3S Lithium-Ion power solution for a project
Your 3s9p cells @ 3Ah /cell may supply 36Ah in 12h to a pack and with 27Ah capacity pack but additional soak time is required to achieve this capacity during CV mode. This is a tradeoff between battery life cycles and maximum capacity and may be defined in the charger design specs as 2 to 5% of CC rate with different CV thresholds from 4.1 to 4.2.  This additional time may take up to 20% or so. Overall power efficiency maybe 80% or so.
So this charger should charge in 12h but it is better not to let batteries reach 0% State of Charge (SoC) in order to get more Ah lifetime capacity.
A balanced current of 45mA/3A= 1.5% is reasonable to extend the life of batteries if they are matched &lt;&lt;1% as aggressive discharge times can increase mismatch tolerance.  Unless each voltage in the string is detected for Undervoltage (UV) cutoff in operation, the rate of discharge will accelerate the rate of a mismatch from the previous use. As the amount of time increases below UV and during CV, controls this ageing effect in addition to cell temperature.