This is an interesting question, and as usual the answer is yes and no. As @meandershas explained, the output of an ordinary inverter can not be mixed with the house mains supplied by the national grid. The AC waveform would need to match exactly in voltage, frequency and phase. An ordinary inverter has no mechanism to match the waveforms, so they can't be mixed.
You have the option of running some house loads via an extension lead from the MH. Possibly with a changeover switch, either manual or automatic, so that the house mains can take over if the batteries go flat.
The inverter you linked to in post#10 is a 'grid-tied' inverter. It is permanently connected to the mains, and takes its waveform from the incoming mains. It 'inverts' the DC power coming from the solar panels. No batteries are involved at any point.
If the grid power fails for any reason, the inverter goes off as well - that's something that's not in the advert. It produces whatever power it can from the solar panels connected to it. You can use that power in the same way as the grid power, and any excess power not used gets fed into the grid.
The Victron Multiplus inverter/charger mentioned in other posts is a different beast entirely. It connects to batteries and can produce 230V AC just like a standard inverter. However if a grid connection is made to it, it can synchronise exactly to the grid waveform, and mix its output with the grid power. It has various operating modes, one of which is to limit the input from a low-amps hookup post and add its own output so that high power appliances can be used. So for example a 6A hookup will normally only supply 6 x 230 = 1380W, but with a Multiplus you could run a 2200W kettle from it, as the difference would be supplied from the batteries via the Multiplus inverter.
But that's just the start of its capabilities. If you like tinkering, the Multiplus input and output can be controlled by a controller like the Cerbo GX, or Venus OS software running on a Raspberry Pi. The Multiplus accepts Modbus commands for input and output. These commands can be sent by a Raspberry Pi script. Or if you use the 'large' version of Venus OS, you can use a NodeRed program. You can program it to do all kinds of things, including exactly what you describe - using battery power to generate mains power to run house appliances within the house. You will need to add some current-measuring sensors clipped round the mains wires, with data transmitted by radio (Zigbee). But yes, entirely doable with a Multiplus.
You have the option of running some house loads via an extension lead from the MH. Possibly with a changeover switch, either manual or automatic, so that the house mains can take over if the batteries go flat.
The inverter you linked to in post#10 is a 'grid-tied' inverter. It is permanently connected to the mains, and takes its waveform from the incoming mains. It 'inverts' the DC power coming from the solar panels. No batteries are involved at any point.
If the grid power fails for any reason, the inverter goes off as well - that's something that's not in the advert. It produces whatever power it can from the solar panels connected to it. You can use that power in the same way as the grid power, and any excess power not used gets fed into the grid.
The Victron Multiplus inverter/charger mentioned in other posts is a different beast entirely. It connects to batteries and can produce 230V AC just like a standard inverter. However if a grid connection is made to it, it can synchronise exactly to the grid waveform, and mix its output with the grid power. It has various operating modes, one of which is to limit the input from a low-amps hookup post and add its own output so that high power appliances can be used. So for example a 6A hookup will normally only supply 6 x 230 = 1380W, but with a Multiplus you could run a 2200W kettle from it, as the difference would be supplied from the batteries via the Multiplus inverter.
But that's just the start of its capabilities. If you like tinkering, the Multiplus input and output can be controlled by a controller like the Cerbo GX, or Venus OS software running on a Raspberry Pi. The Multiplus accepts Modbus commands for input and output. These commands can be sent by a Raspberry Pi script. Or if you use the 'large' version of Venus OS, you can use a NodeRed program. You can program it to do all kinds of things, including exactly what you describe - using battery power to generate mains power to run house appliances within the house. You will need to add some current-measuring sensors clipped round the mains wires, with data transmitted by radio (Zigbee). But yes, entirely doable with a Multiplus.