pvl_reindl_2

Estimate Direct Normal Irradiance from Global Horizontal Irradiance using the REINDL_2 model

Contents

Syntax

DNI = pvl_reindl_2(GHI,Z, doy)

Description

The Reindl-2 model estimates the diffuse fraction DF from global horizontal irradiance through an empirical relationship between DF, the ratio of GHI to extraterrestrial irradiance, Kt, and the true solar zenith angle, Z. pvl_reindl_1 uses the diffuse fraction to compute DHI as

$$DHI = DF \times GHI $$

and direct normal irradiance (DNI) is computed as

$$DNI = {\frac{ GHI - DHI }{ \cos\left(Z \right) }} $$

where $Z$ is the true solar zenith angle.

Inputs

Outputs

Example

This example compares DHI for August 6 from the TMY3 file for Albuquerque, NM, with DHI estimated from GHI from the TMY3 file, using the Reindl-1 model.

TMYData = pvl_readtmy3('723650TY.csv');
TimeMatlab = TMYData.DateNumber;
Time = pvl_maketimestruct(TimeMatlab, ones(size(TimeMatlab))*TMYData.SiteTimeZone);
dayofyear = pvl_date2doy(Time.year, Time.month, Time.day);
DNI = TMYData.DNI; % Read in for comparison with results
DHI = TMYData.DHI; % Read in for comparison with results
GHI = TMYData.GHI;
Location = pvl_makelocationstruct(TMYData.SiteLatitude,TMYData.SiteLongitude,...
TMYData.SiteElevation); %Altitude is optional
PresPa = TMYData.Pressure*100; %Convert pressure from mbar to Pa

% Models that rely on sun position that are run at specific time steps
% (e.g., hourly) run into numerical problems during timesteps when the sun
% straddles the horizon (i.e., spends part of the timestep above and part
% below the horizon).  Since in this example we use TMY day, which is
% hourly and reported at the end of the hour, we adjust the sun position in
% the following two ways.  (1) For hours when the sun is above the horizon
% we adjust sun position so it is for the middle of the hour.  For example,
% sun position reported at 4PM is the sun position at 3:30 PM.  (2) For
% hours where the sun straddles the horizon, we report the position half
% way between the horizon and the position of the sun at the end of the
% hour.  This is appropriate because the GHI data is essentially a sum of the GHI
% measurements made in the past hour.
%
%Run sun position twice:  Once for end of hour positions.
% A second time for mid hour positions.
% Adjust sun elevation and GHI for hours when the sun traverses the horizon
% Include these adjusted values in the mid hour positions
%
[~, ~, AppSunEl, ~] = pvl_ephemeris(Time,Location,PresPa,TMYData.DryBulb);
Time.hour = Time.hour-.5; % shift times back 1/2 hour for sun position calculation because of tmy
% timestamps
[~, ~, AppSunEla, ~] = pvl_ephemeris(Time,Location,PresPa,TMYData.DryBulb);

A=diff(sign(AppSunEl)); %identifies hour before sun straddles horizon (2,-2)
ind1 = find(A==2)+1; % AM hour where sun straddles horizon
ind2 = find(A==-2)+1; % PM hour where sun straddles horizon
%AM Adjustment
    AppSunEl(ind1) = AppSunEl(ind1)/2; %change sun elevation to mid way above the horizon
 %PM Adjustment
    AppSunEl(ind2) = AppSunEl(ind2)/2; %change sun elevation to mid way above the horizon
AppSunEla(ind1)=  AppSunEl(ind1);
AppSunEla(ind2)=  AppSunEl(ind2);

DNI_model = pvl_reindl_2(GHI,90-AppSunEla, dayofyear);

[DNI_model, DHI_model, ~] = pvl_reindl_1(GHI,90-AppSunEla, dayofyear);

figure
tfilter = and(Time.month == 8,Time.day == 6);
plot(Time.hour(tfilter),DHI_model(tfilter),'-s')
hold all
plot(Time.hour(tfilter),DHI(tfilter),'-o')
xlim([0 25])
legend('DHI (Reindl-1 Model)','DHI (TMY3)','Location','NE')
xlabel('Hour of Day')
ylabel('Irradiance (W/m^2)')
title({'Diffuse Horizontal Irradiance Comparison';'Albuquerque, Aug 6'},'FontSize',14)

References

[1] Reindl D.T., Beckman W.A., Duffie J.A., 1990. Diffuse fraction correlations. Solar Energy v45, pp. 1-7.

See also

pvl_disc , pvl_dirint , pvl_erbs , pvl_louche , pvl_orgill_hollands , pvl_reindl_1 , pvl_ephemeris , pvl_date2doy , pvl_alt2pres

Copyright 2014 Sandia National Laboratories