With an off-grid solar system, there won't be any grid connection and we'll have to use batteries to supply our load during the night and on cloudy days.
We can use the following guide to sizing the batteries and charge controllers:
In order to calculate how much electricity your home will use per day, we need to know how many watts each load needs and how long they run for each day. Multiply each device's wattage by its run time, then add all the wattage hours for all the devices to get the total electrical fuel required. To account for losses & inefficiencies, total watt hour should be multiplied by 1.5.
The number of days your battery bank can operate during your load period, and generally it is between 3 and 5 days, we must mention battery days of autonomy.
The total watt hours per day derived from step one referred to above should be multiplied by it's days of autonomy derived from step two referred to above by 2 , since it doesn't have to be fully discharged. In total, the three factors multiply to give the watt hours that the batteries bank is required to provide. Once we have divided this number by the battery voltage, we can determine the AH (ampere hour) of the batteries.
It will be indicated how many batteries shall be used and how they can be connected (parallel and series). You can connect batteries in parallel or in series as you like, but you should keep in mind that the voltage and amperage will add up if you connect them in series or parallel. Generally, to indicate the number of batteries is dependent on how the configuration is set up. For example, if the batteries are in series, how many batteries are parallel is what we mean.
You should also use brand new batteries, as if you use one old battery, the whole system's battery life will be reduced.
Solar charge controller current is described here and voltage is described there. Using watts of total solar array power divided by voltage of batteries, multiplying the number by 1.25 oversizing (safety) factor, we will get maximum charge controller output current.