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pvl_perez.m
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function [SkyDiffuse,SkyDiffuse_Iso,SkyDiffuse_Cir,SkyDiffuse_Hor] = pvl_perez(SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz, AM, varargin)
% PVL_PEREZ Determine diffuse irradiance from the sky on a tilted surface using the Perez model
%
% Syntax
% [SkyDiffuse,SkyDiffuse_Iso,SkyDiffuse_Cir,SkyDiffuse_Hor] = pvl_perez(SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz, AM)
% [SkyDiffuse,SkyDiffuse_Iso,SkyDiffuse_Cir,SkyDiffuse_Hor] = pvl_perez(SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz, AM, model)
%
% Description
% The Perez model [3] determines the sky diffuse irradiance 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. An optional selector may be used to specify
% any of Perez's model coefficient sets.
%
% 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).
% AM - a scalar or vector of relative (not pressure-corrected) airmass
% values. If AM is a vector it must be of the same size as all other
% vector inputs. AM must be >=0 (careful using the 1/sec(z) model of AM
% generation).
% model - 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', or 'albany1988'
%
% Output:
% SkyDiffuse - the total diffuse component of the solar radiation on an
% arbitrarily tilted surface defined by the Perez model as given in
% reference [3].
% 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).
% User is warned if calculated SkyDiffuse is negative or greater than
% extraterrestrial radiation; all outputs are NaN for unreasonable
% calculated SkyDiffuse.
% SkyDiffuse_Iso - the isotropic diffuse component of the solar radiation on an
% arbitrarily tilted surface defined by the Perez model as given in
% reference [3].
% SkyDiffuse_Iso is the isotropic 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).
% SkyDiffuse_Cir - the circumsolar diffuse component of the solar radiation on an
% arbitrarily tilted surface defined by the Perez model as given in
% reference [3].
% SkyDiffuse_Cir is the circumsolar 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).
% SkyDiffuse_Hor - the horizon brightening diffuse component of the solar radiation on an
% arbitrarily tilted surface defined by the Perez model as given in
% reference [3].
% SkyDiffuse_Cir is the horizon brightening 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., 2007. Empirical validation of models to compute
% solar irradiance on inclined surfaces for building energy simulation,
% 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, Sandia National
% Laboratories.
%
% See also PVL_EPHEMERIS PVL_EXTRARADIATION PVL_ISOTROPICSKY
% PVL_HAYDAVIES1980 PVL_REINDL1990 PVL_KLUCHER1979 PVL_KINGDIFFUSE
% PVL_RELATIVEAIRMASS
%
% Notes: pvl_perez original code by Sandia National Laboratories. Extension
% of pvl_perez to output components of sky diffuse irradiance, i.e.,
% circumsolar, horizon brightening and rest-of-sky, contributed by Xingshu
% Sun of Purdue University, 2018.
%
%
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.addRequired('AM', @(x) (all(((isnumeric(x) & x>=0) | isnan(x))) & isvector(x)));
p.addOptional('model', '1990', @(x) ischar(x));
p.parse(SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz, AM, varargin{:});
model = p.Results.model;
SurfTilt = p.Results.SurfTilt(:);
SurfAz = p.Results.SurfAz(:);
DHI = p.Results.DHI(:);
DNI = p.Results.DNI(:);
HExtra = p.Results.HExtra(:);
SunZen = p.Results.SunZen(:);
SunAz = p.Results.SunAz(:);
AM = p.Results.AM(:);
VectorSizes = [numel(SurfTilt), numel(SurfAz), numel(DHI), numel(DNI), ...
numel(HExtra), numel(SunZen), numel(SunAz), numel(AM)];
MaxVectorSize = max(VectorSizes);
if not(all((VectorSizes==MaxVectorSize) | (VectorSizes==1)))
error(['Input parameters SurfTilt, SurfAz, DHI, DNI, HExtra, SunZen, SunAz, and AM'...
' must either be scalars or vectors of the same length.']);
end
% If any input variable is not a scalar, then make any scalar input values
% into a column vector of the correct size.
if MaxVectorSize >1
if VectorSizes(1) < MaxVectorSize
SurfTilt = SurfTilt.*ones(MaxVectorSize , 1);
end
if VectorSizes(2) < MaxVectorSize
SurfAz = SurfAz.*ones(MaxVectorSize, 1);
end
if VectorSizes(3) < MaxVectorSize
DHI = DHI.*ones(MaxVectorSize, 1);
end
if VectorSizes(4) < MaxVectorSize
DNI = DNI.*ones(MaxVectorSize , 1);
end
if VectorSizes(5) < MaxVectorSize
HExtra = HExtra.*ones(MaxVectorSize, 1);
end
if VectorSizes(6) < MaxVectorSize
SunZen = SunZen.*ones(MaxVectorSize, 1);
end
if VectorSizes(7) < MaxVectorSize
SunAz = SunAz.*ones(MaxVectorSize, 1);
end
if VectorSizes(8) < MaxVectorSize
AM = AM.*ones(MaxVectorSize, 1);
end
end
kappa = 1.041; %for SunZen in radians
z = SunZen*pi/180; % convert to radians
e = zeros(length(DHI),1);
Dhfilter = DHI > 0;
e(Dhfilter) = ((DHI(Dhfilter) + DNI(Dhfilter))./DHI(Dhfilter) + kappa.*z(Dhfilter).^3)./(1+kappa.*z(Dhfilter).^3);
ebin = zeros(numel(DHI),1);
% Select which bin e falls into
ebin((e>=1) & (e<1.065)) = 1;
ebin((e>=1.065) & (e<1.23)) = 2;
ebin((e>=1.23) & (e<1.5)) = 3;
ebin((e>=1.5) & (e<1.95)) = 4;
ebin((e>=1.95) & (e<2.8)) = 5;
ebin((e>=2.8) & (e<4.5)) = 6;
ebin((e>=4.5) & (e<6.2)) = 7;
ebin(e>=6.2) = 8;
% This is added because in cases where the sun is below the horizon
% (SunZen > 90) but there is still diffuse horizontal light (DHI>0), it is
% possible that the airmass (AM) could be NaN, which messes up later
% calculations. Instead, if the sun is down, and there is still DHI, we set
% the airmass to the airmass value on the horizon (approximately 37-38).
AM(SunZen >=90 & DHI >0) = 37;
del = DHI.*AM./HExtra;
ebinfilter = ebin > 0;
% The various possible sets of Perez coefficients are contained
% in a subfunction to clean up the code.
[F1c,F2c] = GetPerezCoefficients(model);
F11 = zeros(numel(DHI),1);
F12 = zeros(numel(DHI),1);
F13 = zeros(numel(DHI),1);
F11(ebinfilter) = F1c(ebin(ebinfilter),1);
F12(ebinfilter) = F1c(ebin(ebinfilter),2);
F13(ebinfilter) = F1c(ebin(ebinfilter),3);
F1 = zeros(numel(DHI),1);
F1(ebinfilter)= F11(ebinfilter) + F12(ebinfilter).*del(ebinfilter) + F13(ebinfilter).*z(ebinfilter);
F1(F1<0)=0;
F21 = zeros(numel(DHI),1);
F22 = zeros(numel(DHI),1);
F23 = zeros(numel(DHI),1);
F21(ebinfilter) = F2c(ebin(ebinfilter),1);
F22(ebinfilter) = F2c(ebin(ebinfilter),2);
F23(ebinfilter) = F2c(ebin(ebinfilter),3);
F2 = zeros(length(DHI),1);
F2(ebinfilter) = F21(ebinfilter) + F22(ebinfilter).*del(ebinfilter) + F23(ebinfilter).*z(ebinfilter);
%
% 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.
A = cosd(SurfTilt).*cosd(SunZen) + sind(SurfTilt).*sind(SunZen).*...
cosd(SunAz-SurfAz);
A(A < 0) = 0;
B = cosd(SunZen);
B(B < cosd(85)) = cosd(85);
%Calculate Diffuse POA from sky dome
SkyDiffuse = zeros(length(DHI),1);
% 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.
SkyDiffuse(ebinfilter) = DHI(ebinfilter).* ...
(0.5.* (1-F1(ebinfilter)).*(1+cosd(SurfTilt(ebinfilter))) +...
F1(ebinfilter) .* A(ebinfilter)./ B(ebinfilter) + F2(ebinfilter).* sind(SurfTilt(ebinfilter)));
SkyDiffuse_Iso(ebinfilter) = DHI(ebinfilter).*(0.5.* (1-F1(ebinfilter)).*(1+cosd(SurfTilt(ebinfilter))));
SkyDiffuse_Cir(ebinfilter) = DHI(ebinfilter).*F1(ebinfilter) .* A(ebinfilter)./ B(ebinfilter);
SkyDiffuse_Hor(ebinfilter) = DHI(ebinfilter).*F2(ebinfilter).* sind(SurfTilt(ebinfilter));
% SkyDiffuse(ebinfilter) = DHI(ebinfilter).* 0.5.* (1-F1(ebinfilter)).*(1+cosd(SurfTilt)) +...
% F1(ebinfilter) .* A(ebinfilter)./ B(ebinfilter) + F2(ebinfilter).* sind(SurfTilt);
% con = (SkyDiffuse <= 0);
% SkyDiffuse(con) = 0;
% SkyDiffuse_Iso(con) = 0;
% SkyDiffuse_Cir(con) = 0;
% SkyDiffuse_Hor(con) = 0;
% screen invalid SkyDiffuse and warn user
idx = SkyDiffuse < 0 | SkyDiffuse > max(HExtra);
if any(idx)
SkyDiffuse(idx) = NaN;
SkyDiffuse_Iso(idx) = NaN;
SkyDiffuse_Cir(idx) = NaN;
SkyDiffuse_Hor(idx) = NaN;
warning('NaNs returned for SkyDiffuse < 0 or > max(HExtra).');
end
SkyDiffuse = SkyDiffuse(:);
SkyDiffuse_Iso = SkyDiffuse_Iso(:);
SkyDiffuse_Cir = SkyDiffuse_Cir(:);
SkyDiffuse_Hor = SkyDiffuse_Hor(:);
end
function [F1coeffs,F2coeffs] = GetPerezCoefficients(perezmodel)
switch lower(perezmodel)
case{'allsitescomposite1990','1990'}
PerezCoeffs = ...
[-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];
case{'allsitescomposite1988'}
PerezCoeffs = ...
[-0.0180 0.7050 -0.0710 -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];
case{'sandiacomposite1988'}
PerezCoeffs = ...
[-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];
case{'usacomposite1988'}
PerezCoeffs = ...
[-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];
case{'france1988'}
PerezCoeffs = ...
[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];
case{'phoenix1988'}
PerezCoeffs = ...
[-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];
case{'elmonte1988'}
PerezCoeffs = ...
[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];
case{'osage1988'}
PerezCoeffs = ...
[-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];
case{'albuquerque1988'}
PerezCoeffs = ...
[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];
case{'capecanaveral1988'}
PerezCoeffs = ...
[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];
case{'albany1988'}
PerezCoeffs = ...
[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];
otherwise
error('Incorrect coefficient set name entered for Perez radiation model')
end
F1coeffs = PerezCoeffs(:,1:3);
F2coeffs = PerezCoeffs(:,4:6);
end