Source code for pvlib.soiling

"""
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, surface_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] surface_tilt : numeric 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(surface_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.iloc[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, optional 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)