Add polo spectral factor model (#2491)

* Add polo-smm

Add the polo spectral model for BIPV facades

* Apply suggestions from code review

Co-authored-by: Adam R. Jensen <39184289+AdamRJensen@users.noreply.github.com>

* Update mismatch.py

* Update mismatch.py

* Update mismatch.py

* Update mismatch.py

* Update mismatch.py

* Update mismatch.py

* Update pvlib/spectrum/mismatch.py

Co-authored-by: Echedey Luis <80125792+echedey-ls@users.noreply.github.com>

* Update pvlib/spectrum/mismatch.py

Co-authored-by: Echedey Luis <80125792+echedey-ls@users.noreply.github.com>

* Changes from code review

* Add function to spectrum/__init__.py

* Update test_mismatch.py

* Update test_mismatch.py

* Fix module import in tests

* Update test_mismatch.py

* Fix linter

* Remove tab character

* Update test_mismatch.py

* Update test_mismatch.py

* fix line legth linter error

* Update test_mismatch.py

* Update mismatch.py

* Update mismatch.py

* Apply suggestions from code review

* replace `altitude` parameter with `pressure`

* `albedo : numeric`

* make albedo coefficients user-specified as well

* complete tests

* docstring cleanup

* whatsnew note and contributors

* add to user guide SMM model comparison table

* lint

* minor doc fixes

* Update mismatch.py

* Update mismatch.py

* clip AOI to max of 90 degrees as discussed in review

---------

Co-authored-by: Adam R. Jensen <39184289+AdamRJensen@users.noreply.github.com>
Co-authored-by: Echedey Luis <80125792+echedey-ls@users.noreply.github.com>
Co-authored-by: Kevin Anderson <kevin.anderso@gmail.com>

Author: 4 people

docs/sphinx/source/reference/effects_on_pv_system_output/spectrum.rst

@@ -12,9 +12,10 @@ Spectrum
    spectrum.calc_spectral_mismatch_field
    spectrum.spectral_factor_caballero
    spectrum.spectral_factor_firstsolar
-   spectrum.spectral_factor_sapm
-   spectrum.spectral_factor_pvspec
    spectrum.spectral_factor_jrc
+   spectrum.spectral_factor_polo
+   spectrum.spectral_factor_pvspec
+   spectrum.spectral_factor_sapm
    spectrum.sr_to_qe
    spectrum.qe_to_sr
    spectrum.average_photon_energy

docs/sphinx/source/user_guide/modeling_topics/spectrum.rst

@@ -61,11 +61,21 @@ Reference [2]_.
 |                                                     +-----------------------------+         |    ✓    |  ✓   |      |      |            +   [4]_    |
 |                                                     | clearsky_index              |         |         |      |      |      |            |           |
 +-----------------------------------------------------+-----------------------------+---------+---------+------+------+------+------------+-----------+
+| :py:func:`Polo <spectral_factor_polo>`              | :term:`precipitable_water`, |         |         |      |      |      |            |           |
+|                                                     +-----------------------------+   ✓     |         |  ✓   |  ✓   |  ✓   |            +   [5]_    |
+|                                                     | :term:`airmass_absolute`,   |         |         |      |      |      |            |           |
+|                                                     +-----------------------------+         |         |      |      |      |            |           |
+|                                                     | aod500,                     |         |         |      |      |      |            |           |
+|                                                     +-----------------------------+         |         |      |      |      |            |           |
+|                                                     | :term:`aoi`,                |         |         |      |      |      |            |           |
+|                                                     +-----------------------------+         |         |      |      |      |            |           |
+|                                                     | :term:`pressure`            |         |         |      |      |      |            |           |
++-----------------------------------------------------+-----------------------------+---------+---------+------+------+------+------------+-----------+
 | :py:func:`PVSPEC <spectral_factor_pvspec>`          | :term:`airmass_absolute`,   |         |         |      |      |      |            |           |
-|                                                     +-----------------------------+   ✓     |    ✓    |  ✓   |  ✓   |  ✓   |            |   [5]_    |
+|                                                     +-----------------------------+   ✓     |    ✓    |  ✓   |  ✓   |  ✓   |            |   [6]_    |
 |                                                     | clearsky_index              |         |         |      |      |      |            |           |
 +-----------------------------------------------------+-----------------------------+---------+---------+------+------+------+------------+-----------+
-| :py:func:`SAPM <spectral_factor_sapm>`              | :term:`airmass_absolute`    |         |         |      |      |      |            |   [6]_    |
+| :py:func:`SAPM <spectral_factor_sapm>`              | :term:`airmass_absolute`    |         |         |      |      |      |            |   [7]_    |
 +-----------------------------------------------------+-----------------------------+---------+---------+------+------+------+------------+-----------+
 
 
@@ -88,16 +98,19 @@ References
        PVSPEC Model of Photovoltaic Spectral Mismatch Factor," in Proc. 2020
        IEEE 47th Photovoltaic Specialists Conference (PVSC), Calgary, AB,
        Canada, 2020, pp. 1–6. :doi:`10.1109/PVSC45281.2020.9300932`
-.. [5] D. L. King, W. E. Boyson, and J. A. Kratochvil, Photovoltaic Array
+.. [5] J. Polo and C. Sanz-Saiz, 'Development of spectral mismatch models
+       for BIPV applications in building façades', Renewable Energy, vol. 245,
+       p. 122820, Jun. 2025, :doi:`10.1016/j.renene.2025.122820`
+.. [6] D. L. King, W. E. Boyson, and J. A. Kratochvil, Photovoltaic Array
        Performance Model, Sandia National Laboratories, Albuquerque, NM, USA,
        Tech. Rep. SAND2004-3535, Aug. 2004. :doi:`10.2172/919131`
-.. [6] M. Lee and A. Panchula, "Spectral Correction for Photovoltaic Module
+.. [7] M. Lee and A. Panchula, "Spectral Correction for Photovoltaic Module
        Performance Based on Air Mass and Precipitable Water," 2016 IEEE 43rd
        Photovoltaic Specialists Conference (PVSC), Portland, OR, USA, 2016,
        pp. 3696-3699. :doi:`10.1109/PVSC.2016.7749836`
-.. [7] H. Thomas, S. Tony, and D. Ewan, “A Simple Model for Estimating the
-       Influence of Spectrum Variations on PV Performance,” pp. 3385–3389, Nov.
+.. [8] T. Huld, T. Sample, and E. Dunlop, "A Simple Model for Estimating the
+       Influence of Spectrum Variations on PV Performance," pp. 3385–3389, Nov.
        2009, :doi:`10.4229/24THEUPVSEC2009-4AV.3.27`
-.. [8] IEC 60904-7:2019, Photovoltaic devices — Part 7: Computation of the
+.. [9] IEC 60904-7:2019, Photovoltaic devices — Part 7: Computation of the
        spectral mismatch correction for measurements of photovoltaic devices, 
        International Electrotechnical Commission, Geneva, Switzerland, 2019.

docs/sphinx/source/whatsnew/v0.13.2.rst

@@ -44,6 +44,8 @@ Enhancements
   ERA5 reanalysis data. (:pull:`2573`)
 * Add :py:func:`~pvlib.iotools.get_merra2`, a function for accessing
   MERRA-2 reanalysis data. (:pull:`2572`)
+* Add :py:func:`~pvlib.spectrum.spectral_factor_polo`, a function for estimating
+  spectral mismatch factors for vertical PV façades. (:issue:`2406`, :pull:`2491`)
 
 Documentation
 ~~~~~~~~~~~~~
@@ -79,4 +81,9 @@ Contributors
 * Will Hobbs (:ghuser:`williamhobbs`)
 * Cliff Hansen (:ghuser:`cwhanse`)
 * Joseph Radford (:ghuser:`josephradford`)
+* Jesús Polo (:ghuser:`jesuspolo`)
+* Adam R. Jensen (:ghuser:`adamrjensen`)
+* Echedey Luis (:ghuser:`echedey-ls`)
+* Anton Driesse (:ghuser:`adriesse`)
+* Rajiv Daxini (:ghuser:`RDaxini`)
 * Kevin Anderson (:ghuser:`kandersolar`)

pvlib/spectrum/__init__.py

@@ -3,9 +3,10 @@
     calc_spectral_mismatch_field,
     spectral_factor_caballero,
     spectral_factor_firstsolar,
-    spectral_factor_sapm,
-    spectral_factor_pvspec,
     spectral_factor_jrc,
+    spectral_factor_polo,
+    spectral_factor_pvspec,
+    spectral_factor_sapm,
 )
 from pvlib.spectrum.irradiance import (  # noqa: F401
     get_reference_spectra,

pvlib/spectrum/mismatch.py

@@ -698,3 +698,104 @@ def spectral_factor_jrc(airmass, clearsky_index, module_type=None,
         + coeff[2] * (airmass - 1.5)
     )
     return mismatch
+
+
+def spectral_factor_polo(precipitable_water, airmass_absolute, aod500, aoi,
+                         pressure, module_type=None, coefficients=None,
+                         albedo=0.2):
+    """
+    Estimate the spectral mismatch for BIPV application in vertical facades.
+
+    The model's authors note that this model could also be applied to
+    vertical bifacial ground-mount systems [1]_, although it has not been
+    validated in that context.
+
+    Parameters
+    ----------
+    precipitable_water : numeric
+        Atmospheric precipitable water. [cm]
+    airmass_absolute : numeric
+        Absolute (pressure-adjusted) airmass. See :term:`airmass_absolute`.
+        [unitless]
+    aod500 : numeric
+        Atmospheric aerosol optical depth at 500 nm. [unitless]
+    aoi : numeric
+        Angle of incidence on the vertical surface.  See :term:`aoi`.
+        [degrees]
+    pressure : numeric
+        Atmospheric pressure. See :term:`pressure`. [Pa]
+    module_type : str, optional
+        One of the following PV technology strings from [1]_:
+
+        * ``'cdte'`` - anonymous CdTe module.
+        * ``'monosi'`` - anonymous monocrystalline silicon module.
+        * ``'cigs'`` - anonymous copper indium gallium selenide module.
+        * ``'asi'`` - anonymous amorphous silicon module.
+    coefficients : array-like, optional
+        User-defined coefficients, if not using one of the coefficient
+        sets via the ``module_type`` parameter.  Must have nine elements.
+        The first six elements correspond to the [p1, p2, p3, p4, b, c]
+        parameters of the SMM model.  The last three elements corresponds
+        to the [c1, c2, c3] parameters of the albedo correction factor.
+    albedo : numeric, default 0.2
+        Ground albedo. See :term:`albedo`. [unitless]
+
+    Returns
+    -------
+    modifier: numeric
+        spectral mismatch factor (unitless) which is multiplied
+        with broadband irradiance reaching a module's cells to estimate
+        effective irradiance, i.e., the irradiance that is converted to
+        electrical current.
+
+    Notes
+    -----
+    The Polo model was developed using only SMM values computed for scenarios
+    when the sun is visible from the module's surface (i.e., for ``aoi<90``),
+    and no provision was made in [1]_ for the case of ``aoi>90``. This would
+    create issues in the air mass calculation internal to the model.
+    Following discussion with the model's author, the pvlib implementation
+    handles ``aoi>90`` by truncating the input ``aoi`` to a maximum of
+    90 degrees.
+
+    References
+    ----------
+    .. [1] J. Polo and C. Sanz-Saiz, 'Development of spectral mismatch models
+       for BIPV applications in building façades', Renewable Energy, vol. 245,
+       p. 122820, Jun. 2025, :doi:`10.1016/j.renene.2025.122820`
+    """
+    if module_type is None and coefficients is None:
+        raise ValueError('Must provide either `module_type` or `coefficients`')
+    if module_type is not None and coefficients is not None:
+        raise ValueError('Only one of `module_type` and `coefficients` should '
+                         'be provided')
+    # prevent nan for aoi greater than 90; see docstring Notes
+    aoi = np.clip(aoi, a_min=None, a_max=90)
+    f_aoi_rel = pvlib.atmosphere.get_relative_airmass(aoi,
+                                                      model='kastenyoung1989')
+    f_aoi = pvlib.atmosphere.get_absolute_airmass(f_aoi_rel, pressure)
+    Ram = f_aoi / airmass_absolute
+    _coefficients = {
+        'cdte': (-0.0009, 46.80, 49.20, -0.87, 0.00041, 0.053),
+        'monosi': (0.0027, 10.34, 9.48, 0.31, 0.00077, 0.006),
+        'cigs': (0.0017, 2.33, 1.30, 0.11, 0.00098, -0.018),
+        'asi': (0.0024, 7.32, 7.09, -0.72, -0.0013, 0.089),
+    }
+    c = {
+        'asi': (0.0056, -0.020, 1.014),
+        'cigs': (-0.0009, -0.0003, 1),
+        'cdte': (0.0021, -0.01, 1.01),
+        'monosi': (0, -0.003, 1.0),
+    }
+    if module_type is not None:
+        coeff = _coefficients[module_type]
+        c_albedo = c[module_type]
+    else:
+        coeff = coefficients[:6]
+        c_albedo = coefficients[6:]
+    smm = coeff[0] * Ram + coeff[1] / (coeff[2] + Ram**coeff[3]) \
+        + coeff[4] / aod500 + coeff[5]*np.sqrt(precipitable_water)
+    # Ground albedo correction
+    g = c_albedo[0] * (albedo/0.2)**2 \
+        + c_albedo[1] * (albedo/0.2) + c_albedo[2]
+    return g*smm

tests/spectrum/test_mismatch.py

@@ -288,3 +288,90 @@ def test_spectral_factor_jrc_supplied_ambiguous():
     with pytest.raises(ValueError, match='No valid input provided'):
         spectrum.spectral_factor_jrc(1.0, 0.8, module_type=None,
                                      coefficients=None)
+
+
+@pytest.mark.parametrize("module_type,expected", [
+    ('cdte', np.array(
+        [0.992801, 1.00004, 1.011576, 0.995003, 0.950156, 0.975665])),
+    ('monosi', np.array(
+        [1.000152, 0.969588, 0.984636, 1.015405, 1.024238, 1.005061])),
+    ('cigs', np.array(
+        [1.004621, 0.956719, 0.971668, 1.0254, 1.060066, 1.020196])),
+    ('asi', np.array(
+        [0.986968, 1.049725, 1.051978, 0.957968, 0.842258, 0.941927])),
+])
+def test_spectral_factor_polo(module_type, expected):
+    pws = np.array([0.96, 0.96, 1.85, 1.88, 0.66, 0.66])
+    aods = np.array([0.085, 0.085, 0.16, 0.19, 0.088, 0.088])
+    ams = np.array([1.34, 1.34, 2.2, 2.2, 2.6, 2.6])
+    aois = np.array([46.0, 76.0, 74.0, 28.0, 24.0, 55.0])
+    pressure = np.array([101300, 101400, 100500, 101325, 80000, 120000])
+    alb = np.array([0.15, 0.2, 0.3, 0.18, 0.32, 0.26])
+    out = spectrum.spectral_factor_polo(
+        pws, ams, aods, aois, pressure, module_type=module_type, albedo=alb)
+    np.testing.assert_allclose(out, expected, atol=1e-6)
+
+
+@pytest.fixture
+def polo_inputs():
+    return {'precipitable_water': 0.96,
+            'airmass_absolute': 1.34,
+            'aod500': 0.085,
+            'aoi': 76,
+            'pressure': 101400,
+            'albedo': 0.2}
+
+
+def test_spectral_factor_polo_coefficients(polo_inputs):
+    # test that supplying custom coefficients works as expected
+    coefficients = (
+        (0.0027, 10.34, 9.48, 0.31, 0.00077, 0.006)  # base Si coeffs
+        + (0, -0.003, 1.0)  # Si albedo correction coeffs
+    )
+    out = spectrum.spectral_factor_polo(**polo_inputs,
+                                        coefficients=coefficients)
+    np.testing.assert_allclose(out, 0.969588, atol=1e-6)
+
+
+def test_spectral_factor_polo_errors(polo_inputs):
+    with pytest.raises(ValueError, match='Must provide either'):
+        spectrum.spectral_factor_polo(**polo_inputs)
+    with pytest.raises(ValueError, match='Only one of'):
+        spectrum.spectral_factor_polo(**polo_inputs, module_type='CdTe',
+                                      coefficients=(1, 1, 1, 1, 1, 1))
+
+
+def test_spectral_factor_polo_types(polo_inputs):
+    # float:
+    out = spectrum.spectral_factor_polo(**polo_inputs, module_type='monosi')
+    assert isinstance(out, float)
+    np.testing.assert_allclose(out, 0.969588, atol=1e-6)
+
+    # array:
+    arrays = {k: np.array([v, v]) for k, v in polo_inputs.items()}
+    out = spectrum.spectral_factor_polo(**arrays, module_type='monosi')
+    assert isinstance(out, np.ndarray)
+    np.testing.assert_allclose(out, [0.969588]*2, atol=1e-6)
+
+    # series:
+    series = {k: pd.Series(v) for k, v in arrays.items()}
+    out = spectrum.spectral_factor_polo(**series, module_type='monosi')
+    assert isinstance(out, pd.Series)
+    pd.testing.assert_series_equal(out, pd.Series([0.969588]*2), atol=1e-6)
+
+
+def test_spectral_factor_polo_NaN(polo_inputs):
+    # nan in -> nan out
+    for key in polo_inputs:
+        inputs = polo_inputs.copy()
+        inputs[key] = np.nan
+        out = spectrum.spectral_factor_polo(**inputs, module_type='monosi')
+        assert np.isnan(out)
+
+
+def test_spectral_factor_polo_aoi_gt_90(polo_inputs):
+    polo_inputs['aoi'] = 95
+    out95 = spectrum.spectral_factor_polo(**polo_inputs, module_type='monosi')
+    polo_inputs['aoi'] = 90
+    out90 = spectrum.spectral_factor_polo(**polo_inputs, module_type='monosi')
+    assert out95 == out90