poa_diffuse)
      am = float(airmass_absolute)
      ao = float(aoi)

      module_params = to2d(module_params)
      if not isinstance(module_params, list) or not all(isinstance(row, list) for row in module_params):
        return "Error: module_params must be a 2D list of key-value pairs"

      mod_dict = {}
      for row in module_params:
        if len(row) >= 2:
          key = str(row[0]).strip()
          val = row[1]
          try:
            val = float(val)
          except (TypeError, ValueError):
            pass
          mod_dict[key] = val

      res = result_func(
        poa_direct=eb,
        poa_diffuse=ed,
        airmass_absolute=am,
        aoi=ao,
        module=mod_dict
      )

      return float(res)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Direct irradiance on the plane of array (W/m^2).
Diffuse irradiance on the plane of array (W/m^2).
Absolute airmass (unitless).
Angle of incidence (degrees).
2D list of SAPM coefficients [['key', value], ...].