And then I thought of this:

You could harness all of the energy without a solid sphere, just by making a Niven ring and using it to join two half-spheres of a thin carbon nano-tube fiber mesh with the interior covered with solar panels and threaded with cables leading back to the ring, with a few thinner arches supporting the fabric and carrying the primary conduits.
Gray is the ring, blue is the mesh, and white is the support arches. The relative sizes aren't exact, only to show the concept.
Thoughts on this concept?