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
|
Used in rows arrangements or
tracking: angle between the plane passing by the base of the
collector and the sun, and the ground plane. |
| 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. |
