Solar battery calculator
Bank size is daily consumption times days of autonomy, divided by the usable depth of discharge. Five kilowatt-hours a day with two days of autonomy at 80% usable needs a 12.5 kWh bank — 260 Ah at 48 V.
How to size a battery bank
Days of autonomy is the expensive decision. Each extra day is a linear increase in battery cost, and batteries are usually the largest single line in an off-grid system. Going from two days to five nearly triples the spend, and in a northern winter even five days may not bridge a stubborn anticyclone. Most off-grid systems settle on two or three days of storage plus a generator, because the generator covers the rare deep gap far more cheaply than the batteries that would otherwise be needed.
Questions
Daily use times days of autonomy, divided by usable depth of discharge. Five kWh a day for two days at 80% needs 12.5 kWh.
One for grid backup, two to three off-grid with a generator, five or more only if there is no generator and no tolerance for going dark.
Current. A 5 kW load is 104 A at 48 V but 417 A at 12 V, which needs enormous cable and loses far more to resistance.
The array must refill the bank within the available sun hours, allowing for the load running at the same time. The array figure here does that.
Yes, markedly. Lead-acid loses substantial capacity below freezing and lithium must not be charged below it at all without a heater.