To understand how solar panels work we have to understand the day and night cycle in no mans sky.
Luckily the solar panel provides us with the data necessary to tell when the code considers it day or night.
As they are named in the solar panel- Dark hours and Sunlight are both 15 minute periods that produce a cycle lasting 30 minutes.

Next - power production.
A solar panel does not produce a constant stream of power like its buddies the biofuel reactor and electromagnetic generator.
Instead the solar panel goes off sunlight presence so it generates mostly in the sunlight period but still has lower charge periods at the start and end of Dark Hours.
The solar panel produces a constant 46146 KP of energy per cycle which requires 2 batteries to store.
It comes out to this number always, on all planets.

It has three levels of energy output - 0KPS 25 KPS and 50KPS, the transitions happen roughly in the middle with different planets and locations having varied transition times( if you want to learn more ask in the comments )
0 Kps happens at night, it ends on the last minute of night time, 25 kps lasts 2 minutes and ends on the second minute of daylight, then comes 50kps for the 13 Minutes of daylight. Then 2 more minutes of 25kps and then 0kps until the cycle repeats
(these times are approximate as it varies on the exact time the transition happens on each planet)

Secondary - battery pairing.
One battery holds 45000KP of power which is enough for 30 minutes of constant 25KPs power usage.

Now the optimal set up ( this can be scaled up by any multiple )

2 solar panels combined with one battery can amply provide energy for a constant 50KPS output during a whole day night cycle.

During the day the battery diverts half the power to the user while charging fully or close to fully and then exerting that power at night creating a perfect cycle.

Solar panels are amazing in the convenience they provide and their versatility.

No mans sky uses your computer’s time to calculate base power so if you are using a power grid that has a larger demand for power than ability to generate power and you log out and log in in a few hours, the bases power will be depleted even if you have large power reserves.

Please ask me any questions you have about this and I hope it helps people.

Here is my largest out of 6 testing sites and some data and graphs of power consumption - https://imgur.com/gallery/DqhXBbr