NOCT cell temperature function

docs/sphinx/source/api.rst

@@ -238,6 +238,7 @@ PV temperature models
    temperature.faiman
    temperature.fuentes
    temperature.ross
+   temperature.noct_sam
    pvsystem.PVSystem.sapm_celltemp
    pvsystem.PVSystem.pvsyst_celltemp
    pvsystem.PVSystem.faiman_celltemp

docs/sphinx/source/whatsnew/v0.9.0.rst

@@ -96,6 +96,8 @@ Enhancements
 * :py:meth:`~pvlib.pvsystem.PVSystem.get_ac` is added to calculate AC power
   from DC power. Use parameter ``model`` to specify which inverter model to use.
   (:pull:`1147`, :issue:`998`, :pull:`1150`)
+* Added :py:func:`~pvlib.temperature.noct_sam`, a cell temperature model
+  implemented in SAM (:pull:`1177`)
 
 Bug fixes
 ~~~~~~~~~

pvlib/temperature.py

@@ -706,3 +706,109 @@ def fuentes(poa_global, temp_air, wind_speed, noct_installed, module_height=5,
         sun0 = sun
 
     return pd.Series(tmod_array - 273.15, index=poa_global.index, name='tmod')
+
+
+def _adj_for_mounting_standoff(x):
+    # supports noct cell temperature function. Except for x > 3.5, the SAM code
+    # and documentation aren't clear on the precise intervals. The choice of
+    # < or <= here is pvlib's.
+    return np.piecewise(x, [x <= 0, (x > 0) & (x < 0.5),
+                            (x >= 0.5) & (x < 1.5), (x >= 1.5) & (x < 2.5),
+                            (x >= 2.5) & (x <= 3.5), x > 3.5],
+                        [0., 18., 11., 6., 2., 0.])
+
+
+def noct_sam(poa_global, temp_air, wind_speed, noct, eta_m_ref,
+             effective_irradiance=None, transmittance_absorptance=0.9,
+             array_height=1, mount_standoff=4):
+    r'''
+    Cell temperature model from the System Advisor Model (SAM).
+
+    The model is described in [1]_, Section 10.6.
+
+    Parameters
+    ----------
+    poa_global : numeric
+        Total incident irradiance. [W/m^2]
+
+    temp_air : numeric
+        Ambient dry bulb temperature. [C]
+
+    wind_speed : numeric
+        Wind speed in m/s 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]
+
+    noct : float
+        Nominal operating cell temperature [C], determined at conditions of
+        800 W/m^2 irradiance, 20 C ambient air temperature and 1 m/s wind.
+
+    eta_m_ref : float
+        Module external efficiency [unitless] at reference conditions of
+        1000 W/m^2 and 20C. Calculate as
+        :math:`\eta_{m} = \frac{V_{mp} I_{mp}}{A \times 1000 W/m^2}`
+        where A is module area [m^2].
+
+    effective_irradiance : numeric, default None.
+        The irradiance that is converted to photocurrent. If None,
+        assumed equal to poa_global. [W/m^2]
+
+    transmittance_absorptance : numeric, default 0.9
+        Coefficient for combined transmittance and absorptance effects.
+        [unitless]
+
+    array_height : int, default 1
+        Height of array above ground in stories (one story is about 3m). Must
+        be either 1 or 2. For systems elevated less than one story, use 1.
+        If system is elevated more than two stories, use 2.
+
+    mount_standoff : numeric, default 4
+        Distance between array mounting and mounting surface. Use default
+        if system is ground-mounted. [inches]
+
+    Returns
+    -------
+    cell_temperature : numeric
+        Cell temperature. [C]
+
+    Raises
+    ------
+    ValueError
+        If array_height is an invalid value (must be 1 or 2).
+
+    References
+    ----------
+    .. [1] Gilman, P., Dobos, A., DiOrio, N., Freeman, J., Janzou, S.,
+           Ryberg, D., 2018, "SAM Photovoltaic Model Technical Reference
+           Update", National Renewable Energy Laboratory Report
+           NREL/TP-6A20-67399.
+    '''
+    # in [1] the denominator for irr_ratio isn't precisely clear. From
+    # reproducing output of the SAM function noct_celltemp_t, we determined
+    # that:
+    #  - G_total (SAM) is broadband plane-of-array irradiance before
+    #    reflections. Equivalent to pvlib variable poa_global
+    #  - Geff_total (SAM) is POA irradiance after reflections and
+    #    adjustment for spectrum. Equivalent to effective_irradiance
+    if effective_irradiance is None:
+        irr_ratio = 1.
+    else:
+        irr_ratio = effective_irradiance / poa_global
+
+    if array_height == 1:
+        wind_adj = 0.51 * wind_speed
+    elif array_height == 2:
+        wind_adj = 0.61 * wind_speed
+    else:
+        raise ValueError(
+            f'array_height must be 1 or 2, {array_height} was given')
+
+    noct_adj = noct + _adj_for_mounting_standoff(mount_standoff)
+    tau_alpha = transmittance_absorptance * irr_ratio
+
+    # [1] Eq. 10.37 isn't clear on exactly what "G" is. SAM SSC code uses
+    # poa_global where G appears
+    cell_temp_init = poa_global / 800. * (noct_adj - 20.)
+    heat_loss = 1 - eta_m_ref / tau_alpha
+    wind_loss = 9.5 / (5.7 + 3.8 * wind_adj)
+    return temp_air + cell_temp_init * heat_loss * wind_loss

pvlib/tests/test_temperature.py

@@ -5,7 +5,7 @@
 from conftest import DATA_DIR, assert_series_equal
 from numpy.testing import assert_allclose
 
-from pvlib import temperature
+from pvlib import temperature, tools
 
 
 @pytest.fixture
@@ -212,3 +212,76 @@ def test_fuentes_timezone(tz):
 
     assert_series_equal(out, pd.Series([47.85, 50.85, 50.85], index=index,
                                        name='tmod'))
+
+
+def test_noct_sam():
+    poa_global, temp_air, wind_speed, noct, eta_m_ref = (1000., 25., 1., 45.,
+                                                         0.2)
+    expected = 55.230790492
+    result = temperature.noct_sam(poa_global, temp_air, wind_speed, noct,
+                                  eta_m_ref)
+    assert_allclose(result, expected)
+    # test with different types
+    result = temperature.noct_sam(np.array(poa_global), np.array(temp_air),
+                                  np.array(wind_speed), np.array(noct),
+                                  np.array(eta_m_ref))
+    assert_allclose(result, expected)
+    dr = pd.date_range(start='2020-01-01 12:00:00', end='2020-01-01 13:00:00',
+                       freq='1H')
+    result = temperature.noct_sam(pd.Series(index=dr, data=poa_global),
+                                  pd.Series(index=dr, data=temp_air),
+                                  pd.Series(index=dr, data=wind_speed),
+                                  pd.Series(index=dr, data=noct),
+                                  eta_m_ref)
+    assert_series_equal(result, pd.Series(index=dr, data=expected))
+
+
+def test_noct_sam_against_sam():
+    # test is constructed to reproduce output from SAM v2020.11.29.
+    # SAM calculation is the default Detailed PV System model (CEC diode model,
+    # NOCT cell temperature model), with the only change being the soiling
+    # loss is set to 0. Weather input is TMY3 for Phoenix AZ.
+    # Values are taken from the Jan 1 12:00:00 timestamp.
+    poa_total, temp_air, wind_speed, noct, eta_m_ref = (
+        860.673, 25, 3, 46.4, 0.20551)
+    poa_total_after_refl = 851.458  # from SAM output
+    # compute effective irradiance
+    # spectral loss coefficients fixed in lib_cec6par.cpp
+    a = np.flipud([0.918093, 0.086257, -0.024459, 0.002816, -0.000126])
+    # reproduce SAM air mass calculation
+    zen = 56.4284
+    elev = 358
+    air_mass = 1. / (tools.cosd(zen) + 0.5057 * (96.080 - zen)**-1.634)
+    air_mass *= np.exp(-0.0001184 * elev)
+    f1 = np.polyval(a, air_mass)
+    effective_irradiance = f1 * poa_total_after_refl
+    transmittance_absorptance = 0.9
+    array_height = 1
+    mount_standoff = 4.0
+    result = temperature.noct_sam(poa_total, temp_air, wind_speed, noct,
+                                  eta_m_ref, effective_irradiance,
+                                  transmittance_absorptance, array_height,
+                                  mount_standoff)
+    expected = 43.0655
+    # rtol from limited SAM output precision
+    assert_allclose(result, expected, rtol=1e-5)
+
+
+def test_noct_sam_options():
+    poa_global, temp_air, wind_speed, noct, eta_m_ref = (1000., 25., 1., 45.,
+                                                         0.2)
+    effective_irradiance = 1100.
+    transmittance_absorbtance = 0.8
+    array_height = 2
+    mount_standoff = 2.0
+    result = temperature.noct_sam(poa_global, temp_air, wind_speed, noct,
+                                  eta_m_ref, effective_irradiance,
+                                  transmittance_absorbtance, array_height,
+                                  mount_standoff)
+    expected = 60.477703576
+    assert_allclose(result, expected)
+
+
+def test_noct_sam_errors():
+    with pytest.raises(ValueError):
+        temperature.noct_sam(1000., 25., 1., 34., 0.2, array_height=3)