You are doing a lot of what I say "looking at the leaves" while you need to rise above and look at the whole forest. You cannot, ever, know about all the industries you may be questions on at a case interview. Your job is NOT to know everything about everything but to have the TOOLS to get you there ASAP. What does that mean? Your brain freezes because you've trained it to only answer things that you ALREADY know. You now need to train it to figure out what are the RIGHT questions to ask to get you to a place where you can accurately GUESS at what you don't know. Take your own Q: "what influences variable costs of power plants". I've never read a single document/article on power plants. Here's how I'd approach it.
1. Do I know what variable costs are? Yes. OK, next:
2. Do I know what generally happens to get me power@home? Yes (coal/hydro/solar --> magic happens --> electricity --> national grid --> power lines --> regional grid --> more power lines --> .... -> home). OK, next:
3. Do I know what happens in ANY generic plant/factory? Yes (source --> raw material --> lots of magic --> finished material --> destination). OK, next:
4. Do I know, approx, what the "magic" is? Yes (material, machines, people, etc). OK, next:
Now, TUNE the above to "power plants". Thinking through this, the variable costs are likely going to be:
1. Raw material (if there's no demand, you don't supply == no raw material costs)
2. Transport (see above -- things like people, fuel, etc)
3. Seasonal labor, if applicable (likely -- summers in hot country == more AC; winters in cold countries == more heaters), so more people to dig coal, or transport, etc etc..
That's all I can think of without knowing ins and outs of the industry. You can probably rattle these off without knowing ANYthing about ANY industry and you'll likely be right but your goal is to show you aren't just guessing and have thought through and customized your answer to the industry in question.
So, fun fact: After writing all that above, I just googled up "variable costs of power plants" and came up with this link: https://www.e-education.psu.edu/eme801/node/530 and you'll note, I was almost 100% right. And THAT's how you crack a case interview. Good luck!