I'm at the end of a fairly typical summers weekend in Australia. Not too hot, lots of sun and everything in my house was powered by the solar panels on my roof. Here is my home dashboard right now:
Even though the sun is on the way out my solar is still outputting 1.2kW, it's a tad humid so the aircon is on low and the house is drawing 1.2kW - so net neutral right now. Below that you can see the house (Powerwall 2) and car (Model S) batteries are fully charged (I only charge my car to 90% unless I'm about to go on a very long drive).
In the Smart Meter box you can see the full stats for the entire weekend. Yesterday I consumed $0.04 of power and today I used $0.03 of power. This is caused by spikes in consumption such as the fridge or air conditioner compressors starting up - it takes a split second for the Powerwall to ramp up and for that tiny bit of time the grid provides a little power. This goes away if you disconnect from the grid entirely and is just an artefact of how the Tesla Energy Gateway watches your usage and tries to match it when it's in an on-grid environment.
Finally the column on the right in the Smart Meter box is how much excess power I sold back to the grid, $2.66 yesterday and $0.95 today (I charged the car up today which is why I exported less).
Today I saw an announcement that in South Australia the state government is going to fund 50,000 homes getting a similar system as me (solar+battery) and combine them to create a virtual powerstation! Such an awesome idea, I can only hope more states in Australia follow suit. If all homes had solar and batteries we could easily cover all residential power consumption in Australia.