NREL's Solar Position Algorithm (SPA)

Solar Position Algorithm for Solar Radiation Applications

There have been many published articles describing solar position algorithms for solar radiation applications. The best uncertainty achieved in most of these articles is greater than ±0.01 (deg) in calculating the solar zenith and azimuth angles. For some, the algorithm is valid for a limited number of years varying from 15 years to a hundred years. This program is a step by step procedure for implementing an algorithm to calculate the solar zenith and azimuth angles in the period from the year -2000 to 6000, with uncertainties of ±0.0003 (deg). The algorithm is described by Jean Meeus [1]. This program is written in a step by step format to simplify the complicated steps described in the book, with a focus on the sun instead of the planets and stars in general. It also introduces some changes to accommodate for solar radiation applications. The changes include changing the direction of measuring azimuth angles to be measured from north and eastward instead of being measured from south and eastward, and the direction of measuring the observer’s geographical longitude to be measured as positive eastward from Greenwich meridian instead of negative. This program also includes the calculation of incidence angle for a surface that is tilted to any horizontal and vertical angle, as described by Iqbal [2].
References:
1. Meeus, J. “Astronomical Algorithms”. Second edition 1998, Willmann-Bell, Inc.,Richmond, Virginia, USA.
2. Iqbal, M. “An Introduction to Solar Radiation”. New York: 1983; pp. 23-25.
3. https://www.nrel.gov/midc/spa/