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pvl_haydavies1980.m
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pvl_haydavies1980.m
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function SkyDiffuse = pvl_haydavies1980(SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz)
% PVL_HAYDAVIES1980 Determine diffuse irradiance from the sky on a tilted surface using Hay & Davies' 1980 model
%
% Syntax
% SkyDiffuse = pvl_haydavies1980(SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz)
%
% Description
% 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.
%
% Inputs:
% SurfTilt - a scalar or vector of surface tilt angles in decimal degrees.
% If SurfTilt is a vector it must be of the same size as all other vector
% inputs. SurfTilt must be >=0 and <=180. The tilt angle is defined as
% degrees from horizontal (e.g. surface facing up = 0, surface facing
% horizon = 90)
% SurfAz - a scalar or vector of surface azimuth angles in decimal degrees.
% If SurfAz is a vector it must be of the same size as all other vector
% inputs. SurfAz must be >=0 and <=360. The Azimuth convention is defined
% as degrees east of north (e.g. North = 0, East = 90, West = 270).
% DHI - a scalar or vector of diffuse horizontal irradiance in W/m^2. If DHI
% is a vector it must be of the same size as all other vector inputs.
% DHI must be >=0.
% DNI - a scalar or vector of direct normal irradiance in W/m^2. If DNI
% is a vector it must be of the same size as all other vector inputs.
% DNI must be >=0.
% HExtra - a scalar or vector of extraterrestrial normal irradiance in
% W/m^2. If HExtra is a vector it must be of the same size as
% all other vector inputs. HExtra must be >=0.
% SunZen - a scalar or vector of apparent (refraction-corrected) zenith
% angles in decimal degrees. If SunZen is a vector it must be of the
% same size as all other vector inputs. SunZen must be >=0 and <=180.
% SunAz - a scalar or vector of sun azimuth angles in decimal degrees.
% If SunAz is a vector it must be of the same size as all other vector
% inputs. SunAz must be >=0 and <=360. The Azimuth convention is defined
% as degrees east of north (e.g. North = 0, East = 90, West = 270).
%
% Output:
% SkyDiffuse - the diffuse component of the solar radiation on an
% arbitrarily tilted surface defined by the Hay & Davies model as given in
% Loutzenhiser et. al (2007) equation 7.
% SkyDiffuse is the diffuse component ONLY and does not include the ground
% reflected irradiance or the irradiance due to the beam.
% SkyDiffuse is a column vector vector with a number of elements equal to
% the input vector(s).
%
% 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.
%
% See also PVL_EPHEMERIS PVL_EXTRARADIATION PVL_ISOTROPICSKY
% PVL_REINDL1990 PVL_PEREZ PVL_KLUCHER1979 PVL_KINGDIFFUSE
% PVL_SPA
%
%
%
%
p=inputParser;
p.addRequired('SurfTilt', @(x) (isnumeric(x) && all(x<=180) && all(x>=0) && isvector(x)));
p.addRequired('SurfAz', @(x) isnumeric(x) && all(x<=360) && all(x>=0) && isvector(x));
p.addRequired('DHI', @(x) (isnumeric(x) && isvector(x) && all((x>=0) | isnan(x))));
p.addRequired('DNI', @(x) isnumeric(x) && isvector(x) && all((x>=0) | isnan(x)));
p.addRequired('HExtra', @(x) isnumeric(x) && isvector(x) && all((x>=0) | isnan(x)));
p.addRequired('SunZen', @(x) isnumeric(x) && all(x<=180) && all((x>=0) | isnan(x)) && isvector(x));
p.addRequired('SunAz', @(x) (isnumeric(x) && all(x<=360) && all((x>=0) | isnan(x)) && isvector(x)));
p.parse(SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz);
%COSTT is the cosine of the angle of incidence between beam of the sun
%(defined by SunAz and SunZen)and the normal vector to a surface (defined
% by SurfAz and SurfTilt).
%
% Dec 2012: A bug was identified by Rob Andrews (Queens University) in this equation in PV_LIB
% Version 1.0. Fixed in Version 1.1.
COSTT = cosd(SurfTilt).*cosd(SunZen) + sind(SurfTilt).* ...
sind(SunZen).*cosd(SunAz-SurfAz);
% RB is the ratio of the beam irradiance on the tilted surface to the beam
% irradiance on a horizontal surface, the denominator is set to a minimum
% of 0.01745 corresponding to a zenith angle of 89 degrees
RB = max(COSTT,0)./max(cosd(SunZen),0.01745);
% AI is the Anisotropy index which represents the transmittance through
% atmosphere for beam radiation
AI = DNI./HExtra;
% This is the POAskydiffuse calculation I generated from the Loutzenhiser et al.
% (2007) paper, equation 7. 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 7.
SkyDiffuse = DHI .* (AI .* RB + (1-AI) .* 0.5 .* (1 + cosd(SurfTilt)));
SkyDiffuse = SkyDiffuse(:);
end