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: http://aa.usno.navy.mil/faq/docs/SunApprox.php
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-Hsol | Difference 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 Angle | Angle 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 angle (PrfAng) | Used in rows arrangements or tracking: angle between the plane passing by the base of the collector and the sun, and the ground plane |
| PrfAng = ArcTan ( Tan(HSun) / Cos (AzSun - AzimPl)) |
| Baseline slope | Angle 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 tilt | Tilt of the axis with respect to the horizontal |
| Axis azimuth | Angle between the axis direction and the South (or North). |
| Phi orientation | In 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 angle | Phi angle corresponding to the limit of shading from one tracker to another one. |
| The backtracking angle is depending on the sun position. |
