Hi!
Thanks for all the great answers!
The question of why keep away from batteries is a good one - one that I don’t really have a good answer to.
Things that I have as arguments is that I live where the temperature goes from approx. -30 C in winter to +30 in summer and I’m not sure how the batteries will behave in that kind of cold.
Another one is that I had an idea that the application is only needed in day-time. It’s some sort of (a bit advanced for the actual need) pool-heat-managing device. It started out as a project to build a database with data to practice machine learning on and it has grown from there.
I have an idea of a set-up using relays.
0-5 v burn the energy to heat water.
5-15v a relay kicks in and the arduino is running.
15-24v a relay kicks in the the energy is burned heating water.
The thing is, how do I prevent the arduino from getting more than about 15v? Is there some sort of voltage-roof passage that could be used?
If I’ll use batteries, the 15-24v could be used to charge the battery and the use the eventual excess to heat water.
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On the same subject but in a different application I have another question, let’s call above for number one and this number two. 
If I would get for example two solar panels that gives 100w each during the best prerequisite that my location can offer during the best summer days.
All energy should be used to heat air.
So I have 200w during full summer.
In winter I’ll have perhaps 100 w.
Let’s say I get 8 heater at 25w each.
During summer it’s full blast on all of them - happy days!
But during winter I don’t want 8 lukewarm heaters, I want 4 really hot ones.
Is it the same here, that relays is the best option or is there a smarter way to get this working?
All values are just for example, I’m still at learning phase before I go in to actual calculations.
Thanks for all the help that I have received, this forum is great!
Martin