"""
This module contains functions for soiling models
"""
import datetime
import numpy as np
import pandas as pd
from scipy.special import erf
from pvlib.tools import cosd
[docs]def hsu(rainfall, cleaning_threshold, tilt, pm2_5, pm10,
depo_veloc=None, rain_accum_period=pd.Timedelta('1h')):
"""
Calculates soiling ratio given particulate and rain data using the
Fixed Velocity model from Humboldt State University (HSU).
The HSU soiling model [1]_ returns the soiling ratio, a value between zero
and one which is equivalent to (1 - transmission loss). Therefore a soiling
ratio of 1.0 is equivalent to zero transmission loss.
Parameters
----------
rainfall : Series
Rain accumulated in each time period. [mm]
cleaning_threshold : float
Amount of rain in an accumulation period needed to clean the PV
modules. [mm]
tilt : float
Tilt of the PV panels from horizontal. [degree]
pm2_5 : numeric
Concentration of airborne particulate matter (PM) with
aerodynamic diameter less than 2.5 microns. [g/m^3]
pm10 : numeric
Concentration of airborne particulate matter (PM) with
aerodynamicdiameter less than 10 microns. [g/m^3]
depo_veloc : dict, default {'2_5': 0.0009, '10': 0.004}
Deposition or settling velocity of particulates. [m/s]
rain_accum_period : Timedelta, default 1 hour
Period for accumulating rainfall to check against `cleaning_threshold`
It is recommended that `rain_accum_period` be between 1 hour and
24 hours.
Returns
-------
soiling_ratio : Series
Values between 0 and 1. Equal to 1 - transmission loss.
References
-----------
.. [1] M. Coello and L. Boyle, "Simple Model For Predicting Time Series
Soiling of Photovoltaic Panels," in IEEE Journal of Photovoltaics.
doi: 10.1109/JPHOTOV.2019.2919628
.. [2] Atmospheric Chemistry and Physics: From Air Pollution to Climate
Change. J. Seinfeld and S. Pandis. Wiley and Sons 2001.
"""
# never use mutable input arguments
if depo_veloc is None:
depo_veloc = {'2_5': 0.0009, '10': 0.004}
# accumulate rainfall into periods for comparison with threshold
accum_rain = rainfall.rolling(rain_accum_period, closed='right').sum()
# cleaning is True for intervals with rainfall greater than threshold
cleaning_times = accum_rain.index[accum_rain >= cleaning_threshold]
# determine the time intervals in seconds (dt_sec)
dt = rainfall.index
# subtract shifted values from original and convert to seconds
dt_diff = (dt[1:] - dt[:-1]).total_seconds()
# ensure same number of elements in the array, assuming that the interval
# prior to the first value is equal in length to the first interval
dt_sec = np.append(dt_diff[0], dt_diff).astype('float64')
horiz_mass_rate = (
pm2_5 * depo_veloc['2_5'] + np.maximum(pm10 - pm2_5, 0.)
* depo_veloc['10']) * dt_sec
tilted_mass_rate = horiz_mass_rate * cosd(tilt) # assuming no rain
# tms -> tilt_mass_rate
tms_cumsum = np.cumsum(tilted_mass_rate * np.ones(rainfall.shape))
mass_no_cleaning = pd.Series(index=rainfall.index, data=tms_cumsum)
# specify dtype so pandas doesn't assume object
mass_removed = pd.Series(index=rainfall.index, dtype='float64')
mass_removed[0] = 0.
mass_removed[cleaning_times] = mass_no_cleaning[cleaning_times]
accum_mass = mass_no_cleaning - mass_removed.ffill()
soiling_ratio = 1 - 0.3437 * erf(0.17 * accum_mass**0.8473)
return soiling_ratio
[docs]def kimber(rainfall, cleaning_threshold=6, soiling_loss_rate=0.0015,
grace_period=14, max_soiling=0.3, manual_wash_dates=None,
initial_soiling=0, rain_accum_period=24):
"""
Calculates fraction of energy lost due to soiling given rainfall data and
daily loss rate using the Kimber model.
Kimber soiling model [1]_ assumes soiling builds up at a daily rate unless
the daily rainfall is greater than a threshold. The model also assumes that
if daily rainfall has exceeded the threshold within a grace period, then
the ground is too damp to cause soiling build-up. The model also assumes
there is a maximum soiling build-up. Scheduled manual washes and rain
events are assumed to reset soiling to zero.
Parameters
----------
rainfall: pandas.Series
Accumulated rainfall at the end of each time period. [mm]
cleaning_threshold: float, default 6
Amount of daily rainfall required to clean the panels. [mm]
soiling_loss_rate: float, default 0.0015
Fraction of energy lost due to one day of soiling. [unitless]
grace_period : int, default 14
Number of days after a rainfall event when it's assumed the ground is
damp, and so it's assumed there is no soiling. [days]
max_soiling : float, default 0.3
Maximum fraction of energy lost due to soiling. Soiling will build up
until this value. [unitless]
manual_wash_dates : sequence or None, default None
List or tuple of dates as Python ``datetime.date`` when the panels were
washed manually. Note there is no grace period after a manual wash, so
soiling begins to build up immediately.
initial_soiling : float, default 0
Initial fraction of energy lost due to soiling at time zero in the
`rainfall` series input. [unitless]
rain_accum_period : int, default 24
Period for accumulating rainfall to check against `cleaning_threshold`.
The Kimber model defines this period as one day. [hours]
Returns
-------
pandas.Series
fraction of energy lost due to soiling, has same intervals as input
Notes
-----
The soiling loss rate depends on both the geographical region and the
soiling environment type. Rates measured by Kimber [1]_ are summarized in
the following table:
=================== ======= ========= ======================
Region/Environment Rural Suburban Urban/Highway/Airport
=================== ======= ========= ======================
Central Valley 0.0011 0.0019 0.0020
Northern CA 0.0011 0.0010 0.0016
Southern CA 0 0.0016 0.0019
Desert 0.0030 0.0030 0.0030
=================== ======= ========= ======================
Rainfall thresholds and grace periods may also vary by region. Please
consult [1]_ for more information.
References
----------
.. [1] "The Effect of Soiling on Large Grid-Connected Photovoltaic Systems
in California and the Southwest Region of the United States," Adrianne
Kimber, et al., IEEE 4th World Conference on Photovoltaic Energy
Conference, 2006, :doi:`10.1109/WCPEC.2006.279690`
"""
# convert rain_accum_period to timedelta
rain_accum_period = datetime.timedelta(hours=rain_accum_period)
# convert grace_period to timedelta
grace_period = datetime.timedelta(days=grace_period)
# get indices as numpy datetime64, calculate timestep as numpy timedelta64,
# and convert timestep to fraction of days
rain_index_vals = rainfall.index.values
timestep_interval = (rain_index_vals[1] - rain_index_vals[0])
day_fraction = timestep_interval / np.timedelta64(24, 'h')
# accumulate rainfall
accumulated_rainfall = rainfall.rolling(
rain_accum_period, closed='right').sum()
# soiling rate
soiling = np.ones_like(rainfall.values) * soiling_loss_rate * day_fraction
soiling[0] = initial_soiling
soiling = np.cumsum(soiling)
soiling = pd.Series(soiling, index=rainfall.index, name='soiling')
# rainfall events that clean the panels
rain_events = accumulated_rainfall > cleaning_threshold
# grace periods windows during which ground is assumed damp, so no soiling
grace_windows = rain_events.rolling(grace_period, closed='right').sum() > 0
# clean panels by subtracting soiling for indices in grace period windows
cleaning = pd.Series(float('NaN'), index=rainfall.index)
cleaning.iloc[0] = 0.0
cleaning[grace_windows] = soiling[grace_windows]
# manual wash dates
if manual_wash_dates is not None:
rain_tz = rainfall.index.tz
# convert manual wash dates to datetime index in the timezone of rain
manual_wash_dates = pd.DatetimeIndex(manual_wash_dates, tz=rain_tz)
cleaning[manual_wash_dates] = soiling[manual_wash_dates]
# remove soiling by foward filling cleaning where NaN
soiling -= cleaning.ffill()
# check if soiling has reached the maximum
return soiling.where(soiling < max_soiling, max_soiling)