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ivcorrection.py
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy import interpolate
from typing import Union
from pvlib.pvsystem import calcparams_desoto, singlediode
from pvlib.ivtools.sdm import fit_desoto
from pvlib.ivtools.sde import fit_sandia_simple
from matplotlib.colors import LinearSegmentedColormap
from mpl_toolkits.axes_grid1 import make_axes_locatable
from collections.abc import Sized
"""
The current version works for the correction of I-V curves of c-Si PV modules.
The performance on other PV technologies will be updated later.
"""
irradiance_STC = 1000
temperature_STC = 25
colors = ["lightseagreen", "lawngreen", "gold", "darkorange"]
cmap = LinearSegmentedColormap.from_list("mycmap", colors)
def simu_IV_curve(G : Union[list, float],
T : Union[list, float],
alpha_isc_abs : float,
SDMparams : dict,
rs_degra: float = None,
rsh_degra: float = None,
ivcurve_pnts : int =100,
singlediode_method : str ='lambertw'):
"""
Simulate I-V curves at specified environmental conditions
Parameters
----------
G : float or list
Irradiance [W/m2]
T : float or list
Module temperature [C]
alpha_isc_abs : float
Absolute temperature coefficient of Isc (A/C)
SDMparams: dict
Dict including the five single-diode model (SDM) parameters
The five parameters (keys of the dict) are:
I_L_ref: Light-generated current at reference conditions [A]
I_o_ref: Diode saturation current at reference conditions [A]
R_s: Series resistance [ohm]
R_sh_ref: Shunt resistance at reference conditions [ohm]
a_ref: Modified ideality factor at reference conditions.
The product of the usual diode ideality factor (n, unitless),
number of cells in series (Ns), and cell thermal voltage at
specified effective irradiance and cell temperature.
rs_degra: float [ohms]
To simulate IV curves under Rs degradation,
rs_degra is an additional resistance in series to the PV module
rsh_degra: float [ohms]
To simulate IV curves under Rsh degradation,
rsh_degra is an additional resistance in paralle to the PV module
ivcurve_pnts : int
Number of points in the desired IV curve. If None or 0, no IV curves will be produced.
singlediode_method : str
Determines the method used to calculate points on the IV curve.
The options are 'lambertw', 'newton', or 'brentq'.
Output
------
ivcurves: dict
Dict including the generated 'v', 'i' and 'G', 'T'
"""
if (not isinstance(G, list)) & (not isinstance(G, np.ndarray)):
G = [G]
if (not isinstance(T, list)) & (not isinstance(T, np.ndarray)):
T = [T]
G = np.array(G)
T = np.array(T)
Eg_ref = 1.121
dEgdT = -0.0002677
# update rs when rs_degra exits
R_s = SDMparams['R_s']
if rs_degra:
R_s = SDMparams['R_s'] + rs_degra
iph, io, rs, rsh, nNsVth = calcparams_desoto(
G,
T,
alpha_sc = alpha_isc_abs,
a_ref = SDMparams['a_ref'],
I_L_ref = SDMparams['I_L_ref'],
I_o_ref = SDMparams['I_o_ref'],
R_sh_ref = SDMparams['R_sh_ref'],
R_s = R_s,
EgRef=Eg_ref,
dEgdT=dEgdT,
irrad_ref=irradiance_STC,
temp_ref=temperature_STC
)
if singlediode_method in ['lambertw', 'brentq', 'newton']:
out = singlediode(iph,
io,
rs,
rsh,
nNsVth,
method=singlediode_method,
ivcurve_pnts=ivcurve_pnts,
)
else:
raise Exception(
'Method must be "lambertw", "brentq", or "newton"')
ivcurves = {}
alli = {}
allv = {}
nIV = G.size
for n in range(nIV):
i = out['i'][n]
v = out['v'][n]
# update current when rsh_degra exits
if rsh_degra:
i = i - v/rsh_degra
alli[n] = i
allv[n] = v
ivcurves['G'] = G
ivcurves['T'] = T
ivcurves['v'] = allv
ivcurves['i'] = alli
return ivcurves
def get_corrected_IV_P1 (iv_initial : dict,
alpha_isc_abs : float,
beta_voc_abs : float,
rs : float = 0.35,
k : float = 0
):
"""
Get the corrected I-V curves using Procedure 1 of IEC 60891:2021 [1]
Parameters
----------
iv_initial : dict
Dict including the 'v', 'i' of the I-V curves to correct,
and G, T where the I-V curve is measured under
alpha_isc_abs : float
Absolute temperature coefficient of short circuit current [A/C]
beta_voc_abs : float
Absolute temperature coefficient of open circuit voltage [V/C]
rs : float
Correction coefficient of the internal series resistance [ohm]
k : float
Correction coefficient of the curve correction factor
Output
------
iv_corrected: dict
Dict including the 'v', 'i' of the corrected I-V curves,
and 'G', 'T' where the initial I-V curve is measured under
Reference
---------
[1] IEC 60891:2021, Photovoltaic devices - Procedures for temperature
and irradiance corrections to measured I-V characteristics
"""
iv_corrected = {key: iv_initial[key] for key in ['G', 'T']}
alli_corr = {}
allv_corr = {}
nIV = np.array(iv_initial['G']).size
for n in range(nIV):
i = iv_initial['i'][n]
v = iv_initial['v'][n]
G = iv_initial['G'][n]
T = iv_initial['T'][n]
isc = np.max(i)
i_corr = i+isc*(1000/G-1) + alpha_isc_abs*(25-T)
v_corr = v - rs*(i_corr-i) - k*i_corr*(25-T) + beta_voc_abs*(25-T)
alli_corr[n] = i_corr
allv_corr[n] = v_corr
iv_corrected['v'] = allv_corr
iv_corrected['i'] = alli_corr
return iv_corrected
def get_corrected_IV_P2 (iv_initial : dict,
alpha_isc_rel : float,
beta_voc_rel : float,
voc_ref : float,
rs : float = 0.35,
k : float = 0,
B1 : float = 0,
B2 : float = 0):
"""
Get the corrected I-V curves using Procedure 2 of IEC 60891:2021 [1]
Parameters
----------
iv_initial : dict
Dict including the 'v', 'i' of the I-V curves to correct,
and G, T where the I-V curve is measured under
alpha_isc_rel : float
Relative temperature coefficient of short circuit current [A/%]
beta_voc_rel : float
Relative temperature coefficient of open circuit voltage [V/%]
voc_ref : float
Open-circuit voltage at STC [V]
rs : float
Correction coefficient of the internal series resistance [ohm]
k : float
Correction coefficient of the curve correction factor
B1 : float
Correction coefficient of the irradiance correction factor 1
B2 : float
Correction coefficient of the irradiance correction factor 2
Output
------
iv_corrected: dict
Dict including the 'v', 'i' of the corrected I-V curves,
and 'G', 'T' where the initial I-V curve is measured under
Reference
---------
[1] IEC 60891:2021, Photovoltaic devices - Procedures for temperature
and irradiance corrections to measured I-V characteristics
"""
iv_corrected = {key: iv_initial[key] for key in ['G', 'T']}
alli_corr = {}
allv_corr = {}
nIV = np.array(iv_initial['G']).size
for n in range(nIV):
i = iv_initial['i'][n]
v = iv_initial['v'][n]
G = iv_initial['G'][n]
T = iv_initial['T'][n]
i_corr = i*1000/G/(1 + alpha_isc_rel*(T-25))
rs1 = rs + k*(T-25)
fG1 = B2*(np.log(1000/G)**2) + B1*np.log(1000/G) + 1
v_corr = v - rs1*(i_corr-i) - k*i_corr*(25-T) + \
voc_ref*(beta_voc_rel*(25-T)*fG1 + 1 - 1/fG1)
alli_corr[n] = i_corr
allv_corr[n] = v_corr
iv_corrected['v'] = allv_corr
iv_corrected['i'] = alli_corr
return iv_corrected
def get_corrected_IV_P4 (iv_initial : dict,
alpha_isc_abs : float,
N_cells : int,
rs : float = 0.35,
epsilon : float = 1.232):
"""
Get the corrected I-V curves using Procedure 4 of IEC 60891:2021 [1]
Parameters
----------
iv_initial : dict
Dict including the 'v', 'i' of the I-V curves to correct,
and G, T where the I-V curve is measured under
alpha_isc_abs : float
Absolute temperature coefficient of short circuit current [A/C]
N_cells : int
Number of cells of PV module
rs : float
Correction coefficient of the internal series resistance [ohm]
epsilon : float
Bandgap of the PV module, default for cs-Si module: 1.232
Output
------
iv_corrected: dict
Dict including the 'v', 'i' of the corrected I-V curves,
and 'G', 'T' where the initial I-V curve is measured under
Reference
---------
[1] IEC 60891:2021, Photovoltaic devices - Procedures for temperature
and irradiance corrections to measured I-V characteristics
"""
iv_corrected = {key: iv_initial[key] for key in ['G', 'T']}
alli_corr = {}
allv_corr = {}
nIV = np.array(iv_initial['G']).size
for n in range(nIV):
i = iv_initial['i'][n]
v = iv_initial['v'][n]
G = iv_initial['G'][n]
T = iv_initial['T'][n]
isc = np.max(i)
try:
rs = get_rs_sandia(v,i)
except:
alli_corr[n] = i_corr
allv_corr[n] = v_corr
else:
itemp = i + isc*(1000/G-1)
vtemp = v - rs*(itemp-i)
i_corr = itemp + alpha_isc_abs*(25-T)
v_corr = vtemp + (25-T)/(T+273.15)*(vtemp-epsilon*N_cells)
alli_corr[n] = i_corr
allv_corr[n] = v_corr
iv_corrected['v'] = allv_corr
iv_corrected['i'] = alli_corr
return iv_corrected
def get_corrected_IV_Pdyna (iv_initial : dict,
alpha_isc_rel : float,
beta_voc_rel : float,
voc_ref : float,
rs : float = 0.35,
k : float = 0,
B1 : float = 0,
B2 : float = 0):
"""
Get the corrected I-V curves using Procedure dynamic (Pdyna)
Parameters
----------
iv_initial : dict
Dict including the 'v', 'i' of the I-V curves to correct,
and 'G', 'T' where the I-V curve is measured under
alpha_isc_rel : float
Relative temperature coefficient of short circuit current [A/%]
beta_voc_rel : float
Relative temperature coefficient of open circuit voltage [V/%]
voc_ref : float
Open-circuit voltage at STC [V]
rs : float
Correction coefficient of the internal series resistance [ohm]
It is calculatd using the sample_simple funcition from the raw I-V curve [1]
k : float
Correction coefficient of the curve correction factor
B1 : float
Correction coefficient of the irradiance correction factor 1
B2 : float
Correction coefficient of the irradiance correction factor 2
Output
------
iv_corrected: dict
Dict including the 'v', 'i' of the corrected I-V curves,
and 'G', 'T' where the initial I-V curve is measured under
Reference
---------
[1] C. B. Jones and C. W. Hansen, “Single Diode Parameter Extraction from In-Field
Photovoltaic I-V Curves on a Single Board Computer,” Conference Record of the IEEE
Photovoltaic Specialists Conference, pp. 382–387, Jun. 2019, doi: 10.1109/PVSC40753.2019.8981330.
"""
iv_corrected = {key: iv_initial[key] for key in ['G', 'T']}
alli_corr = {}
allv_corr = {}
nIV = np.array(iv_initial['G']).size
for n in range(nIV):
i = iv_initial['i'][n]
v = iv_initial['v'][n]
G = iv_initial['G'][n]
T = iv_initial['T'][n]
try:
rs = get_rs_sandia(v[i>0],i[i>0]) # dynamic rs
rsh = get_rsh_sandia(v[i>0],i[i>0]) # dynamic rsh
if rsh > 100: # neglect rsh when it is large
rsh = 1e5
except:
alli_corr[n] = np.nan
allv_corr[n] = np.nan
else:
itemp = (i+v/rsh)*1000/G/(1 + alpha_isc_rel*(T-25))
rs1 = rs + k*(T-25)
fG1 = B2*(np.log(1000/G)**2) + B1*np.log(1000/G) + 1
v_corr = v - rs1*(itemp-i-v/rsh) - k*itemp*(25-T) + \
voc_ref*(beta_voc_rel*(25-T)*fG1 + 1 - 1/fG1)
i_corr = itemp -v_corr/rsh
alli_corr[n] = i_corr
allv_corr[n] = v_corr
iv_corrected['v'] = allv_corr
iv_corrected['i'] = alli_corr
return iv_corrected
def get_rs_coef(SDMparams : dict,
alpha_isc_abs : float,
beta_voc_abs : float = 0,
alpha_isc_rel : float = 0,
beta_voc_rel : float = 0,
voc_ref : float = 0,
B1 : float = 0,
B2 : float = 0,
correction_method : str = None):
"""
Estimate the correction coefficient rs for Procedure 1 and 2 based on IEC 60891:2021 standard [1]
Parameters
----------
SDMparams: dict
Dict including the five single-diode model (SDM) parameters
The five parameters (keys of the dict) are:
I_L_ref: Light-generated current at reference conditions [A]
I_o_ref: Diode saturation current at reference conditions [A]
R_s: Series resistance [ohm]
R_sh_ref: Shunt resistance at reference conditions [ohm]
a_ref: Modified ideality factor at reference conditions.
The product of the usual diode ideality factor (n, unitless),
number of cells in series (Ns), and cell thermal voltage at
specified effective irradiance and cell temperature.
alpha_isc_abs : float
Absolute temperature coefficient of short-circuit current (A/C)
beta_voc_abs : float
Absolute temperature coefficient of open circuit voltage [V/C]
alpha_isc_rel : float
Relative temperature coefficient of short circuit current [A/%]
beta_voc_rel : float
Relative temperature coefficient of open circuit voltage [V/%]
voc_ref : float
Open-circuit voltage at STC [V]
B1 : float
Correction coefficient of the irradiance correction factor 1 for Procedure 2
B2 : float
Correction coefficient of the irradiance correction factor 2 for Procedure 2
correction_method : str
Correction method name, choose from 'P1' or 'P2'
Output
------
rs_best: float
Optimal correction coefficient rs
Reference
---------
[1] IEC 60891:2021, Photovoltaic devices - Procedures for temperature
and irradiance corrections to measured I-V characteristics
"""
# Simulate IV curves at varying irradiance with temperature = 25
G = np.arange(200, 1201, 100)
T = np.ones(len(G))*25
ivcurves = simu_IV_curve(G, T, alpha_isc_abs, SDMparams)
ivcurve_STC = simu_IV_curve([irradiance_STC], [temperature_STC], alpha_isc_abs, SDMparams)
if correction_method is None:
raise ValueError('Correction method must be "P1" or "P2"')
rs_range = np.arange(0.1, 2, 0.01)
rs_results = {}
rs_results['rs'] = rs_range
rs_results['pmp_err_mean'] = [np.nan] * len(rs_range)
rs_results['pmp_err_std'] = [np.nan] * len(rs_range)
for i in range(len(rs_range)):
if correction_method == 'P1':
ivcurves_corr = get_corrected_IV_P1(ivcurves,
alpha_isc_abs = alpha_isc_abs,
beta_voc_abs = beta_voc_abs,
rs = rs_range[i])
elif correction_method == 'P2':
ivcurves_corr = get_corrected_IV_P2(ivcurves,
alpha_isc_rel = alpha_isc_rel,
beta_voc_rel = beta_voc_rel,
voc_ref= voc_ref,
B1 = B1,
B2 = B2,
rs = rs_range[i])
allpmp_err = np.abs(calc_mpp_error(ivcurves_corr, ivcurve_STC))
rs_results['pmp_err_mean'][i] = np.mean(allpmp_err)
rs_results['pmp_err_std'][i] = np.std(allpmp_err)
rs_best = rs_results['rs'][np.argmin(rs_results['pmp_err_mean'])]
return rs_best, rs_results
def get_k_coef(SDMparams : dict,
alpha_isc_abs : float,
beta_voc_abs : float = 0,
alpha_isc_rel : float = 0,
beta_voc_rel : float = 0,
voc_ref : float = 0,
B1 : float = 0,
B2 : float = 0,
rs : float = 0,
correction_method : str = None):
"""
Estimate the correction coefficient k for Procedure 1 or 2 based on IEC 60891:2021 standard [1]
Parameters
----------
SDMparams: dict
Dict including the five single-diode model (SDM) parameters
The five parameters (keys of the dict) are:
I_L_ref: Light-generated current at reference conditions [A]
I_o_ref: Diode saturation current at reference conditions [A]
R_s: Series resistance [ohm]
R_sh_ref: Shunt resistance at reference conditions [ohm]
a_ref: Modified ideality factor at reference conditions.
The product of the usual diode ideality factor (n, unitless),
number of cells in series (Ns), and cell thermal voltage at
specified effective irradiance and cell temperature.
alpha_isc_abs : float
Absolute temperature coefficient of short-circuit current (A/C)
beta_voc_abs : float
Absolute temperature coefficient of open circuit voltage [V/C]
alpha_isc_rel : float
Relative temperature coefficient of short circuit current [A/%]
beta_voc_rel : float
Relative temperature coefficient of open circuit voltage [V/%]
voc_ref : float
Open-circuit voltage at STC [V]
B1 : float
Correction coefficient of the irradiance correction factor 1 for Procedure 2
B2 : float
Correction coefficient of the irradiance correction factor 2 for Procedure 2
rs: float
Correction coefficient rs
correction_method : str
Correction method name, choose from 'P1' or 'P2'
Output
------
k_best: float
Optimal correction coefficient k
Reference
---------
[1] IEC 60891:2021, Photovoltaic devices - Procedures for temperature
and irradiance corrections to measured I-V characteristics
"""
# Simulate IV curves at varying temperature with irradiance = 1000W/m2
T = np.arange(10, 71, 5)
G = np.ones(len(T))*1000
ivcurves = simu_IV_curve(G, T, alpha_isc_abs, SDMparams)
ivcurve_STC = simu_IV_curve([irradiance_STC], [temperature_STC], alpha_isc_abs, SDMparams)
if correction_method is None:
raise ValueError('Correction method must be "P1" or "P2"')
k_range = np.arange(0, 0.01, 0.0001)
k_results = {}
k_results['k'] = k_range
k_results['pmp_err_mean'] = [np.nan] * len(k_range)
k_results['pmp_err_std'] = [np.nan] * len(k_range)
for i in range(len(k_range)):
if correction_method == 'P1':
ivcurves_corr = get_corrected_IV_P1(ivcurves,
alpha_isc_abs = alpha_isc_abs,
beta_voc_abs = beta_voc_abs,
rs = rs,
k = k_range[i])
elif correction_method == 'P2':
ivcurves_corr = get_corrected_IV_P2(ivcurves,
alpha_isc_rel = alpha_isc_rel,
beta_voc_rel = beta_voc_rel,
voc_ref= voc_ref,
B1 = B1,
B2 = B2,
rs = rs,
k = k_range[i])
allpmp_err = np.abs(calc_mpp_error(ivcurves_corr, ivcurve_STC))
k_results['pmp_err_mean'][i] = np.mean(allpmp_err)
k_results['pmp_err_std'][i] = np.std(allpmp_err)
k_best = k_range[np.argmin(k_results['pmp_err_std'])]
return k_best, k_results
def get_rs_sandia(v : list, i : list):
"""
Estimate the correction coefficient rs from the raw I-V curve using sandia_simple [1]
Parameters
----------
v : list
Voltage of I-V curve [V]
i : list
Current of I-V curve [A]
Output
------
rs: float
Correction coefficient rs [ohms]
Reference
---------
[1] C. B. Jones and C. W. Hansen, “Single Diode Parameter Extraction from In-Field
Photovoltaic I-V Curves on a Single Board Computer,” Conference Record of the IEEE
Photovoltaic Specialists Conference, pp. 382–387, Jun. 2019, doi: 10.1109/PVSC40753.2019.8981330.
"""
rs = fit_sandia_simple(v, i)[2]
return rs
def get_rsh_sandia(v : list, i : list):
"""
Estimate the correction coefficient rsh from the raw I-V curve using sandia_simple [1]
Parameters
----------
v : list
Voltage of I-V curve [V]
i : list
Current of I-V curve [A]
Output
------
rsh: float
Correction coefficient rsh [ohms]
Reference
---------
[1] C. B. Jones and C. W. Hansen, “Single Diode Parameter Extraction from In-Field
Photovoltaic I-V Curves on a Single Board Computer,” Conference Record of the IEEE
Photovoltaic Specialists Conference, pp. 382–387, Jun. 2019, doi: 10.1109/PVSC40753.2019.8981330.
"""
rsh = fit_sandia_simple(v, i)[3]
return rsh
def get_B1B2_coef(alpha_isc_abs : float,
voc_ref : float,
SDMparams : dict):
"""
Estimate the correction coefficient B1 and B2 for Procedure 2 based on IEC 60891:2021 standard [1]
Parameters
----------
alpha_isc_abs : float
Absolute temperature coefficient of short-circuit current (A/C)
voc_ref : float
Open-circuit voltage at STC [V]
SDMparams: dict
Dict including the five single-diode model (SDM) parameters
The five parameters (keys of the dict) are:
I_L_ref: Light-generated current at reference conditions [A]
I_o_ref: Diode saturation current at reference conditions [A]
R_s: Series resistance [ohm]
R_sh_ref: Shunt resistance at reference conditions [ohm]
a_ref: Modified ideality factor at reference conditions.
The product of the usual diode ideality factor (n, unitless),
number of cells in series (Ns), and cell thermal voltage at
specified effective irradiance and cell temperature.
Output
------
B1 : float
Correction coefficient of the irradiance correction factor 1
B2 : float
Correction coefficient of the irradiance correction factor 2
Reference
---------
[1] IEC 60891:2021, Photovoltaic devices - Procedures for temperature
and irradiance corrections to measured I-V characteristics
"""
# Simulate IV curves at varying irradiance with temperature = 25
G = np.arange(400, 1101, 100)
T = np.ones(len(G))*25
ivcurves = simu_IV_curve(G, T, alpha_isc_abs, SDMparams)
allvoc = [np.max(ivcurves['v'][n]) for n in range(len(G))]
x = np.log(1000/G)
y = voc_ref/np.array(allvoc)
para = np.polyfit(x, y, 2)
B1 = para[1]
B2 = para[0]
return B1, B2
def get_P1_coefs(alpha_isc_abs : float,
beta_voc_abs : float,
SDMparams : dict):
"""
Run pipeline to get rs and k for Procedure 1
Parameters
----------
alpha_isc_abs : float
Absolute temperature coefficient of short-circuit current (A/C)
beta_voc_abs : float
Absolute temperature coefficient of open circuit voltage [V/C]
SDMparams: dict
Dict including the five single-diode model (SDM) parameters
The five parameters (keys of the dict) are:
I_L_ref: Light-generated current at reference conditions [A]
I_o_ref: Diode saturation current at reference conditions [A]
R_s: Series resistance [ohm]
R_sh_ref: Shunt resistance at reference conditions [ohm]
a_ref: Modified ideality factor at reference conditions.
The product of the usual diode ideality factor (n, unitless),
number of cells in series (Ns), and cell thermal voltage at
specified effective irradiance and cell temperature.
Output
------
coeff : dict
Dict including rs and k
"""
coeff = {}
coeff['rs'], _ = get_rs_coef(SDMparams = SDMparams,
alpha_isc_abs = alpha_isc_abs,
beta_voc_abs = beta_voc_abs,
correction_method= 'P1')
coeff['k'], _ = get_k_coef(SDMparams = SDMparams,
alpha_isc_abs = alpha_isc_abs,
beta_voc_abs = beta_voc_abs,
rs = coeff['rs'],
correction_method='P1')
return coeff
def get_P2_coefs(alpha_isc_abs : float,
alpha_isc_rel : float,
beta_voc_rel : float,
voc_ref : float,
SDMparams : dict):
"""
Run pipeline to get B1, B2, rs and k for Procedure 2
Parameters
----------
alpha_isc_abs : float
Absolute temperature coefficient of short-circuit current (A/C)
alpha_isc_rel : float
Relative temperature coefficient of short circuit current [A/%]
beta_voc_rel : float
Relative temperature coefficient of open circuit voltage [V/%]
voc_ref : float
Open-circuit voltage at STC [V]
SDMparams: dict
Dict including the five single-diode model (SDM) parameters
The five parameters (keys of the dict) are:
I_L_ref: Light-generated current at reference conditions [A]
I_o_ref: Diode saturation current at reference conditions [A]
R_s: Series resistance [ohm]
R_sh_ref: Shunt resistance at reference conditions [ohm]
a_ref: Modified ideality factor at reference conditions.
The product of the usual diode ideality factor (n, unitless),
number of cells in series (Ns), and cell thermal voltage at
specified effective irradiance and cell temperature.
Output
------
coeff : dict
Dict including B1, B2, rs and k
"""
coeff = {}
coeff['B1'], coeff['B2'] = get_B1B2_coef(SDMparams = SDMparams,
alpha_isc_abs = alpha_isc_abs,
voc_ref = voc_ref)
coeff['rs'], _ = get_rs_coef(SDMparams = SDMparams,
alpha_isc_abs = alpha_isc_abs,
alpha_isc_rel = alpha_isc_rel,
beta_voc_rel = beta_voc_rel,
voc_ref = voc_ref,
B1 = coeff['B1'],
B2 = coeff['B2'],
correction_method = 'P2')
coeff['k'], _ = get_k_coef(SDMparams = SDMparams,
alpha_isc_abs = alpha_isc_abs,
alpha_isc_rel = alpha_isc_rel,
beta_voc_rel = beta_voc_rel,
voc_ref = voc_ref,
B1 = coeff['B1'],
B2 = coeff['B2'],
rs = coeff['rs'],
correction_method='P2')
return coeff
def calc_mpp_error(ivcurves : dict,
ivcurve_ref : dict,
method : str = 'optimized'):
"""
Calculate the maximum power point error
Parameters
----------
ivcurves : dict
Dict including the 'v', 'i' of the corrected I-V curves and 'G', 'T'
ivcurve_ref : dict
Dict including the 'v', 'i' of the reference I-V curve and 'G', 'T'
method: str (default: 'optimized')
'standard': calculate the pmp error
'optimized': calculate the RMSE of vmp and imp error,
which considers both vmp and imp and can make the
maximum power point of corrected curves closer to
the reference one
Output
------
allpmp_err : list
Ratio of the pmp error compared to the reference pmp [%]
"""
allmpp_err = []
i_ref = ivcurve_ref['i'][0]
v_ref = ivcurve_ref['v'][0]
for n in range(len(ivcurves['G'])):
i = ivcurves['i'][n]
v = ivcurves['v'][n]
if method == 'standard':
pmp = np.max(v*i)
pmp_ref = np.max(ivcurve_ref['v'][0]*ivcurve_ref['i'][0])
mpp_err = np.abs((pmp-pmp_ref)/pmp_ref*100)
if method == 'optimized':
idpmp = np.argmax(v*i)
idpmp_ref = np.argmax(v_ref*i_ref)
vmp_err = (v[idpmp]-v_ref[idpmp_ref])/v_ref[idpmp_ref]
imp_err = (i[idpmp]-i_ref[idpmp_ref])/i_ref[idpmp_ref]
mpp_err = np.sqrt((vmp_err**2+imp_err**2)/2)
allmpp_err.append(mpp_err)
return allmpp_err
def calc_correction_error(ivcurves : dict,
iv_ref: dict):
"""
Calculate the area error between the corrected and the reference I-V curve
Area error is a ratio of the area size of the difference to the area size of the reference curve [1]
Parameters
----------
ivcurves : dict
Dict including the 'v', 'i' of the corrected I-V curves and 'G', 'T'
ivcurve_ref : dict
Dict including the 'v', 'i' of the reference I-V curve and 'G', 'T'
Output
------
area_err : list
List of area errors of the corrected I-V curves [%]
Reference
---------
[1] J. C. H. Phang and D. S. H. Chan, “A review of curve fitting error criteria
for solar cell I-V characteristics,” Solar Cells, vol. 18, no. 1, pp. 1–12,
Jul. 1986, doi: 10.1016/0379-6787(86)90002-5.
"""
area_err = []
nIV = np.array(ivcurves['G']).size
for n in range(nIV):
i = ivcurves['i'][n]
v = ivcurves['v'][n]
i_ref = iv_ref['i'][0]
v_ref = iv_ref['v'][0]
vmin = max(0, np.min(v))
if np.min(i) > 0:
vreftemp = np.interp(np.min(i), np.flip(i_ref), np.flip(v_ref))
vmax = max(np.max(v), vreftemp)
else:
voc = np.interp(0, i, v)
vmax = max(voc, max(v_ref))
vi = np.arange(vmin, vmax+1e-3, (vmax-vmin)/1000)
ii = np.interp(vi, v, i)
irefi = np.interp(vi, v_ref, i_ref)
icut = max(0, min(i))
irefi[irefi<icut] = icut
ii[ii<icut] = icut
area_err.append(np.sum(np.abs(ii-irefi))/np.sum(irefi-icut)*100)
return area_err
def plot_iv_corrected (ivcurves : dict,
iv_ref : dict = None,
lw : float = 2,
plot_ref : bool = True,
xmax : float = None,
ymax : float = None,
errorshow : bool = True):
"""
Plot the corrected I-V curves
Parameters
----------
ivcurves : dict
Dict including the 'v', 'i' of the corrected I-V curves and 'G', 'T'
iv_ref : dict
Dict including the 'v', 'i' of the reference I-V curve and 'G', 'T'
lw : float
Line width of the corrected I-V curves
plot_ref : bool
Plot the reference curve if True
xmax : float
Max of the x-axis of figure
ymax : float
Max of the y-axis of figure
errorshow : bool
Calculate and display the correction error if True
"""
plt.rcParams.update({'font.size': 15})