I'm certain that a self-contained habitation for a year is a solvable problem; nuclear submarines can be away in the ocean for a comparable time.
A habitat self-sustained for potentially indefinite time (at least half century), while producing its own food and oxygen, is a much taller order.
Unlike Amundsen's, such a station can have a nuclear reactor, with decades worth of fuel.
Tangentially, McMurdo (the coastal Antarctica base) did have a nuclear reactor for a bit. It didn't go great.
Though my hopes must be tempered by the prospect of greed. It would be better if the government(s) created an open design which could reuse off the shelf or components that any corporation could compete to create.
I'm assuming a Martian reactor would need some other approach give the relative scarcity of water? Sure ambient temperatures are lower, but equally the atmosphere is not very dense.
Thinking about it, burning diesel is also not attractive (lack of oxygen) and solar is weaker than earth. But I'm not seeing a lot of alternatives to solar...
https://www.researchgate.net/publication/334411420_Estimatio...
GHI is quite low (your array needs to be very spread out) and seasonality is 1/0, but if seasonal storage were available then a solar array in antarctica is fine.
Mars GHI is about 550W/m^2, but there are no clouds. An array there would perform about as well as france or spain.
I remember a pretty popular book and a Hollywood starring Matt Damon which primarily focused on this exact problem.
It really has nothing at all to do with developing a sustainable base on any planet. It's about some clever survival strategies, all of which are considered temporary at best.
Every time I see people get excited about Martian human habitation, I note a lack of discussion of the essential intermediate step: a fully self-sustaining base in the most inhospitable parts of Earth.
Where are the Biosphere++ projects?
And Amundsen-Scott has it easy: pressure, oxygen levels, and dust aren't a problem! (granted: Martian equator has easier temperatures).
Also, I've long wondered what is the comparable level of yearly insolation (for viability of solar power) in the South Pole compares to Mars' equator?