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pvl_klucher1979.m
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pvl_klucher1979.m
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function SkyDiffuse = pvl_klucher1979(SurfTilt, SurfAz, DHI, GHI, SunZen, SunAz)
% PVL_KLUCHER1979 Determine diffuse irradiance from the sky on a tilted surface using Klucher's 1979 model
%
% Syntax
% SkyDiffuse = pvl_klucher1979(SurfTilt, SurfAz, DHI, GHI, SunZen, SunAz)
%
% Description
% 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.
%
% 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. Values of DHI which are < GHI will be set to GHI.
% GHI - a scalar or vector of global horizontal irradiance in W/m^2. If GHI
% is a vector it must be of the same size as all other vector inputs.
% GHI 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 Klucher model as given in
% Loutzenhiser et. al (2007) equation 4.
% 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] Klucher, T.M., 1979. Evaluation of models to predict insolation on tilted
% surfaces. Solar Energy 23 (2), 111–114.
%
% See also PVL_EPHEMERIS PVL_EXTRARADIATION PVL_ISOTROPICSKY
% PVL_HAYDAVIES1980 PVL_PEREZ PVL_REINDL1990 PVL_KINGDIFFUSE
%
%
%
%
p = inputParser;
p.addRequired('SurfTilt', @(x) all(isnumeric(x) & x<=180 & x>=0 & isvector(x)));
p.addRequired('SurfAz', @(x) all(isnumeric(x) & x<=360 & x>=0 & isvector(x)));
p.addRequired('DHI', @(x) all(isnumeric(x) & isvector(x) & x>=0));
p.addRequired('GHI', @(x) all(isnumeric(x) & isvector(x) & x>=0));
p.addRequired('SunZen', @(x) all(isnumeric(x) & x<=180 & x>=0 & isvector(x)));
p.addRequired('SunAz', @(x) all(isnumeric(x) & x<=360 & x>=0 & isvector(x)));
p.parse(SurfTilt, SurfAz, DHI, GHI, SunZen, SunAz);
GHI(GHI<DHI) = DHI(GHI<DHI); %Global horizontal should be >= Diffuse horizontal
GHI(GHI < 1E-6) = 1E-6; % Prevent division by 0
% 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 is cos(angle between sun vector and array normal)
COSTT = cosd(SurfTilt).*cosd(SunZen) + sind(SurfTilt).* ...
sind(SunZen).*cosd(SunAz-SurfAz);
% Aug 2018: Restrict COSTT>=0, so that circumsolar irradiance is not added
% to total sky diffuse when the sun is behind the array
COSTT(COSTT<0) = 0.0;
F = 1 - ((DHI./GHI).^2);
SkyDiffuse = DHI ...
.* (0.5 .* (1 + cosd(SurfTilt))) ...
.* (1 + F .* ((sind(SurfTilt ./ 2)).^3)) ...
.* (1 + F .* ((COSTT).^2) .* ((sind(SunZen)).^3));
SkyDiffuse = SkyDiffuse(:); % Make the column vector, regardless of input vector type