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I assume the issues you are having is that the load is cutting out, either momentarily when you first connect said loads, or indefinitely as long as those loads are connected.
The former (shorter disconnect) occurs when you connect a load with a capacitive circuit/behaviour and is caused by the surge of the capacitor taking a large amount of current very suddenly. In my case this happens when I connect my macbook air 12v charger, or my 12v compressor fridge. In both cases the actual load of each device (even both together) is less than the 20A limit of the charge controller and so I just ignore the problem safely.
If the controller keeps the loads switched off as long as the device is still connected (ie. more than a couple of seconds) then either there is a fault with that device, or it is drawing more current than the rated 20A of the output terminals on the controller. Any inverter or other load over around 200w is (or simultaneous smaller loads adding up to more than that) is too much current to connect to the lout output terminals and should instead be connected to the battery via suitably thick fused wiring.
The only way a relay is going to help your situation, is if you want to use the low voltage disconnect feature of the 100/20 to switch off your loads if your battery discharges too much. In that case you’d need a relay big enough to handle the currents that your loads require. The control side of the relay would then be connected to the load output terminals on your MPPT which acts as a control signal for the relay.
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