In the literature there are different equations available to calculate solar energy at different angle and find the optimum tilt angle at any location. you can read the literature other wise you can get data of solar energy at different tilt angle for your location from NASA SSE data using longitude and latitude of your location.
So you are not looking for optimal power generation, but more for an aesthetic implementation that can generate power too...It really depends on the physical model you are using... There are so many variables when you are considering a tree, such as shadowing - time of the day, angles, ...
I hate to discourage you, but I think you are making life difficult for yourself !
You need to do the resource analysis including each and every panel that you install on your "tree" ! And that entirely depends on the exact position and height you install each panel at !!
The analysis across diurnal variation and seasonal variations can be simply hellish !!
Reliability is questionable, since the expectation that every MPPT controller will operate ideally is simply Utopian!!
Last but not the least, you are making the entire setup frightfully expensive ! Is that acceptable to you ??
Abdullah, I have to agree with Sasnjay - but at the same time I don't think that the situation is totally lost. Plants tend to grow with leaves facing many different directions, although they are all turned approximately towards the light. However, the situation in a chloroplast in a leaf is very very different from a solar cell in a solar array. The output of the chloroplast is a carbohydrate, which is not charged; the output of a solar cells is charged and has a potential relative to other structures. So if you build a solar tree - it would work a little, but the shading and variation in cell direction would make unifying all the power from the solar tree extremely difficult. You might do one as a research project but I can't see such a structure every being commercially viable. Good luck with your research!
Electrothermal performance and environmental effects of optimal photovoltaic–thermal system on this paper, at the solar calculation section, it has been explained. please take a look and let me know if you need further information.
Abdullah,
That isn't so much difficult that you think. except shadow effect which I haven't work on that, for the rest, you can see my paper for calculation of solar radiation on a plate with various direction: