The answer to your question is complicated.I'm doing exactly what you are doing except with different controller and a 4s battery. Even with a BMS you will have to adjust the boost/bulk voltage constantly as the battery gets full. If the bulk voltage is too low, it will slow charge, if its too high it will fast charge. If you get active balancers you will need to do less adjustments. If you introduce an overvoltage relay (like I did)to control everythingyou can leave the battery unattended practically 24/7. Also there is voltage drop, if the controller reads 28.8 volts but you measure the voltage at the battery terminals and it reads 28 vollts, you got .8 volts difference, you need to increase the boost/bulk by .8 volts to get what you need.
Example : If your solar system can put out 20 amps at 24 volts, but your only seeing 10 amps when you haveboost set28.8 volts, you can live with that or you can raise the boost to a higher voltage and see if you can get all the 20 amps. Thats what I mean if the boost is set toolow it will slow charge the battery. You need to find the voltage that will work on your system. The 28.8 volts is just the recommendation. The equalize voltage if you cannot disable keep it as low as possible.
I had many problems with my lifepo4 battery going out of balance when charging. I wouldn't charge without a BMS or someway to monitor the balancing (overvoltage alarm). Even if you setthe bulk to a lower setting then the max, if the batterybecomes unbalanced, one cell might go over its limits.
At 28.8 volts for the boost(bulk) that will be 3.6 volts per cell, in a perfectly balance battery that would be acceptable. But I think too high for a battery with no BMS. Float at 27 volts equal to 3.37 volts per cell, also probably too high because if left unattended, an unbalance cell can easily reach its max voltage. In your situation I would get active balancers if I was going to rely on the overall voltage to charge the battery, its a 200 dollar investment but for a 2000 ah battery worth it. I use them on my 4s 220 ah lifepo4, would not charge them without them, if your solar system is large enough that it can charge at high amps, active balancers are the only ones that can keep up with that.I also have a cheap 6 dollar 30A4s BMS as last line of defense to protect battery.
Do you have a way to monitor the voltage on every cell? Also how will you balance the battery pack, all my batteries li-ion and lifepo4 have gone out out of balance when fast charging. Even the packs that I thought where in perfect balance drift out of balance when near the max overall voltage. Before getting the active balancers and overvoltage relays the BMS was always triggered to shutoff the charging when I charged with solar. You never want the BMS to shutoff charging, that always creates voltage surges with solar.
active balancers
overvoltage relay
