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Words of wisdom: “Three stage chargers are easier on your batteries, charge them faster, fuller and help you use less water”1) – HandyBob
Smart chargers, whether solar charge controllers, converters, or shore power chargers, use three stages to charge lead-acid batteries.
In some chargers these voltages and other setpoints can be configured by the user to better match battery maker recommendations, offset voltage loss in cables between charger and battery posts, etc.
Accurate charging requires the charger know the temperature of the batteries being charged. In hot temps a full charge will require somewhat lower voltage. In the cold the charging voltage can be very high4), enough to trip overvoltage protection in some 12v gear.
Flooded lead-acid batteries can, over time and in certain conditions, end up with stratified electrolyte. The way to remix the electrolyte is to charge at a rate high enough to intentionally cause off-gassing. The bubbles will mix the electrolyte and afterward the water level can be replenished.
Note that equalization is usually done with house circuits disconnected as the overvoltage might confuse or damage electronics.
Solar charge controllers and smart converters handle charging under load gracefully. As long as there is enough solar power coming in to hold the absorption or float voltage steady those charging stages will not be disturbed. If there is not enough power to hold the prescribed voltage the charger may drop back a stage or restart the process. This behavior may be configurable by the user.
Mains chargers, even smart ones, can get confused by load during charging.5)
Manual chargers will not be affected by load as they are controlled by the user.