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It depends on how long you require your system to run on batteries without any assistance? There are many types of 5KW off grid solar inverters on the market, what we see are usually two types:
1. Solar panel input is less than 5000W 1. Off-grid solar power system with solar panel input less than 5000W (48V battery system)
2. Solar panel input is greater than 5000W.
Assuming your solar panel is 3000W, the electricity generated is 3kWh per hour, which means that you need 48V60AH battery to store. If your location has 5 hours of sunshine, the electricity generated every day needs 48V300AH battery to store, that is 15kWh, when the off-grid solar power system you design runs for a day, when the battery is full, the energy obtained from the solar energy will be directly converted into AC power for the load. The battery is always in a full state and is used at night when there is no solar energy. 15kWh, supplying 1000W load can be used for 15 hours. The cost of this system is low and practical. If it is a configured lithium iron phosphate battery, the life will be very long.2. Off-grid solar power system with solar panel input greater than or equal to 5000W (48V battery system)
This kind of design is generally for commercial or industrial use, which uses a lot of electricity during the day and basically does not need to be used at night. We designed 5000W solar panel input, which can generate 5kWh per hour, and most of the power is directly converted to the load, and a small part is stored in the battery. Calculated on a daily basis for 5 hours of sunshine, it can generate 25kWh of power a day, and what capacity of the battery you need depends on the load usage at night, but it produces 5kWh of electricity per hour, even if you use a 1C lithium iron phosphate battery, it needs at least 48V120AH.
Summary: what capacity the battery needed for an 5kw off-grid system? In addition to calculating the usage of the load when there is no solar or no grid, it also needs to calculate the power to charge the battery per hour to achieve the best state of the battery. If the capacity of the battery is too small, it will be damaged very quickly.