Annex60.BoundaryConditions.SolarIrradiation.BaseClasses

IEA EBC Annex 60

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses

Package with base classes for Annex60.BoundaryConditions.SolarIrradiation

Information

This package contains base classes that are used to construct the models in Annex60.BoundaryConditions.SolarIrradiation.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

Package Content

Name	Description
BrighteningCoefficient	Circumsolar and horizon brightening coefficients
DiffuseIsotropic	Diffuse solar irradiation on a tilted surface with an isotropic model
DiffusePerez	Hemispherical diffuse irradiation on a tilted surface with Perez's anisotropic model
DirectTiltedSurface	Direct solar irradiation on a tilted surface
PartialSolarIrradiation	Partial model that is used to compute the direct and diffuse solar irradiation
RelativeAirMass	Relative air mass
SkyBrightness	Sky brightness
SkyClearness	Sky clearness
Examples	Collection of models that illustrate model use and test models

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.BrighteningCoefficient

Circumsolar and horizon brightening coefficients

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.BrighteningCoefficient

Information

This component computes the circumsolar and horizon brightening coefficients.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Connectors

Type	Name	Description
input RealInput	zen	Zenith angle of the sun beam [rad]
input RealInput	skyCle	Sky clearness. skyCle=1: overcast sky; skyCle=8 clear sky
input RealInput	skyBri	Sky brightness [0,1]
output RealOutput	F1	Circumsolar brightening coefficient
output RealOutput	F2	Horizon brightening coefficient

Modelica definition

block BrighteningCoefficient "Circumsolar and horizon brightening coefficients" extends Modelica.Blocks.Icons.Block; import H = Annex60.Utilities.Math.Functions.regStep; Modelica.Blocks.Interfaces.RealInput zen( quantity="Angle", unit="rad", displayUnit="degree") "Zenith angle of the sun beam"; Modelica.Blocks.Interfaces.RealInput skyCle "Sky clearness. skyCle=1: overcast sky; skyCle=8 clear sky"; Modelica.Blocks.Interfaces.RealInput skyBri "Sky brightness [0,1]"; Modelica.Blocks.Interfaces.RealOutput F1 "Circumsolar brightening coefficient"; Modelica.Blocks.Interfaces.RealOutput F2 "Horizon brightening coefficient"; protected Real F11; Real F12; Real F13; Real F21; Real F22; Real F23; Real d=0.01; Real a1; Real a2; Real a3; Real a4; Real a5; Real a6; Real a7; Real a8; Real b1; Real b2; Real b3; Real b4; Real b5; Real b6; Real b7; Real b8; equation b1 = H( y1=1, y2=0, x=1.065 - skyCle, x_small=d); b2 = H( y1=1, y2=0, x=1.23 - skyCle, x_small=d); b3 = H( y1=1, y2=0, x=1.50 - skyCle, x_small=d); b4 = H( y1=1, y2=0, x=1.95 - skyCle, x_small=d); b5 = H( y1=1, y2=0, x=2.80 - skyCle, x_small=d); b6 = H( y1=1, y2=0, x=4.50 - skyCle, x_small=d); b7 = H( y1=1, y2=0, x=6.20 - skyCle, x_small=d); b8 = H( y1=1, y2=0, x=skyCle - 6.20, x_small=d); a1 = b1; a2 = b2 - b1; a3 = b3 - b2; a4 = b4 - b3; a5 = b5 - b4; a6 = b6 - b5; a7 = b7 - b6; a8 = b8; F11 = -0.0083117*a1 + 0.1299457*a2 + 0.3296958*a3 + 0.5682053*a4 + 0.8730280* a5 + 1.1326077*a6 + 1.0601591*a7 + 0.6777470*a8; F12 = 0.5877285*a1 + 0.6825954*a2 + 0.4868735*a3 + 0.1874525*a4 - 0.3920403* a5 - 1.2367284*a6 - 1.5999137*a7 - 0.3272588*a8; F13 = -0.0620636*a1 - 0.1513725*a2 - 0.2210958*a3 - 0.2951290*a4 - 0.3616149* a5 - 0.4118494*a6 - 0.3589221*a7 - 0.2504286*a8; F21 = -0.0596012*a1 - 0.0189325*a2 + 0.0554140*a3 + 0.1088631*a4 + 0.2255647* a5 + 0.2877813*a6 + 0.2642124*a7 + 0.1561313*a8; F22 = 0.0721249*a1 + 0.0659650*a2 - 0.0639588*a3 - 0.1519229*a4 - 0.4620442* a5 - 0.8230357*a6 - 1.1272340*a7 - 1.3765031*a8; F23 = -0.0220216*a1 - 0.0288748*a2 - 0.0260542*a3 - 0.0139754*a4 + 0.0012448* a5 + 0.0558651*a6 + 0.1310694*a7 + 0.2506212*a8; F1 = Annex60.Utilities.Math.Functions.smoothMax( 0, F11 + F12*skyBri + F13*zen, 0.01); F2 = F21 + F22*skyBri + F23*zen; end BrighteningCoefficient;

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.DiffuseIsotropic

Diffuse solar irradiation on a tilted surface with an isotropic model

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.DiffuseIsotropic

Information

This component computes the hemispherical diffuse irradiation on a tilted surface. The irradiation is composed of the diffuse horizontal solar irradiation and the irradiation that has been reflected by the ground. Both components are adjusted to take into account the tilt of the receiving surface.

References

P. Ineichen, R. Perez and R. Seals (1987). The Importance of Correct Albedo Determination for Adequately Modeling Energy Received by Tilted Surface, Solar Energy, 39(4): 301-305.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Type	Name	Default	Description
Real	rho	0.2	Ground reflectance
Angle	til		Surface tilt angle [rad]

Connectors

Type	Name	Description
input RealInput	HDifHor	Horizontal diffuse solar radiation [W/m2]
input RealInput	HGloHor	Horizontal global radiation [W/m2]
output RealOutput	HGroDifTil	Diffuse solar irradiation on a tilted surface from the ground [W/m2]
output RealOutput	HSkyDifTil	Diffuse solar irradiation on a tilted surface from the sky [W/m2]

Modelica definition

block DiffuseIsotropic "Diffuse solar irradiation on a tilted surface with an isotropic model" extends Modelica.Blocks.Icons.Block; parameter Real rho=0.2 "Ground reflectance"; parameter Modelica.SIunits.Angle til(displayUnit="deg") "Surface tilt angle"; Modelica.Blocks.Interfaces.RealInput HDifHor(quantity= "RadiantEnergyFluenceRate", unit="W/m2") "Horizontal diffuse solar radiation"; Modelica.Blocks.Interfaces.RealInput HGloHor(quantity= "RadiantEnergyFluenceRate", unit="W/m2") "Horizontal global radiation"; Modelica.Blocks.Interfaces.RealOutput HGroDifTil(final quantity="RadiantEnergyFluenceRate", final unit="W/m2") "Diffuse solar irradiation on a tilted surface from the ground"; Modelica.Blocks.Interfaces.RealOutput HSkyDifTil(final quantity="RadiantEnergyFluenceRate", final unit="W/m2") "Diffuse solar irradiation on a tilted surface from the sky"; protected Real til_c "Cosine of tilt angle"; equation til_c = Modelica.Math.cos(til); HSkyDifTil = 0.5*HDifHor*(1 + til_c); HGroDifTil = 0.5*HGloHor*rho*(1 - til_c); end DiffuseIsotropic;

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.DiffusePerez

Hemispherical diffuse irradiation on a tilted surface with Perez's anisotropic model

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.DiffusePerez

Information

This component computes the hemispherical diffuse irradiation on a tilted surface by using an anisotropic model proposed by Perez.

References

P. Ineichen, R. Perez and R. Seals (1987). The Importance of Correct Albedo Determination for Adequately Modeling Energy Received by Tilted Surface, Solar Energy, 39(4): 301-305.
R. Perez, R. Seals, P. Ineichen, R. Stewart and D. Menicucci (1987). A New Simplified Version of the Perez Diffuse Irradiance Model for Tilted Surface, Solar Energy, 39(3): 221-231.
R. Perez, P. Ineichen, R. Seals, J. Michalsky and R. Stewart (1990). Modeling Dyalight Availability and Irradiance Componets From Direct and Global Irradiance, Solar Energy, 44(5):271-289.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Type	Name	Default	Description
Real	rho	0.2	Ground reflectance
Angle	til		Surface tilt angle [rad]

Connectors

Type	Name	Description
input RealInput	briCof1	Brightening Coeffcient F1
input RealInput	briCof2	Brightening Coeffcient F2
input RealInput	HDifHor	Diffuse horizontal solar radiation [W/m2]
input RealInput	HGloHor	Global horizontal radiation [W/m2]
input RealInput	zen	Zenith angle of the sun beam [rad]
input RealInput	incAng	Solar incidence angle on the surface [rad]
output RealOutput	HGroDifTil	Hemispherical diffuse solar irradiation on a tilted surface from the ground [W/m2]
output RealOutput	HSkyDifTil	Hemispherical diffuse solar irradiation on a tilted surface from the sky [W/m2]

Modelica definition

block DiffusePerez "Hemispherical diffuse irradiation on a tilted surface with Perez's anisotropic model" extends Modelica.Blocks.Icons.Block; parameter Real rho=0.2 "Ground reflectance"; parameter Modelica.SIunits.Angle til(displayUnit="deg") "Surface tilt angle"; Modelica.Blocks.Interfaces.RealInput briCof1 "Brightening Coeffcient F1"; Modelica.Blocks.Interfaces.RealInput briCof2 "Brightening Coeffcient F2"; Modelica.Blocks.Interfaces.RealInput HDifHor(quantity= "RadiantEnergyFluenceRate", unit="W/m2") "Diffuse horizontal solar radiation"; Modelica.Blocks.Interfaces.RealInput HGloHor(quantity= "RadiantEnergyFluenceRate", unit="W/m2") "Global horizontal radiation"; Modelica.Blocks.Interfaces.RealInput zen( quantity="Angle", unit="rad", displayUnit="degree") "Zenith angle of the sun beam"; Modelica.Blocks.Interfaces.RealInput incAng( quantity="Angle", unit="rad", displayUnit="degree") "Solar incidence angle on the surface"; Modelica.Blocks.Interfaces.RealOutput HGroDifTil(final quantity= "RadiantEnergyFluenceRate", final unit="W/m2") "Hemispherical diffuse solar irradiation on a tilted surface from the ground"; Modelica.Blocks.Interfaces.RealOutput HSkyDifTil(final quantity= "RadiantEnergyFluenceRate", final unit="W/m2") "Hemispherical diffuse solar irradiation on a tilted surface from the sky"; protected Real a; Real b; constant Real bMin=Modelica.Math.cos(Modelica.Constants.pi*85/180) "Lower bound for b"; equation a = Annex60.Utilities.Math.Functions.smoothMax( 0, Modelica.Math.cos(incAng), 0.01); b = Annex60.Utilities.Math.Functions.smoothMax( bMin, Modelica.Math.cos(zen), 0.01); HSkyDifTil = HDifHor*(0.5*(1 - briCof1)*(1 + Modelica.Math.cos(til)) + briCof1*a/b + briCof2*Modelica.Math.sin(til)); HGroDifTil = HGloHor*0.5*rho*(1 - Modelica.Math.cos(til)); end DiffusePerez;

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.DirectTiltedSurface

Direct solar irradiation on a tilted surface

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.DirectTiltedSurface

Information

This component computes the direct solar irradiation on a tilted surface.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Connectors

Type	Name	Description
input RealInput	incAng	Incidence angle of the sun beam on a tilted surface [rad]
input RealInput	HDirNor	Direct normal radiation [W/m2]
output RealOutput	HDirTil	Direct solar irradiation on a tilted surface [W/m2]

Modelica definition

block DirectTiltedSurface "Direct solar irradiation on a tilted surface" extends Modelica.Blocks.Icons.Block; Modelica.Blocks.Interfaces.RealInput incAng( quantity="Angle", unit="rad", displayUnit="degree") "Incidence angle of the sun beam on a tilted surface"; Modelica.Blocks.Interfaces.RealInput HDirNor(quantity= "RadiantEnergyFluenceRate", unit="W/m2") "Direct normal radiation"; Modelica.Blocks.Interfaces.RealOutput HDirTil(final quantity= "RadiantEnergyFluenceRate", final unit="W/m2") "Direct solar irradiation on a tilted surface"; equation HDirTil = max(0, Modelica.Math.cos(incAng)*HDirNor); end DirectTiltedSurface;

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.PartialSolarIrradiation

Partial model that is used to compute the direct and diffuse solar irradiation

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.PartialSolarIrradiation

Information

This is a partial model that is used to implement the direct and diffuse irradiation.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Type	Name	Default	Description
Angle	til		Surface tilt [rad]

Connectors

Type	Name	Description
output RealOutput	H	Radiation per unit area [W/m2]
Bus	weaBus	Bus with weather data

Modelica definition

partial block PartialSolarIrradiation "Partial model that is used to compute the direct and diffuse solar irradiation" extends Modelica.Blocks.Icons.Block; parameter Modelica.SIunits.Angle til(displayUnit="deg") "Surface tilt"; Modelica.Blocks.Interfaces.RealOutput H( final quantity="RadiantEnergyFluenceRate", final unit="W/m2") "Radiation per unit area"; WeatherData.Bus weaBus "Bus with weather data"; end PartialSolarIrradiation;

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.RelativeAirMass

Relative air mass

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.RelativeAirMass

Information

This component computes the relative air mass for sky brightness.

References

R. Perez (1999). Fortran Function irrpz.f, Emailed by R. Perez to F.C. Winkelmann on May 21, 1999.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Connectors

Type	Name	Description
input RealInput	zen	Zenith angle of the sun beam [rad]
output RealOutput	relAirMas	Relative air mass

Modelica definition

block RelativeAirMass "Relative air mass" extends Modelica.Blocks.Icons.Block; Modelica.Blocks.Interfaces.RealInput zen( quantity="Angle", unit="rad", displayUnit="degree") "Zenith angle of the sun beam"; Modelica.Blocks.Interfaces.RealOutput relAirMas "Relative air mass"; protected Real zenLim "Zenith angle bounded from above by 90 degree"; Real zenDeg "Zenith angle in degree"; equation zenLim = Annex60.Utilities.Math.Functions.smoothMin( zen, Modelica.Constants.pi/2, 0.01); zenDeg = zenLim*180/Modelica.Constants.pi; relAirMas = 1/(Modelica.Math.cos(zenLim) + 0.15*(93.9 - zenDeg)^(-1.253)); end RelativeAirMass;

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.SkyBrightness

Sky brightness

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.SkyBrightness

Information

This component computes the sky brightness.

References

R. Perez, P. Ineichen, R. Seals, J. Michalsky and R. Stewart (1990). Modeling Dyalight Availability and Irradiance Componets From Direct and Global Irradiance, Solar Energy, 44(5):271-289.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Connectors

Type	Name	Description
input RealInput	relAirMas	Relative air mass
input RealInput	HDifHor	Horizontal diffuse solar radiation [W/m2]
output RealOutput	skyBri	Sky brightness

Modelica definition

block SkyBrightness "Sky brightness" extends Modelica.Blocks.Icons.Block; Modelica.Blocks.Interfaces.RealInput relAirMas "Relative air mass"; Modelica.Blocks.Interfaces.RealInput HDifHor(quantity= "RadiantEnergyFluenceRate", unit="W/m2") "Horizontal diffuse solar radiation"; Modelica.Blocks.Interfaces.RealOutput skyBri "Sky brightness"; equation skyBri = Annex60.Utilities.Math.Functions.smoothMin( HDifHor*relAirMas/1367, 1, 0.025); end SkyBrightness;

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.SkyClearness

Sky clearness

Annex60.BoundaryConditions.SolarIrradiation.BaseClasses.SkyClearness

Information

This component computes the sky clearness.

Implementation

In the Annex60 library, HGloHor is always larger than 1E-4, minus some small undershoot due to regularization. Hence, the implementation is not simplified for HGloHor < Modelica.Constants.small.

The function call Annex60.Utilities.Math.Functions.smoothMax is such that the regularization is usually not triggered.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Connectors

Type	Name	Description
input RealInput	zen	Zenith angle of the sun beam [rad]
input RealInput	HDifHor	Horizontal diffuse solar radiation [W/m2]
input RealInput	HGloHor	Horizontal global solar radiation [W/m2]
output RealOutput	skyCle	Sky clearness. skyCle=1: overast sky; skyCle=8: clear sky

Modelica definition

block SkyClearness "Sky clearness" extends Modelica.Blocks.Icons.Block; Modelica.Blocks.Interfaces.RealInput zen( quantity="Angle", unit="rad", displayUnit="degreeC") "Zenith angle of the sun beam"; Modelica.Blocks.Interfaces.RealInput HDifHor(quantity= "RadiantEnergyFluenceRate", unit="W/m2") "Horizontal diffuse solar radiation"; Modelica.Blocks.Interfaces.RealInput HGloHor(quantity= "RadiantEnergyFluenceRate", unit="W/m2") "Horizontal global solar radiation"; Modelica.Blocks.Interfaces.RealOutput skyCle "Sky clearness. skyCle=1: overast sky; skyCle=8: clear sky"; // Set hSmall so that hSmall + deltaX < 1E-4. See info section. protected constant Modelica.SIunits.Irradiance hSmall = 0.5e-4 "Small radiation for regularization"; constant Modelica.SIunits.Irradiance deltaX = hSmall/2 "Small radiation for regularization"; constant Real k = 5.534e-6*(180/Modelica.Constants.pi)^3 "Constant factor"; Real tmp1 "Intermediate variable"; Modelica.SIunits.Irradiance HDifHorBou "Diffuse horizontal irradiation, bounded away from zero"; equation tmp1 = k*zen^3; HDifHorBou = Annex60.Utilities.Math.Functions.smoothMax( x1 = HDifHor, x2 = hSmall, deltaX = deltaX); // In the Buildings library, HGloHor is always larger than 1E-4 // (minus some small undershoot due to regularization. Hence, // it makes no sense to simplify the equation for // HGloHor < Modelica.Constants.small. skyCle = Annex60.Utilities.Math.Functions.smoothLimit( x = (HGloHor/HDifHorBou + tmp1)/(1 + tmp1), l = 1, u = 8, deltaX = 0.01); end SkyClearness;

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