Source code for pvlib.irradiance

"""
The ``irradiance`` module contains functions for modeling global
horizontal irradiance, direct normal irradiance, diffuse horizontal
irradiance, and total irradiance under various conditions.
"""

import datetime
from collections import OrderedDict
from functools import partial

import numpy as np
import pandas as pd

from pvlib import atmosphere, solarposition, tools


# see References section of get_ground_diffuse function
SURFACE_ALBEDOS = {'urban': 0.18,
                   'grass': 0.20,
                   'fresh grass': 0.26,
                   'soil': 0.17,
                   'sand': 0.40,
                   'snow': 0.65,
                   'fresh snow': 0.75,
                   'asphalt': 0.12,
                   'concrete': 0.30,
                   'aluminum': 0.85,
                   'copper': 0.74,
                   'fresh steel': 0.35,
                   'dirty steel': 0.08,
                   'sea': 0.06}


[docs]def get_extra_radiation(datetime_or_doy, solar_constant=1366.1, method='spencer', epoch_year=2014, **kwargs): """ Determine extraterrestrial radiation from day of year. Parameters ---------- datetime_or_doy : numeric, array, date, datetime, Timestamp, DatetimeIndex Day of year, array of days of year, or datetime-like object solar_constant : float, default 1366.1 The solar constant. method : string, default 'spencer' The method by which the ET radiation should be calculated. Options include ``'pyephem', 'spencer', 'asce', 'nrel'``. epoch_year : int, default 2014 The year in which a day of year input will be calculated. Only applies to day of year input used with the pyephem or nrel methods. kwargs : Passed to solarposition.nrel_earthsun_distance Returns ------- dni_extra : float, array, or Series The extraterrestrial radiation present in watts per square meter on a surface which is normal to the sun. Pandas Timestamp and DatetimeIndex inputs will yield a Pandas TimeSeries. All other inputs will yield a float or an array of floats. References ---------- .. [1] M. Reno, C. Hansen, and J. Stein, "Global Horizontal Irradiance Clear Sky Models: Implementation and Analysis", Sandia National Laboratories, SAND2012-2389, 2012. .. [2] <http://solardat.uoregon.edu/SolarRadiationBasics.html>, Eqs. SR1 and SR2 .. [3] Partridge, G. W. and Platt, C. M. R. 1976. Radiative Processes in Meteorology and Climatology. .. [4] Duffie, J. A. and Beckman, W. A. 1991. Solar Engineering of Thermal Processes, 2nd edn. J. Wiley and Sons, New York. .. [5] ASCE, 2005. The ASCE Standardized Reference Evapotranspiration Equation, Environmental and Water Resources Institute of the American Civil Engineers, Ed. R. G. Allen et al. """ to_doy, to_datetimeindex, to_output = \ _handle_extra_radiation_types(datetime_or_doy, epoch_year) # consider putting asce and spencer methods in their own functions method = method.lower() if method == 'asce': B = solarposition._calculate_simple_day_angle(to_doy(datetime_or_doy), offset=0) RoverR0sqrd = 1 + 0.033 * np.cos(B) elif method == 'spencer': B = solarposition._calculate_simple_day_angle(to_doy(datetime_or_doy)) RoverR0sqrd = (1.00011 + 0.034221 * np.cos(B) + 0.00128 * np.sin(B) + 0.000719 * np.cos(2 * B) + 7.7e-05 * np.sin(2 * B)) elif method == 'pyephem': times = to_datetimeindex(datetime_or_doy) RoverR0sqrd = solarposition.pyephem_earthsun_distance(times) ** (-2) elif method == 'nrel': times = to_datetimeindex(datetime_or_doy) RoverR0sqrd = \ solarposition.nrel_earthsun_distance(times, **kwargs) ** (-2) else: raise ValueError('Invalid method: %s', method) Ea = solar_constant * RoverR0sqrd Ea = to_output(Ea) return Ea
def _handle_extra_radiation_types(datetime_or_doy, epoch_year): # This block will set the functions that can be used to convert the # inputs to either day of year or pandas DatetimeIndex, and the # functions that will yield the appropriate output type. It's # complicated because there are many day-of-year-like input types, # and the different algorithms need different types. Maybe you have # a better way to do it. if isinstance(datetime_or_doy, pd.DatetimeIndex): to_doy = tools._pandas_to_doy # won't be evaluated unless necessary def to_datetimeindex(x): return x # noqa: E306 to_output = partial(pd.Series, index=datetime_or_doy) elif isinstance(datetime_or_doy, pd.Timestamp): to_doy = tools._pandas_to_doy to_datetimeindex = \ tools._datetimelike_scalar_to_datetimeindex to_output = tools._scalar_out elif isinstance(datetime_or_doy, (datetime.date, datetime.datetime, np.datetime64)): to_doy = tools._datetimelike_scalar_to_doy to_datetimeindex = \ tools._datetimelike_scalar_to_datetimeindex to_output = tools._scalar_out elif np.isscalar(datetime_or_doy): # ints and floats of various types def to_doy(x): return x # noqa: E306 to_datetimeindex = partial(tools._doy_to_datetimeindex, epoch_year=epoch_year) to_output = tools._scalar_out else: # assume that we have an array-like object of doy def to_doy(x): return x # noqa: E306 to_datetimeindex = partial(tools._doy_to_datetimeindex, epoch_year=epoch_year) to_output = tools._array_out return to_doy, to_datetimeindex, to_output
[docs]def aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth): """ Calculates the dot product of the sun position unit vector and the surface normal unit vector; in other words, the cosine of the angle of incidence. Usage note: When the sun is behind the surface the value returned is negative. For many uses negative values must be set to zero. Input all angles in degrees. Parameters ---------- surface_tilt : numeric Panel tilt from horizontal. surface_azimuth : numeric Panel azimuth from north. solar_zenith : numeric Solar zenith angle. solar_azimuth : numeric Solar azimuth angle. Returns ------- projection : numeric Dot product of panel normal and solar angle. """ projection = ( tools.cosd(surface_tilt) * tools.cosd(solar_zenith) + tools.sind(surface_tilt) * tools.sind(solar_zenith) * tools.cosd(solar_azimuth - surface_azimuth)) # GH 1185 projection = np.clip(projection, -1, 1) try: projection.name = 'aoi_projection' except AttributeError: pass return projection
[docs]def aoi(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth): """ Calculates the angle of incidence of the solar vector on a surface. This is the angle between the solar vector and the surface normal. Input all angles in degrees. Parameters ---------- surface_tilt : numeric Panel tilt from horizontal. surface_azimuth : numeric Panel azimuth from north. solar_zenith : numeric Solar zenith angle. solar_azimuth : numeric Solar azimuth angle. Returns ------- aoi : numeric Angle of incidence in degrees. """ projection = aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth) aoi_value = np.rad2deg(np.arccos(projection)) try: aoi_value.name = 'aoi' except AttributeError: pass return aoi_value
[docs]def poa_horizontal_ratio(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth): """ Calculates the ratio of the beam components of the plane of array irradiance and the horizontal irradiance. Input all angles in degrees. Parameters ---------- surface_tilt : numeric Panel tilt from horizontal. surface_azimuth : numeric Panel azimuth from north. solar_zenith : numeric Solar zenith angle. solar_azimuth : numeric Solar azimuth angle. Returns ------- ratio : numeric Ratio of the plane of array irradiance to the horizontal plane irradiance """ cos_poa_zen = aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth) cos_solar_zenith = tools.cosd(solar_zenith) # ratio of tilted and horizontal beam irradiance ratio = cos_poa_zen / cos_solar_zenith try: ratio.name = 'poa_ratio' except AttributeError: pass return ratio
[docs]def beam_component(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth, dni): """ Calculates the beam component of the plane of array irradiance. Parameters ---------- surface_tilt : numeric Panel tilt from horizontal. surface_azimuth : numeric Panel azimuth from north. solar_zenith : numeric Solar zenith angle. solar_azimuth : numeric Solar azimuth angle. dni : numeric Direct Normal Irradiance Returns ------- beam : numeric Beam component """ beam = dni * aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth) beam = np.maximum(beam, 0) return beam
[docs]def get_total_irradiance(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth, dni, ghi, dhi, dni_extra=None, airmass=None, albedo=0.25, surface_type=None, model='isotropic', model_perez='allsitescomposite1990'): r""" Determine total in-plane irradiance and its beam, sky diffuse and ground reflected components, using the specified sky diffuse irradiance model. .. math:: I_{tot} = I_{beam} + I_{sky diffuse} + I_{ground} Sky diffuse models include: * isotropic (default) * klucher * haydavies * reindl * king * perez Parameters ---------- surface_tilt : numeric Panel tilt from horizontal. [degree] surface_azimuth : numeric Panel azimuth from north. [degree] solar_zenith : numeric Solar zenith angle. [degree] solar_azimuth : numeric Solar azimuth angle. [degree] dni : numeric Direct Normal Irradiance. [W/m2] ghi : numeric Global horizontal irradiance. [W/m2] dhi : numeric Diffuse horizontal irradiance. [W/m2] dni_extra : None or numeric, default None Extraterrestrial direct normal irradiance. [W/m2] airmass : None or numeric, default None Relative airmass (not adjusted for pressure). [unitless] albedo : numeric, default 0.25 Ground surface albedo. [unitless] surface_type : None or str, default None Surface type. See :py:func:`~pvlib.irradiance.get_ground_diffuse` for the list of accepted values. model : str, default 'isotropic' Irradiance model. Can be one of ``'isotropic'``, ``'klucher'``, ``'haydavies'``, ``'reindl'``, ``'king'``, ``'perez'``. model_perez : str, default 'allsitescomposite1990' Used only if ``model='perez'``. See :py:func:`~pvlib.irradiance.perez`. Returns ------- total_irrad : OrderedDict or DataFrame Contains keys/columns ``'poa_global', 'poa_direct', 'poa_diffuse', 'poa_sky_diffuse', 'poa_ground_diffuse'``. Notes ----- Models ``'haydavies'``, ``'reindl'``, or ``'perez'`` require ``'dni_extra'``. Values can be calculated using :py:func:`~pvlib.irradiance.get_extra_radiation`. The ``'perez'`` model requires relative airmass (``airmass``) as input. If ``airmass`` is not provided, it is calculated using the defaults in :py:func:`~pvlib.atmosphere.get_relative_airmass`. """ poa_sky_diffuse = get_sky_diffuse( surface_tilt, surface_azimuth, solar_zenith, solar_azimuth, dni, ghi, dhi, dni_extra=dni_extra, airmass=airmass, model=model, model_perez=model_perez) poa_ground_diffuse = get_ground_diffuse(surface_tilt, ghi, albedo, surface_type) aoi_ = aoi(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth) irrads = poa_components(aoi_, dni, poa_sky_diffuse, poa_ground_diffuse) return irrads
[docs]def get_sky_diffuse(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth, dni, ghi, dhi, dni_extra=None, airmass=None, model='isotropic', model_perez='allsitescomposite1990'): r""" Determine in-plane sky diffuse irradiance component using the specified sky diffuse irradiance model. Sky diffuse models include: * isotropic (default) * klucher * haydavies * reindl * king * perez Parameters ---------- surface_tilt : numeric Panel tilt from horizontal. [degree] surface_azimuth : numeric Panel azimuth from north. [degree] solar_zenith : numeric Solar zenith angle. [degree] solar_azimuth : numeric Solar azimuth angle. [degree] dni : numeric Direct Normal Irradiance. [W/m2] ghi : numeric Global horizontal irradiance. [W/m2] dhi : numeric Diffuse horizontal irradiance. [W/m2] dni_extra : None or numeric, default None Extraterrestrial direct normal irradiance. [W/m2] airmass : None or numeric, default None Relative airmass (not adjusted for pressure). [unitless] model : str, default 'isotropic' Irradiance model. Can be one of ``'isotropic'``, ``'klucher'``, ``'haydavies'``, ``'reindl'``, ``'king'``, ``'perez'``. model_perez : str, default 'allsitescomposite1990' Used only if ``model='perez'``. See :py:func:`~pvlib.irradiance.perez`. Returns ------- poa_sky_diffuse : numeric Sky diffuse irradiance in the plane of array. [W/m2] Raises ------ ValueError If model is one of ``'haydavies'``, ``'reindl'``, or ``'perez'`` and ``dni_extra`` is ``None``. Notes ----- Models ``'haydavies'``, ``'reindl'``, and ``'perez``` require 'dni_extra'. Values can be calculated using :py:func:`~pvlib.irradiance.get_extra_radiation`. The ``'perez'`` model requires relative airmass (``airmass``) as input. If ``airmass`` is not provided, it is calculated using the defaults in :py:func:`~pvlib.atmosphere.get_relative_airmass`. """ model = model.lower() if (model in {'haydavies', 'reindl', 'perez'}) and (dni_extra is None): raise ValueError(f'dni_extra is required for model {model}') if model == 'isotropic': sky = isotropic(surface_tilt, dhi) elif model == 'klucher': sky = klucher(surface_tilt, surface_azimuth, dhi, ghi, solar_zenith, solar_azimuth) elif model == 'haydavies': sky = haydavies(surface_tilt, surface_azimuth, dhi, dni, dni_extra, solar_zenith, solar_azimuth) elif model == 'reindl': sky = reindl(surface_tilt, surface_azimuth, dhi, dni, ghi, dni_extra, solar_zenith, solar_azimuth) elif model == 'king': sky = king(surface_tilt, dhi, ghi, solar_zenith) elif model == 'perez': if airmass is None: airmass = atmosphere.get_relative_airmass(solar_zenith) sky = perez(surface_tilt, surface_azimuth, dhi, dni, dni_extra, solar_zenith, solar_azimuth, airmass, model=model_perez) else: raise ValueError(f'invalid model selection {model}') return sky
[docs]def poa_components(aoi, dni, poa_sky_diffuse, poa_ground_diffuse): r''' Determine in-plane irradiance components. Combines DNI with sky diffuse and ground-reflected irradiance to calculate total, direct and diffuse irradiance components in the plane of array. Parameters ---------- aoi : numeric Angle of incidence of solar rays with respect to the module surface, from :func:`aoi`. dni : numeric Direct normal irradiance (W/m^2), as measured from a TMY file or calculated with a clearsky model. poa_sky_diffuse : numeric Diffuse irradiance (W/m^2) in the plane of the modules, as calculated by a diffuse irradiance translation function poa_ground_diffuse : numeric Ground reflected irradiance (W/m^2) in the plane of the modules, as calculated by an albedo model (eg. :func:`grounddiffuse`) Returns ------- irrads : OrderedDict or DataFrame Contains the following keys: * ``poa_global`` : Total in-plane irradiance (W/m^2) * ``poa_direct`` : Total in-plane beam irradiance (W/m^2) * ``poa_diffuse`` : Total in-plane diffuse irradiance (W/m^2) * ``poa_sky_diffuse`` : In-plane diffuse irradiance from sky (W/m^2) * ``poa_ground_diffuse`` : In-plane diffuse irradiance from ground (W/m^2) Notes ------ Negative beam irradiation due to aoi :math:`> 90^{\circ}` or AOI :math:`< 0^{\circ}` is set to zero. ''' poa_direct = np.maximum(dni * np.cos(np.radians(aoi)), 0) poa_diffuse = poa_sky_diffuse + poa_ground_diffuse poa_global = poa_direct + poa_diffuse irrads = OrderedDict() irrads['poa_global'] = poa_global irrads['poa_direct'] = poa_direct irrads['poa_diffuse'] = poa_diffuse irrads['poa_sky_diffuse'] = poa_sky_diffuse irrads['poa_ground_diffuse'] = poa_ground_diffuse if isinstance(poa_direct, pd.Series): irrads = pd.DataFrame(irrads) return irrads
[docs]def get_ground_diffuse(surface_tilt, ghi, albedo=.25, surface_type=None): ''' Estimate diffuse irradiance from ground reflections given irradiance, albedo, and surface tilt. Function to determine the portion of irradiance on a tilted surface due to ground reflections. Any of the inputs may be DataFrames or scalars. Parameters ---------- surface_tilt : numeric Surface tilt angles in decimal degrees. Tilt must be >=0 and <=180. The tilt angle is defined as degrees from horizontal (e.g. surface facing up = 0, surface facing horizon = 90). ghi : numeric Global horizontal irradiance. [W/m^2] albedo : numeric, default 0.25 Ground reflectance, typically 0.1-0.4 for surfaces on Earth (land), may increase over snow, ice, etc. May also be known as the reflection coefficient. Must be >=0 and <=1. Will be overridden if surface_type is supplied. surface_type: None or string, default None If not None, overrides albedo. String can be one of 'urban', 'grass', 'fresh grass', 'snow', 'fresh snow', 'asphalt', 'concrete', 'aluminum', 'copper', 'fresh steel', 'dirty steel', 'sea'. Returns ------- grounddiffuse : numeric Ground reflected irradiance. [W/m^2] References ---------- .. [1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation" 2007, Solar Energy vol. 81. pp. 254-267. The calculation is the last term of equations 3, 4, 7, 8, 10, 11, and 12. .. [2] albedos from: http://files.pvsyst.com/help/albedo.htm and http://en.wikipedia.org/wiki/Albedo and https://doi.org/10.1175/1520-0469(1972)029<0959:AOTSS>2.0.CO;2 ''' if surface_type is not None: albedo = SURFACE_ALBEDOS[surface_type] diffuse_irrad = ghi * albedo * (1 - np.cos(np.radians(surface_tilt))) * 0.5 try: diffuse_irrad.name = 'diffuse_ground' except AttributeError: pass return diffuse_irrad
[docs]def isotropic(surface_tilt, dhi): r''' Determine diffuse irradiance from the sky on a tilted surface using the isotropic sky model. .. math:: I_{d} = DHI \frac{1 + \cos\beta}{2} Hottel and Woertz's model treats the sky as a uniform source of diffuse irradiance. Thus the diffuse irradiance from the sky (ground reflected irradiance is not included in this algorithm) on a tilted surface can be found from the diffuse horizontal irradiance and the tilt angle of the surface. Parameters ---------- surface_tilt : numeric Surface tilt angle in decimal degrees. Tilt must be >=0 and <=180. The tilt angle is defined as degrees from horizontal (e.g. surface facing up = 0, surface facing horizon = 90) dhi : numeric Diffuse horizontal irradiance in W/m^2. DHI must be >=0. Returns ------- diffuse : numeric The sky diffuse component of the solar radiation. References ---------- .. [1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation" 2007, Solar Energy vol. 81. pp. 254-267 .. [2] Hottel, H.C., Woertz, B.B., 1942. Evaluation of flat-plate solar heat collector. Trans. ASME 64, 91. ''' sky_diffuse = dhi * (1 + tools.cosd(surface_tilt)) * 0.5 return sky_diffuse
[docs]def klucher(surface_tilt, surface_azimuth, dhi, ghi, solar_zenith, solar_azimuth): r''' Determine diffuse irradiance from the sky on a tilted surface using Klucher's 1979 model .. math:: I_{d} = DHI \frac{1 + \cos\beta}{2} (1 + F' \sin^3(\beta/2)) (1 + F' \cos^2\theta\sin^3\theta_z) where .. math:: F' = 1 - (I_{d0} / GHI)^2 Klucher's 1979 model determines the diffuse irradiance from the sky (ground reflected irradiance is not included in this algorithm) on a tilted surface using the surface tilt angle, surface azimuth angle, diffuse horizontal irradiance, direct normal irradiance, global horizontal irradiance, extraterrestrial irradiance, sun zenith angle, and sun azimuth angle. Parameters ---------- surface_tilt : numeric Surface tilt angles in decimal degrees. surface_tilt must be >=0 and <=180. The tilt angle is defined as degrees from horizontal (e.g. surface facing up = 0, surface facing horizon = 90) surface_azimuth : numeric Surface azimuth angles in decimal degrees. surface_azimuth must be >=0 and <=360. The Azimuth convention is defined as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270). dhi : numeric Diffuse horizontal irradiance in W/m^2. DHI must be >=0. ghi : numeric Global irradiance in W/m^2. DNI must be >=0. solar_zenith : numeric Apparent (refraction-corrected) zenith angles in decimal degrees. solar_zenith must be >=0 and <=180. solar_azimuth : numeric Sun azimuth angles in decimal degrees. solar_azimuth must be >=0 and <=360. The Azimuth convention is defined as degrees east of north (e.g. North = 0, East = 90, West = 270). Returns ------- diffuse : numeric The sky diffuse component of the solar radiation. References ---------- .. [1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation" 2007, Solar Energy vol. 81. pp. 254-267 .. [2] Klucher, T.M., 1979. Evaluation of models to predict insolation on tilted surfaces. Solar Energy 23 (2), 111-114. ''' # zenith angle with respect to panel normal. cos_tt = aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth) cos_tt = np.maximum(cos_tt, 0) # GH 526 # silence warning from 0 / 0 with np.errstate(invalid='ignore'): F = 1 - ((dhi / ghi) ** 2) try: # fails with single point input F.fillna(0, inplace=True) except AttributeError: F = np.where(np.isnan(F), 0, F) term1 = 0.5 * (1 + tools.cosd(surface_tilt)) term2 = 1 + F * (tools.sind(0.5 * surface_tilt) ** 3) term3 = 1 + F * (cos_tt ** 2) * (tools.sind(solar_zenith) ** 3) sky_diffuse = dhi * term1 * term2 * term3 return sky_diffuse
[docs]def haydavies(surface_tilt, surface_azimuth, dhi, dni, dni_extra, solar_zenith=None, solar_azimuth=None, projection_ratio=None): r''' Determine diffuse irradiance from the sky on a tilted surface using Hay & Davies' 1980 model .. math:: I_{d} = DHI ( A R_b + (1 - A) (\frac{1 + \cos\beta}{2}) ) Hay and Davies' 1980 model determines the diffuse irradiance from the sky (ground reflected irradiance is not included in this algorithm) on a tilted surface using the surface tilt angle, surface azimuth angle, diffuse horizontal irradiance, direct normal irradiance, extraterrestrial irradiance, sun zenith angle, and sun azimuth angle. Parameters ---------- surface_tilt : numeric Surface tilt angles in decimal degrees. The tilt angle is defined as degrees from horizontal (e.g. surface facing up = 0, surface facing horizon = 90) surface_azimuth : numeric Surface azimuth angles in decimal degrees. The azimuth convention is defined as degrees east of north (e.g. North=0, South=180, East=90, West=270). dhi : numeric Diffuse horizontal irradiance in W/m^2. dni : numeric Direct normal irradiance in W/m^2. dni_extra : numeric Extraterrestrial normal irradiance in W/m^2. solar_zenith : None or numeric, default None Solar apparent (refraction-corrected) zenith angles in decimal degrees. Must supply ``solar_zenith`` and ``solar_azimuth`` or supply ``projection_ratio``. solar_azimuth : None or numeric, default None Solar azimuth angles in decimal degrees. Must supply ``solar_zenith`` and ``solar_azimuth`` or supply ``projection_ratio``. projection_ratio : None or numeric, default None Ratio of angle of incidence projection to solar zenith angle projection. Must supply ``solar_zenith`` and ``solar_azimuth`` or supply ``projection_ratio``. Returns -------- sky_diffuse : numeric The sky diffuse component of the solar radiation. Notes ------ When supplying ``projection_ratio``, consider constraining its values when zenith angle approaches 90 degrees or angle of incidence projection is negative. See code for details. References ----------- .. [1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation" 2007, Solar Energy vol. 81. pp. 254-267 .. [2] Hay, J.E., Davies, J.A., 1980. Calculations of the solar radiation incident on an inclined surface. In: Hay, J.E., Won, T.K. (Eds.), Proc. of First Canadian Solar Radiation Data Workshop, 59. Ministry of Supply and Services, Canada. ''' # if necessary, calculate ratio of titled and horizontal beam irradiance if projection_ratio is None: cos_tt = aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth) cos_tt = np.maximum(cos_tt, 0) # GH 526 cos_solar_zenith = tools.cosd(solar_zenith) Rb = cos_tt / np.maximum(cos_solar_zenith, 0.01745) # GH 432 else: Rb = projection_ratio # Anisotropy Index AI = dni / dni_extra # these are the () and [] sub-terms of the second term of eqn 7 term1 = 1 - AI term2 = 0.5 * (1 + tools.cosd(surface_tilt)) sky_diffuse = dhi * (AI * Rb + term1 * term2) sky_diffuse = np.maximum(sky_diffuse, 0) return sky_diffuse
[docs]def reindl(surface_tilt, surface_azimuth, dhi, dni, ghi, dni_extra, solar_zenith, solar_azimuth): r''' Determine diffuse irradiance from the sky on a tilted surface using Reindl's 1990 model .. math:: I_{d} = DHI (A R_b + (1 - A) (\frac{1 + \cos\beta}{2}) (1 + \sqrt{\frac{I_{hb}}{I_h}} \sin^3(\beta/2)) ) Reindl's 1990 model determines the diffuse irradiance from the sky (ground reflected irradiance is not included in this algorithm) on a tilted surface using the surface tilt angle, surface azimuth angle, diffuse horizontal irradiance, direct normal irradiance, global horizontal irradiance, extraterrestrial irradiance, sun zenith angle, and sun azimuth angle. Parameters ---------- surface_tilt : numeric Surface tilt angles in decimal degrees. The tilt angle is defined as degrees from horizontal (e.g. surface facing up = 0, surface facing horizon = 90) surface_azimuth : numeric Surface azimuth angles in decimal degrees. The azimuth convention is defined as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270). dhi : numeric diffuse horizontal irradiance in W/m^2. dni : numeric direct normal irradiance in W/m^2. ghi: numeric Global irradiance in W/m^2. dni_extra : numeric Extraterrestrial normal irradiance in W/m^2. solar_zenith : numeric Apparent (refraction-corrected) zenith angles in decimal degrees. solar_azimuth : numeric Sun azimuth angles in decimal degrees. The azimuth convention is defined as degrees east of north (e.g. North = 0, East = 90, West = 270). Returns ------- poa_sky_diffuse : numeric The sky diffuse component of the solar radiation. Notes ----- The poa_sky_diffuse calculation is generated from the Loutzenhiser et al. (2007) paper, equation 8. Note that I have removed the beam and ground reflectance portion of the equation and this generates ONLY the diffuse radiation from the sky and circumsolar, so the form of the equation varies slightly from equation 8. References ---------- .. [1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation" 2007, Solar Energy vol. 81. pp. 254-267 .. [2] Reindl, D.T., Beckmann, W.A., Duffie, J.A., 1990a. Diffuse fraction correlations. Solar Energy 45(1), 1-7. .. [3] Reindl, D.T., Beckmann, W.A., Duffie, J.A., 1990b. Evaluation of hourly tilted surface radiation models. Solar Energy 45(1), 9-17. ''' cos_tt = aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth) cos_tt = np.maximum(cos_tt, 0) # GH 526 # do not apply cos(zen) limit here (needed for HB below) cos_solar_zenith = tools.cosd(solar_zenith) # ratio of titled and horizontal beam irradiance Rb = cos_tt / np.maximum(cos_solar_zenith, 0.01745) # GH 432 # Anisotropy Index AI = dni / dni_extra # DNI projected onto horizontal HB = dni * cos_solar_zenith HB = np.maximum(HB, 0) # these are the () and [] sub-terms of the second term of eqn 8 term1 = 1 - AI term2 = 0.5 * (1 + tools.cosd(surface_tilt)) with np.errstate(invalid='ignore', divide='ignore'): hb_to_ghi = np.where(ghi == 0, 0, np.divide(HB, ghi)) term3 = 1 + np.sqrt(hb_to_ghi) * (tools.sind(0.5 * surface_tilt)**3) sky_diffuse = dhi * (AI * Rb + term1 * term2 * term3) sky_diffuse = np.maximum(sky_diffuse, 0) return sky_diffuse
[docs]def king(surface_tilt, dhi, ghi, solar_zenith): ''' Determine diffuse irradiance from the sky on a tilted surface using the King model. King's model determines the diffuse irradiance from the sky (ground reflected irradiance is not included in this algorithm) on a tilted surface using the surface tilt angle, diffuse horizontal irradiance, global horizontal irradiance, and sun zenith angle. Note that this model is not well documented and has not been published in any fashion (as of January 2012). Parameters ---------- surface_tilt : numeric Surface tilt angles in decimal degrees. The tilt angle is defined as degrees from horizontal (e.g. surface facing up = 0, surface facing horizon = 90) dhi : numeric Diffuse horizontal irradiance in W/m^2. ghi : numeric Global horizontal irradiance in W/m^2. solar_zenith : numeric Apparent (refraction-corrected) zenith angles in decimal degrees. Returns -------- poa_sky_diffuse : numeric The diffuse component of the solar radiation. ''' sky_diffuse = (dhi * (1 + tools.cosd(surface_tilt)) / 2 + ghi * (0.012 * solar_zenith - 0.04) * (1 - tools.cosd(surface_tilt)) / 2) sky_diffuse = np.maximum(sky_diffuse, 0) return sky_diffuse
[docs]def perez(surface_tilt, surface_azimuth, dhi, dni, dni_extra, solar_zenith, solar_azimuth, airmass, model='allsitescomposite1990', return_components=False): ''' Determine diffuse irradiance from the sky on a tilted surface using one of the Perez models. Perez models determine the diffuse irradiance from the sky (ground reflected irradiance is not included in this algorithm) on a tilted surface using the surface tilt angle, surface azimuth angle, diffuse horizontal irradiance, direct normal irradiance, extraterrestrial irradiance, sun zenith angle, sun azimuth angle, and relative (not pressure-corrected) airmass. Optionally a selector may be used to use any of Perez's model coefficient sets. Parameters ---------- surface_tilt : numeric Surface tilt angles in decimal degrees. surface_tilt must be >=0 and <=180. The tilt angle is defined as degrees from horizontal (e.g. surface facing up = 0, surface facing horizon = 90) surface_azimuth : numeric Surface azimuth angles in decimal degrees. surface_azimuth must be >=0 and <=360. The azimuth convention is defined as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270). dhi : numeric Diffuse horizontal irradiance in W/m^2. DHI must be >=0. dni : numeric Direct normal irradiance in W/m^2. DNI must be >=0. dni_extra : numeric Extraterrestrial normal irradiance in W/m^2. solar_zenith : numeric apparent (refraction-corrected) zenith angles in decimal degrees. solar_zenith must be >=0 and <=180. solar_azimuth : numeric Sun azimuth angles in decimal degrees. solar_azimuth must be >=0 and <=360. The azimuth convention is defined as degrees east of north (e.g. North = 0, East = 90, West = 270). airmass : numeric Relative (not pressure-corrected) airmass values. If AM is a DataFrame it must be of the same size as all other DataFrame inputs. AM must be >=0 (careful using the 1/sec(z) model of AM generation) model : string (optional, default='allsitescomposite1990') A string which selects the desired set of Perez coefficients. If model is not provided as an input, the default, '1990' will be used. All possible model selections are: * '1990' * 'allsitescomposite1990' (same as '1990') * 'allsitescomposite1988' * 'sandiacomposite1988' * 'usacomposite1988' * 'france1988' * 'phoenix1988' * 'elmonte1988' * 'osage1988' * 'albuquerque1988' * 'capecanaveral1988' * 'albany1988' return_components: bool (optional, default=False) Flag used to decide whether to return the calculated diffuse components or not. Returns -------- numeric, OrderedDict, or DataFrame Return type controlled by `return_components` argument. If ``return_components=False``, `sky_diffuse` is returned. If ``return_components=True``, `diffuse_components` is returned. sky_diffuse : numeric The sky diffuse component of the solar radiation on a tilted surface. diffuse_components : OrderedDict (array input) or DataFrame (Series input) Keys/columns are: * sky_diffuse: Total sky diffuse * isotropic * circumsolar * horizon References ---------- .. [1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation" 2007, Solar Energy vol. 81. pp. 254-267 .. [2] Perez, R., Seals, R., Ineichen, P., Stewart, R., Menicucci, D., 1987. A new simplified version of the Perez diffuse irradiance model for tilted surfaces. Solar Energy 39(3), 221-232. .. [3] Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R., 1990. Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy 44 (5), 271-289. .. [4] Perez, R. et. al 1988. "The Development and Verification of the Perez Diffuse Radiation Model". SAND88-7030 ''' kappa = 1.041 # for solar_zenith in radians z = np.radians(solar_zenith) # convert to radians # delta is the sky's "brightness" delta = dhi * airmass / dni_extra # epsilon is the sky's "clearness" with np.errstate(invalid='ignore'): eps = ((dhi + dni) / dhi + kappa * (z ** 3)) / (1 + kappa * (z ** 3)) # numpy indexing below will not work with a Series if isinstance(eps, pd.Series): eps = eps.values # Perez et al define clearness bins according to the following # rules. 1 = overcast ... 8 = clear (these names really only make # sense for small zenith angles, but...) these values will # eventually be used as indicies for coeffecient look ups ebin = np.digitize(eps, (0., 1.065, 1.23, 1.5, 1.95, 2.8, 4.5, 6.2)) ebin = np.array(ebin) # GH 642 ebin[np.isnan(eps)] = 0 # correct for 0 indexing in coeffecient lookup # later, ebin = -1 will yield nan coefficients ebin -= 1 # The various possible sets of Perez coefficients are contained # in a subfunction to clean up the code. F1c, F2c = _get_perez_coefficients(model) # results in invalid eps (ebin = -1) being mapped to nans nans = np.array([np.nan, np.nan, np.nan]) F1c = np.vstack((F1c, nans)) F2c = np.vstack((F2c, nans)) F1 = (F1c[ebin, 0] + F1c[ebin, 1] * delta + F1c[ebin, 2] * z) F1 = np.maximum(F1, 0) F2 = (F2c[ebin, 0] + F2c[ebin, 1] * delta + F2c[ebin, 2] * z) A = aoi_projection(surface_tilt, surface_azimuth, solar_zenith, solar_azimuth) A = np.maximum(A, 0) B = tools.cosd(solar_zenith) B = np.maximum(B, tools.cosd(85)) # Calculate Diffuse POA from sky dome term1 = 0.5 * (1 - F1) * (1 + tools.cosd(surface_tilt)) term2 = F1 * A / B term3 = F2 * tools.sind(surface_tilt) sky_diffuse = np.maximum(dhi * (term1 + term2 + term3), 0) # we've preserved the input type until now, so don't ruin it! if isinstance(sky_diffuse, pd.Series): sky_diffuse[np.isnan(airmass)] = 0 else: sky_diffuse = np.where(np.isnan(airmass), 0, sky_diffuse) if return_components: diffuse_components = OrderedDict() diffuse_components['sky_diffuse'] = sky_diffuse # Calculate the different components diffuse_components['isotropic'] = dhi * term1 diffuse_components['circumsolar'] = dhi * term2 diffuse_components['horizon'] = dhi * term3 # Set values of components to 0 when sky_diffuse is 0 mask = sky_diffuse == 0 if isinstance(sky_diffuse, pd.Series): diffuse_components = pd.DataFrame(diffuse_components) diffuse_components.loc[mask] = 0 else: diffuse_components = {k: np.where(mask, 0, v) for k, v in diffuse_components.items()} return diffuse_components else: return sky_diffuse
[docs]def clearsky_index(ghi, clearsky_ghi, max_clearsky_index=2.0): """ Calculate the clearsky index. The clearsky index is the ratio of global to clearsky global irradiance. Negative and non-finite clearsky index values will be truncated to zero. Parameters ---------- ghi : numeric Global horizontal irradiance in W/m^2. clearsky_ghi : numeric Modeled clearsky GHI max_clearsky_index : numeric, default 2.0 Maximum value of the clearsky index. The default, 2.0, allows for over-irradiance events typically seen in sub-hourly data. Returns ------- clearsky_index : numeric Clearsky index """ clearsky_index = ghi / clearsky_ghi # set +inf, -inf, and nans to zero clearsky_index = np.where(~np.isfinite(clearsky_index), 0, clearsky_index) # but preserve nans in the input arrays input_is_nan = ~np.isfinite(ghi) | ~np.isfinite(clearsky_ghi) clearsky_index = np.where(input_is_nan, np.nan, clearsky_index) clearsky_index = np.maximum(clearsky_index, 0) clearsky_index = np.minimum(clearsky_index, max_clearsky_index) # preserve input type if isinstance(ghi, pd.Series): clearsky_index = pd.Series(clearsky_index, index=ghi.index) return clearsky_index
[docs]def clearness_index(ghi, solar_zenith, extra_radiation, min_cos_zenith=0.065, max_clearness_index=2.0): """ Calculate the clearness index. The clearness index is the ratio of global to extraterrestrial irradiance on a horizontal plane [1]_. Parameters ---------- ghi : numeric Global horizontal irradiance in W/m^2. solar_zenith : numeric True (not refraction-corrected) solar zenith angle in decimal degrees. extra_radiation : numeric Irradiance incident at the top of the atmosphere min_cos_zenith : numeric, default 0.065 Minimum value of cos(zenith) to allow when calculating global clearness index `kt`. Equivalent to zenith = 86.273 degrees. max_clearness_index : numeric, default 2.0 Maximum value of the clearness index. The default, 2.0, allows for over-irradiance events typically seen in sub-hourly data. NREL's SRRL Fortran code used 0.82 for hourly data. Returns ------- kt : numeric Clearness index References ---------- .. [1] Maxwell, E. L., "A Quasi-Physical Model for Converting Hourly Global Horizontal to Direct Normal Insolation", Technical Report No. SERI/TR-215-3087, Golden, CO: Solar Energy Research Institute, 1987. """ cos_zenith = tools.cosd(solar_zenith) I0h = extra_radiation * np.maximum(cos_zenith, min_cos_zenith) # consider adding # with np.errstate(invalid='ignore', divide='ignore'): # to kt calculation, but perhaps it's good to allow these # warnings to the users that override min_cos_zenith kt = ghi / I0h kt = np.maximum(kt, 0) kt = np.minimum(kt, max_clearness_index) return kt
[docs]def clearness_index_zenith_independent(clearness_index, airmass, max_clearness_index=2.0): """ Calculate the zenith angle independent clearness index. See [1]_ for details. Parameters ---------- clearness_index : numeric Ratio of global to extraterrestrial irradiance on a horizontal plane airmass : numeric Airmass max_clearness_index : numeric, default 2.0 Maximum value of the clearness index. The default, 2.0, allows for over-irradiance events typically seen in sub-hourly data. NREL's SRRL Fortran code used 0.82 for hourly data. Returns ------- kt_prime : numeric Zenith independent clearness index References ---------- .. [1] Perez, R., P. Ineichen, E. Maxwell, R. Seals and A. Zelenka, (1992). "Dynamic Global-to-Direct Irradiance Conversion Models". ASHRAE Transactions-Research Series, pp. 354-369 """ # Perez eqn 1 kt_prime = clearness_index / _kt_kt_prime_factor(airmass) kt_prime = np.maximum(kt_prime, 0) kt_prime = np.minimum(kt_prime, max_clearness_index) return kt_prime
def _kt_kt_prime_factor(airmass): """ Calculate the conversion factor between kt and kt prime. Function is useful because DIRINT and GTI-DIRINT both use this. """ # consider adding # airmass = np.maximum(airmass, 12) # GH 450 return 1.031 * np.exp(-1.4 / (0.9 + 9.4 / airmass)) + 0.1
[docs]def disc(ghi, solar_zenith, datetime_or_doy, pressure=101325, min_cos_zenith=0.065, max_zenith=87, max_airmass=12): """ Estimate Direct Normal Irradiance from Global Horizontal Irradiance using the DISC model. The DISC algorithm converts global horizontal irradiance to direct normal irradiance through empirical relationships between the global and direct clearness indices. The pvlib implementation limits the clearness index to 1. The original report describing the DISC model [1]_ uses the relative airmass rather than the absolute (pressure-corrected) airmass. However, the NREL implementation of the DISC model [2]_ uses absolute airmass. PVLib Matlab also uses the absolute airmass. pvlib python defaults to absolute airmass, but the relative airmass can be used by supplying `pressure=None`. Parameters ---------- ghi : numeric Global horizontal irradiance in W/m^2. solar_zenith : numeric True (not refraction-corrected) solar zenith angles in decimal degrees. datetime_or_doy : int, float, array, pd.DatetimeIndex Day of year or array of days of year e.g. pd.DatetimeIndex.dayofyear, or pd.DatetimeIndex. pressure : None or numeric, default 101325 Site pressure in Pascal. If None, relative airmass is used instead of absolute (pressure-corrected) airmass. min_cos_zenith : numeric, default 0.065 Minimum value of cos(zenith) to allow when calculating global clearness index `kt`. Equivalent to zenith = 86.273 degrees. max_zenith : numeric, default 87 Maximum value of zenith to allow in DNI calculation. DNI will be set to 0 for times with zenith values greater than `max_zenith`. max_airmass : numeric, default 12 Maximum value of the airmass to allow in Kn calculation. Default value (12) comes from range over which Kn was fit to airmass in the original paper. Returns ------- output : OrderedDict or DataFrame Contains the following keys: * ``dni``: The modeled direct normal irradiance in W/m^2 provided by the Direct Insolation Simulation Code (DISC) model. * ``kt``: Ratio of global to extraterrestrial irradiance on a horizontal plane. * ``airmass``: Airmass References ---------- .. [1] Maxwell, E. L., "A Quasi-Physical Model for Converting Hourly Global Horizontal to Direct Normal Insolation", Technical Report No. SERI/TR-215-3087, Golden, CO: Solar Energy Research Institute, 1987. .. [2] Maxwell, E. "DISC Model", Excel Worksheet. https://www.nrel.gov/grid/solar-resource/disc.html See Also -------- dirint """ # this is the I0 calculation from the reference # SSC uses solar constant = 1367.0 (checked 2018 08 15) I0 = get_extra_radiation(datetime_or_doy, 1370., 'spencer') kt = clearness_index(ghi, solar_zenith, I0, min_cos_zenith=min_cos_zenith, max_clearness_index=1) am = atmosphere.get_relative_airmass(solar_zenith, model='kasten1966') if pressure is not None: am = atmosphere.get_absolute_airmass(am, pressure) Kn, am = _disc_kn(kt, am, max_airmass=max_airmass) dni = Kn * I0 bad_values = (solar_zenith > max_zenith) | (ghi < 0) | (dni < 0) dni = np.where(bad_values, 0, dni) output = OrderedDict() output['dni'] = dni output['kt'] = kt output['airmass'] = am if isinstance(datetime_or_doy, pd.DatetimeIndex): output = pd.DataFrame(output, index=datetime_or_doy) return output
def _disc_kn(clearness_index, airmass, max_airmass=12): """ Calculate Kn for `disc` Parameters ---------- clearness_index : numeric airmass : numeric max_airmass : float airmass > max_airmass is set to max_airmass before being used in calculating Kn. Returns ------- Kn : numeric am : numeric airmass used in the calculation of Kn. am <= max_airmass. """ # short names for equations kt = clearness_index am = airmass am = np.minimum(am, max_airmass) # GH 450 # powers of kt will be used repeatedly, so compute only once kt2 = kt * kt # about the same as kt ** 2 kt3 = kt2 * kt # 5-10x faster than kt ** 3 bools = (kt <= 0.6) a = np.where(bools, 0.512 - 1.56*kt + 2.286*kt2 - 2.222*kt3, -5.743 + 21.77*kt - 27.49*kt2 + 11.56*kt3) b = np.where(bools, 0.37 + 0.962*kt, 41.4 - 118.5*kt + 66.05*kt2 + 31.9*kt3) c = np.where(bools, -0.28 + 0.932*kt - 2.048*kt2, -47.01 + 184.2*kt - 222.0*kt2 + 73.81*kt3) delta_kn = a + b * np.exp(c*am) Knc = 0.866 - 0.122*am + 0.0121*am**2 - 0.000653*am**3 + 1.4e-05*am**4 Kn = Knc - delta_kn return Kn, am
[docs]def dirint(ghi, solar_zenith, times, pressure=101325., use_delta_kt_prime=True, temp_dew=None, min_cos_zenith=0.065, max_zenith=87): """ Determine DNI from GHI using the DIRINT modification of the DISC model. Implements the modified DISC model known as "DIRINT" introduced in [1]_. DIRINT predicts direct normal irradiance (DNI) from measured global horizontal irradiance (GHI). DIRINT improves upon the DISC model by using time-series GHI data and dew point temperature information. The effectiveness of the DIRINT model improves with each piece of information provided. The pvlib implementation limits the clearness index to 1. Parameters ---------- ghi : array-like Global horizontal irradiance in W/m^2. solar_zenith : array-like True (not refraction-corrected) solar_zenith angles in decimal degrees. times : DatetimeIndex pressure : float or array-like, default 101325.0 The site pressure in Pascal. Pressure may be measured or an average pressure may be calculated from site altitude. use_delta_kt_prime : bool, default True If True, indicates that the stability index delta_kt_prime is included in the model. The stability index adjusts the estimated DNI in response to dynamics in the time series of GHI. It is recommended that delta_kt_prime is not used if the time between GHI points is 1.5 hours or greater. If use_delta_kt_prime=True, input data must be Series. temp_dew : None, float, or array-like, default None Surface dew point temperatures, in degrees C. Values of temp_dew may be numeric or NaN. Any single time period point with a temp_dew=NaN does not have dew point improvements applied. If temp_dew is not provided, then dew point improvements are not applied. min_cos_zenith : numeric, default 0.065 Minimum value of cos(zenith) to allow when calculating global clearness index `kt`. Equivalent to zenith = 86.273 degrees. max_zenith : numeric, default 87 Maximum value of zenith to allow in DNI calculation. DNI will be set to 0 for times with zenith values greater than `max_zenith`. Returns ------- dni : array-like The modeled direct normal irradiance in W/m^2 provided by the DIRINT model. Notes ----- DIRINT model requires time series data (ie. one of the inputs must be a vector of length > 2). References ---------- .. [1] Perez, R., P. Ineichen, E. Maxwell, R. Seals and A. Zelenka, (1992). "Dynamic Global-to-Direct Irradiance Conversion Models". ASHRAE Transactions-Research Series, pp. 354-369 .. [2] Maxwell, E. L., "A Quasi-Physical Model for Converting Hourly Global Horizontal to Direct Normal Insolation", Technical Report No. SERI/TR-215-3087, Golden, CO: Solar Energy Research Institute, 1987. """ disc_out = disc(ghi, solar_zenith, times, pressure=pressure, min_cos_zenith=min_cos_zenith, max_zenith=max_zenith) airmass = disc_out['airmass'] kt = disc_out['kt'] kt_prime = clearness_index_zenith_independent( kt, airmass, max_clearness_index=1) delta_kt_prime = _delta_kt_prime_dirint(kt_prime, use_delta_kt_prime, times) w = _temp_dew_dirint(temp_dew, times) dirint_coeffs = _dirint_coeffs(times, kt_prime, solar_zenith, w, delta_kt_prime) # Perez eqn 5 dni = disc_out['dni'] * dirint_coeffs return dni
def _dirint_from_dni_ktprime(dni, kt_prime, solar_zenith, use_delta_kt_prime, temp_dew): """ Calculate DIRINT DNI from supplied DISC DNI and Kt'. Supports :py:func:`gti_dirint` """ times = dni.index delta_kt_prime = _delta_kt_prime_dirint(kt_prime, use_delta_kt_prime, times) w = _temp_dew_dirint(temp_dew, times) dirint_coeffs = _dirint_coeffs(times, kt_prime, solar_zenith, w, delta_kt_prime) dni_dirint = dni * dirint_coeffs return dni_dirint def _delta_kt_prime_dirint(kt_prime, use_delta_kt_prime, times): """ Calculate delta_kt_prime (Perez eqn 2 and eqn 3), or return a default value for use with :py:func:`_dirint_bins`. """ if use_delta_kt_prime: # Perez eqn 2 kt_next = kt_prime.shift(-1) kt_previous = kt_prime.shift(1) # replace nan with values that implement Perez Eq 3 for first and last # positions. Use kt_previous and kt_next to handle series of length 1 kt_next.iloc[-1] = kt_previous.iloc[-1] kt_previous.iloc[0] = kt_next.iloc[0] delta_kt_prime = 0.5 * ((kt_prime - kt_next).abs().add( (kt_prime - kt_previous).abs(), fill_value=0)) else: # do not change unless also modifying _dirint_bins delta_kt_prime = pd.Series(-1, index=times) return delta_kt_prime def _temp_dew_dirint(temp_dew, times): """ Calculate precipitable water from surface dew point temp (Perez eqn 4), or return a default value for use with :py:func:`_dirint_bins`. """ if temp_dew is not None: # Perez eqn 4 w = pd.Series(np.exp(0.07 * temp_dew - 0.075), index=times) else: # do not change unless also modifying _dirint_bins w = pd.Series(-1, index=times) return w def _dirint_coeffs(times, kt_prime, solar_zenith, w, delta_kt_prime): """ Determine the DISC to DIRINT multiplier `dirint_coeffs`. dni = disc_out['dni'] * dirint_coeffs Parameters ---------- times : pd.DatetimeIndex kt_prime : Zenith-independent clearness index solar_zenith : Solar zenith angle w : precipitable water estimated from surface dew-point temperature delta_kt_prime : stability index Returns ------- dirint_coeffs : array-like """ kt_prime_bin, zenith_bin, w_bin, delta_kt_prime_bin = \ _dirint_bins(times, kt_prime, solar_zenith, w, delta_kt_prime) # get the coefficients coeffs = _get_dirint_coeffs() # subtract 1 to account for difference between MATLAB-style bin # assignment and Python-style array lookup. dirint_coeffs = coeffs[kt_prime_bin-1, zenith_bin-1, delta_kt_prime_bin-1, w_bin-1] # convert unassigned bins to nan dirint_coeffs = np.where((kt_prime_bin == 0) | (zenith_bin == 0) | (w_bin == 0) | (delta_kt_prime_bin == 0), np.nan, dirint_coeffs) return dirint_coeffs def _dirint_bins(times, kt_prime, zenith, w, delta_kt_prime): """ Determine the bins for the DIRINT coefficients. Parameters ---------- times : pd.DatetimeIndex kt_prime : Zenith-independent clearness index zenith : Solar zenith angle w : precipitable water estimated from surface dew-point temperature delta_kt_prime : stability index Returns ------- tuple of kt_prime_bin, zenith_bin, w_bin, delta_kt_prime_bin """ # @wholmgren: the following bin assignments use MATLAB's 1-indexing. # Later, we'll subtract 1 to conform to Python's 0-indexing. # Create kt_prime bins kt_prime_bin = pd.Series(0, index=times, dtype=np.int64) kt_prime_bin[(kt_prime >= 0) & (kt_prime < 0.24)] = 1 kt_prime_bin[(kt_prime >= 0.24) & (kt_prime < 0.4)] = 2 kt_prime_bin[(kt_prime >= 0.4) & (kt_prime < 0.56)] = 3 kt_prime_bin[(kt_prime >= 0.56) & (kt_prime < 0.7)] = 4 kt_prime_bin[(kt_prime >= 0.7) & (kt_prime < 0.8)] = 5 kt_prime_bin[(kt_prime >= 0.8) & (kt_prime <= 1)] = 6 # Create zenith angle bins zenith_bin = pd.Series(0, index=times, dtype=np.int64) zenith_bin[(zenith >= 0) & (zenith < 25)] = 1 zenith_bin[(zenith >= 25) & (zenith < 40)] = 2 zenith_bin[(zenith >= 40) & (zenith < 55)] = 3 zenith_bin[(zenith >= 55) & (zenith < 70)] = 4 zenith_bin[(zenith >= 70) & (zenith < 80)] = 5 zenith_bin[(zenith >= 80)] = 6 # Create the bins for w based on dew point temperature w_bin = pd.Series(0, index=times, dtype=np.int64) w_bin[(w >= 0) & (w < 1)] = 1 w_bin[(w >= 1) & (w < 2)] = 2 w_bin[(w >= 2) & (w < 3)] = 3 w_bin[(w >= 3)] = 4 w_bin[(w == -1)] = 5 # Create delta_kt_prime binning. delta_kt_prime_bin = pd.Series(0, index=times, dtype=np.int64) delta_kt_prime_bin[(delta_kt_prime >= 0) & (delta_kt_prime < 0.015)] = 1 delta_kt_prime_bin[(delta_kt_prime >= 0.015) & (delta_kt_prime < 0.035)] = 2 delta_kt_prime_bin[(delta_kt_prime >= 0.035) & (delta_kt_prime < 0.07)] = 3 delta_kt_prime_bin[(delta_kt_prime >= 0.07) & (delta_kt_prime < 0.15)] = 4 delta_kt_prime_bin[(delta_kt_prime >= 0.15) & (delta_kt_prime < 0.3)] = 5 delta_kt_prime_bin[(delta_kt_prime >= 0.3) & (delta_kt_prime <= 1)] = 6 delta_kt_prime_bin[delta_kt_prime == -1] = 7 return kt_prime_bin, zenith_bin, w_bin, delta_kt_prime_bin
[docs]def dirindex(ghi, ghi_clearsky, dni_clearsky, zenith, times, pressure=101325., use_delta_kt_prime=True, temp_dew=None, min_cos_zenith=0.065, max_zenith=87): """ Determine DNI from GHI using the DIRINDEX model. The DIRINDEX model [1]_ modifies the DIRINT model implemented in :py:func:`pvlib.irradiance.dirint` by taking into account information from a clear sky model. It is recommended that ``ghi_clearsky`` be calculated using the Ineichen clear sky model :py:func:`pvlib.clearsky.ineichen` with ``perez_enhancement=True``. The pvlib implementation limits the clearness index to 1. Parameters ---------- ghi : array-like Global horizontal irradiance in W/m^2. ghi_clearsky : array-like Global horizontal irradiance from clear sky model, in W/m^2. dni_clearsky : array-like Direct normal irradiance from clear sky model, in W/m^2. zenith : array-like True (not refraction-corrected) zenith angles in decimal degrees. If Z is a vector it must be of the same size as all other vector inputs. Z must be >=0 and <=180. times : DatetimeIndex pressure : float or array-like, default 101325.0 The site pressure in Pascal. Pressure may be measured or an average pressure may be calculated from site altitude. use_delta_kt_prime : bool, default True If True, indicates that the stability index delta_kt_prime is included in the model. The stability index adjusts the estimated DNI in response to dynamics in the time series of GHI. It is recommended that delta_kt_prime is not used if the time between GHI points is 1.5 hours or greater. If use_delta_kt_prime=True, input data must be Series. temp_dew : None, float, or array-like, default None Surface dew point temperatures, in degrees C. Values of temp_dew may be numeric or NaN. Any single time period point with a temp_dew=NaN does not have dew point improvements applied. If temp_dew is not provided, then dew point improvements are not applied. min_cos_zenith : numeric, default 0.065 Minimum value of cos(zenith) to allow when calculating global clearness index `kt`. Equivalent to zenith = 86.273 degrees. max_zenith : numeric, default 87 Maximum value of zenith to allow in DNI calculation. DNI will be set to 0 for times with zenith values greater than `max_zenith`. Returns ------- dni : array-like The modeled direct normal irradiance in W/m^2. Notes ----- DIRINDEX model requires time series data (ie. one of the inputs must be a vector of length > 2). References ---------- .. [1] Perez, R., Ineichen, P., Moore, K., Kmiecik, M., Chain, C., George, R., & Vignola, F. (2002). A new operational model for satellite-derived irradiances: description and validation. Solar Energy, 73(5), 307-317. """ dni_dirint = dirint(ghi, zenith, times, pressure=pressure, use_delta_kt_prime=use_delta_kt_prime, temp_dew=temp_dew, min_cos_zenith=min_cos_zenith, max_zenith=max_zenith) dni_dirint_clearsky = dirint(ghi_clearsky, zenith, times, pressure=pressure, use_delta_kt_prime=use_delta_kt_prime, temp_dew=temp_dew, min_cos_zenith=min_cos_zenith, max_zenith=max_zenith) dni_dirindex = dni_clearsky * dni_dirint / dni_dirint_clearsky dni_dirindex[dni_dirindex < 0] = 0. return dni_dirindex
[docs]def gti_dirint(poa_global, aoi, solar_zenith, solar_azimuth, times, surface_tilt, surface_azimuth, pressure=101325., use_delta_kt_prime=True, temp_dew=None, albedo=.25, model='perez', model_perez='allsitescomposite1990', calculate_gt_90=True, max_iterations=30): """ Determine GHI, DNI, DHI from POA global using the GTI DIRINT model. The GTI DIRINT model is described in [1]_. .. warning:: Model performance is poor for AOI greater than approximately 80 degrees `and` plane of array irradiance greater than approximately 200 W/m^2. Parameters ---------- poa_global : array-like Plane of array global irradiance in W/m^2. aoi : array-like Angle of incidence of solar rays with respect to the module surface normal. solar_zenith : array-like True (not refraction-corrected) solar zenith angles in decimal degrees. solar_azimuth : array-like Solar azimuth angles in decimal degrees. times : DatetimeIndex Time indices for the input array-like data. surface_tilt : numeric Surface tilt angles in decimal degrees. Tilt must be >=0 and <=180. The tilt angle is defined as degrees from horizontal (e.g. surface facing up = 0, surface facing horizon = 90). surface_azimuth : numeric Surface azimuth angles in decimal degrees. surface_azimuth must be >=0 and <=360. The Azimuth convention is defined as degrees east of north (e.g. North = 0, South=180 East = 90, West = 270). pressure : numeric, default 101325.0 The site pressure in Pascal. Pressure may be measured or an average pressure may be calculated from site altitude. use_delta_kt_prime : bool, default True If True, indicates that the stability index delta_kt_prime is included in the model. The stability index adjusts the estimated DNI in response to dynamics in the time series of GHI. It is recommended that delta_kt_prime is not used if the time between GHI points is 1.5 hours or greater. If use_delta_kt_prime=True, input data must be Series. temp_dew : None, float, or array-like, default None Surface dew point temperatures, in degrees C. Values of temp_dew may be numeric or NaN. Any single time period point with a temp_dew=NaN does not have dew point improvements applied. If temp_dew is not provided, then dew point improvements are not applied. albedo : numeric, default 0.25 Ground surface albedo. [unitless] model : String, default 'perez' Irradiance model. See :py:func:`get_sky_diffuse` for allowed values. model_perez : String, default 'allsitescomposite1990' Used only if model='perez'. See :py:func:`perez`. calculate_gt_90 : bool, default True Controls if the algorithm evaluates inputs with AOI >= 90 degrees. If False, returns nan for AOI >= 90 degrees. Significant speed ups can be achieved by setting this parameter to False. max_iterations : int, default 30 Maximum number of iterations for the aoi < 90 deg algorithm. Returns ------- data : DataFrame Contains the following keys/columns: * ``ghi``: the modeled global horizontal irradiance in W/m^2. * ``dni``: the modeled direct normal irradiance in W/m^2. * ``dhi``: the modeled diffuse horizontal irradiance in W/m^2. References ---------- .. [1] B. Marion, A model for deriving the direct normal and diffuse horizontal irradiance from the global tilted irradiance, Solar Energy 122, 1037-1046. :doi:`10.1016/j.solener.2015.10.024` """ aoi_lt_90 = aoi < 90 # for AOI less than 90 degrees ghi, dni, dhi, kt_prime = _gti_dirint_lt_90( poa_global, aoi, aoi_lt_90, solar_zenith, solar_azimuth, times, surface_tilt, surface_azimuth, pressure=pressure, use_delta_kt_prime=use_delta_kt_prime, temp_dew=temp_dew, albedo=albedo, model=model, model_perez=model_perez, max_iterations=max_iterations) # for AOI greater than or equal to 90 degrees if calculate_gt_90: ghi_gte_90, dni_gte_90, dhi_gte_90 = _gti_dirint_gte_90( poa_global, aoi, solar_zenith, solar_azimuth, surface_tilt, times, kt_prime, pressure=pressure, temp_dew=temp_dew, albedo=albedo) else: ghi_gte_90, dni_gte_90, dhi_gte_90 = np.nan, np.nan, np.nan # put the AOI < 90 and AOI >= 90 conditions together output = OrderedDict() output['ghi'] = ghi.where(aoi_lt_90, ghi_gte_90) output['dni'] = dni.where(aoi_lt_90, dni_gte_90) output['dhi'] = dhi.where(aoi_lt_90, dhi_gte_90) output = pd.DataFrame(output, index=times) return output
def _gti_dirint_lt_90(poa_global, aoi, aoi_lt_90, solar_zenith, solar_azimuth, times, surface_tilt, surface_azimuth, pressure=101325., use_delta_kt_prime=True, temp_dew=None, albedo=.25, model='perez', model_perez='allsitescomposite1990', max_iterations=30): """ GTI-DIRINT model for AOI < 90 degrees. See Marion 2015 Section 2.1. See gti_dirint signature for parameter details. """ I0 = get_extra_radiation(times, 1370, 'spencer') cos_zenith = tools.cosd(solar_zenith) # I0h as in Marion 2015 eqns 1, 3 I0h = I0 * np.maximum(0.065, cos_zenith) airmass = atmosphere.get_relative_airmass(solar_zenith, model='kasten1966') airmass = atmosphere.get_absolute_airmass(airmass, pressure) # these coeffs and diff variables and the loop below # implement figure 1 of Marion 2015 # make coeffs that is at least 30 elements long so that all # coeffs can be assigned as specified in Marion 2015. # slice below will limit iterations if necessary coeffs = np.empty(max(30, max_iterations)) coeffs[0:3] = 1 coeffs[3:10] = 0.5 coeffs[10:20] = 0.25 coeffs[20:] = 0.125 coeffs = coeffs[:max_iterations] # covers case where max_iterations < 30 # initialize diff diff = pd.Series(9999, index=times) best_diff = diff # initialize poa_global_i poa_global_i = poa_global for iteration, coeff in enumerate(coeffs): # test if difference between modeled GTI and # measured GTI (poa_global) is less than 1 W/m^2 # only test for aoi less than 90 deg best_diff_lte_1 = best_diff <= 1 best_diff_lte_1_lt_90 = best_diff_lte_1[aoi_lt_90] if best_diff_lte_1_lt_90.all(): # all aoi < 90 points have a difference <= 1, so break loop break # calculate kt and DNI from GTI kt = clearness_index(poa_global_i, aoi, I0) # kt from Marion eqn 2 disc_dni = np.maximum(_disc_kn(kt, airmass)[0] * I0, 0) kt_prime = clearness_index_zenith_independent(kt, airmass) # dirint DNI in Marion eqn 3 dni = _dirint_from_dni_ktprime(disc_dni, kt_prime, solar_zenith, use_delta_kt_prime, temp_dew) # calculate DHI using Marion eqn 3 (identify 1st term on RHS as GHI) # I0h has a minimum zenith projection, but multiplier of DNI does not ghi = kt * I0h # Kt * I0 * max(0.065, cos(zen)) dhi = ghi - dni * cos_zenith # no cos(zen) restriction here # following SSC code dni = np.maximum(dni, 0) ghi = np.maximum(ghi, 0) dhi = np.maximum(dhi, 0) # use DNI and DHI to model GTI # GTI-DIRINT uses perez transposition model, but we allow for # any model here all_irrad = get_total_irradiance( surface_tilt, surface_azimuth, solar_zenith, solar_azimuth, dni, ghi, dhi, dni_extra=I0, airmass=airmass, albedo=albedo, model=model, model_perez=model_perez) gti_model = all_irrad['poa_global'] # calculate new diff diff = gti_model - poa_global # determine if the new diff is smaller in magnitude # than the old diff diff_abs = diff.abs() smallest_diff = diff_abs < best_diff # save the best differences best_diff = diff_abs.where(smallest_diff, best_diff) # on first iteration, the best values are the only values if iteration == 0: best_ghi = ghi best_dni = dni best_dhi = dhi best_kt_prime = kt_prime else: # save new DNI, DHI, DHI if they provide the best consistency # otherwise use the older values. best_ghi = ghi.where(smallest_diff, best_ghi) best_dni = dni.where(smallest_diff, best_dni) best_dhi = dhi.where(smallest_diff, best_dhi) best_kt_prime = kt_prime.where(smallest_diff, best_kt_prime) # calculate adjusted inputs for next iteration. Marion eqn 4 poa_global_i = np.maximum(1.0, poa_global_i - coeff * diff) else: # we are here because we ran out of coeffs to loop over and # therefore we have exceeded max_iterations import warnings failed_points = best_diff[aoi_lt_90][~best_diff_lte_1_lt_90] warnings.warn( ('%s points failed to converge after %s iterations. best_diff:\n%s' % (len(failed_points), max_iterations, failed_points)), RuntimeWarning) # return the best data, whether or not the solution converged return best_ghi, best_dni, best_dhi, best_kt_prime def _gti_dirint_gte_90(poa_global, aoi, solar_zenith, solar_azimuth, surface_tilt, times, kt_prime, pressure=101325., temp_dew=None, albedo=.25): """ GTI-DIRINT model for AOI >= 90 degrees. See Marion 2015 Section 2.2. See gti_dirint signature for parameter details. """ kt_prime_gte_90 = _gti_dirint_gte_90_kt_prime(aoi, solar_zenith, solar_azimuth, times, kt_prime) I0 = get_extra_radiation(times, 1370, 'spencer') airmass = atmosphere.get_relative_airmass(solar_zenith, model='kasten1966') airmass = atmosphere.get_absolute_airmass(airmass, pressure) kt = kt_prime_gte_90 * _kt_kt_prime_factor(airmass) disc_dni = np.maximum(_disc_kn(kt, airmass)[0] * I0, 0) dni_gte_90 = _dirint_from_dni_ktprime(disc_dni, kt_prime, solar_zenith, False, temp_dew) dni_gte_90_proj = dni_gte_90 * tools.cosd(solar_zenith) cos_surface_tilt = tools.cosd(surface_tilt) # isotropic sky plus ground diffuse dhi_gte_90 = ( (2 * poa_global - dni_gte_90_proj * albedo * (1 - cos_surface_tilt)) / (1 + cos_surface_tilt + albedo * (1 - cos_surface_tilt))) ghi_gte_90 = dni_gte_90_proj + dhi_gte_90 return ghi_gte_90, dni_gte_90, dhi_gte_90 def _gti_dirint_gte_90_kt_prime(aoi, solar_zenith, solar_azimuth, times, kt_prime): """ Determine kt' values to be used in GTI-DIRINT AOI >= 90 deg case. See Marion 2015 Section 2.2. For AOI >= 90 deg: average of the kt_prime values for 65 < AOI < 80 in each day's morning and afternoon. Morning and afternoon are treated separately. For AOI < 90 deg: NaN. See gti_dirint signature for parameter details. Returns ------- kt_prime_gte_90 : Series Index is `times`. """ # kt_prime values from DIRINT calculation for AOI < 90 case # set the kt_prime from sunrise to AOI=90 to be equal to # the kt_prime for 65 < AOI < 80 during the morning. # similar for the afternoon. repeat for every day. aoi_gte_90 = aoi >= 90 aoi_65_80 = (aoi > 65) & (aoi < 80) zenith_lt_90 = solar_zenith < 90 morning = solar_azimuth < 180 afternoon = solar_azimuth > 180 aoi_65_80_morning = aoi_65_80 & morning aoi_65_80_afternoon = aoi_65_80 & afternoon zenith_lt_90_aoi_gte_90_morning = zenith_lt_90 & aoi_gte_90 & morning zenith_lt_90_aoi_gte_90_afternoon = zenith_lt_90 & aoi_gte_90 & afternoon kt_prime_gte_90 = [] for date, data in kt_prime.groupby(times.date): kt_prime_am_avg = data[aoi_65_80_morning].mean() kt_prime_pm_avg = data[aoi_65_80_afternoon].mean() kt_prime_by_date = pd.Series(np.nan, index=data.index) kt_prime_by_date[zenith_lt_90_aoi_gte_90_morning] = kt_prime_am_avg kt_prime_by_date[zenith_lt_90_aoi_gte_90_afternoon] = kt_prime_pm_avg kt_prime_gte_90.append(kt_prime_by_date) kt_prime_gte_90 = pd.concat(kt_prime_gte_90) return kt_prime_gte_90
[docs]def erbs(ghi, zenith, datetime_or_doy, min_cos_zenith=0.065, max_zenith=87): r""" Estimate DNI and DHI from GHI using the Erbs model. The Erbs model [1]_ estimates the diffuse fraction DF from global horizontal irradiance through an empirical relationship between DF and the ratio of GHI to extraterrestrial irradiance, Kt. The function uses the diffuse fraction to compute DHI as .. math:: DHI = DF \times GHI DNI is then estimated as .. math:: DNI = (GHI - DHI)/\cos(Z) where Z is the zenith angle. Parameters ---------- ghi: numeric Global horizontal irradiance in W/m^2. zenith: numeric True (not refraction-corrected) zenith angles in decimal degrees. datetime_or_doy : int, float, array, pd.DatetimeIndex Day of year or array of days of year e.g. pd.DatetimeIndex.dayofyear, or pd.DatetimeIndex. min_cos_zenith : numeric, default 0.065 Minimum value of cos(zenith) to allow when calculating global clearness index `kt`. Equivalent to zenith = 86.273 degrees. max_zenith : numeric, default 87 Maximum value of zenith to allow in DNI calculation. DNI will be set to 0 for times with zenith values greater than `max_zenith`. Returns ------- data : OrderedDict or DataFrame Contains the following keys/columns: * ``dni``: the modeled direct normal irradiance in W/m^2. * ``dhi``: the modeled diffuse horizontal irradiance in W/m^2. * ``kt``: Ratio of global to extraterrestrial irradiance on a horizontal plane. References ---------- .. [1] D. G. Erbs, S. A. Klein and J. A. Duffie, Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation, Solar Energy 28(4), pp 293-302, 1982. Eq. 1 See also -------- dirint disc """ dni_extra = get_extra_radiation(datetime_or_doy) kt = clearness_index(ghi, zenith, dni_extra, min_cos_zenith=min_cos_zenith, max_clearness_index=1) # For Kt <= 0.22, set the diffuse fraction df = 1 - 0.09*kt # For Kt > 0.22 and Kt <= 0.8, set the diffuse fraction df = np.where((kt > 0.22) & (kt <= 0.8), 0.9511 - 0.1604*kt + 4.388*kt**2 - 16.638*kt**3 + 12.336*kt**4, df) # For Kt > 0.8, set the diffuse fraction df = np.where(kt > 0.8, 0.165, df) dhi = df * ghi dni = (ghi - dhi) / tools.cosd(zenith) bad_values = (zenith > max_zenith) | (ghi < 0) | (dni < 0) dni = np.where(bad_values, 0, dni) # ensure that closure relationship remains valid dhi = np.where(bad_values, ghi, dhi) data = OrderedDict() data['dni'] = dni data['dhi'] = dhi data['kt'] = kt if isinstance(datetime_or_doy, pd.DatetimeIndex): data = pd.DataFrame(data, index=datetime_or_doy) return data
[docs]def campbell_norman(zenith, transmittance, pressure=101325.0, dni_extra=1367.0): ''' Determine DNI, DHI, GHI from extraterrestrial flux, transmittance, and atmospheric pressure. Parameters ---------- zenith: pd.Series True (not refraction-corrected) zenith angles in decimal degrees. If Z is a vector it must be of the same size as all other vector inputs. Z must be >=0 and <=180. transmittance: float Atmospheric transmittance between 0 and 1. pressure: float, default 101325.0 Air pressure dni_extra: float, default 1367.0 Direct irradiance incident at the top of the atmosphere. Returns ------- irradiance: DataFrame Modeled direct normal irradiance, direct horizontal irradiance, and global horizontal irradiance in W/m^2 References ---------- .. [1] Campbell, G. S., J. M. Norman (1998) An Introduction to Environmental Biophysics. 2nd Ed. New York: Springer. ''' tau = transmittance airmass = atmosphere.get_relative_airmass(zenith, model='simple') airmass = atmosphere.get_absolute_airmass(airmass, pressure=pressure) dni = dni_extra*tau**airmass cos_zen = tools.cosd(zenith) dhi = 0.3 * (1.0 - tau**airmass) * dni_extra * cos_zen ghi = dhi + dni * cos_zen irrads = OrderedDict() irrads['ghi'] = ghi irrads['dni'] = dni irrads['dhi'] = dhi if isinstance(ghi, pd.Series): irrads = pd.DataFrame(irrads) return irrads
def _liujordan(zenith, transmittance, airmass, dni_extra=1367.0): ''' Determine DNI, DHI, GHI from extraterrestrial flux, transmittance, and optical air mass number. Liu and Jordan, 1960, developed a simplified direct radiation model. DHI is from an empirical equation for diffuse radiation from Liu and Jordan, 1960. Parameters ---------- zenith: pd.Series True (not refraction-corrected) zenith angles in decimal degrees. If Z is a vector it must be of the same size as all other vector inputs. Z must be >=0 and <=180. transmittance: float Atmospheric transmittance between 0 and 1. pressure: float, default 101325.0 Air pressure dni_extra: float, default 1367.0 Direct irradiance incident at the top of the atmosphere. Returns ------- irradiance: DataFrame Modeled direct normal irradiance, direct horizontal irradiance, and global horizontal irradiance in W/m^2 References ---------- .. [1] Campbell, G. S., J. M. Norman (1998) An Introduction to Environmental Biophysics. 2nd Ed. New York: Springer. .. [2] Liu, B. Y., R. C. Jordan, (1960). "The interrelationship and characteristic distribution of direct, diffuse, and total solar radiation". Solar Energy 4:1-19 ''' tau = transmittance dni = dni_extra*tau**airmass dhi = 0.3 * (1.0 - tau**airmass) * dni_extra * np.cos(np.radians(zenith)) ghi = dhi + dni * np.cos(np.radians(zenith)) irrads = OrderedDict() irrads['ghi'] = ghi irrads['dni'] = dni irrads['dhi'] = dhi if isinstance(ghi, pd.Series): irrads = pd.DataFrame(irrads) return irrads def _get_perez_coefficients(perezmodel): ''' Find coefficients for the Perez model Parameters ---------- perezmodel : string (optional, default='allsitescomposite1990') a character string which selects the desired set of Perez coefficients. If model is not provided as an input, the default, '1990' will be used. All possible model selections are: * '1990' * 'allsitescomposite1990' (same as '1990') * 'allsitescomposite1988' * 'sandiacomposite1988' * 'usacomposite1988' * 'france1988' * 'phoenix1988' * 'elmonte1988' * 'osage1988' * 'albuquerque1988' * 'capecanaveral1988' * 'albany1988' Returns -------- F1coeffs, F2coeffs : (array, array) F1 and F2 coefficients for the Perez model References ---------- .. [1] Loutzenhiser P.G. et. al. "Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation" 2007, Solar Energy vol. 81. pp. 254-267 .. [2] Perez, R., Seals, R., Ineichen, P., Stewart, R., Menicucci, D., 1987. A new simplified version of the Perez diffuse irradiance model for tilted surfaces. Solar Energy 39(3), 221-232. .. [3] Perez, R., Ineichen, P., Seals, R., Michalsky, J., Stewart, R., 1990. Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy 44 (5), 271-289. .. [4] Perez, R. et. al 1988. "The Development and Verification of the Perez Diffuse Radiation Model". SAND88-7030 ''' coeffdict = { 'allsitescomposite1990': [ [-0.0080, 0.5880, -0.0620, -0.0600, 0.0720, -0.0220], [0.1300, 0.6830, -0.1510, -0.0190, 0.0660, -0.0290], [0.3300, 0.4870, -0.2210, 0.0550, -0.0640, -0.0260], [0.5680, 0.1870, -0.2950, 0.1090, -0.1520, -0.0140], [0.8730, -0.3920, -0.3620, 0.2260, -0.4620, 0.0010], [1.1320, -1.2370, -0.4120, 0.2880, -0.8230, 0.0560], [1.0600, -1.6000, -0.3590, 0.2640, -1.1270, 0.1310], [0.6780, -0.3270, -0.2500, 0.1560, -1.3770, 0.2510]], 'allsitescomposite1988': [ [-0.0180, 0.7050, -0.071, -0.0580, 0.1020, -0.0260], [0.1910, 0.6450, -0.1710, 0.0120, 0.0090, -0.0270], [0.4400, 0.3780, -0.2560, 0.0870, -0.1040, -0.0250], [0.7560, -0.1210, -0.3460, 0.1790, -0.3210, -0.0080], [0.9960, -0.6450, -0.4050, 0.2600, -0.5900, 0.0170], [1.0980, -1.2900, -0.3930, 0.2690, -0.8320, 0.0750], [0.9730, -1.1350, -0.3780, 0.1240, -0.2580, 0.1490], [0.6890, -0.4120, -0.2730, 0.1990, -1.6750, 0.2370]], 'sandiacomposite1988': [ [-0.1960, 1.0840, -0.0060, -0.1140, 0.1800, -0.0190], [0.2360, 0.5190, -0.1800, -0.0110, 0.0200, -0.0380], [0.4540, 0.3210, -0.2550, 0.0720, -0.0980, -0.0460], [0.8660, -0.3810, -0.3750, 0.2030, -0.4030, -0.0490], [1.0260, -0.7110, -0.4260, 0.2730, -0.6020, -0.0610], [0.9780, -0.9860, -0.3500, 0.2800, -0.9150, -0.0240], [0.7480, -0.9130, -0.2360, 0.1730, -1.0450, 0.0650], [0.3180, -0.7570, 0.1030, 0.0620, -1.6980, 0.2360]], 'usacomposite1988': [ [-0.0340, 0.6710, -0.0590, -0.0590, 0.0860, -0.0280], [0.2550, 0.4740, -0.1910, 0.0180, -0.0140, -0.0330], [0.4270, 0.3490, -0.2450, 0.0930, -0.1210, -0.0390], [0.7560, -0.2130, -0.3280, 0.1750, -0.3040, -0.0270], [1.0200, -0.8570, -0.3850, 0.2800, -0.6380, -0.0190], [1.0500, -1.3440, -0.3480, 0.2800, -0.8930, 0.0370], [0.9740, -1.5070, -0.3700, 0.1540, -0.5680, 0.1090], [0.7440, -1.8170, -0.2560, 0.2460, -2.6180, 0.2300]], 'france1988': [ [0.0130, 0.7640, -0.1000, -0.0580, 0.1270, -0.0230], [0.0950, 0.9200, -0.1520, 0, 0.0510, -0.0200], [0.4640, 0.4210, -0.2800, 0.0640, -0.0510, -0.0020], [0.7590, -0.0090, -0.3730, 0.2010, -0.3820, 0.0100], [0.9760, -0.4000, -0.4360, 0.2710, -0.6380, 0.0510], [1.1760, -1.2540, -0.4620, 0.2950, -0.9750, 0.1290], [1.1060, -1.5630, -0.3980, 0.3010, -1.4420, 0.2120], [0.9340, -1.5010, -0.2710, 0.4200, -2.9170, 0.2490]], 'phoenix1988': [ [-0.0030, 0.7280, -0.0970, -0.0750, 0.1420, -0.0430], [0.2790, 0.3540, -0.1760, 0.0300, -0.0550, -0.0540], [0.4690, 0.1680, -0.2460, 0.0480, -0.0420, -0.0570], [0.8560, -0.5190, -0.3400, 0.1760, -0.3800, -0.0310], [0.9410, -0.6250, -0.3910, 0.1880, -0.3600, -0.0490], [1.0560, -1.1340, -0.4100, 0.2810, -0.7940, -0.0650], [0.9010, -2.1390, -0.2690, 0.1180, -0.6650, 0.0460], [0.1070, 0.4810, 0.1430, -0.1110, -0.1370, 0.2340]], 'elmonte1988': [ [0.0270, 0.7010, -0.1190, -0.0580, 0.1070, -0.0600], [0.1810, 0.6710, -0.1780, -0.0790, 0.1940, -0.0350], [0.4760, 0.4070, -0.2880, 0.0540, -0.0320, -0.0550], [0.8750, -0.2180, -0.4030, 0.1870, -0.3090, -0.0610], [1.1660, -1.0140, -0.4540, 0.2110, -0.4100, -0.0440], [1.1430, -2.0640, -0.2910, 0.0970, -0.3190, 0.0530], [1.0940, -2.6320, -0.2590, 0.0290, -0.4220, 0.1470], [0.1550, 1.7230, 0.1630, -0.1310, -0.0190, 0.2770]], 'osage1988': [ [-0.3530, 1.4740, 0.0570, -0.1750, 0.3120, 0.0090], [0.3630, 0.2180, -0.2120, 0.0190, -0.0340, -0.0590], [-0.0310, 1.2620, -0.0840, -0.0820, 0.2310, -0.0170], [0.6910, 0.0390, -0.2950, 0.0910, -0.1310, -0.0350], [1.1820, -1.3500, -0.3210, 0.4080, -0.9850, -0.0880], [0.7640, 0.0190, -0.2030, 0.2170, -0.2940, -0.1030], [0.2190, 1.4120, 0.2440, 0.4710, -2.9880, 0.0340], [3.5780, 22.2310, -10.7450, 2.4260, 4.8920, -5.6870]], 'albuquerque1988': [ [0.0340, 0.5010, -0.0940, -0.0630, 0.1060, -0.0440], [0.2290, 0.4670, -0.1560, -0.0050, -0.0190, -0.0230], [0.4860, 0.2410, -0.2530, 0.0530, -0.0640, -0.0220], [0.8740, -0.3930, -0.3970, 0.1810, -0.3270, -0.0370], [1.1930, -1.2960, -0.5010, 0.2810, -0.6560, -0.0450], [1.0560, -1.7580, -0.3740, 0.2260, -0.7590, 0.0340], [0.9010, -4.7830, -0.1090, 0.0630, -0.9700, 0.1960], [0.8510, -7.0550, -0.0530, 0.0600, -2.8330, 0.3300]], 'capecanaveral1988': [ [0.0750, 0.5330, -0.1240, -0.0670, 0.0420, -0.0200], [0.2950, 0.4970, -0.2180, -0.0080, 0.0030, -0.0290], [0.5140, 0.0810, -0.2610, 0.0750, -0.1600, -0.0290], [0.7470, -0.3290, -0.3250, 0.1810, -0.4160, -0.0300], [0.9010, -0.8830, -0.2970, 0.1780, -0.4890, 0.0080], [0.5910, -0.0440, -0.1160, 0.2350, -0.9990, 0.0980], [0.5370, -2.4020, 0.3200, 0.1690, -1.9710, 0.3100], [-0.8050, 4.5460, 1.0720, -0.2580, -0.9500, 0.7530]], 'albany1988': [ [0.0120, 0.5540, -0.0760, -0.0520, 0.0840, -0.0290], [0.2670, 0.4370, -0.1940, 0.0160, 0.0220, -0.0360], [0.4200, 0.3360, -0.2370, 0.0740, -0.0520, -0.0320], [0.6380, -0.0010, -0.2810, 0.1380, -0.1890, -0.0120], [1.0190, -1.0270, -0.3420, 0.2710, -0.6280, 0.0140], [1.1490, -1.9400, -0.3310, 0.3220, -1.0970, 0.0800], [1.4340, -3.9940, -0.4920, 0.4530, -2.3760, 0.1170], [1.0070, -2.2920, -0.4820, 0.3900, -3.3680, 0.2290]], } array = np.array(coeffdict[perezmodel]) F1coeffs = array[:, 0:3] F2coeffs = array[:, 3:7] return F1coeffs, F2coeffs def _get_dirint_coeffs(): """ A place to stash the dirint coefficients. Returns ------- np.array with shape ``(6, 6, 7, 5)``. Ordering is ``[kt_prime_bin, zenith_bin, delta_kt_prime_bin, w_bin]`` """ # To allow for maximum copy/paste from the MATLAB 1-indexed code, # we create and assign values to an oversized array. # Then, we return the [1:, 1:, :, :] slice. coeffs = np.zeros((7, 7, 7, 5)) coeffs[1, 1, :, :] = [ [0.385230, 0.385230, 0.385230, 0.462880, 0.317440], [0.338390, 0.338390, 0.221270, 0.316730, 0.503650], [0.235680, 0.235680, 0.241280, 0.157830, 0.269440], [0.830130, 0.830130, 0.171970, 0.841070, 0.457370], [0.548010, 0.548010, 0.478000, 0.966880, 1.036370], [0.548010, 0.548010, 1.000000, 3.012370, 1.976540], [0.582690, 0.582690, 0.229720, 0.892710, 0.569950]] coeffs[1, 2, :, :] = [ [0.131280, 0.131280, 0.385460, 0.511070, 0.127940], [0.223710, 0.223710, 0.193560, 0.304560, 0.193940], [0.229970, 0.229970, 0.275020, 0.312730, 0.244610], [0.090100, 0.184580, 0.260500, 0.687480, 0.579440], [0.131530, 0.131530, 0.370190, 1.380350, 1.052270], [1.116250, 1.116250, 0.928030, 3.525490, 2.316920], [0.090100, 0.237000, 0.300040, 0.812470, 0.664970]] coeffs[1, 3, :, :] = [ [0.587510, 0.130000, 0.400000, 0.537210, 0.832490], [0.306210, 0.129830, 0.204460, 0.500000, 0.681640], [0.224020, 0.260620, 0.334080, 0.501040, 0.350470], [0.421540, 0.753970, 0.750660, 3.706840, 0.983790], [0.706680, 0.373530, 1.245670, 0.864860, 1.992630], [4.864400, 0.117390, 0.265180, 0.359180, 3.310820], [0.392080, 0.493290, 0.651560, 1.932780, 0.898730]] coeffs[1, 4, :, :] = [ [0.126970, 0.126970, 0.126970, 0.126970, 0.126970], [0.810820, 0.810820, 0.810820, 0.810820, 0.810820], [3.241680, 2.500000, 2.291440, 2.291440, 2.291440], [4.000000, 3.000000, 2.000000, 0.975430, 1.965570], [12.494170, 12.494170, 8.000000, 5.083520, 8.792390], [21.744240, 21.744240, 21.744240, 21.744240, 21.744240], [3.241680, 12.494170, 1.620760, 1.375250, 2.331620]] coeffs[1, 5, :, :] = [ [0.126970, 0.126970, 0.126970, 0.126970, 0.126970], [0.810820, 0.810820, 0.810820, 0.810820, 0.810820], [3.241680, 2.500000, 2.291440, 2.291440, 2.291440], [4.000000, 3.000000, 2.000000, 0.975430, 1.965570], [12.494170, 12.494170, 8.000000, 5.083520, 8.792390], [21.744240, 21.744240, 21.744240, 21.744240, 21.744240], [3.241680, 12.494170, 1.620760, 1.375250, 2.331620]] coeffs[1, 6, :, :] = [ [0.126970, 0.126970, 0.126970, 0.126970, 0.126970], [0.810820, 0.810820, 0.810820, 0.810820, 0.810820], [3.241680, 2.500000, 2.291440, 2.291440, 2.291440], [4.000000, 3.000000, 2.000000, 0.975430, 1.965570], [12.494170, 12.494170, 8.000000, 5.083520, 8.792390], [21.744240, 21.744240, 21.744240, 21.744240, 21.744240], [3.241680, 12.494170, 1.620760, 1.375250, 2.331620]] coeffs[2, 1, :, :] = [ [0.337440, 0.337440, 0.969110, 1.097190, 1.116080], [0.337440, 0.337440, 0.969110, 1.116030, 0.623900], [0.337440, 0.337440, 1.530590, 1.024420, 0.908480], [0.584040, 0.584040, 0.847250, 0.914940, 1.289300], [0.337440, 0.337440, 0.310240, 1.435020, 1.852830], [0.337440, 0.337440, 1.015010, 1.097190, 2.117230], [0.337440, 0.337440, 0.969110, 1.145730, 1.476400]] coeffs[2, 2, :, :] = [ [0.300000, 0.300000, 0.700000, 1.100000, 0.796940], [0.219870, 0.219870, 0.526530, 0.809610, 0.649300], [0.386650, 0.386650, 0.119320, 0.576120, 0.685460], [0.746730, 0.399830, 0.470970, 0.986530, 0.785370], [0.575420, 0.936700, 1.649200, 1.495840, 1.335590], [1.319670, 4.002570, 1.276390, 2.644550, 2.518670], [0.665190, 0.678910, 1.012360, 1.199940, 0.986580]] coeffs[2, 3, :, :] = [ [0.378870, 0.974060, 0.500000, 0.491880, 0.665290], [0.105210, 0.263470, 0.407040, 0.553460, 0.582590], [0.312900, 0.345240, 1.144180, 0.854790, 0.612280], [0.119070, 0.365120, 0.560520, 0.793720, 0.802600], [0.781610, 0.837390, 1.270420, 1.537980, 1.292950], [1.152290, 1.152290, 1.492080, 1.245370, 2.177100], [0.424660, 0.529550, 0.966910, 1.033460, 0.958730]] coeffs[2, 4, :, :] = [ [0.310590, 0.714410, 0.252450, 0.500000, 0.607600], [0.975190, 0.363420, 0.500000, 0.400000, 0.502800], [0.175580, 0.196250, 0.476360, 1.072470, 0.490510], [0.719280, 0.698620, 0.657770, 1.190840, 0.681110], [0.426240, 1.464840, 0.678550, 1.157730, 0.978430], [2.501120, 1.789130, 1.387090, 2.394180, 2.394180], [0.491640, 0.677610, 0.685610, 1.082400, 0.735410]] coeffs[2, 5, :, :] = [ [0.597000, 0.500000, 0.300000, 0.310050, 0.413510], [0.314790, 0.336310, 0.400000, 0.400000, 0.442460], [0.166510, 0.460440, 0.552570, 1.000000, 0.461610], [0.401020, 0.559110, 0.403630, 1.016710, 0.671490], [0.400360, 0.750830, 0.842640, 1.802600, 1.023830], [3.315300, 1.510380, 2.443650, 1.638820, 2.133990], [0.530790, 0.745850, 0.693050, 1.458040, 0.804500]] coeffs[2, 6, :, :] = [ [0.597000, 0.500000, 0.300000, 0.310050, 0.800920], [0.314790, 0.336310, 0.400000, 0.400000, 0.237040], [0.166510, 0.460440, 0.552570, 1.000000, 0.581990], [0.401020, 0.559110, 0.403630, 1.016710, 0.898570], [0.400360, 0.750830, 0.842640, 1.802600, 3.400390], [3.315300, 1.510380, 2.443650, 1.638820, 2.508780], [0.204340, 1.157740, 2.003080, 2.622080, 1.409380]] coeffs[3, 1, :, :] = [ [1.242210, 1.242210, 1.242210, 1.242210, 1.242210], [0.056980, 0.056980, 0.656990, 0.656990, 0.925160], [0.089090, 0.089090, 1.040430, 1.232480, 1.205300], [1.053850, 1.053850, 1.399690, 1.084640, 1.233340], [1.151540, 1.151540, 1.118290, 1.531640, 1.411840], [1.494980, 1.494980, 1.700000, 1.800810, 1.671600], [1.018450, 1.018450, 1.153600, 1.321890, 1.294670]] coeffs[3, 2, :, :] = [ [0.700000, 0.700000, 1.023460, 0.700000, 0.945830], [0.886300, 0.886300, 1.333620, 0.800000, 1.066620], [0.902180, 0.902180, 0.954330, 1.126690, 1.097310], [1.095300, 1.075060, 1.176490, 1.139470, 1.096110], [1.201660, 1.201660, 1.438200, 1.256280, 1.198060], [1.525850, 1.525850, 1.869160, 1.985410, 1.911590], [1.288220, 1.082810, 1.286370, 1.166170, 1.119330]] coeffs[3, 3, :, :] = [ [0.600000, 1.029910, 0.859890, 0.550000, 0.813600], [0.604450, 1.029910, 0.859890, 0.656700, 0.928840], [0.455850, 0.750580, 0.804930, 0.823000, 0.911000], [0.526580, 0.932310, 0.908620, 0.983520, 0.988090], [1.036110, 1.100690, 0.848380, 1.035270, 1.042380], [1.048440, 1.652720, 0.900000, 2.350410, 1.082950], [0.817410, 0.976160, 0.861300, 0.974780, 1.004580]] coeffs[3, 4, :, :] = [ [0.782110, 0.564280, 0.600000, 0.600000, 0.665740], [0.894480, 0.680730, 0.541990, 0.800000, 0.669140], [0.487460, 0.818950, 0.841830, 0.872540, 0.709040], [0.709310, 0.872780, 0.908480, 0.953290, 0.844350], [0.863920, 0.947770, 0.876220, 1.078750, 0.936910], [1.280350, 0.866720, 0.769790, 1.078750, 0.975130], [0.725420, 0.869970, 0.868810, 0.951190, 0.829220]] coeffs[3, 5, :, :] = [ [0.791750, 0.654040, 0.483170, 0.409000, 0.597180], [0.566140, 0.948990, 0.971820, 0.653570, 0.718550], [0.648710, 0.637730, 0.870510, 0.860600, 0.694300], [0.637630, 0.767610, 0.925670, 0.990310, 0.847670], [0.736380, 0.946060, 1.117590, 1.029340, 0.947020], [1.180970, 0.850000, 1.050000, 0.950000, 0.888580], [0.700560, 0.801440, 0.961970, 0.906140, 0.823880]] coeffs[3, 6, :, :] = [ [0.500000, 0.500000, 0.586770, 0.470550, 0.629790], [0.500000, 0.500000, 1.056220, 1.260140, 0.658140], [0.500000, 0.500000, 0.631830, 0.842620, 0.582780], [0.554710, 0.734730, 0.985820, 0.915640, 0.898260], [0.712510, 1.205990, 0.909510, 1.078260, 0.885610], [1.899260, 1.559710, 1.000000, 1.150000, 1.120390], [0.653880, 0.793120, 0.903320, 0.944070, 0.796130]] coeffs[4, 1, :, :] = [ [1.000000, 1.000000, 1.050000, 1.170380, 1.178090], [0.960580, 0.960580, 1.059530, 1.179030, 1.131690], [0.871470, 0.871470, 0.995860, 1.141910, 1.114600], [1.201590, 1.201590, 0.993610, 1.109380, 1.126320], [1.065010, 1.065010, 0.828660, 0.939970, 1.017930], [1.065010, 1.065010, 0.623690, 1.119620, 1.132260], [1.071570, 1.071570, 0.958070, 1.114130, 1.127110]] coeffs[4, 2, :, :] = [ [0.950000, 0.973390, 0.852520, 1.092200, 1.096590], [0.804120, 0.913870, 0.980990, 1.094580, 1.042420], [0.737540, 0.935970, 0.999940, 1.056490, 1.050060], [1.032980, 1.034540, 0.968460, 1.032080, 1.015780], [0.900000, 0.977210, 0.945960, 1.008840, 0.969960], [0.600000, 0.750000, 0.750000, 0.844710, 0.899100], [0.926800, 0.965030, 0.968520, 1.044910, 1.032310]] coeffs[4, 3, :, :] = [ [0.850000, 1.029710, 0.961100, 1.055670, 1.009700], [0.818530, 0.960010, 0.996450, 1.081970, 1.036470], [0.765380, 0.953500, 0.948260, 1.052110, 1.000140], [0.775610, 0.909610, 0.927800, 0.987800, 0.952100], [1.000990, 0.881880, 0.875950, 0.949100, 0.893690], [0.902370, 0.875960, 0.807990, 0.942410, 0.917920], [0.856580, 0.928270, 0.946820, 1.032260, 0.972990]] coeffs[4, 4, :, :] = [ [0.750000, 0.857930, 0.983800, 1.056540, 0.980240], [0.750000, 0.987010, 1.013730, 1.133780, 1.038250], [0.800000, 0.947380, 1.012380, 1.091270, 0.999840], [0.800000, 0.914550, 0.908570, 0.999190, 0.915230], [0.778540, 0.800590, 0.799070, 0.902180, 0.851560], [0.680190, 0.317410, 0.507680, 0.388910, 0.646710], [0.794920, 0.912780, 0.960830, 1.057110, 0.947950]] coeffs[4, 5, :, :] = [ [0.750000, 0.833890, 0.867530, 1.059890, 0.932840], [0.979700, 0.971470, 0.995510, 1.068490, 1.030150], [0.858850, 0.987920, 1.043220, 1.108700, 1.044900], [0.802400, 0.955110, 0.911660, 1.045070, 0.944470], [0.884890, 0.766210, 0.885390, 0.859070, 0.818190], [0.615680, 0.700000, 0.850000, 0.624620, 0.669300], [0.835570, 0.946150, 0.977090, 1.049350, 0.979970]] coeffs[4, 6, :, :] = [ [0.689220, 0.809600, 0.900000, 0.789500, 0.853990], [0.854660, 0.852840, 0.938200, 0.923110, 0.955010], [0.938600, 0.932980, 1.010390, 1.043950, 1.041640], [0.843620, 0.981300, 0.951590, 0.946100, 0.966330], [0.694740, 0.814690, 0.572650, 0.400000, 0.726830], [0.211370, 0.671780, 0.416340, 0.297290, 0.498050], [0.843540, 0.882330, 0.911760, 0.898420, 0.960210]] coeffs[5, 1, :, :] = [ [1.054880, 1.075210, 1.068460, 1.153370, 1.069220], [1.000000, 1.062220, 1.013470, 1.088170, 1.046200], [0.885090, 0.993530, 0.942590, 1.054990, 1.012740], [0.920000, 0.950000, 0.978720, 1.020280, 0.984440], [0.850000, 0.908500, 0.839940, 0.985570, 0.962180], [0.800000, 0.800000, 0.810080, 0.950000, 0.961550], [1.038590, 1.063200, 1.034440, 1.112780, 1.037800]] coeffs[5, 2, :, :] = [ [1.017610, 1.028360, 1.058960, 1.133180, 1.045620], [0.920000, 0.998970, 1.033590, 1.089030, 1.022060], [0.912370, 0.949930, 0.979770, 1.020420, 0.981770], [0.847160, 0.935300, 0.930540, 0.955050, 0.946560], [0.880260, 0.867110, 0.874130, 0.972650, 0.883420], [0.627150, 0.627150, 0.700000, 0.774070, 0.845130], [0.973700, 1.006240, 1.026190, 1.071960, 1.017240]] coeffs[5, 3, :, :] = [ [1.028710, 1.017570, 1.025900, 1.081790, 1.024240], [0.924980, 0.985500, 1.014100, 1.092210, 0.999610], [0.828570, 0.934920, 0.994950, 1.024590, 0.949710], [0.900810, 0.901330, 0.928830, 0.979570, 0.913100], [0.761030, 0.845150, 0.805360, 0.936790, 0.853460], [0.626400, 0.546750, 0.730500, 0.850000, 0.689050], [0.957630, 0.985480, 0.991790, 1.050220, 0.987900]] coeffs[5, 4, :, :] = [ [0.992730, 0.993880, 1.017150, 1.059120, 1.017450], [0.975610, 0.987160, 1.026820, 1.075440, 1.007250], [0.871090, 0.933190, 0.974690, 0.979840, 0.952730], [0.828750, 0.868090, 0.834920, 0.905510, 0.871530], [0.781540, 0.782470, 0.767910, 0.764140, 0.795890], [0.743460, 0.693390, 0.514870, 0.630150, 0.715660], [0.934760, 0.957870, 0.959640, 0.972510, 0.981640]] coeffs[5, 5, :, :] = [ [0.965840, 0.941240, 0.987100, 1.022540, 1.011160], [0.988630, 0.994770, 0.976590, 0.950000, 1.034840], [0.958200, 1.018080, 0.974480, 0.920000, 0.989870], [0.811720, 0.869090, 0.812020, 0.850000, 0.821050], [0.682030, 0.679480, 0.632450, 0.746580, 0.738550], [0.668290, 0.445860, 0.500000, 0.678920, 0.696510], [0.926940, 0.953350, 0.959050, 0.876210, 0.991490]] coeffs[5, 6, :, :] = [ [0.948940, 0.997760, 0.850000, 0.826520, 0.998470], [1.017860, 0.970000, 0.850000, 0.700000, 0.988560], [1.000000, 0.950000, 0.850000, 0.606240, 0.947260], [1.000000, 0.746140, 0.751740, 0.598390, 0.725230], [0.922210, 0.500000, 0.376800, 0.517110, 0.548630], [0.500000, 0.450000, 0.429970, 0.404490, 0.539940], [0.960430, 0.881630, 0.775640, 0.596350, 0.937680]] coeffs[6, 1, :, :] = [ [1.030000, 1.040000, 1.000000, 1.000000, 1.049510], [1.050000, 0.990000, 0.990000, 0.950000, 0.996530], [1.050000, 0.990000, 0.990000, 0.820000, 0.971940], [1.050000, 0.790000, 0.880000, 0.820000, 0.951840], [1.000000, 0.530000, 0.440000, 0.710000, 0.928730], [0.540000, 0.470000, 0.500000, 0.550000, 0.773950], [1.038270, 0.920180, 0.910930, 0.821140, 1.034560]] coeffs[6, 2, :, :] = [ [1.041020, 0.997520, 0.961600, 1.000000, 1.035780], [0.948030, 0.980000, 0.900000, 0.950360, 0.977460], [0.950000, 0.977250, 0.869270, 0.800000, 0.951680], [0.951870, 0.850000, 0.748770, 0.700000, 0.883850], [0.900000, 0.823190, 0.727450, 0.600000, 0.839870], [0.850000, 0.805020, 0.692310, 0.500000, 0.788410], [1.010090, 0.895270, 0.773030, 0.816280, 1.011680]] coeffs[6, 3, :, :] = [ [1.022450, 1.004600, 0.983650, 1.000000, 1.032940], [0.943960, 0.999240, 0.983920, 0.905990, 0.978150], [0.936240, 0.946480, 0.850000, 0.850000, 0.930320], [0.816420, 0.885000, 0.644950, 0.817650, 0.865310], [0.742960, 0.765690, 0.561520, 0.700000, 0.827140], [0.643870, 0.596710, 0.474460, 0.600000, 0.651200], [0.971740, 0.940560, 0.714880, 0.864380, 1.001650]] coeffs[6, 4, :, :] = [ [0.995260, 0.977010, 1.000000, 1.000000, 1.035250], [0.939810, 0.975250, 0.939980, 0.950000, 0.982550], [0.876870, 0.879440, 0.850000, 0.900000, 0.917810], [0.873480, 0.873450, 0.751470, 0.850000, 0.863040], [0.761470, 0.702360, 0.638770, 0.750000, 0.783120], [0.734080, 0.650000, 0.600000, 0.650000, 0.715660], [0.942160, 0.919100, 0.770340, 0.731170, 0.995180]] coeffs[6, 5, :, :] = [ [0.952560, 0.916780, 0.920000, 0.900000, 1.005880], [0.928620, 0.994420, 0.900000, 0.900000, 0.983720], [0.913070, 0.850000, 0.850000, 0.800000, 0.924280], [0.868090, 0.807170, 0.823550, 0.600000, 0.844520], [0.769570, 0.719870, 0.650000, 0.550000, 0.733500], [0.580250, 0.650000, 0.600000, 0.500000, 0.628850], [0.904770, 0.852650, 0.708370, 0.493730, 0.949030]] coeffs[6, 6, :, :] = [ [0.911970, 0.800000, 0.800000, 0.800000, 0.956320], [0.912620, 0.682610, 0.750000, 0.700000, 0.950110], [0.653450, 0.659330, 0.700000, 0.600000, 0.856110], [0.648440, 0.600000, 0.641120, 0.500000, 0.695780], [0.570000, 0.550000, 0.598800, 0.400000, 0.560150], [0.475230, 0.500000, 0.518640, 0.339970, 0.520230], [0.743440, 0.592190, 0.603060, 0.316930, 0.794390]] return coeffs[1:, 1:, :, :]
[docs]def dni(ghi, dhi, zenith, clearsky_dni=None, clearsky_tolerance=1.1, zenith_threshold_for_zero_dni=88.0, zenith_threshold_for_clearsky_limit=80.0): """ Determine DNI from GHI and DHI. When calculating the DNI from GHI and DHI the calculated DNI may be unreasonably high or negative for zenith angles close to 90 degrees (sunrise/sunset transitions). This function identifies unreasonable DNI values and sets them to NaN. If the clearsky DNI is given unreasonably high values are cut off. Parameters ---------- ghi : Series Global horizontal irradiance. dhi : Series Diffuse horizontal irradiance. zenith : Series True (not refraction-corrected) zenith angles in decimal degrees. Angles must be >=0 and <=180. clearsky_dni : None or Series, default None Clearsky direct normal irradiance. clearsky_tolerance : float, default 1.1 If 'clearsky_dni' is given this parameter can be used to allow a tolerance by how much the calculated DNI value can be greater than the clearsky value before it is identified as an unreasonable value. zenith_threshold_for_zero_dni : float, default 88.0 Non-zero DNI values for zenith angles greater than or equal to 'zenith_threshold_for_zero_dni' will be set to NaN. zenith_threshold_for_clearsky_limit : float, default 80.0 DNI values for zenith angles greater than or equal to 'zenith_threshold_for_clearsky_limit' and smaller the 'zenith_threshold_for_zero_dni' that are greater than the clearsky DNI (times allowed tolerance) will be corrected. Only applies if 'clearsky_dni' is not None. Returns ------- dni : Series The modeled direct normal irradiance. """ # calculate DNI dni = (ghi - dhi) / tools.cosd(zenith) # cutoff negative values dni[dni < 0] = float('nan') # set non-zero DNI values for zenith angles >= # zenith_threshold_for_zero_dni to NaN dni[(zenith >= zenith_threshold_for_zero_dni) & (dni != 0)] = float('nan') # correct DNI values for zenith angles greater or equal to the # zenith_threshold_for_clearsky_limit and smaller than the # upper_cutoff_zenith that are greater than the clearsky DNI (times # clearsky_tolerance) if clearsky_dni is not None: max_dni = clearsky_dni * clearsky_tolerance dni[(zenith >= zenith_threshold_for_clearsky_limit) & (zenith < zenith_threshold_for_zero_dni) & (dni > max_dni)] = max_dni return dni