Solar Position

The amount of solar irradiance incident on a solar surface --at any moment and location-- depends fundamentally on the Solar Incidence angle. This angle governs how much sunlight actually reaches the surface and, consequently, the generated photovoltaic power.

To calculcate the critical solar incidence angle, PVGIS requires the relative Latitude and Longitude coordinates of the surface in question, its Surface Tilt and Surface Orientation angles, as well as the Solar Declination and the Solar Hour angles both of which are derived from the Timestamp of interest.

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In order to calculcate the solar incidence angle, we go through a series of solar position angles in the following order :

1. Fractional year
2. Equation of Time
3. Time Offset
4. True Solar Time
5. Solar declination
6. Solar zenith
7. Solar altitude
8. Solar azimuth
9. Solar incidence

Fractional Year¶

The position of the Earth in its orbit around the sun is expressed through the Fractional Year angle, measured in radians based solely on a moment in time (timestamp).

Equation of Time¶

The Equation of Time measured in minutes that corrects for the eccentricity (or else non-circularity) of the Earth's orbit and axial tilt. This correction helps align civil time with actual solar position.

Time Offset¶

The Time Offset measured in minutes, incorporates the Equation of Time and accounts for the variation of the Local Solar Time (LST) within a given time zone due to the longitude variations within the time zone.

True Solar Time¶

Next is the True solar time, also known as the Apparent solar time upon which depends the calculation of the Solar hour angle.

Solar Hour Angle¶

The Solar Hour angle measures the Earth's rotation and indicates the time of the day relative to the position of the sun. It bases on the longitude and timestamp and by definition, the solar hour angle is :

- 0° at solar noon
- negative in the morning
- positive in the afternoon

Solar Declination¶

The Solar Declination angle, depending on the algorithm, requires only the Fractional Year or in addition the Eccentricity correction factor and the Perigee offset.

Solar Zenith¶

The Solar Zenith angle links time, position, and solar geometry used for both direct and indirect irradiance models.

Solar Altitude¶

The Solar Altitude is the complement of the Solar Zenith angle. It defines how high the sun is above the horizon.

Solar Azimuth¶

The Solar Azimuth specifies the compass direction toward the sun. It combines the hour angle, latitude, and declination.

Solar Incidence¶

The solar incidence angle comprises all previous angles and defines the projection of sunlight onto the plane of the solar surface.

Default algoriths¶

The default algoriths for solar timing, positioning and the definition of the incidence angle are :

• solar_time_model is set to Milne1921 (see in pvgisprototype.constants: SOLAR_TIME_ALGORITHM_DEFAULT).

  • Calculate the apparent solar time based on the equation of time by Milne 1921

• solar_position_model is set to NOAA's equation for .. (see : SOLAR_POSITION_ALGORITHM_DEFAULT).

• solar_incidence_model is set to Iqbal (see : SolarIncidenceModel.iqbal).

Atmospheric refraction¶

Following the NOAA solar geometry equations, the calculation of the solar incidence anlge requires all of the following angular quantities :

• altitude which in turn requires the hour angle and the zenith angle
• zenith which in turn requires the solar declination angle (sun-earth)
• azimuth
• surface tilt
• latitude
• hour angle
• relative longitude

Mathematicall speaking, the point where refraction plays a role is the solar zenith angle. The zenith angle is adjusted based on some method of atmospheric refraction and the solar altitude angle (high altitude above horizon, low altitude above horizon and altitude below horizon). While the adjustment isn't large in absolute terms, it is part of the solar geometry system and may impact the analysis, especially when it comes to the amount of irradiance close to sun- rise and set.