"""Collection of functions for degradation calculations."""
import numpy as np
import pandas as pd
from typing import Union
from pvdeg import humidity
from . import (
temperature,
spectral,
decorators,
)
R_GAS = 0.00831446261815324 # Gas Constant in [kJ/mol*K]
def _extract_param(parameters, key, default=None):
"""Helper to extract parameter value from nested dict."""
if parameters is not None and key in parameters:
value = parameters[key].get("value", None)
if value is not None:
return value
return default
[docs]
def arrhenius(
weather_df=None,
temperature=None,
RH=None,
irradiance=None,
elapsed_time=None,
Ro=1,
Ea=0,
p=0,
n=0,
C2=0,
parameters=None,
):
"""
Calculate the degradation rate using an Arrhenius function with power law
functions for humidity and irradiance dependence.
D = R_0 ∫[RH(t)]^n·e^[-E_a/RT(t)] {∫[e^(-C_2∙λ)∙G(λ,t)]^p dλ}dt
Parameters
----------
weather_df : pd.DataFrame
Dataframe containing temperature, humidity, and irradiance data.
Defaults to module surface temperature, surface humidity, and POA global
irradiance.
temperature : pd.DataFrame
Temperature data for Arrhenius degradation calculation. If not specified,
uses module surface temperature from weather_df. If Ea=0, temperature is
not needed.
RH : pd.DataFrame
Relative humidity data for Arrhenius degradation calculation. If not
specified, uses module surface relative humidity from weather_df. If n=0,
humidity is not needed.
irradiance : pd.DataFrame
Irradiance data for Arrhenius degradation calculation. If not specified,
uses module POA irradiance from weather_df. If p=0, irradiance is not
needed.
If C2 is provided, wavelength spectral intensity data must be provided.
The header should start with "spectra", followed by wavelength points.
Each element is a list of intensity values at each wavelength [W/m²/nm].
elapsed_time : pd.DataFrame
If the time step for each interval is not constant, this can be used to
provide a different elapsed time value for each element. If it is included
in the weather_df, it must be under a column named "elapsed_time".
Ro : float
Degradation rate prefactor [e.g. %/h/%RH/(1000 W/m²)]. Defaults to 1 if
not provided.
Ea : float
Degradation Activation Energy [kJ/mol]. If Ea=0, no temperature dependence and
degradation will proceed according to the amount of light an humidity.
p : float
Power law coefficient for irradiance dependence. If p=0, ignores light.
Small p (e.g. 0.0001) means little dependence of degradation on irradiance,
but only daylight is considered.
n : float
Power law coefficient for humidity dependence. If n=0, ignores humidity.
C2 : float
Coefficient for spectral response dependence on wavelength.
parameters : json
Database containing parameters for Arrhenius calculation. If Ea, n, or p
are not provided, values are taken from this json database.
Returns
-------
degradation : float
Total degradation with units as determined by Ro.
"""
# override defaults with parameters if provided
if parameters is not None:
Ro = _extract_param(parameters, "R_0", Ro)
Ea = _extract_param(parameters, "E_a", Ea)
n = _extract_param(parameters, "n", n)
p = _extract_param(parameters, "p", p)
C2 = _extract_param(parameters, "C_2", C2)
if temperature is None and Ea != 0:
if weather_df is not None:
if "temperature" in weather_df:
temperature = weather_df["temperature"]
elif "temp_module" in weather_df:
temperature = weather_df["temp_module"]
print("Using temp_module from weather_df for temperature.")
else:
raise ValueError("Temperature data must be provided if Ea is provided.")
if n != 0 and RH is None:
print(n)
if "RH_surface_outside" in weather_df:
RH = weather_df["RH_surface_outside"]
elif (
"relative_humidity" in weather_df
and "temp_air" in weather_df
and "temp_module" in weather_df
):
RH = humidity.surface_relative(
weather_df["relative_humidity"],
weather_df["temp_air"],
weather_df["temp_module"],
)
else:
raise ValueError(
"Relative Humidity data must be provided if n is provided."
)
if RH is not None:
print("Using RH_surface_outside from weather_df for humidity.")
if irradiance is None:
if C2 != 0 or p != 0:
if weather_df is not None:
for col in weather_df.columns:
if "SPECTRA" in (col[:7]).upper():
irradiance = weather_df[col].copy()
irradiance = pd.DataFrame(irradiance)
break
if irradiance is None:
if "poa_global" in weather_df:
irradiance = weather_df["poa_global"]
print("Using poa_global from weather_df for irradiance.")
if C2 != 0:
raise ValueError(
"Irradiance data not provided. Please provide "
"irradiance data in weather_df."
)
# In the future the spectra will be created using AM1.5.
else:
raise ValueError(
"Irradiance data not provided. Please provide it in "
"irradiance or weather_df."
)
else:
raise ValueError(
"Irradiance data must be provided when C2 or p are used."
)
if elapsed_time is None:
if weather_df is not None:
if "elapsed_time" in weather_df:
elapsed_time = weather_df["elapsed_time"]
if C2 != 0:
wavelengths = [
float(i)
for i in irradiance.columns[0].split("[")[1].split("]")[0].split(",")
]
wavelengths = np.array(wavelengths)
bin_widths = (
np.append(wavelengths, [0, 0]) - np.append([0, 0], wavelengths)
) / 2
bin_widths = bin_widths[1:]
bin_widths = bin_widths[:-1]
# assumes the first and last bin widths are the width of that between the next
# or previous bin, respectively.
bin_widths[0] = bin_widths[1]
bin_widths[-1] = bin_widths[-2]
bin_widths = pd.Series(bin_widths)
wavelengths = pd.Series(wavelengths)
if isinstance(irradiance, pd.DataFrame):
irradiance = irradiance.T.to_numpy().reshape(
-1,
)
irradiance = pd.Series(irradiance)
if p == 0:
if Ea != 0:
if n == 0:
degradation = Ro * np.exp(-(Ea / (R_GAS * (temperature + 273.15))))
else:
degradation = (
Ro * np.exp(-(Ea / (R_GAS * (temperature + 273.15)))) * (RH**n)
)
else:
if n == 0:
degradation = (
Ro * weather_df.iloc[:, 0] / weather_df.iloc[:, 0]
) # This makes sure it sums over the corect number of time
# intervals.
else:
degradation = (
Ro * (RH**n) * weather_df.iloc[:, 0] / weather_df.iloc[:, 0]
)
else:
degradation = bin_widths * ((np.exp(-C2 * wavelengths) * irradiance) ** p)
if Ea != 0:
if n == 0:
degradation = (
degradation
* Ro
* np.exp(-(Ea / (R_GAS * (temperature + 273.15))))
)
else:
degradation = (
degradation
* Ro
* np.exp(-(Ea / (R_GAS * (temperature + 273.15))))
* (RH**n)
)
else:
if n == 0:
degradation = degradation * Ro
else:
degradation = degradation * Ro * (RH**n)
elif Ea != 0:
if n == 0 and p == 0:
degradation = Ro * np.exp(-(Ea / (R_GAS * (temperature + 273.15))))
elif n == 0 and p != 0:
degradation = (
Ro * np.exp(-(Ea / (R_GAS * (temperature + 273.15)))) * (irradiance**p)
)
elif n != 0 and p == 0:
degradation = (
Ro * np.exp(-(Ea / (R_GAS * (temperature + 273.15)))) * (RH**n)
)
else:
degradation = (
Ro
* np.exp(-(Ea / (R_GAS * (temperature + 273.15))))
* (RH**n)
* (irradiance**p)
)
else:
if n == 0 and p == 0:
degradation = Ro * weather_df.iloc[:, 0] / weather_df.iloc[:, 0]
elif n == 0 and p != 0:
degradation = Ro * (irradiance**p)
elif n != 0 and p == 0:
degradation = Ro * (RH**n)
else:
degradation = Ro * (RH**n) * (irradiance**p)
if elapsed_time is not None:
if isinstance(elapsed_time, pd.DataFrame):
elapsed_time = elapsed_time.T.to_numpy().reshape(
-1,
)
elapsed_time = pd.Series(elapsed_time)
degradation = degradation * elapsed_time
return degradation.sum(axis=0, skipna=True)
[docs]
def vantHoff_deg(
weather_df,
meta,
I_chamber,
temp_chamber,
poa=None,
temp=None,
p=0.5,
Tf=1.41,
temp_model="sapm",
conf="open_rack_glass_polymer",
wind_factor=0.33,
irradiance_kwarg={},
model_kwarg={},
):
"""
Calculate Van't Hoff Irradiance Degradation acceleration factor.
In this calculation, the rate of degradation kinetics is calculated using
the Van't Hoff model.
Parameters
----------
weather_df : pd.DataFrame
DataFrame containing at least dni, dhi, ghi, temperature, wind_speed
meta : dict
Location meta-data containing at least latitude, longitude, altitude
I_chamber : float
Irradiance of Controlled Condition [W/m²]
temp_chamber : float
Reference temperature [°C] ("Chamber Temperature")
poa : pd.Series or pd.DataFrame, optional
Series or DataFrame containing 'poa_global', Global Plane of Array Irradiance
[W/m²]
temp : pd.Series, optional
Solar module temperature or Cell temperature [°C]. If not provided, it will
be generated using the default parameters of pvdeg.temperature.cell
p : float
Fit parameter
Tf : float
Multiplier for the increase in degradation for every 10[°C] temperature increase
temp_model : (str, optional)
Specify which temperature model from pvlib to use. Current options:
conf : (str)
The configuration of the PV module architecture and mounting
configuration. Currently only used for 'sapm' and 'pvsys'.
With different options for each.
'sapm' options: ``open_rack_glass_polymer`` (default),
``open_rack_glass_glass``, ``close_mount_glass_glass``,
``insulated_back_glass_polymer``
'pvsys' options: ``freestanding``, ``insulated``
wind_factor : float, optional
Wind speed correction exponent to account for different wind speed measurement
heights between weather database (e.g. NSRDB) and the temperature model
(e.g. SAPM)
The NSRDB provides calculations at 2 m (i.e module height) but SAPM uses a 10 m
height. It is recommended that a power-law relationship between height and wind
speed of 0.33 be used*. This results in a wind speed that is 1.7 times higher.
It is acknowledged that this can vary significantly.
irradiance_kwarg : (dict, optional)
keyword argument dictionary used for the poa irradiance calculation.
options: ``sol_position``, ``tilt``, ``azimuth``, ``sky_model``. See
``pvdeg.spectral.poa_irradiance``.
model_kwarg : (dict, optional)
keyword argument dictionary used for the pvlib temperature model calculation.
See https://pvlib-python.readthedocs.io/en/stable/reference/pv_modeling/temperature.html # noqa
for more.
Returns
-------
accelerationFactor : float or pd.Series
Degradation acceleration factor
"""
if poa is None:
poa = spectral.poa_irradiance(weather_df, meta, **irradiance_kwarg)
if isinstance(poa, pd.DataFrame):
poa_global = poa["poa_global"]
if temp is None:
temp = temperature.temperature(
cell_or_mod="cell",
temp_model=temp_model,
weather_df=weather_df,
meta=meta,
poa=poa,
conf=conf,
wind_factor=wind_factor,
model_kwarg=model_kwarg,
)
rateOfDegEnv = (poa_global**p) * (Tf ** ((temp - temp_chamber) / 10))
avgOfDegEnv = rateOfDegEnv.mean()
rateOfDegChamber = I_chamber**p
accelerationFactor = rateOfDegChamber / avgOfDegEnv
return accelerationFactor
[docs]
@decorators.geospatial_quick_shape("numeric", ["Iwa"])
def IwaVantHoff(
weather_df,
meta,
poa=None,
temp=None,
Teq=None,
p=0.5,
Tf=1.41,
temp_model="sapm",
conf="open_rack_glass_polymer",
wind_factor=0.33,
model_kwarg={},
irradiance_kwarg={},
):
"""
Calculate IWa: Environment Characterization [W/m²].
For one year of degradation, the controlled environment lamp settings will need to
be set to IWa.
Parameters
----------
weather_df : pd.DataFrame
DataFrame containing at least dni, dhi, ghi, temperature, wind_speed
meta : dict
Location meta-data containing at least latitude, longitude, altitude
poa : pd.Series or pd.DataFrame, optional
Series or DataFrame containing 'poa_global', Global Plane of Array Irradiance
[W/m²]
temp : pd.Series, optional
Solar module temperature or Cell temperature [°C]
Teq : pd.Series, optional
VantHoff equivalent temperature [°C]
p : float
Fit parameter
Tf : float
Multiplier for the increase in degradation for every 10[°C] temperature increase
temp_model : (str, optional)
Specify which temperature model from pvlib to use. Current options:
conf : (str)
The configuration of the PV module architecture and mounting
configuration. Currently only used for 'sapm' and 'pvsys'.
With different options for each.
'sapm' options: ``open_rack_glass_polymer`` (default),
``open_rack_glass_glass``, ``close_mount_glass_glass``,
``insulated_back_glass_polymer``
'pvsys' options: ``freestanding``, ``insulated``
wind_factor : float, optional
Wind speed correction exponent to account for different wind speed measurement
heights between weather database (e.g. NSRDB) and the temperature model
(e.g. SAPM)
The NSRDB provides calculations at 2 m (i.e module height) but SAPM uses a 10 m
height. It is recommended that a power-law relationship between height and wind
speed of 0.33 be used*. This results in a wind speed that is 1.7 times higher.
It is acknowledged that this can vary significantly.
irradiance_kwarg : (dict, optional)
keyword argument dictionary used for the poa irradiance calculation.
options: ``sol_position``, ``tilt``, ``azimuth``, ``sky_model``. See
``pvdeg.spectral.poa_irradiance``.
model_kwarg : (dict, optional)
keyword argument dictionary used for the pvlib temperature model calculation.
See https://pvlib-python.readthedocs.io/en/stable/reference/pv_modeling/temperature.html # noqa
for more.
Returns
-------
Iwa : float
Environment Characterization [W/m²]
"""
if poa is None:
poa = spectral.poa_irradiance(weather_df, meta, **irradiance_kwarg)
if temp is None:
temp = temperature.temperature(
cell_or_mod="cell",
temp_model=temp_model,
weather_df=weather_df,
meta=meta,
poa=poa,
conf=conf,
wind_factor=wind_factor,
model_kwarg=model_kwarg,
)
if Teq is None:
toSum = Tf ** (temp / 10)
summation = toSum.sum(axis=0, skipna=True)
Teq = (10 / np.log(Tf)) * np.log(summation / len(temp))
if isinstance(poa, pd.DataFrame):
poa_global = poa["poa_global"]
else:
poa_global = poa
toSum = (poa_global**p) * (Tf ** ((temp - Teq) / 10))
summation = toSum.sum(axis=0, skipna=True)
Iwa = (summation / len(poa_global)) ** (1 / p)
return Iwa
[docs]
def arrhenius_deg(
weather_df: pd.DataFrame,
meta: dict,
rh_outdoor,
I_chamber,
rh_chamber,
Ea,
temp_chamber,
poa=None,
temp=None,
p=0.5,
n=1,
temp_model="sapm",
conf="open_rack_glass_polymer",
wind_factor=0.33,
model_kwarg={},
irradiance_kwarg={},
):
"""
Calculate the Acceleration Factor between the rate of degradation of a
modeled environment versus a modeled controlled environment.
Example: If AF=25, then 1 year of Controlled Environment exposure is equal to
25 years in the field.
Parameters
----------
weather_df : pd.DataFrame
DataFrame containing at least dni, dhi, ghi, temperature, wind_speed
meta : dict
Location meta-data containing at least latitude, longitude, altitude
rh_outdoor : pd.Series
Relative Humidity of material of interest.
Acceptable relative humiditys can be calculated from these functions:
- pvdeg.humidity.backsheet()
- pvdeg.humidity.back_encapsulant()
- pvdeg.humidity.front_encapsulant()
- pvdeg.humidity.surface_relative()
I_chamber : float
Irradiance of Controlled Condition [W/m²]
rh_chamber : float
Relative Humidity of Controlled Condition [%].
EXAMPLE: "50 = 50% NOT .5 = 50%"
temp_chamber : float
Reference temperature [°C] ("Chamber Temperature")
Ea : float
Degradation Activation Energy [kJ/mol]
if Ea=0 is used there will be not dependence on temperature and degradation will
proceed according to the amount of light and humidity.
poa : pd.DataFrame, optional
Global Plane of Array Irradiance [W/m²]
temp : pd.Series, optional
Solar module temperature or Cell temperature [°C]. If no cell temperature is
given, it will be generated using the default parameters from
pvdeg.temperature.cell
p : float
Fit parameter
When p=0 the dependence on light will be ignored and degradation will happen
both day and night. As a caution or a feature, a very small value of p
(e.g. p=0.0001) will provide very little degradation dependence on irradiance,
but degradation will only be accounted for during daylight. i.e. averages will
be computed over half of the time only.
n : float
Fit parameter for relative humidity
When n=0 the degradation rate will not be dependent on humidity.
temp_model : (str, optional)
Specify which temperature model from pvlib to use. Current options:
conf : (str)
The configuration of the PV module architecture and mounting
configuration. Currently only used for 'sapm' and 'pvsys'.
With different options for each.
'sapm' options: ``open_rack_glass_polymer`` (default),
``open_rack_glass_glass``, ``close_mount_glass_glass``,
``insulated_back_glass_polymer``
'pvsys' options: ``freestanding``, ``insulated``
wind_factor : float, optional
Wind speed correction exponent to account for different wind speed measurement
heights between weather database (e.g. NSRDB) and the temperature model
(e.g. SAPM)
The NSRDB provides calculations at 2 m (i.e module height) but SAPM uses a 10 m
height. It is recommended that a power-law relationship between height and wind
speed of 0.33 be used*. This results in a wind speed that is 1.7 times higher.
It is acknowledged that this can vary significantly.
irradiance_kwarg : (dict, optional)
keyword argument dictionary used for the poa irradiance calculation.
options: ``sol_position``, ``tilt``, ``azimuth``, ``sky_model``. See
``pvdeg.spectral.poa_irradiance``.
model_kwarg : (dict, optional)
keyword argument dictionary used for the pvlib temperature model calculation.
See https://pvlib-python.readthedocs.io/en/stable/reference/pv_modeling/temperature.html # noqa
for more.
Returns
-------
accelerationFactor : float or pd.Series
Degradation acceleration factor
"""
if poa is None:
poa = spectral.poa_irradiance(weather_df, meta, **irradiance_kwarg)
if temp is None:
temp = temperature.temperature(
cell_or_mod="cell",
temp_model=temp_model,
weather_df=weather_df,
meta=meta,
poa=poa,
conf=conf,
wind_factor=wind_factor,
model_kwarg=model_kwarg,
)
if isinstance(poa, pd.DataFrame):
poa_global = poa["poa_global"]
else:
poa_global = poa
# rate of degradation of the environment
arrheniusDenominator = (
(poa_global**p) * (rh_outdoor**n) * np.exp(-Ea / (R_GAS * (temp + 273.15)))
)
AvgOfDenominator = arrheniusDenominator.mean()
# rate of degradation of the simulated chamber
arrheniusNumerator = (
(I_chamber**p)
* (rh_chamber**n)
* np.exp(-Ea / (R_GAS * (temp_chamber + 273.15)))
)
accelerationFactor = arrheniusNumerator / AvgOfDenominator
return accelerationFactor
def _T_eq_arrhenius(temp, Ea):
"""
Get Temperature equivalent required for the settings of the controlled environment.
Calculation is used in determining Arrhenius Environmental Characterization
Parameters
-----------
temp : pandas series
Solar module temperature or Cell temperature [°C]
Ea : float
Degradation Activation Energy [kJ/mol]
Returns
-------
Teq : float
Temperature equivalent (Celsius) required
for the settings of the controlled environment
"""
summationFrame = np.exp(-(Ea / (R_GAS * (temp + 273.15))))
sumForTeq = summationFrame.sum(axis=0, skipna=True)
Teq = -((Ea) / (R_GAS * np.log(sumForTeq / len(temp))))
# Convert to celsius
Teq = Teq - 273.15
return Teq
def _RH_wa_arrhenius(rh_outdoor, temp, Ea, Teq=None, n=1):
"""
NOTE
Get the Relative Humidity Weighted Average.
Calculation is used in determining Arrhenius Environmental Characterization
Parameters
-----------
rh_outdoor : pandas series
Relative Humidity of material of interest.
Acceptable relative humiditys can be calculated from these functions:
- pvdeg.humidity.backsheet()
- pvdeg.humidity.back_encapsulant()
- pvdeg.humidity.front_encapsulant()
- pvdeg.humidity.surface_relative()
temp : pandas series
solar module temperature or Cell temperature [°C]
Ea : float
Degradation Activation Energy [kJ/mol]
Teq : series
Equivalent Arrhenius temperature [°C]
n : float
Fit parameter for relative humidity
Returns
--------
RHwa : float
Relative Humidity Weighted Average [%]
"""
if Teq is None:
Teq = _T_eq_arrhenius(temp, Ea)
summationFrame = (rh_outdoor**n) * np.exp(-(Ea / (R_GAS * (temp + 273.15))))
sumForRHwa = summationFrame.sum(axis=0, skipna=True)
RHwa = (
sumForRHwa / (len(summationFrame) * np.exp(-(Ea / (R_GAS * (Teq + 273.15)))))
) ** (1 / n)
return RHwa
# TODO: CHECK
# STANDARDIZE
[docs]
def IwaArrhenius(
weather_df: pd.DataFrame,
meta: dict,
rh_outdoor: pd.Series,
Ea: float,
poa: pd.DataFrame = None,
temp: pd.Series = None,
RHwa: float = None,
Teq: float = None,
p: float = 0.5,
n: float = 1,
temp_model="sapm",
conf="open_rack_glass_polymer",
wind_factor=0.33,
model_kwarg={},
irradiance_kwarg={},
) -> float:
"""
Function to calculate IWa, the Environment Characterization [W/m²].
For one year of degradation the controlled environment lamp settings will
need to be set at IWa.
Parameters
----------
weather_df : pd.DataFrame
Dataframe containing at least dni, dhi, ghi, temperature, wind_speed
meta : dict
Location meta-data containing at least latitude, longitude, altitude
rh_outdoor : pd.Series
Relative Humidity of material of interest
Acceptable relative humiditys can be calculated from these functions:
- pvdeg.humidity.backsheet()
- pvdeg.humidity.back_encapsulant()
- pvdeg.humidity.front_encapsulant()
- pvdeg.humidity.surface_relative()
Ea : float
Degradation Activation Energy [kJ/mol]
poa : pd.DataFrame, optional
must contain 'poa_global', Global Plane of Array irradiance [W/m²]
temp : pd.Series, optional
Solar module temperature or Cell temperature [°C]
RHwa : float, optional
Relative Humidity Weighted Average [%]
Teq : float, optional
Temperature equivalent (Celsius) required
for the settings of the controlled environment
p : float
Fit parameter
n : float
Fit parameter for relative humidity
temp_model : (str, optional)
Specify which temperature model from pvlib to use. Current options:
conf : (str)
The configuration of the PV module architecture and mounting
configuration. Currently only used for 'sapm' and 'pvsys'.
With different options for each.
'sapm' options: ``open_rack_glass_polymer`` (default),
``open_rack_glass_glass``, ``close_mount_glass_glass``,
``insulated_back_glass_polymer``
'pvsys' options: ``freestanding``, ``insulated``
wind_factor : float, optional
Wind speed correction exponent to account for different wind speed measurement
heights between weather database (e.g. NSRDB) and the temperature model
(e.g. SAPM)
The NSRDB provides calculations at 2 m (i.e module height) but SAPM uses a 10 m
height. It is recommended that a power-law relationship between height and wind
speed of 0.33 be used*. This results in a wind speed that is 1.7 times higher.
It is acknowledged that this can vary significantly.
irradiance_kwarg : (dict, optional)
keyword argument dictionary used for the poa irradiance calculation.
options: ``sol_position``, ``tilt``, ``azimuth``, ``sky_model``. See
``pvdeg.spectral.poa_irradiance``.
model_kwarg : (dict, optional)
keyword argument dictionary used for the pvlib temperature model calculation.
See https://pvlib-python.readthedocs.io/en/stable/reference/pv_modeling/temperature.html # noqa
for more.
Returns
--------
Iwa : float
Environment Characterization [W/m²]
"""
if poa is None:
poa = spectral.poa_irradiance(weather_df, meta, **irradiance_kwarg)
if temp is None:
temp = temperature.temperature(
cell_or_mod="cell",
temp_model=temp_model,
weather_df=weather_df,
meta=meta,
poa=poa,
conf=conf,
wind_factor=wind_factor,
model_kwarg=model_kwarg,
)
if Teq is None:
Teq = _T_eq_arrhenius(temp, Ea)
if RHwa is None:
RHwa = _RH_wa_arrhenius(rh_outdoor, temp, Ea)
if isinstance(poa, pd.DataFrame):
poa_global = poa["poa_global"]
else:
poa_global = poa
numerator = (
poa_global ** (p)
* rh_outdoor ** (n)
* np.exp(-(Ea / (R_GAS * (temp + 273.15))))
)
sumOfNumerator = numerator.sum(axis=0, skipna=True)
denominator = (
(len(numerator)) * ((RHwa) ** n) * (np.exp(-(Ea / (R_GAS * (Teq + 273.15)))))
)
IWa = (sumOfNumerator / denominator) ** (1 / p)
return IWa
[docs]
def degradation_spectral(
spectra: pd.Series,
rh: pd.Series,
temp: pd.Series,
wavelengths: Union[int, np.ndarray],
time: pd.Series,
Ea: float = 0.0,
n: float = 0.0,
p: float = 0.6,
C2: float = 0.07,
R_0: float = 1.0,
) -> float:
"""
Compute degradation as double integral of Arrhenius (Activation
Energy, RH, Temperature) and spectral (wavelength, irradiance)
functions over wavelength and time.
Parameters
----------
spectra : pd.Series type=Float
front or rear irradiance at each wavelength in "wavelengths" [W/m² nm]
rh : pd.Series type=Float
RH, time indexed [%]
temp : pd.Series type=Float
temperature, time indexed [°C]
wavelengths : int-array
integer array (or list) of wavelengths tested w/ uniform delta
in nanometers [nm]
time : time indicator in [h]
if not included it will assume 1 h for each dataframe entry.
Ea : float [kJ/mol]
Arrhenius activation energy. The default is 0 ofr no dependence
n : float
Power law fit paramter for RH sensitivity. The default is 0 for no dependence.
p : float
Power law fit parameter for irradiance sensitivity. Typically
0.6 +- 0.22. Here it is applied separately for each wavelength bin.
C2 : float
Exponential fit parameter for sensitivity to wavelength.
Typically 0.07 [1/nm]
R_0 : float
Prefactor for degradation. Units can vary, but would be something like [%/h]
Default 1.0
Returns
-------
degradation : float
Total degradation over time and wavelength. Units are determined from R_0 and
time.
"""
# --- TO DO ---
# unpack input-dataframe
# spectra = df['spectra']
# temp_module = df['temp_module']
# rh_module = df['rh_module']
wav_bin = list(np.diff(wavelengths))
wav_bin.append(wav_bin[-1]) # Adding a bin for the last wavelength
try:
irr = pd.DataFrame(spectra.tolist(), index=spectra.index)
irr.columns = wavelengths
except Exception:
print("Removing brackets from spectral irradiance data")
irr = spectra.str.strip("[]").str.split(",", expand=True).astype(float)
irr.columns = wavelengths
sensitivitywavelengths = np.exp(-C2 * np.array(wavelengths))
irr = irr * sensitivitywavelengths
irr *= np.array(wav_bin)
irr = irr**p
data = pd.DataFrame(index=spectra.index)
data["G_integral"] = irr.sum(axis=1)
EApR = -Ea / R_GAS
C4 = np.exp(EApR / temp)
RHn = rh**n
data["Arr_integrand"] = C4 * RHn
data["dD"] = data["G_integral"] * data["Arr_integrand"]
degradation = R_0 * data["dD"].sum(axis=0)
return degradation
[docs]
def vecArrhenius(
poa_global: np.ndarray, module_temp: np.ndarray, ea: float, x: float, lnr0: float
) -> float:
"""
Calculates degradation using :math:`R_D = R_0 * I^X * e^{-Ea/(kT)}`
Parameters
----------
poa_global : numpy.ndarray
Plane of array irradiance [W/m²]
module_temp : numpy.ndarray
Cell temperature [°C].
ea : float
Activation energy [kJ/mol]
x : float
Irradiance relation [unitless]
lnr0 : float
prefactor [ln(%/h)]
Returns
----------
degradation : float
Degradation Rate [%/h]
"""
mask = poa_global >= 25
poa_global = poa_global[mask]
module_temp = module_temp[mask]
ea_scaled = ea / 8.31446261815324e-03
R0 = np.exp(lnr0)
poa_global_scaled = poa_global / 1000
degradation = 0
for entry in range(len(poa_global_scaled)):
degradation += (
R0
* np.exp(-ea_scaled / (273.15 + module_temp[entry]))
* np.power(poa_global_scaled[entry], x)
)
return degradation / len(poa_global)
