Solar Geometry

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Solar Geometry

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The calculations of PVsyst use simplified expressions (accuracy some few arc-minutes).

If you need more accurate calculations you can refer to the site of the US navy:

Here are some definitions and calculations   (see also the corresponding variables names in the simulation):

Time definitions :

Ecliptic angle (Ecl)Tilt of the earth's axis with respect to the ecliptic plane  = 23° 26'   (or 23.433°).
Declination (Decl)is the angle between the earth's rotation axis and the earth-sun line.
Computed using NoDay = Day of year from 1st January
the year's origin (around 21 of March) : NoDayOrig = 79 +  (Year MOD 4) / 4     (i.e. 79, 79.25, 79.5, 79.75)
and the number of days in the year NDaysY  (365, or 366 for leap years)
Decl = ArcSin  ( sin(Ecl) * sin (2*π * (NoDay - NoDayOrig) / NDaysY) )
If  (NoDay > 172)  then   Decl = Decl + 1.5 * sin( 2*π * (NoDay-173) / NDaysY)
Equation of Time (TE)Correction between  Solar Time and "constant" time, due to the ellipticity of the earth's trajectory and the Obliquity of the earth's axis (Ecliptic angle).  
Let us define the year angle YAngle = 2 * π * (NoDay-1) / 365.25
TE  =  0.0072 * Cos (YAngle) - 0.0528 * Cos (2*YAngle ) - 0.0012 * Cos (3*YAngle ) - 0.1229 * Sin (YAngle) - 0.1565 * Sin (2*YAngle) - 0.0041 * Sin (3*YAngle)
Diff Hleg-HsolDifference between Legal time and Solar time
DHLegHSol  =  TimeZone - Longitude[°] / 15 - TE    [hours]
Solar Time (ST)ST = Legal Time [hour of day] - DHLegHSol
Hourly Angle (HA) Projection on the equator plane of the sun's direction with respect to latitude of the site  (sun at midday)
HA =  15°  *  (ST - 12)         angle with respect to midday

Sun's position geometry :

Sun height   (HSun)Angle between the sun's direction and the horizontal plane
Sin (HSun)  =   Sin (Lat) * Sin (Decl) + Cos (Lat) * Cos (Decl) * Cos (HA)

Sun azimuth (AzSun) Angle with respect to south in the Northern hemisphere, and the North in the Southern Hemisphere

   (opposite to the Architect's convention, but largely adopted in the Solar Industry).
The azimuth is counted positively towards West  (counterclockwise in the Northern hemisphere, clockwise in the southern hemisphere)          
Sin (AzSun) =  Cos (Decl) * Sin(HA)  /  Cos (HSun)

Collector plane geometry :

Plane tilt         (TiltPl)Angle between the collector plane and the ground plane.
Plane azimuth (AzimPl)Angle of the perpendicular to the base of the collector plane and the south (in northern hemisphere) or the north (in the southern hemisphere).
Incidence AngleAngle between the sun's ray and the normal to the plane
cos (IA)  =  cos  (AzSun - AzimPl)  *  cos (HSun) * sin (InclPl)  +  sin (HSun) * cos (InclPl)
Profile angleUsed in rows arrangements or tracking: angle between the plane passing by the base of the collector and the sun, and the ground plane.
Baseline slopeAngle between the base of a  "table" of collectors, and the horizontal.
A not null baseline slope involves a modification of the real Tilt and Azimuth of the plane.

Tracking systems :

Axis tiltTilt of the axis with respect to the horizontal
Axis azimuthAngle between the axis direction and the South (or North).
Phi orientationIn one-axis systems, angle between the tracking plane and the "rest position".        
With horizontal axis: the "rest position" is the horizontal
With tilted axis: the "rest position" is the direction of the axis azimuth.
NB:The "N/S horizontal axis"  means a tracking from east to west.
Backtracking anglePhi angle corresponding to the limit of shading from one tracker to another one.
The backtracking angle is depending on the sun position.