Function to calculate temperature coefficient of power for pvsyst (pvlib#1190)

* initial implementation of function to calculate pvsyst temperature coefficient

* add reference

* add test for pvsyst_tempco

* correct test reference

* api, whatsnews

* add to whatsnew

* change to 1/C, edit test

* fix bad merge

* change from W/C to 1/C

Author: cwhanse

docs/sphinx/source/api.rst

@@ -268,6 +268,7 @@ Functions relevant for single diode models.
    pvsystem.singlediode
    pvsystem.v_from_i
    pvsystem.max_power_point
+   ivtools.sdm.pvsyst_temperature_coeff
 
 Low-level functions for solving the single diode equation.
 
@@ -334,6 +335,7 @@ Pvsyst model
    temperature.pvsyst_cell
    pvsystem.calcparams_pvsyst
    pvsystem.singlediode
+   ivtools.sdm.pvsyst_temperature_coeff
    pvsystem.dc_ohms_from_percent
    pvsystem.dc_ohmic_losses
 

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

@@ -102,7 +102,10 @@ Enhancements
   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`, :pull:`1195`)
+  implemented in SAM. (:pull:`1177`, :pull:`1195`)
+* Added :py:func:`~pvlib.ivtools.sdm.pvsyst_temperature_coeff` to calculate
+  the temperature coefficient of power for the pvsyst module model.
+   (:pull:`1190`)
 
 Bug fixes
 ~~~~~~~~~

pvlib/ivtools/sdm.py

@@ -11,8 +11,10 @@
 import scipy.constants
 from scipy import optimize
 from scipy.special import lambertw
+from scipy.misc import derivative
 
-from pvlib.pvsystem import singlediode, v_from_i
+from pvlib.pvsystem import calcparams_pvsyst, singlediode, v_from_i
+from pvlib.singlediode import bishop88_mpp
 
 from pvlib.ivtools.utils import rectify_iv_curve, _numdiff
 from pvlib.ivtools.sde import _fit_sandia_cocontent
@@ -1252,3 +1254,91 @@ def _calc_theta_phi_exact(vmp, imp, iph, io, rs, rsh, nnsvth):
     theta = np.transpose(theta)
 
     return theta, phi
+
+
+def pvsyst_temperature_coeff(alpha_sc, gamma_ref, mu_gamma, I_L_ref, I_o_ref,
+                             R_sh_ref, R_sh_0, R_s, cells_in_series,
+                             R_sh_exp=5.5, EgRef=1.121, irrad_ref=1000,
+                             temp_ref=25):
+    r"""
+    Calculates the temperature coefficient of power for a pvsyst single
+    diode model.
+
+    The temperature coefficient is determined as the numerical derivative
+    :math:`\frac{dP}{dT}` at the maximum power point at reference conditions
+    [1]_.
+
+    Parameters
+    ----------
+    alpha_sc : float
+        The short-circuit current temperature coefficient of the module. [A/C]
+
+    gamma_ref : float
+        The diode ideality factor. [unitless]
+
+    mu_gamma : float
+        The temperature coefficient for the diode ideality factor. [1/K]
+
+    I_L_ref : float
+        The light-generated current (or photocurrent) at reference conditions.
+        [A]
+
+    I_o_ref : float
+        The dark or diode reverse saturation current at reference conditions.
+        [A]
+
+    R_sh_ref : float
+        The shunt resistance at reference conditions. [ohm]
+
+    R_sh_0 : float
+        The shunt resistance at zero irradiance conditions. [ohm]
+
+    R_s : float
+        The series resistance at reference conditions. [ohm]
+
+    cells_in_series : int
+        The number of cells connected in series.
+
+    R_sh_exp : float, default 5.5
+        The exponent in the equation for shunt resistance. [unitless]
+
+    EgRef : float, default 1.121
+        The energy bandgap of the module's cells at reference temperature.
+        Default of 1.121 eV is for crystalline silicon. Must be positive. [eV]
+
+    irrad_ref : float, default 1000
+        Reference irradiance. [W/m^2].
+
+    temp_ref : float, default 25
+        Reference cell temperature. [C]
+
+
+    Returns
+    -------
+    gamma_pdc : float
+        Temperature coefficient of power at maximum power point at reference
+        conditions. [1/C]
+
+    References
+    ----------
+    .. [1] K. Sauer, T. Roessler, C. W. Hansen, Modeling the Irradiance and
+       Temperature Dependence of Photovoltaic Modules in PVsyst, IEEE Journal
+       of Photovoltaics v5(1), January 2015.
+    """
+
+    def maxp(temp_cell, irrad_ref, alpha_sc, gamma_ref, mu_gamma, I_L_ref,
+             I_o_ref, R_sh_ref, R_sh_0, R_s, cells_in_series, R_sh_exp, EgRef,
+             temp_ref):
+        params = calcparams_pvsyst(
+            irrad_ref, temp_cell, alpha_sc, gamma_ref, mu_gamma, I_L_ref,
+            I_o_ref, R_sh_ref, R_sh_0, R_s, cells_in_series, R_sh_exp, EgRef,
+            irrad_ref, temp_ref)
+        res = bishop88_mpp(*params)
+        return res[2]
+
+    args = (irrad_ref, alpha_sc, gamma_ref, mu_gamma, I_L_ref,
+            I_o_ref, R_sh_ref, R_sh_0, R_s, cells_in_series, R_sh_exp, EgRef,
+            temp_ref)
+    pmp = maxp(temp_ref, *args)
+    gamma_pdc = derivative(maxp, temp_ref, args=args)
+    return gamma_pdc / pmp

pvlib/tests/ivtools/test_sdm.py

@@ -2,6 +2,7 @@
 import pandas as pd
 
 import pytest
+from numpy.testing import assert_allclose
 
 from pvlib.ivtools import sdm
 from pvlib import pvsystem
@@ -306,7 +307,7 @@ def test__update_rsh_fixed_pt_nans(vmp, imp, iph, io, rs, rsh, nnsvth,
 def test__update_rsh_fixed_pt_vmp0():
     outrsh = sdm._update_rsh_fixed_pt(vmp=0., imp=2., iph=2., io=2., rs=2.,
                                       rsh=2., nnsvth=2.)
-    np.testing.assert_allclose(outrsh, np.array([502.]), atol=.0001)
+    assert_allclose(outrsh, np.array([502.]), atol=.0001)
 
 
 def test__update_rsh_fixed_pt_vector():
@@ -318,7 +319,7 @@ def test__update_rsh_fixed_pt_vector():
                                       imp=np.array([.2, .2, -1., 2.]),
                                       vmp=np.array([0., -1, 0., 0.]))
     assert np.all(np.isnan(outrsh[0:3]))
-    np.testing.assert_allclose(outrsh[3], np.array([502.]), atol=.0001)
+    assert_allclose(outrsh[3], np.array([502.]), atol=.0001)
 
 
 @pytest.mark.parametrize('voc, iph, io, rs, rsh, nnsvth, expected', [
@@ -329,7 +330,7 @@ def test__update_rsh_fixed_pt_vector():
     (0., 2., 2., 2., 2., 2., 17.9436)])
 def test__update_io(voc, iph, io, rs, rsh, nnsvth, expected):
     outio = sdm._update_io(voc, iph, io, rs, rsh, nnsvth)
-    np.testing.assert_allclose(outio, expected, atol=.0001)
+    assert_allclose(outio, expected, atol=.0001)
 
 
 @pytest.mark.parametrize('voc, iph, io, rs, rsh, nnsvth', [
@@ -347,8 +348,8 @@ def test__update_io_nan(voc, iph, io, rs, rsh, nnsvth):
     (0., 2., 2., 2., 2., 2., 2., (1.5571, 2.))])
 def test__calc_theta_phi_exact(vmp, imp, iph, io, rs, rsh, nnsvth, expected):
     theta, phi = sdm._calc_theta_phi_exact(vmp, imp, iph, io, rs, rsh, nnsvth)
-    np.testing.assert_allclose(theta, expected[0], atol=.0001)
-    np.testing.assert_allclose(phi, expected[1], atol=.0001)
+    assert_allclose(theta, expected[0], atol=.0001)
+    assert_allclose(phi, expected[1], atol=.0001)
 
 
 @pytest.mark.parametrize('vmp, imp, iph, io, rs, rsh, nnsvth', [
@@ -365,7 +366,7 @@ def test__calc_theta_phi_exact_one_nan():
     theta, phi = sdm._calc_theta_phi_exact(imp=2., iph=2., vmp=2., io=2.,
                                            nnsvth=2., rs=0., rsh=2.)
     assert np.isnan(theta)
-    np.testing.assert_allclose(phi, 2., atol=.0001)
+    assert_allclose(phi, 2., atol=.0001)
 
 
 def test__calc_theta_phi_exact_vector():
@@ -379,4 +380,23 @@ def test__calc_theta_phi_exact_vector():
     assert np.isnan(theta[0])
     assert np.isnan(theta[1])
     assert np.isnan(phi[0])
-    np.testing.assert_allclose(phi[1], 2.2079, atol=.0001)
+    assert_allclose(phi[1], 2.2079, atol=.0001)
+
+
+def test_pvsyst_temperature_coeff():
+    # test for consistency with dP/dT estimated with secant rule
+    params = {'alpha_sc': 0., 'gamma_ref': 1.1, 'mu_gamma': 0.,
+              'I_L_ref': 6., 'I_o_ref': 5.e-9, 'R_sh_ref': 200.,
+              'R_sh_0': 2000., 'R_s': 0.5, 'cells_in_series': 60}
+    expected = -0.004886706494879083
+    # params defines a Pvsyst model for a notional module.
+    # expected value is created by calculating power at 1000 W/m2, and cell
+    # temperature of 24 and 26C, using pvsystem.calcparams_pvsyst and
+    # pvsystem.singlediode. The derivative (value for expected) is estimated
+    # as the slope (p_mp at 26C - p_mp at 24C) / 2
+    # using the secant rule for derivatives.
+    gamma_pdc = sdm.pvsyst_temperature_coeff(
+        params['alpha_sc'], params['gamma_ref'], params['mu_gamma'],
+        params['I_L_ref'], params['I_o_ref'], params['R_sh_ref'],
+        params['R_sh_0'], params['R_s'], params['cells_in_series'])
+    assert_allclose(gamma_pdc, expected, rtol=0.0005)