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So, in a totally non-technical way, the inverter can make 5 kW and it powers the house first and exports the surplus to the grid, with a maximum of 5kW accepted by the power grid.
Say the house needs 1kW to operate, leaving 4 kW to export, a total of 5 kW.
But if the inverter can make up to 8 kW, then it can send 1kW to power the house and 5 kW to the grid, a total of 6kW. So the householder gets the feed in tariff on 5kW, not 4 kW.
Anyway, I think that's right.
Power will flow to the local appliances more easily than back through the transformer so the house always gets first dibs. If our kettle is switched on then there is a reduction in export power but if the sun is shining enough then the inverter will increase output up to the maximum capacity of the panels or the export limit, whichever occurs first while the kettle is consuming power, then reduce output after the kettle is switched off until export is reduced to the export limit.
However in times of cool weather and bright sunshine the lack of grid usage will cause grid voltage to rise to the trigger level where inverters start reducing output, effectively reducing export, until the grid voltage gets low enough assuming the inverter is appropriately configured. Ours has not been correctly configured since being installed in May last year even though some changes have been made as recently as 2 weeks ago when the derating voltage threshold was lowered to below the instant shut-down voltage at my request after the installers consulted the inverter technical support people (they had previously set it higher than any other voltage ensuring that derating would never occur) because the solar installers don't know how to configure it, so it shuts down every time an appliance is switched off due to being over-voltage on cool, sunny days. If only I knew the password I'd fix it as the installers don't want to make the necessary changes because they don't know what those parameters control, but hopefully it will be sorted in the next couple of weeks.