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 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 ```` 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 = # 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)