Add method to fit Huld model

docs/sphinx/source/reference/pv_modeling/system_models.rst

@@ -56,3 +56,4 @@ PVGIS model
    :toctree: ../generated/
 
     pvarray.huld
+    pvarray.fit_huld

docs/sphinx/source/whatsnew/v0.11.0.rst

@@ -9,6 +9,7 @@ Breaking changes
 ~~~~~~~~~~~~~~~~
 * The deprecated ``pvlib.modelchain.basic_chain`` has now been removed. (:pull:`1862`)
 * Remove the `poa_horizontal_ratio` function and all of its references. (:issue:`1697`, :pull:`2021`)
+* Parameter ``temp_mod`` in :py:func:`pvlib.pvarray.huld` is renamed to ``temp_module``. (:pull:`1979`)
 * The `leap_day` parameter in :py:func:`~pvlib.iotools.get_psm3`
   now defaults to True instead of False. (:issue:`1481`, :pull:`1991`)
 
@@ -23,7 +24,7 @@ Enhancements
   shade perpendicular to ``axis_azimuth``. The function is applicable to both
   fixed-tilt and one-axis tracking systems.
   (:issue:`1689`, :pull:`1725`, :pull:`1962`)
-
+* Added a method to fit the Huld PV model. (:pull:`1979`)
 
 Bug fixes
 ~~~~~~~~~

pvlib/pvarray.py

@@ -242,7 +242,7 @@ def _infer_k_huld(cell_type, pdc0):
     return k
 
 
-def huld(effective_irradiance, temp_mod, pdc0, k=None, cell_type=None):
+def huld(effective_irradiance, temp_module, pdc0, k=None, cell_type=None):
     r"""
     Power (DC) using the Huld model.
 
@@ -263,13 +263,13 @@ def huld(effective_irradiance, temp_mod, pdc0, k=None, cell_type=None):
     ----------
     effective_irradiance : numeric
         The irradiance that is converted to photocurrent. [:math:`W/m^2`]
-    temp_mod: numeric
+    temp_module: numeric
         Module back-surface temperature. [C]
     pdc0: numeric
         Power of the modules at reference conditions 1000 :math:`W/m^2`
         and :math:`25^{\circ}C`. [W]
     k : tuple, optional
-        Empirical coefficients used in the power model. Length 6. If ``k`` is
+        Empirical coefficients used in the Huld model. Length 6. If ``k`` is
         not provided, ``cell_type`` must be specified.
     cell_type : str, optional
         If provided, must be one of ``'cSi'``, ``'CIS'``, or ``'CdTe'``.
@@ -332,6 +332,10 @@ def huld(effective_irradiance, temp_mod, pdc0, k=None, cell_type=None):
            E. Dunlop. A power-rating model for crystalline silicon PV modules.
            Solar Energy Materials and Solar Cells 95, (2011), pp. 3359-3369.
            :doi:`10.1016/j.solmat.2011.07.026`.
+
+    See Also
+    --------
+    pvlib.pvarray.fit_huld
     """
     if k is None:
         if cell_type is not None:
@@ -340,7 +344,7 @@ def huld(effective_irradiance, temp_mod, pdc0, k=None, cell_type=None):
             raise ValueError('Either k or cell_type must be specified')
 
     gprime = effective_irradiance / 1000
-    tprime = temp_mod - 25
+    tprime = temp_module - 25
     # accomodate gprime<=0
     with np.errstate(divide='ignore'):
         logGprime = np.log(gprime, out=np.zeros_like(gprime),
@@ -350,3 +354,99 @@ def huld(effective_irradiance, temp_mod, pdc0, k=None, cell_type=None):
                     k[2] * tprime + k[3] * tprime * logGprime +
                     k[4] * tprime * logGprime**2 + k[5] * tprime**2)
     return pdc
+
+
+def _build_iec61853():
+    ee = np.array([100, 100, 200, 200, 400, 400, 400, 600, 600, 600, 600,
+                   800, 800, 800, 800, 1000, 1000, 1000, 1000, 1100, 1100,
+                   1100], dtype=np.float64).T
+    tc = np.array([15, 25, 15, 25, 15, 25, 50, 15, 25, 50, 75,
+                   15, 25, 50, 75, 15, 25, 50, 75, 25, 50, 75],
+                  dtype=np.float64).T
+    return ee, tc
+
+
+def fit_huld(effective_irradiance, temp_module, pdc, method='ols'):
+    r'''
+    Fit the Huld model to the input data.
+
+    Parameters
+    ----------
+    effective_irradiance : array-like
+        The irradiance that is converted to photocurrent. [:math:`W/m^2`]
+    temp_module: array-like
+        Module back-surface temperature. [C]
+    pdc: array-like
+        DC power at ``effective_irradiance`` and ``temp_module``. [W]
+    method : string, default 'ols'
+        The regression method. Must be either ``'ols'`` or ``'robust'``.
+
+    Returns
+    -------
+    pdc0: numeric
+        Power of the modules at reference conditions 1000 :math:`W/m^2`
+        and :math:`25^{\circ}C`. [W]
+    k : tuple
+        Empirical coefficients used in the Huld model. Length 6.
+
+    Notes
+    -----
+    Requires ``statsmodels``.
+
+    Input data ``effective_irradiance``, ``temp_module`` and ``pdc`` must be
+    equal length. Data are aligned as columns and any row with a NaN in any
+    column is dropped. Remaining data must be at least length 7.
+
+    Huld [1]_ describes fitting by least-squares but doesn't detail the
+    procedure, although it is reasonable that ordinary least-squares regression
+    was used. Ordinary least-squares regression can be unduly influenced by
+    data points with large deviations from the mean of the dependent variable
+    ``pdc``. For example, these data may occur when short-duration shading is
+    present. If filtering is applied to exclude such data, a suitable model
+    can be obtained with ordinary least-squares regression. As an alternative,
+    this function also provides a 'robust' regression option (an iteratively
+    reweighted least-squares method) that is more tolerant of outliers in the
+    dependent variable.
+
+    References
+    ----------
+    .. [1] T. Huld, G. Friesen, A. Skoczek, R. Kenny, T. Sample, M. Field,
+           E. Dunlop. A power-rating model for crystalline silicon PV modules.
+           Solar Energy Materials and Solar Cells 95, (2011), pp. 3359-3369.
+           :doi:`10.1016/j.solmat.2011.07.026`.
+
+    See Also
+    --------
+    pvlib.pvarray.huld
+    '''
+
+    try:
+        import statsmodels.api as sm
+    except ImportError:
+        raise ImportError(
+            'fit_huld requires statsmodels')
+
+    gprime = effective_irradiance / 1000
+    tprime = temp_module - 25
+    # accomodate gprime<=0
+    logGprime = np.log(gprime, out=np.nan*gprime,
+                       where=np.array(gprime > 0))
+    with np.errstate(divide='ignore'):
+        Y = np.divide(pdc, gprime, out=np.nan*gprime,
+                      where=np.array(gprime > 0))
+
+    X = np.stack((logGprime, logGprime**2, tprime, tprime*logGprime,
+                  tprime*logGprime**2, tprime**2), axis=0).T
+    X = sm.add_constant(X)
+
+    if method == 'ols':
+        model = sm.OLS(Y, X, missing='drop')
+    elif method == 'robust':
+        model = sm.RLM(Y, X, missing='drop')
+    else:
+        raise ValueError("method must be ols or robust")
+
+    result = model.fit()
+    pdc0 = result.params[0]
+    k = result.params[1:]
+    return pdc0, k

pvlib/tests/test_pvarray.py

@@ -3,7 +3,7 @@
 from numpy.testing import assert_allclose
 from .conftest import assert_series_equal
 import pytest
-
+from pvlib.tests.conftest import requires_statsmodels
 from pvlib import pvarray
 
 
@@ -69,3 +69,40 @@ def test_huld():
     with pytest.raises(ValueError,
                        match='Either k or cell_type must be specified'):
         res = pvarray.huld(1000, 25, 100)
+
+
+@pytest.mark.parametrize('method', ['ols', 'robust'])
+@requires_statsmodels
+def test_fit_huld(method):
+    # test is to recover the parameters in _infer_huld_k for each cell type
+    # IEC61853 conditions to make data for fitting
+    ee, tc = pvarray._build_iec61853()
+    techs = ['csi', 'cis', 'cdte']
+    pdc0 = 250
+    for tech in techs:
+        k0 = pvarray._infer_k_huld(tech, pdc0)
+        pdc = pvarray.huld(ee, tc, pdc0, cell_type=tech)
+        m_pdc0, k = pvarray.fit_huld(ee, tc, pdc, method=method)
+        expected = np.array([pdc0, ] + [v for v in k0], dtype=float)
+        modeled = np.hstack((m_pdc0, k))
+        assert_allclose(expected, modeled, rtol=1e-8)
+    # once more to check that NaNs are handled
+    ee[7] = np.nan
+    tc[9] = np.nan
+    k0 = pvarray._infer_k_huld('csi', pdc0)
+    pdc = pvarray.huld(ee, tc, pdc0, cell_type='csi')
+    pdc[11] = np.nan
+    m_pdc0, k = pvarray.fit_huld(ee, tc, pdc, method='ols')
+    expected = np.array([pdc0, ] + [v for v in k0], dtype=float)
+    modeled = np.hstack((m_pdc0, k))
+    assert_allclose(expected, modeled, rtol=1e-8)
+
+
+@requires_statsmodels
+def test_fit_huld_method_error():
+    ee, tc = pvarray._build_iec61853()
+    pdc0 = 250
+    pdc = pvarray.huld(ee, tc, pdc0, cell_type='csi')
+    method = 'brute_force'
+    with pytest.raises(ValueError, match="method must be ols or robust"):
+        m_pdc0, k = pvarray.fit_huld(ee, tc, pdc, method=method)