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Sure, "mining" the sun is going to be tricky, but solar collectors at a safe distance should be pretty feasible. Once you've got enough you'll be harnessing a sizable portion of the star's energy. You could then have local factories using wasteful processes to create materials with a bit more dense energy load to make it more transportable.

Any star should have enough energy for a couple of points. Ideally it should be modded to be more complex than just plodding down a mining station at every star.

Maybe a mechanic where you place a station similar to a terraforming station, but instead of terraforming the star it creates solar collectors. Each year's worth adds perhaps 0.1 more energy, maybe less for low quality stars. At high mineral cost, perhaps with mineral maintenance instead of energy (replacing faulty collectors).

If fractions aren't possible let it take 10 years to complete each "cycle" and then add 1 more energy output.
 
Wonder if there is a way to make an event that gets called whenever you build a mining station, which can then check if that station is built on a specific type of star (one of the modded stars, I guess). If it is that specific star, append X for every Y years passing and have that be the energy you get from it. Then again, you'd also have to remove that variable if the station gets removed.

I know in 00_on_actions.txt there's a on_building_mining_station = { } section that triggers a few events.
 
Actually, it wouldn't be, because it's dirt simple:
1: Get ye Solar Panel Array
2: Place ye Solar Panel Array in Close Proximity to Star
3: Get ye energy back from Solar Panel Array
4: Profit

No, I have not skipped a step there. It is literally that simple. We could do this today, the only problem is that we don't have easy access to space nor do we have a reliably tested microwave transmission mechanism.
 
On top of that, the fact that your Stellaris empire does have easy access to space means they probably have prefabricated mirror arrays ready to be sent out whenever a construction ship approaches an unharvested star.
 
I like the premise of the mod. I have played 110 years in a heavily modded game now, where I have dozens of new techs and ship classes, I have around 30 planets and around 450 naval cap used. Half of the planets are dedicated to energy production but if I would launch all of my navy I would still be bankrupt in ~15 months. So for me it will be really useful.:)