An often used algorithm for the calculation of the apparent sun position (given a date and latitude/longitude of the observer) is SPA of Reda et al. [1]. If you're interested, I wrote an Android app (Sun Locator [2]) that implemented this algorithm.
[1] https://www.sciencedirect.com/science/article/abs/pii/S00380...
[2] https://play.google.com/store/apps/details?id=com.genewarrio...