Source code for pvlib.snow

"""
The ``snow`` module contains functions that model module snow cover and the
associated effects on PV module output
"""

import numpy as np
import pandas as pd
from pvlib.tools import sind, cosd, tand


def _time_delta_in_hours(times):
    delta = times.to_series().diff()
    return delta.dt.total_seconds().div(3600)


[docs]def fully_covered_nrel(snowfall, threshold_snowfall=1.): ''' Calculates the timesteps when the row's slant height is fully covered by snow. Parameters ---------- snowfall : Series Accumulated snowfall in each time period [cm] threshold_snowfall : float, default 1.0 Hourly snowfall above which snow coverage is set to the row's slant height. [cm/hr] Returns ---------- boolean: Series True where the snowfall exceeds the defined threshold to fully cover the panel. Notes ----- Implements the model described in [1]_ with minor improvements in [2]_. References ---------- .. [1] Marion, B.; Schaefer, R.; Caine, H.; Sanchez, G. (2013). "Measured and modeled photovoltaic system energy losses from snow for Colorado and Wisconsin locations." Solar Energy 97; pp.112-121. .. [2] Ryberg, D; Freeman, J. "Integration, Validation, and Application of a PV Snow Coverage Model in SAM" (2017) NREL Technical Report NREL/TP-6A20-68705 ''' timestep = _time_delta_in_hours(snowfall.index) hourly_snow_rate = snowfall / timestep # if we can infer a time frequency, use first snowfall value # otherwise the first snowfall value is ignored freq = pd.infer_freq(snowfall.index) if freq is not None: timedelta = pd.tseries.frequencies.to_offset(freq) / pd.Timedelta('1h') hourly_snow_rate.iloc[0] = snowfall[0] / timedelta else: # can't infer frequency from index hourly_snow_rate[0] = 0 # replaces NaN return hourly_snow_rate > threshold_snowfall
[docs]def coverage_nrel(snowfall, poa_irradiance, temp_air, surface_tilt, initial_coverage=0, threshold_snowfall=1., can_slide_coefficient=-80., slide_amount_coefficient=0.197): ''' Calculates the fraction of the slant height of a row of modules covered by snow at every time step. Implements the model described in [1]_ with minor improvements in [2]_, with the change that the output is in fraction of the row's slant height rather than in tenths of the row slant height. As described in [1]_, model validation focused on fixed tilt systems. Parameters ---------- snowfall : Series Accumulated snowfall within each time period. [cm] poa_irradiance : Series Total in-plane irradiance [W/m^2] temp_air : Series Ambient air temperature [C] surface_tilt : numeric Tilt of module's from horizontal, e.g. surface facing up = 0, surface facing horizon = 90. [degrees] initial_coverage : float, default 0 Fraction of row's slant height that is covered with snow at the beginning of the simulation. [unitless] threshold_snowfall : float, default 1.0 Hourly snowfall above which snow coverage is set to the row's slant height. [cm/hr] can_slide_coefficient : float, default -80. Coefficient to determine if snow can slide given irradiance and air temperature. [W/(m^2 C)] slide_amount_coefficient : float, default 0.197 Coefficient to determine fraction of snow that slides off in one hour. [unitless] Returns ------- snow_coverage : Series The fraction of the slant height of a row of modules that is covered by snow at each time step. Notes ----- In [1]_, `can_slide_coefficient` is termed `m`, and the value of `slide_amount_coefficient` is given in tenths of a module's slant height. References ---------- .. [1] Marion, B.; Schaefer, R.; Caine, H.; Sanchez, G. (2013). "Measured and modeled photovoltaic system energy losses from snow for Colorado and Wisconsin locations." Solar Energy 97; pp.112-121. .. [2] Ryberg, D; Freeman, J. (2017). "Integration, Validation, and Application of a PV Snow Coverage Model in SAM" NREL Technical Report NREL/TP-6A20-68705 ''' # find times with new snowfall new_snowfall = fully_covered_nrel(snowfall, threshold_snowfall) # set up output Series snow_coverage = pd.Series(np.nan, index=poa_irradiance.index) # determine amount that snow can slide in each timestep can_slide = temp_air > poa_irradiance / can_slide_coefficient slide_amt = slide_amount_coefficient * sind(surface_tilt) * \ _time_delta_in_hours(poa_irradiance.index) slide_amt[~can_slide] = 0. # don't slide during snow events slide_amt[new_snowfall] = 0. # don't slide in the interval preceding the snowfall data slide_amt.iloc[0] = 0 # build time series of cumulative slide amounts sliding_period_ID = new_snowfall.cumsum() cumulative_sliding = slide_amt.groupby(sliding_period_ID).cumsum() # set up time series of snow coverage without any sliding applied snow_coverage[new_snowfall] = 1.0 if np.isnan(snow_coverage.iloc[0]): snow_coverage.iloc[0] = initial_coverage snow_coverage.ffill(inplace=True) snow_coverage -= cumulative_sliding # clean up periods where row is completely uncovered return snow_coverage.clip(lower=0)
[docs]def dc_loss_nrel(snow_coverage, num_strings): ''' Calculates the fraction of DC capacity lost due to snow coverage. DC capacity loss assumes that if a string is partially covered by snow, the string's capacity is lost; see [1]_, Eq. 11.8. Module orientation is accounted for by specifying the number of cell strings in parallel along the slant height. For example, a typical 60-cell module has 3 parallel strings, each comprising 20 cells in series, with the cells arranged in 6 columns of 10 cells each. For a row consisting of single modules, if the module is mounted in portrait orientation, i.e., the row slant height is along a column of 10 cells, there is 1 string in parallel along the row slant height, so `num_strings=1`. In contrast, if the module is mounted in landscape orientation with the row slant height comprising 6 cells, there are 3 parallel strings along the row slant height, so `num_strings=3`. Parameters ---------- snow_coverage : numeric The fraction of row slant height covered by snow at each time step. num_strings: int The number of parallel-connected strings along a row slant height. Returns ------- loss : numeric fraction of DC capacity loss due to snow coverage at each time step. References ---------- .. [1] Gilman, P. et al., (2018). "SAM Photovoltaic Model Technical Reference Update", NREL Technical Report NREL/TP-6A20-67399. Available at https://www.nrel.gov/docs/fy18osti/67399.pdf ''' return np.ceil(snow_coverage * num_strings) / num_strings
def _townsend_effective_snow(snow_total, snow_events): ''' Calculates effective snow using the total snowfall received each month and the number of snowfall events each month. Parameters ---------- snow_total : array-like Snow received each month. Referred to as S in [1]_. [cm] snow_events : array-like Number of snowfall events each month. Referred to as N in [1]_. [-] Returns ------- effective_snowfall : array-like Effective snowfall as defined in the Townsend model. [cm] References ---------- .. [1] Townsend, Tim & Powers, Loren. (2011). Photovoltaics and snow: An update from two winters of measurements in the SIERRA. 37th IEEE Photovoltaic Specialists Conference, Seattle, WA, USA. :doi:`10.1109/PVSC.2011.6186627` ''' snow_events_no_zeros = np.maximum(snow_events, 1) effective_snow = 0.5 * snow_total * (1 + 1 / snow_events_no_zeros) return np.where(snow_events > 0, effective_snow, 0)
[docs]def loss_townsend(snow_total, snow_events, surface_tilt, relative_humidity, temp_air, poa_global, slant_height, lower_edge_height, angle_of_repose=40): ''' Calculates monthly snow loss based on the Townsend monthly snow loss model [1]_. Parameters ---------- snow_total : array-like Snow received each month. Referred to as S in [1]_. [cm] snow_events : array-like Number of snowfall events each month. Referred to as N in [1]_. [-] surface_tilt : float Tilt angle of the array. [deg] relative_humidity : array-like Monthly average relative humidity. [%] temp_air : array-like Monthly average ambient temperature. [C] poa_global : array-like Monthly plane of array insolation. [Wh/m2] slant_height : float Row length in the slanted plane of array dimension. [m] lower_edge_height : float Distance from array lower edge to the ground. [m] angle_of_repose : float, default 40 Piled snow angle, assumed to stabilize at 40°, the midpoint of 25°-55° avalanching slope angles. [deg] Returns ------- loss : array-like Monthly average DC capacity loss fraction due to snow coverage. Notes ----- This model has not been validated for tracking arrays; however, for tracking arrays [1]_ suggests using the maximum rotation angle in place of ``surface_tilt``. References ---------- .. [1] Townsend, Tim & Powers, Loren. (2011). Photovoltaics and snow: An update from two winters of measurements in the SIERRA. 37th IEEE Photovoltaic Specialists Conference, Seattle, WA, USA. :doi:`10.1109/PVSC.2011.6186627` ''' C1 = 5.7e04 C2 = 0.51 snow_total_prev = np.roll(snow_total, 1) snow_events_prev = np.roll(snow_events, 1) effective_snow = _townsend_effective_snow(snow_total, snow_events) effective_snow_prev = _townsend_effective_snow( snow_total_prev, snow_events_prev ) effective_snow_weighted = ( 1 / 3 * effective_snow_prev + 2 / 3 * effective_snow ) effective_snow_weighted_m = effective_snow_weighted / 100 lower_edge_height_clipped = np.maximum(lower_edge_height, 0.01) gamma = ( slant_height * effective_snow_weighted_m * cosd(surface_tilt) / (lower_edge_height_clipped**2 - effective_snow_weighted_m**2) * 2 * tand(angle_of_repose) ) ground_interference_term = 1 - C2 * np.exp(-gamma) relative_humidity_fraction = relative_humidity / 100 temp_air_kelvin = temp_air + 273.15 effective_snow_weighted_in = effective_snow_weighted / 2.54 poa_global_kWh = poa_global / 1000 # Calculate Eqn. 3 in the reference. # Although the reference says Eqn. 3 calculates percentage loss, the y-axis # of Figure 7 indicates Eqn. 3 calculates fractional loss. Since the slope # of the line in Figure 7 is the same as C1 in Eqn. 3, it is assumed that # Eqn. 3 calculates fractional loss. loss_fraction = ( C1 * effective_snow_weighted_in * cosd(surface_tilt)**2 * ground_interference_term * relative_humidity_fraction / temp_air_kelvin**2 / poa_global_kWh**0.67 ) return np.clip(loss_fraction, 0, 1)