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‎pvlib/ivtools/convert.py‎

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"""
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The ``sdm`` module contains functions to fit single diode models.
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Function names should follow the pattern "fit_" + name of model + "_" +
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fitting method.
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"""
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import numpy as np
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import pandas as pd
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from scipy import constants
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from scipy import optimize
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from pvlib.pvsystem import (calcparams_pvsyst, calcparams_cec, singlediode)
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CONSTANTS = {'E0': 1000.0, 'T0': 25.0, 'k': constants.k, 'q': constants.e}
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IEC61853 = pd.DataFrame(
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columns=['effective_irradiance', 'temp_cell'],
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data=np.array(
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[[100, 100, 100, 100, 200, 200, 200, 200, 400, 400, 400, 400,
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600, 600, 600, 600, 800, 800, 800, 800, 1000, 1000, 1000, 1000,
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1100, 1100, 1100, 1100],
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[15, 25, 50, 75, 15, 25, 50, 75, 15, 25, 50, 75, 15, 25, 50, 75,
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15, 25, 50, 75, 15, 25, 50, 75, 15, 25, 50, 75]]).T,
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dtype=np.float64)
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def _pvsyst_objfun(pvs_mod, cec_ivs, ee, tc, cs):
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# translate the guess into named args that are used in the functions
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# order : [alpha_sc, gamma_ref, mu_gamma, I_L_ref, I_o_ref,
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# R_sh_mult, R_sh_ref, R_s]
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# cec_ivs : DataFrame with columns i_sc, v_oc, i_mp, v_mp, p_mp
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# ee : effective irradiance
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# tc : cell temperature
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# cs : cells in series
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alpha_sc = pvs_mod[0]
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gamma_ref = pvs_mod[1]
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mu_gamma = pvs_mod[2]
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I_L_ref = pvs_mod[3]
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I_o_ref = pvs_mod[4]
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R_sh_mult = pvs_mod[5]
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R_sh_ref = pvs_mod[6]
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R_s = pvs_mod[7]
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R_sh_0 = R_sh_ref * R_sh_mult
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pvs_params = calcparams_pvsyst(
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ee, tc, alpha_sc, gamma_ref, mu_gamma, I_L_ref, I_o_ref, R_sh_ref,
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R_sh_0, R_s, cs)
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pvsyst_ivs = singlediode(*pvs_params)
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isc_diff = np.abs((pvsyst_ivs['i_sc'] - cec_ivs['i_sc']) /
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cec_ivs['i_sc']).mean()
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imp_diff = np.abs((pvsyst_ivs['i_mp'] - cec_ivs['i_mp']) /
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cec_ivs['i_mp']).mean()
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voc_diff = np.abs((pvsyst_ivs['v_oc'] - cec_ivs['v_oc']) /
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cec_ivs['v_oc']).mean()
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vmp_diff = np.abs((pvsyst_ivs['v_mp'] - cec_ivs['v_mp']) /
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cec_ivs['v_mp']).mean()
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pmp_diff = np.abs((pvsyst_ivs['p_mp'] - cec_ivs['p_mp']) /
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cec_ivs['p_mp']).mean()
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mean_abs_diff = (isc_diff + imp_diff + voc_diff + vmp_diff + pmp_diff) / 5
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return mean_abs_diff
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def convert_cec_pvsyst(cec_model, cells_in_series, method='Nelder-Mead',
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options=None):
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r"""
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Convert a set of CEC model parameters to an equivalent set of PVsyst model
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parameters.
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Parameter conversion uses optimization as described in [1]_ to fit the
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PVsyst model to :math:`I_{sc}`, :math:`V_{oc}`, :math:`V_{mp}`,
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:math:`I_{mp}`, and :math:`P_{mp}`, calculated using the input CEC model
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at the IEC 61853-3 conditions [2]_.
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Parameters
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----------
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cec_model : dict or DataFrame
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Must include keys: 'alpha_sc', 'a_ref', 'I_L_ref', 'I_o_ref',
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'R_sh_ref', 'R_s', 'Adjust'
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cell_in_series : int
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Number of cells in series.
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method : str, default 'Nelder-Mead'
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Method for scipy.optimize.minimize.
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options : dict, optional
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Solver options passed to scipy.optimize.minimize.
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Returns
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-------
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dict with the following elements:
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alpha_sc : float
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Short-circuit current temperature coefficient [A/C] .
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I_L_ref : float
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The light-generated current (or photocurrent) at reference
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conditions [A].
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I_o_ref : float
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The dark or diode reverse saturation current at reference
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conditions [A].
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EgRef : float
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The energy bandgap at reference temperature [eV].
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R_s : float
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The series resistance at reference conditions [ohm].
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R_sh_ref : float
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The shunt resistance at reference conditions [ohm].
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R_sh_0 : float
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Shunt resistance at zero irradiance [ohm].
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R_sh_exp : float
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Exponential factor defining decrease in shunt resistance with
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increasing effective irradiance [unitless].
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gamma_ref : float
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Diode (ideality) factor at reference conditions [unitless].
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mu_gamma : float
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Temperature coefficient for diode (ideality) factor at reference
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conditions [1/K].
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cells_in_series : int
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Number of cells in series.
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Notes
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-----
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Reference conditions are irradiance of 1000 W/m⁻² and cell temperature of
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25 °C.
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See Also
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--------
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pvlib.ivtools.sdm.convert_pvsyst_cec
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References
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----------
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.. [1] L. Deville et al., "Parameter Translation for Photovoltaic Single
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Diode Models", submitted. 2024
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.. [2] "IEC 61853-3 Photovoltaic (PV) module performance testing and energy
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rating - Part 3: Energy rating of PV modules". IEC, Geneva, 2018.
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"""
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if options is None:
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options = {'maxiter': 5000, 'maxfev': 5000, 'xatol': 0.001}
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# calculate target IV curve values
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cec_params = calcparams_cec(
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IEC61853['effective_irradiance'],
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IEC61853['temp_cell'],
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**cec_model)
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cec_ivs = singlediode(*cec_params)
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# initial guess at PVsyst parameters
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# Order in list is alpha_sc, gamma_ref, mu_gamma, I_L_ref, I_o_ref,
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# Rsh_mult = R_sh_0 / R_sh_ref, R_sh_ref, R_s
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initial = [0, 1.2, 0.001, cec_model['I_L_ref'], cec_model['I_o_ref'],
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12, 1000, cec_model['R_s']]
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# bounds for PVsyst parameters
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b_alpha = (-1, 1)
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b_gamma = (1, 2)
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b_mu = (-1, 1)
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b_IL = (1e-12, 100)
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b_Io = (1e-24, 0.1)
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b_Rmult = (1, 20)
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b_Rsh = (100, 1e6)
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b_Rs = (1e-12, 10)
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bounds = [b_alpha, b_gamma, b_mu, b_IL, b_Io, b_Rmult, b_Rsh, b_Rs]
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# optimization to find PVsyst parameters
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result = optimize.minimize(
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_pvsyst_objfun, initial,
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args=(cec_ivs, IEC61853['effective_irradiance'],
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IEC61853['temp_cell'], cells_in_series),
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method='Nelder-Mead',
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bounds=bounds,
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options=options)
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alpha_sc, gamma, mu_gamma, I_L_ref, I_o_ref, Rsh_mult, R_sh_ref, R_s = \
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result.x
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R_sh_0 = Rsh_mult * R_sh_ref
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R_sh_exp = 5.5
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EgRef = 1.121 # default for all modules in the CEC model
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return {'alpha_sc': alpha_sc,
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'I_L_ref': I_L_ref, 'I_o_ref': I_o_ref, 'EgRef': EgRef, 'R_s': R_s,
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'R_sh_ref': R_sh_ref, 'R_sh_0': R_sh_0, 'R_sh_exp': R_sh_exp,
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'gamma_ref': gamma, 'mu_gamma': mu_gamma,
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'cells_in_series': cells_in_series,
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}
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def _cec_objfun(cec_mod, pvs_ivs, ee, tc, alpha_sc):
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# translate the guess into named args that are used in the functions
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# order : [I_L_ref, I_o_ref, a_ref, R_sh_ref, R_s, alpha_sc, Adjust]
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# pvs_ivs : DataFrame with columns i_sc, v_oc, i_mp, v_mp, p_mp
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# ee : effective irradiance
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# tc : cell temperature
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# alpha_sc : temperature coefficient for Isc
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I_L_ref = cec_mod[0]
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I_o_ref = cec_mod[1]
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a_ref = cec_mod[2]
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R_sh_ref = cec_mod[3]
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R_s = cec_mod[4]
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Adjust = cec_mod[5]
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alpha_sc = alpha_sc
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cec_params = calcparams_cec(
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ee, tc, alpha_sc, a_ref, I_L_ref, I_o_ref, R_sh_ref, R_s, Adjust)
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cec_ivs = singlediode(*cec_params)
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isc_rss = np.sqrt(sum((cec_ivs['i_sc'] - pvs_ivs['i_sc'])**2))
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imp_rss = np.sqrt(sum((cec_ivs['i_mp'] - pvs_ivs['i_mp'])**2))
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voc_rss = np.sqrt(sum((cec_ivs['v_oc'] - pvs_ivs['v_oc'])**2))
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vmp_rss = np.sqrt(sum((cec_ivs['v_mp'] - pvs_ivs['v_mp'])**2))
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pmp_rss = np.sqrt(sum((cec_ivs['p_mp'] - pvs_ivs['p_mp'])**2))
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mean_diff = (isc_rss+imp_rss+voc_rss+vmp_rss+pmp_rss) / 5
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return mean_diff
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def convert_pvsyst_cec(pvsyst_model, method='Nelder-Mead', options=None):
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r"""
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Convert a set of PVsyst model parameters to an equivalent set of CEC model
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parameters.
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Parameter conversion uses optimization as described in [1]_ to fit the
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CEC model to :math:`I_{sc}`, :math:`V_{oc}`, :math:`V_{mp}`,
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:math:`I_{mp}`, and :math:`P_{mp}`, calculated using the input PVsyst model
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at the IEC 61853-3 conditions [2]_.
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Parameters
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----------
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pvsyst_model : dict or DataFrame
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Must include keys: 'alpha_sc', 'I_L_ref', 'I_o_ref', 'EgRef', 'R_s',
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'R_sh_ref', 'R_sh_0', 'R_sh_exp', 'gamma_ref', 'mu_gamma',
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'cells_in_series'
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method : str, default 'Nelder-Mead'
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Method for scipy.optimize.minimize.
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options : dict, optional
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Solver options passed to scipy.optimize.minimize.
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Returns
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-------
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dict with the following elements:
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I_L_ref : float
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The light-generated current (or photocurrent) at reference
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conditions [A].
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I_o_ref : float
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The dark or diode reverse saturation current at reference
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conditions [A].
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R_s : float
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The series resistance at reference conditions [ohm].
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R_sh_ref : float
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The shunt resistance at reference conditions [ohm].
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a_ref : float
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The product of the usual diode ideality factor ``n`` (unitless),
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number of cells in series ``Ns``, and cell thermal voltage at
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reference conditions [V].
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Adjust : float
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The adjustment to the temperature coefficient for short circuit
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current, in percent.
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EgRef : float
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The energy bandgap at reference temperature [eV].
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dEgdT : float
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The temperature dependence of the energy bandgap at reference
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conditions [1/K].
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Notes
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-----
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Reference conditions are irradiance of 1000 W/m⁻² and cell temperature of
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25 °C.
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See Also
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--------
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pvlib.ivtools.sdm.convert_cec_pvsyst
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References
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----------
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.. [1] L. Deville et al., "Parameter Translation for Photovoltaic Single
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Diode Models", submitted. 2024.
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.. [2] "IEC 61853-3 Photovoltaic (PV) module performance testing and energy
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rating - Part 3: Energy rating of PV modules". IEC, Geneva, 2018.
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"""
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if options is None:
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options = {'maxiter': 5000, 'maxfev': 5000, 'xatol': 0.001}
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# calculate target IV curve values
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pvs_params = calcparams_pvsyst(
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IEC61853['effective_irradiance'],
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IEC61853['temp_cell'],
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**pvsyst_model)
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pvsyst_ivs = singlediode(*pvs_params)
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# set EgRef and dEgdT to CEC defaults
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EgRef = 1.121
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dEgdT = -0.0002677
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# initial guess
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# order must match _pvsyst_objfun
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# order : [I_L_ref, I_o_ref, a_ref, R_sh_ref, R_s, alpha_sc, Adjust]
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nNsVth = pvsyst_model['gamma_ref'] * pvsyst_model['cells_in_series'] \
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* 0.025
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initial = [pvsyst_model['I_L_ref'], pvsyst_model['I_o_ref'],
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nNsVth, pvsyst_model['R_sh_ref'], pvsyst_model['R_s'],
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0]
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# bounds for PVsyst parameters
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b_IL = (1e-12, 100)
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b_Io = (1e-24, 0.1)
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b_aref = (1e-12, 1000)
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b_Rsh = (100, 1e6)
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b_Rs = (1e-12, 10)
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b_Adjust = (-100, 100)
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bounds = [b_IL, b_Io, b_aref, b_Rsh, b_Rs, b_Adjust]
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result = optimize.minimize(
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_cec_objfun, initial,
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args=(pvsyst_ivs, IEC61853['effective_irradiance'],
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IEC61853['temp_cell'], pvsyst_model['alpha_sc']),
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method='Nelder-Mead',
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bounds=bounds,
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options=options)
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I_L_ref, I_o_ref, a_ref, R_sh_ref, R_s, Adjust = result.x
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return {'alpha_sc': pvsyst_model['alpha_sc'],
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'a_ref': a_ref, 'I_L_ref': I_L_ref, 'I_o_ref': I_o_ref,
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'R_sh_ref': R_sh_ref, 'R_s': R_s, 'Adjust': Adjust,
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'EgRef': EgRef, 'dEgdT': dEgdT
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}

‎tests/ivtools/test_convert.py‎

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import numpy as np
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from pvlib.ivtools import sdm
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def test_convert_cec_pvsyst():
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cells_in_series = 66
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trina660_cec = {'I_L_ref': 18.4759, 'I_o_ref': 5.31e-12,
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'EgRef': 1.121, 'dEgdT': -0.0002677,
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'R_s': 0.159916, 'R_sh_ref': 113.991, 'a_ref': 1.59068,
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'Adjust': 6.42247, 'alpha_sc': 0.00629}
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trina660_pvsyst_est = sdm.convert_cec_pvsyst(trina660_cec,
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cells_in_series)
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pvsyst_expected = {'alpha_sc': 0.007478218748188788,
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'I_L_ref': 18.227679597516214,
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'I_o_ref': 2.7418999402908e-11,
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'EgRef': 1.121,
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'R_s': 0.16331908293164496,
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'R_sh_ref': 5267.928954454954,
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'R_sh_0': 60171.206687871425,
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'R_sh_exp': 5.5,
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'gamma_ref': 1.0,
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'mu_gamma': -6.349173477135307e-05,
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'cells_in_series': 66}
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assert np.all([np.isclose(trina660_pvsyst_est[k], pvsyst_expected[k],
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rtol=1e-3)
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for k in pvsyst_expected])
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def test_convert_pvsyst_cec():
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trina660_pvsyst = {'alpha_sc': 0.0074, 'I_o_ref': 3.3e-11, 'EgRef': 1.121,
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'R_s': 0.156, 'R_sh_ref': 200, 'R_sh_0': 800,
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'R_sh_exp': 5.5, 'gamma_ref': 1.002, 'mu_gamma': 1e-3,
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'cells_in_series': 66}
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trina660_cec_est = sdm.convert_pvsyst_cec(trina660_pvsyst)
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cec_expected = {'alpha_sc': 0.0074,
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'I_L_ref': 18.05154226834071,
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'I_o_ref': 2.6863417875143392e-14,
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'EgRef': 1.121,
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'dEgdT': -0.0002677,
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'R_s': 0.09436341848926795,
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'a_ref': 1.2954800250731866,
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'Adjust': 0.0011675969492410047,
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'cells_in_series': 66}
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assert np.all([np.isclose(trina660_cec_est[k], cec_expected[k],
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rtol=1e-3)
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for k in cec_expected])

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