Implement enhanced Faiman temperature model

docs/sphinx/source/reference/pv_modeling.rst

@@ -40,6 +40,7 @@ PV temperature models
    temperature.sapm_cell_from_module
    temperature.pvsyst_cell
    temperature.faiman
+   temperature.faiman_rad
    temperature.fuentes
    temperature.ross
    temperature.noct_sam

pvlib/temperature.py

@@ -419,7 +419,7 @@ def faiman(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84):
     u1 : numeric, default 6.84
         Combined heat loss factor influenced by wind. The default value is one
         determined by Faiman for 7 silicon modules.
-        :math:`\left[ \frac{\text{W}/\text{m}^2}{\text{C}\ \left( \text{m/s} \right)} \right]`
+        :math:`\left[ \frac{\text{W}/\text{m}^2}{\text{C}\ \left( \text{m/s} \right)} \right]`  # noQA: E501
 
     Returns
     -------
@@ -457,6 +457,106 @@ def faiman(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84):
     return temp_air + temp_difference
 
 
+def faiman_rad(poa_global, temp_air, wind_speed=1.0, ir_down=None,
+               u0=25.0, u1=6.84, sky_view=1.0, emissivity=0.88):
+    r'''
+    Calculate cell or module temperature using the Faiman model augmented
+    with a radiative loss term.
+
+    The Faiman model uses an empirical heat loss factor model [1]_ and is
+    adopted in the IEC 61853 standards [2]_ and [3]_.  The radiative loss
+    term was developed in [4]_.
+
+    The model can be used to represent cell or module temperature.
+
+    Parameters
+    ----------
+    poa_global : numeric
+        Total incident irradiance [W/m^2].
+
+    temp_air : numeric
+        Ambient dry bulb temperature [C].
+
+    wind_speed : numeric, default 1.0
+        Wind speed measured at the same height for which the wind loss
+        factor was determined.  The default value 1.0 m/s is the wind
+        speed at module height used to determine NOCT. [m/s]
+
+    ir_down : numeric, default 0.0
+        Downwelling infrared radiation from the sky, measured on a horizontal
+        surface. [W/m^2]
+
+    u0 : numeric, default 25.0
+        Combined heat loss factor coefficient. The default value is one
+        determined by Faiman for 7 silicon modules.
+        :math:`\left[\frac{\text{W}/{\text{m}^2}}{\text{C}}\right]`
+
+    u1 : numeric, default 6.84
+        Combined heat loss factor influenced by wind. The default value is one
+        determined by Faiman for 7 silicon modules.
+        :math:`\left[ \frac{\text{W}/\text{m}^2}{\text{C}\ \left( \text{m/s} \right)} \right]`  # noQA: E501
+
+    sky_view : numeric, default 1.0
+        Effective view factor limiting the radiative exchange between the
+        module and the sky. For a tilted array the expressions
+        (1 + 3*cos(tilt)) / 4 can be used as a first estimate for sky_view
+        as discussed in [4]_. The default value is for a horizontal module.
+        [unitless]
+
+    emissivity : numeric, default 0.88
+        Infrared emissivity of the module surface facing the sky. The default
+        value represents the middle of a range of values found in the
+        literature. [unitless]
+
+    Returns
+    -------
+    numeric, values in degrees Celsius
+
+    Notes
+    -----
+    All arguments may be scalars or vectors. If multiple arguments
+    are vectors they must be the same length.
+
+    If the input `ir_down` is not supplied the model output is the same as the
+    original Faiman model.
+
+    References
+    ----------
+    .. [1] Faiman, D. (2008). "Assessing the outdoor operating temperature of
+       photovoltaic modules." Progress in Photovoltaics 16(4): 307-315.
+
+    .. [2] "IEC 61853-2 Photovoltaic (PV) module performance testing and energy
+       rating - Part 2: Spectral responsivity, incidence angle and module
+       operating temperature measurements". IEC, Geneva, 2018.
+
+    .. [3] "IEC 61853-3 Photovoltaic (PV) module performance testing and energy
+       rating - Part 3: Energy rating of PV modules". IEC, Geneva, 2018.
+
+    .. [4] Driesse, A. et al (2022) "Improving Common PV Module Temperature
+       Models by Incorporating Radiative Losses to the Sky". SAND2022-11604.
+
+    '''
+    # Contributed by Anton Driesse (@adriesse), PV Performance Labs. Nov., 2022
+
+    u0 = np.asanyarray(u0)
+    u1 = np.asanyarray(u1)
+    emissivity = np.asanyarray(emissivity)
+
+    abs_zero = np.array(-273.15)
+    kstefbolz = np.array(5.670367e-8)
+
+    if ir_down is None:
+        qrad_sky = np.array(0.0)
+    else:
+        ir_up = kstefbolz * ((temp_air - abs_zero)**4)
+        qrad_sky = emissivity * sky_view * (ir_up - ir_down)
+
+    heat_input = poa_global - qrad_sky
+    total_loss_factor = u0 + u1 * wind_speed
+    temp_difference = heat_input / total_loss_factor
+    return temp_air + temp_difference
+
+
 def ross(poa_global, temp_air, noct):
     r'''
     Calculate cell temperature using the Ross model.

pvlib/tests/test_temperature.py

@@ -108,12 +108,12 @@ def test_pvsyst_cell_eta_m_deprecated():
 
 def test_faiman_default():
     result = temperature.faiman(900, 20, 5)
-    assert_allclose(result, 35.203, 0.001)
+    assert_allclose(result, 35.203, atol=0.001)
 
 
 def test_faiman_kwargs():
     result = temperature.faiman(900, 20, wind_speed=5.0, u0=22.0, u1=6.)
-    assert_allclose(result, 37.308, 0.001)
+    assert_allclose(result, 37.308, atol=0.001)
 
 
 def test_faiman_list():
@@ -122,7 +122,7 @@ def test_faiman_list():
     winds = [10, 5, 0]
     result = temperature.faiman(irrads, temps, wind_speed=winds)
     expected = np.array([0.0, 18.446, 5.0])
-    assert_allclose(expected, result, 3)
+    assert_allclose(expected, result, atol=0.001)
 
 
 def test_faiman_ndarray():
@@ -131,7 +131,32 @@ def test_faiman_ndarray():
     winds = np.array([10, 5, 0])
     result = temperature.faiman(irrads, temps, wind_speed=winds)
     expected = np.array([0.0, 18.446, 5.0])
-    assert_allclose(expected, result, 3)
+    assert_allclose(expected, result, atol=0.001)
+
+
+def test_faiman_rad_no_ir():
+    expected = temperature.faiman(900, 20, 5)
+    result = temperature.faiman_rad(900, 20, 5)
+    assert_allclose(result, expected)
+
+
+def test_faiman_rad_ir():
+    ir_down = [0, 100, 200, 315.6574, 400]
+    expected = [-11.111, -7.591, -4.071, -0.000, 2.969]
+    result = temperature.faiman_rad(0, 0, 0, ir_down)
+    assert_allclose(result, expected, atol=0.001)
+
+    sky_view = [1.0, 0.5, 0.0]
+    expected = [-4.071, -2.036, 0.000]
+    result = temperature.faiman_rad(0, 0, 0, ir_down=200,
+                                    sky_view=sky_view)
+    assert_allclose(result, expected, atol=0.001)
+
+    emissivity = [1.0, 0.88, 0.5, 0.0]
+    expected = [-4.626, -4.071, -2.313, 0.000]
+    result = temperature.faiman_rad(0, 0, 0, ir_down=200,
+                                    emissivity=emissivity)
+    assert_allclose(result, expected, atol=0.001)
 
 
 def test_ross():