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Are there any commercial aircraft that use solar energy in terms of auxiliary (not as main power source, as of now) power source ?
If Yes, In what forms is the solar power used?
If No, Why isn't solar energy used in commercial aircraft as an auxiliary power source?
The sun's energy is a max of about 1000 W/m2 at sea level (sun directly overhead, clear day). A solar power installation may have around 15% efficiency, yielding a max of 150 W/m2. Let's just see roughly what that gives us for a 737, to see if it's even that much.
The wing area of a 737 is 124 m^2, and the fuselage is 42 m long and 3.76 m wide. This gives a total area of 280 m2 if the sun is directly overhead. Covering all of this with solar panels gives a total (extremely optimistic) output of 42,375 W. The fuselage tapers at both ends though, and needs to have openings for the windows, antennas, etc. The wings will probably only have the fixed panels covered in solar panels (not flaps, slats, etc) so you would be looking at significantly less for a realistic installation. The Solar Impulse 1 was in the same ballpark (200 m2 for a peak of 45 kW).
The APU on a 737 is rated at 90 kVA. Of course you will usually use less than that, but we are looking at solar only providing maybe 20% of the capacity for any considerable part of the day. Since solar is not always available, you cannot even downsize the APU.
Another important function of the APU is to provide bleed air. This can be used to run the air conditioning packs and to start the engines. Photovoltaic panels would be a very inefficient way to provide bleed air.
An airplane will probably look strange being covered in solar panels, but covering so much area also causes some issues. Inspecting the aircraft for damage will be difficult. This means the solar installation should be easily removable (also for repairing damage to the solar cells), and the structure may need to be more damage tolerant. The panels would also need to be attached well so that they would not depart the plane even if damaged. This all adds more weight.
You would be adding a lot of weight to install solar that only helps a little bit sometimes. You may get a small benefit by reducing the generator load on the engines, but probably not nearly enough to make up for the increase in weight.
Airlines are big on reducing fuel usage, and are willing to add weight to save fuel overall (such as with winglets), but we haven't seen solar put to use on any airliners yet. The most efficient way overall to provide regular power is to extract it from the engines that are already running. For auxiliary power, a small turbine generator, which can provide both bleed air and electricity. And for emergencies, a RAT.
No. The APU has to work on night flights as well as it works during the day. (Granted, it can be inoperative and deferred for either, but the general expectation is that the equipment, when operative, is available 24x7, rather than 12x7.) Anything that's always inoperative from sunset to sunrise is a novelty at best, and excess weight for sure.
