There are two core parameters to determine battery bank size:
The maximum DC load when the Integrel system is not running. Typically, you want to calculate the worst-case overnight loads, which in many applications is air conditioning loads, and then, if using advanced AGM lead-acid batteries, double that for the battery capacity, and if using lithium-ion, multiply by 1.2, to establish a minimum battery capacity.
The charge acceptance rate of the batteries. If the batteries cannot absorb the output of the Integrel system, you lose a lot of the benefits of the system. With lithium-ion, we like to keep the charge rate no higher than the 1C, which is a charge rate equal to the rated capacity of the batteries, so a ~7.5 kWh battery capacity rating fits nicely with the 7-8 kW output of the Integrel system. For lead-acid batteries, you really need at least 10 kWh capacity to optimize the system, and even then the charge acceptance rate will taper off once the batteries are much above 50 percent charged (this is one reason we do not recommend using lead-acid batteries).