I am working on a project where I need to model the output of solar panels during the day. Because the sun moves across the horizon it won't always shine straight at the panels. For this reason, I wanted to calculate the area equivalent if the panel were to point directly at the sun. For example, if the panel were to point straight up and the sun was at a zenith angle of 45deg the effective area would be $0.5\sqrt2$
I have been using a model where I calculate the difference between the azimuth and zenith angles of the sun and panels and multiplying the cos of these angles to get an area. The problem is that this breaks down the moment I use a flat panel. In the case of a flat panel the azimuth shouldn't matter, yet it does in my model, e.g.: cos(AZpanel - AZsun) * cos(ZENpanel - ZENsun). I have not managed to find any documentation of what formula's I should be using.
I am looking for the solution to my problem given the solar angles and panel angles. Does anybody have a model, formula, or documentation which can help me with my issue?
Thank you for reading and I hope you can help.
Euristically, what you are looking for is the scalar product between two unit vectors, the first one normal to your solar panel and the second one pointing towards the sun from the center of your solar panel. Then you multiply by it's area.Then you multiply by it's area. In other words $$A_{eff} = \cos(\text{angle})\times A_{\text{solar panel}}$$ The Angle being the one described above and $A$ standing for Area.
Now, if the sun is on the other side of the plane, you will get a negative effective Area. Technicaly, you should just say that the actual effective area is zero whenever get a negative number.