Most Dutch homes will use a similar amount of energy in the form of gas for heating and cooking so we can double the OP's number to 7000 kWh/annum.
Because of interest in PV for my own place (I use less than 1500 kWh/year) I had a look around and found this site bidgely.com, they can log your power consumption, analyse it and compare it to others.
The software they use is trained on US consumption and doesn't work for European homes, as an example a typical US freezer consumes 300 Watts, a European one consumes 100 Watts.
Having frequently travelled the US and other hot & cold places I can say the US can save a hell of a lot by insulating.
Take Denmark as an example, per building code you have to have a minimum of 30cms (12") of insulation in the roof and floor, a little less in the walls and it really makes a difference!
But that doesn't mean the same isn't going to happen with solar, luckily PV is spread out all over but weather can over a few hundred kms be quite different.
The connection of PV to the grid is also regulated via the Voltage, regulations allow a fluctuation of 10%, as soon as that 255V barrier is reached the PV plant has to throttle or even switch of.
That's one reason I've put in bigger wires for my own, to keep the Voltage as low as practically possible and continue output for the maximum.
For me it's only a 50mtrs stretch (x2!) but I already gain some 5 Volts, for the power company with kilometers to the next transformer it is standard proper engineering practice.
Then, to increase reliability you lay (string in the US) some lines to your neighbours and don't have a problem if one of your generators or batteries is out for maintenance.
Oh wait, that starts sounding like a grid...
But the systems I know are by design, at times of excess wind or solar output power goes from The Netherlands, Germany and Denmark to pump up storage in Norway and at times of demand it is returned.
Any utility that builds such a system one way deserves to fail.
Of course we can still work on better solutions and that would be a large intercontinental grid and storage.
Myself I'm looking at adding an electric heating element to my gas fired water heater and when available use excess solar power.
That part of the world has a very high standard of reliability for their power grid, things like a UPS are al but unknown.
Another big factor is that except for the large trunk lines everything is underground making it far more reliable than the US system of stringing wires to dead trees.
One is to build a larger backbone of transmission lines but that's seriously delayed by lot's of NIMBY's.
The other is to build more (expensive) gas turbines that can be started up in minutes if not seconds if demand needs it.
An important measure is to regulate the inverters that sit between the PV panels and the net, they will automatically cut off when the Voltage get's too high and in future they will be centrally controlled.
Domestic smart meters are already being rolled out for years and they also help utilities to monitor and control generation and distribution.
A next and simple step would be that it's a gradual down-turning of the output, say 100% output below 245V, 50% at 250V or even more finely regulated.
But such systems are already existing on large plants
I was recently shopping around for PV panels and found out Germany requires a controller for domestic use to have an interface for a future monitoring and controlling system.
In Europe the generator and distributor are already separate entities and it's the generator that has to pay x cents per KWh for transport.
I fear I would then end up with two bills, one covering the cost of the energy I want and another to allow the delivery of that energy to the location I desire...
I really don't understand what worries you, over here the lines do belong to a separate company and I can shop around for a supplier of electricity
Exactly the same as with internet or telephone, many providers to choose from, one utility that does the delivery.
I pay one bill that has the KWh's and transmission as separate items, transmission is then paid by the electric supplier/provider to the cable company, it's not my worry at all.
Oh yeah, surprise, there's a third item on that bill, taxes ):