Just to confirm with dwh, 'cause he's more experienced with this stuff, but there's no problem connecting multiple "chargers" to a battery, right?
It seems like there shouldn't be, but I worry about the times when two might be trying to put power in at the same time (like when the sun is shining and you're connected to mains or driving down the road). At the worst, adding a few cutoff switches so only any one system was in use at a time would keep things happy...
It's generally not a problem. First, they all protect themselves from backflow from the battery, so it's not like one charger will overwhelm another. They won't butt heads.
The only real issue, is when the battery is low. If one charger is supplying 13.8v to the bus and the other is supplying 14.4v, then power will flow from them both into the battery until the battery voltage hits 13.8 and then power will only flow from the higher voltage charger.
That's a non-issue if the chargers are constant voltage type, since the battery is just going to absorb whatever it can absorb, regardless of whatever the max capability of the charger is. But if they were both constant current type trying to stuff their full amperage into the battery, then it could be more charge current (amps) than the battery is rated for.
That won't happen with alternator + solar charger since the alternator is constant voltage type charger. It also won't happen with a normal car charger + a solar charger, since the normal car charger is also a constant voltage type charger.
The only time it could happen, is if the mains charger and the solar charge controller are both multi-stage and are both in bulk stage (constant current mode).
If the battery was rated for say 30a max charge current and you had a 15a solar and a 15a mains charger hooked up, then no problemo. If you have a 30a mains and a 15a solar then you could supply too much IF both are in bulk stage.
So it depends on how much the battery can handle, how much the chargers can put out, and what type of chargers they are.
