Charging Batteries Overnight Using APS Grid Electricity

Hi everyone. My evening rate for APS is 5.23 cents a kWh. Does it make sense to charge up my batteries immediately after discharging 10 percent, or is waiting for the sun to come up to recharge ok? If this makes sense, what kind of charger should I get?

My limited experience with lithium batteries are that they are quite happy hanging around for days at charge capacity between 10-90%. No sense charging your batteries using grid power, if the batteries can be charged using solar before being needed for the peak hours. There will be cloudy days where You may wish to charge your batteries during the low peak hours on the grid. 12volt 50 amp lithium chargers are about $250