I thought of going to 240 volt battery bank.
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Joel, possibly I'm missing something, but what would the correlation be between the battery bank Voltage and how long one can ride out those overcast days?
How long you can keep the lights on with nothing coming into the batteries depends on the capacity of the battery bank (and how fast you're draining them). How may kWh's of energy are stored in it. The Voltage has nothing to do with this. A 12V battery bank can store as much energy as a 240V battery bank, it's a matter of the size of those batteries that make up the bank.
Voltage comes into play when you need to move power/energy; at a higher Voltage it requires less current, and therefore thinner wires. Current limited charge controllers can move more power if they run at a higher Voltage, i.e. a 60A controller will do roughly 800 Watt at 12 Volt, while that same controller can handle a 3,200 Watt PV array at 48 Volt. That makes higher Voltage battery banks a little more cost-efficient for larger installations.
-RoB-