# Know your Solar Zenith and Azimuth Angles Solar photovoltaic (PV) modules and systems convert sunlight to electric energy.  The amount of sunlight incident on a PV module is of paramount importance to the electric energy produced.  In order to estimate the amount of incident sunlight on a PV module at any given time, we need to determine the position of the sun in the sky.

The position of the sun in the sky depends on two rotations.  First, the earth makes one rotation daily on its tilted axis.  Second, the tilted earth makes one rotation around the sun annually.  These two rotations affect the angle of sunlight at any point on the earth at a given time.  Since the earth rotates 360° in approximately 24 hours, it rotates approximately 15° each hour.  The earth also revolves 360° around the sun in approximately 365 days.  Depending on the day of the year, the declination of the sun is defined as the highest solar position of the sun at the equator.  In the northern hemisphere, solar noon, on any day, is the time when the sun it at its highest point and due South at the Greenwich Meridian (GST) hemisphere.  So for any given position on the earth, we can calculate local time at GST solar noon, given longitude, time zone, and daylight savings information.  The equation of time (EOT) is the difference between noon (1200 hours) and local solar noon.  EOT is affected by eccentricities in the Earth’s orbit and by the simultaneous rotation of the earth on own its axis and the revolution around the sun.  Given the hour angle (longitude, time zone, and EOT), declination (day of year), and latitude, the solar position is given by the azimuth angle, which is measured from due south, and the zenith angle, which is measured from the vertical.

The National Renewable Energy Laboratories (NREL) has published a solar position algorithm (SPA) for solar radiation applications.  SPA is an astronomical algorithm that calculates solar zenith and azimuth angles.  The algorithm is accurate for the years -2000 to +6000 with uncertainties of ±0.0003°.  An online version can be found at: http://www.nrel.gov/midc/solpos/spa.html. 