PVsyst 8 ephemeris

Method

The sun position comes from a simplified ephemeris. The declination of the sun follows the United States Naval Observatory's approximate formula, evaluated once per day, at 12:00 UT of the date (1). The equation of time is a Fourier series in the day of the year (2). The hour angle follows from the local standard time, the time zone, the longitude and the equation of time (3), and the sun height and azimuth follow from the latitude, the declination and the hour angle (4, 5). No atmospheric refraction is added.

The math

1. Declination
2. Equation of time
3. Hour angle
4. Sun height
5. Sun azimuth

$$\sin\delta = \sin\epsilon\,\sin\lambda,\qquad \lambda = L_{mean} + 1.915°\sin g + 0.020°\sin 2g,\qquad \epsilon = 23.439° - 3.6 \times 10^{-7}\,d \tag{1}$$ $$E_t = 0.0072\cos y - 0.0528\cos 2y - 0.0012\cos 3y - 0.1229\sin y - 0.1565\sin 2y - 0.0041\sin 3y,\qquad y = \frac{2\pi\,n}{365.25} \tag{2}$$ $$\omega = 15°\,\big(t_{loc} - Z + \text{lon}/15° + E_t - 12\big) \tag{3}$$ $$\sin\alpha = \sin\varphi\,\sin\delta + \cos\varphi\,\cos\delta\,\cos\omega \tag{4}$$ $$\gamma_s = \operatorname{atan2}\big(-\cos\delta\,\sin\omega,\ \sin\delta\,\cos\varphi - \cos\delta\,\sin\varphi\,\cos\omega\big) \tag{5}$$

where

Symbol	Meaning	Unit
$\delta$	the declination of the sun, its angle above the equator	degrees
$\epsilon$	the obliquity of the ecliptic	degrees
$\lambda$	the ecliptic longitude of the sun	degrees
$L_{mean}$	the mean longitude of the sun, $280.459° + 0.98564736°\,d$	degrees
$g$	the mean anomaly of the sun, $357.529° + 0.98560028°\,d$	degrees
$d$	the whole Julian day of the date minus 2451545, the day of 1 January 2000 at 12:00 UT	days
$E_t$	the equation of time, apparent minus mean solar time	h
$y$	the day angle	rad
$n$	the day of the year, 1 on 1 January	—
$\omega$	the hour angle, 15° per hour from solar noon	degrees
$t_{loc}$	the local standard time of the instant the sun is placed at	h
$Z$	the time zone of the site, hours ahead of UT	h
$\text{lon}$	the longitude of the site, east positive	degrees
$\alpha$	the elevation of the sun above the horizon	degrees
$\varphi$	the latitude of the site	degrees
$\gamma_s$	the sun's azimuth, clockwise from true north	degrees

References

1. United States Naval Observatory, Approximate Solar Coordinates (aa.usno.navy.mil)
2. PVsyst 8 help, Solar geometry and time definition

API

site.sun_model = pvsyst

Symbols follow the symbol registry.