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Is solar power combined with battery storage not an option?
Not really. Current battery technology is to put it lightly not the type of thing you want to rely on for long term life support. Lithium ion the current go to for rechargeable batteries physically degrades as you charge it. One of the main things you can do to reduce this is don't fully charge the battery. For example if the battery degradation from 0%* to 100%** is a cycle then 50% to 80% is only 21% of a cycle. That'll extend the lifetime of the battery (not the capacity) by about 5 times! That's pretty significant but you lose out on 20% of the batteries capacity permanently, even as the capacity decreases from degradation.
You've probably seen the hype about Sodium batteries which are currently 50% less energy dense which just immediately means NOPE for use in space.
* Lithium ion batteries are extremely difficult to actually fully discharge (controller won't let you)
**Lithium ion batteries should never be fully charged it causes them excessive damage so the controller prevents this from happening
They do it on the ISS though?
Although Li-Ion batteries typically have shorter lifetimes than Ni-H2 batteries as they cannot sustain as many charge/discharge cycles before suffering notable degradation, the ISS Li-Ion batteries have been designed for 60,000 cycles and ten years of lifetime, much longer than the original Ni-H2 batteries' design life span of 6.5 years.
Electrical system of the international space station, batteries
Also related:
Peak of eternal light, Lunar North Pole
ISS doesn’t have a two week long Lunar Night where solar panels dont work
The eternal light idea is fascinating but even in the best case scenarios, you’d need batteries to supply all power for two full days. In the more prudent case since lives depend on it, you’d need significantly more to cover any outages
Meanwhile, 2-3 nuclear reactors strung out on different sides and with redundant connections, and you’re good for 20 years and many types of outages
Much less power for the weight, and weight is the big deal when you're sending things from earth.