I just skimmed, but noticed one small discrepancy in one of the pictures. It shows an inverter connected to the “load” terminals on the solar charge controller. This is not the way to do it, because the inverter draws way too much power.
The inverter should be connected directly to the battery with low gauge wire.
It depends on the hardware you have, as the charger and inverter can interfere with each other in a number of ways.
For an RV with a couple lead-acid batteries, separate devices all connected to the battery usually work fine.
For more sophisticated set-ups (at least around here) all-in-one devices incorporating both charger and inverter are preferred. You also get load managenent this way.
If you have a separate inverter and charger that are designed to talk to each other and have good MPPT, you connect them both to the PV panels so the inverter doesn’t sabotage the charger’s ability to measure the battery’s state of charge or charge it optimally. This is ‘preferable’ for lead batteries and critical for lithium batteries.
As I said, it depends. There are inverters made specifically to be connected to PV panels, and there are inverters made for a fixed input voltage that you connect to a battery (the DIY store kind are usually the latter).
Though if you want to build a self-contained PV system without having to think about it too much, you’re probably best off with an all-in-one device where you can just plug in your panels, your battery and your devices and let it worry about the rest.
There’s another aspect, and I sadly lack the technical vocabulary here, but basically what you want to do for optimum efficiency is to convert the voltage as few times as possible. So: panels–>inverter–>load resp. panels–>charger–>battery, but not panels–>charger–>inverter–>load. The latter decreases your general efficiency and introduces roughly twice the losses.
The charger may also reduce its power output to much less than what the panels could deliver once it thinks the battery is full.
But then again, it all depends on your use case: where you use the system, what the environmental conditions are, and of course what your budget is. There simply is no one-size-fits-all PV system. You may not even need an inverter if all you want to do is charge your phone and laptop.
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