Buildings.BoundaryConditions.SolarGeometry.BaseClasses

Information

This package contains base classes that are used to construct the models in Buildings.BoundaryConditions.SolarGeometry.

Package Content

Name	Description
Declination	Declination angle
IncidenceAngle	The solar incidence angle on a tilted surface
SolarAzimuth	Solar azimuth
SolarHourAngle	Solar hour angle
ZenithAngle	Zenith angle
AltitudeAngle	Solar altitude angle
WallSolarAzimuth	Angle measured in a horizontal plane between the projection of the sun's rays and the normal to a vertical surface
Examples	Collection of models that illustrate model use and test models

Buildings.BoundaryConditions.SolarGeometry.BaseClasses.Declination

Information

This component computes the angle between the equatorial plane and the solar beam.

Connectors

Type	Name	Description
input RealInput	nDay	One-based day number in seconds [s]
output RealOutput	decAng	Declination angle [rad]

Modelica definition

block Declination "Declination angle"
  extends Modelica.Blocks.Interfaces.BlockIcon;
public 
  Modelica.Blocks.Interfaces.RealInput nDay(quantity="Time", unit="s") 
    "One-based day number in seconds";
  Modelica.Blocks.Interfaces.RealOutput decAng(
    final quantity="Angle",
    final unit="rad",
    displayUnit="deg") "Declination angle";
equation 
  decAng = Modelica.Math.asin(-sin(23.45*2*Modelica.Constants.pi/360)*
    Modelica.Math.cos((nDay/86400 + 10)*2*Modelica.Constants.pi/365.25)) 
    "(A4.5)";
end Declination;

Buildings.BoundaryConditions.SolarGeometry.BaseClasses.IncidenceAngle

Information

This component computes the solar incidence angle on a tilted surface using the solar hour angle and the declination angle as input.

Parameters

Type	Name	Default	Description
Angle	lat		Latitude [rad]
Angle	azi		Surface azimuth. azi=-90 degree if surface outward unit normal points toward east; azi=0 if it points toward south [rad]
Angle	til		Surface tilt. til=90 degree for walls; til=0 for ceilings; til=180 for roof [rad]

Connectors

Type	Name	Description
input RealInput	solHouAng	Solar hour angle [rad]
input RealInput	decAng	Declination [rad]
output RealOutput	incAng	Incidence angle on a tilted surfce [rad]

Modelica definition

block IncidenceAngle "The solar incidence angle on a tilted surface"
  extends Modelica.Blocks.Interfaces.BlockIcon;
public 
  parameter Modelica.SIunits.Angle lat "Latitude";
  parameter Modelica.SIunits.Angle azi(displayUnit="degree") 
    "Surface azimuth. azi=-90 degree if surface outward unit normal points toward east; azi=0 if it points toward south";
  parameter Modelica.SIunits.Angle til(displayUnit="degree") 
    "Surface tilt. til=90 degree for walls; til=0 for ceilings; til=180 for roof";
  Modelica.Blocks.Interfaces.RealInput solHouAng(quantity="Angle", unit="rad") 
    "Solar hour angle";
  Modelica.Blocks.Interfaces.RealInput decAng(quantity="Angle", unit="rad") 
    "Declination";
  Modelica.Blocks.Interfaces.RealOutput incAng(
    final quantity="Angle",
    final unit="rad",
    displayUnit="deg") "Incidence angle on a tilted surfce";
protected 
  Real dec_c=Modelica.Math.cos(decAng);
  Real dec_s=Modelica.Math.sin(decAng);
  Real sol_c=Modelica.Math.cos(solHouAng);
  Real sol_s=Modelica.Math.sin(solHouAng);
  Real lat_c=Modelica.Math.cos(lat);
  Real lat_s=Modelica.Math.sin(lat);
equation 
  incAng = Modelica.Math.acos(Modelica.Math.cos(til)*(dec_c*sol_c*lat_c + dec_s
    *lat_s) + Modelica.Math.sin(til)*(Modelica.Math.sin(azi)*dec_c*sol_s +
    Modelica.Math.cos(azi)*(dec_c*sol_c*lat_s - dec_s*lat_c))) "(A.4.13)";
end IncidenceAngle;

Buildings.BoundaryConditions.SolarGeometry.BaseClasses.SolarAzimuth

Information

This component computes the solar azimuth angle.

Parameters

Type	Name	Default	Description
Angle	lat		Latitude [rad]

Connectors

Type	Name	Description
input RealInput	zen	Zenith angle [rad]
input RealInput	solTim	Solar time [s]
output RealOutput	solAzi	Solar Azimuth [rad]
input RealInput	decAng	Decline angle [rad]

Modelica definition

block SolarAzimuth "Solar azimuth"
  extends Modelica.Blocks.Interfaces.BlockIcon;
public 
  parameter Modelica.SIunits.Angle lat "Latitude";
  Modelica.Blocks.Interfaces.RealInput zen(quantity="Angle", unit="rad") 
    "Zenith angle";
  Modelica.Blocks.Interfaces.RealInput solTim(quantity="Time", unit="s") 
    "Solar time";
  Modelica.Blocks.Interfaces.RealOutput solAzi(
    final quantity="Angle",
    final unit="rad",
    displayUnit="deg") "Solar Azimuth";
  Modelica.Blocks.Interfaces.RealInput decAng(quantity="Angle", unit="rad") 
    "Decline angle";

protected 
  Real arg "cos(solAzi) after data validity check";
  Real tmp "cos(solAzi) before data validity check";
  constant Modelica.SIunits.Time day=86400 "Number of seconds in a day";
  constant Modelica.SIunits.Angle polarCircle = 1.1617 
    "Latitude of polar circle (66 degree 33 min 44 sec)";
  final parameter Boolean outsidePolarCircle = lat < polarCircle and lat > -polarCircle 
    "Flag, true if latitude is outside polar region";
algorithm 
  tmp :=(Modelica.Math.sin(lat)*Modelica.Math.cos(zen) - Modelica.Math.sin(
    decAng))/(Modelica.Math.cos(lat)*Modelica.Math.sin(zen));

  arg :=min(1.0, max(-1.0, tmp));

  solAzi := Modelica.Math.acos(arg); // Solar azimuth (A4.9a and b) as a positive number

  if outsidePolarCircle then
    // Outside the polar circle, the only non-differentiability is at night when the sun is set.
    // Hence, we use noEvent.
    if noEvent(solTim - integer(solTim/day)*day < 43200) then
      solAzi :=-solAzi;
    end if;
  else
    // Inside the polar circle, there is a jump at (solar-)midnight when the sun can
    // be above the horizon. Hence, we do not use noEvent(...)
    if solTim - integer(solTim/day)*day < 43200 then
      solAzi :=-solAzi;
    end if;
  end if;

end SolarAzimuth;

Buildings.BoundaryConditions.SolarGeometry.BaseClasses.SolarHourAngle

Information

This component computes the solar hour angle, which is defined as the angle between the circle that passes through an observer, the north pole and the south pole, and the circle that passes through the sun, the north and the south pole.

Connectors

Type	Name	Description
input RealInput	solTim	Solar time [s]
output RealOutput	solHouAng	Solar hour angle [rad]

Modelica definition

block SolarHourAngle "Solar hour angle"
  extends Modelica.Blocks.Interfaces.BlockIcon;
public 
  Modelica.Blocks.Interfaces.RealInput solTim(quantity="Time", unit="s") 
    "Solar time";
  Modelica.Blocks.Interfaces.RealOutput solHouAng(
    final quantity="Angle",
    final unit="rad",
    displayUnit="deg") "Solar hour angle";
equation 
  solHouAng = (solTim/3600 - 12)*2*Modelica.Constants.pi/24 
    "Our unit is s instead of h in (A4.6)";
end SolarHourAngle;

Buildings.BoundaryConditions.SolarGeometry.BaseClasses.ZenithAngle

Information

This component computes the zenith angle, which is the angle between the earth surface normal and the sun's beam. Input are the solar hour angle and the declination angle.

Parameters

Type	Name	Default	Description
Angle	lat		Latitude [rad]

Connectors

Type	Name	Description
input RealInput	solHouAng	Solar hour angle [rad]
input RealInput	decAng	Declination [rad]
output RealOutput	zen	Zenith angle [rad]

Modelica definition

block ZenithAngle "Zenith angle"
  extends Modelica.Blocks.Interfaces.BlockIcon;
public 
  parameter Modelica.SIunits.Angle lat "Latitude";
  Modelica.Blocks.Interfaces.RealInput solHouAng(quantity="Angle", unit="rad") 
    "Solar hour angle";
  Modelica.Blocks.Interfaces.RealInput decAng(quantity="Angle", unit="rad") 
    "Declination";
  Modelica.Blocks.Interfaces.RealOutput zen(
    final quantity="Angle",
    final unit="rad",
    displayUnit="deg") "Zenith angle";
equation 
  zen =  Modelica.Math.acos(Modelica.Math.cos(lat)*Modelica.Math.cos(decAng)*
    Modelica.Math.cos(solHouAng) + Modelica.Math.sin(lat)*Modelica.Math.sin(
    decAng)) "(A4.8)";
end ZenithAngle;

Buildings.BoundaryConditions.SolarGeometry.BaseClasses.AltitudeAngle

Information

This block computes the altitude angle of the sun with respect to a horizontal surface. The altitude angle is the angle between the sun ray and the projection of the ray on a horizontal surface. It is the complementory angle to the zenith angle.

Connectors

Type	Name	Description
input RealInput	zen	Zenith angle [rad]
output RealOutput	alt	Altitude angle [rad]

Modelica definition

block AltitudeAngle "Solar altitude angle"
  extends Modelica.Blocks.Interfaces.BlockIcon;
public 
  Modelica.Blocks.Interfaces.RealInput zen(quantity="Angle", unit="rad") 
    "Zenith angle";
  Modelica.Blocks.Interfaces.RealOutput alt(
    final quantity="Angle",
    final unit="rad",
    displayUnit="deg") "Altitude angle";
equation 
  alt = (Modelica.Constants.pi/2) - zen;
end AltitudeAngle;

Buildings.BoundaryConditions.SolarGeometry.BaseClasses.WallSolarAzimuth

Information

This block computes the wall solar azimuth angle. It is the angle between the projection of the sun ray on a horizontal surface and the line perpendicular to the wall. The value of this angle varies from 0 to 180 degrees. In the northern hemisphere at solar noon, the value of the wall solar azimuth angle is zero if the wall is facing south.

Connectors

Type	Name	Description
input RealInput	incAng	Solar incidence angle [rad]
input RealInput	alt	Solar altitude angle (angle between sun ray and horizontal surface) [rad]
output RealOutput	verAzi	Angle between projection of sun's rays and normal to vertical surface [rad]

Modelica definition

block WallSolarAzimuth 
  "Angle measured in a horizontal plane between the projection of the sun's rays and the normal to a vertical surface"
  extends Modelica.Blocks.Interfaces.BlockIcon;

  Modelica.Blocks.Interfaces.RealInput incAng(quantity="Angle",
                                              unit="rad",
                                              displayUnit="rad") 
    "Solar incidence angle";
Modelica.Blocks.Interfaces.RealInput alt(quantity="Angle",
                                         unit="rad",
                                         displayUnit="rad") 
    "Solar altitude angle (angle between sun ray and horizontal surface)";
Modelica.Blocks.Interfaces.RealOutput verAzi(
    final quantity="Angle",
    final unit="rad",
    displayUnit="deg") 
    "Angle between projection of sun's rays and normal to vertical surface";
protected 
  constant Modelica.SIunits.Angle delta = 1*Modelica.Constants.pi/180 
    "Small angle";
  constant Modelica.SIunits.Angle ninety= Modelica.Constants.pi/2-delta 
    "+89 degree";
  constant Real deltaX = 1E-4 "Small number used for smoothing";
  Real alt_c "Cosine of altitude, bounded away from zero";
  Real rat "Ratio of cosines";
equation 
  alt_c=Modelica.Math.cos(Buildings.Utilities.Math.Functions.smoothLimit(
        x=alt, l=-ninety, u=ninety, deltaX=delta));
  rat = Modelica.Math.cos(incAng)/alt_c;
  // Due to the smoothLimit, rat can be about 1E-3 greater than 1 or smaller than -1.
  // Hence, below we use another call to smoothLimit to ensure that the argument of
  // acos(.) is inside the interval [-1, 1].
  verAzi=Modelica.Math.acos(
       Buildings.Utilities.Math.Functions.smoothLimit(x=rat, l=-1+deltaX, u=1-deltaX, deltaX=deltaX/10));

end WallSolarAzimuth;