I think all inverters these days have an adjustable upper export limit, the reast can be used in the house from both the solar available and drawn back out of the battery/s as required, then replace by solar or cheaper o/night power ......
Over this way, that cheap overnight power will soon be a thing of the past. Once the last of the spinning mass frequency and voltage stabilisers as shut down, the newer, faster to react, battery backed, frequency and voltage forming inverters will completely take over.
Coal fired stations are being shut down because they are well past their service life after they were bought up by interests who were looking for quick returns and didn't maintain the infrastructure with longevity in mind, fix it if and when it broke worked well for a while, with next to no maintenance shut down periods, those breakdowns are getting far more frequent.
For some reason, only known to those that made the decision, South Australia has a gas fired power station that runs 24/7 .... why, in a state that sells excess renewable energy to the other states via the interconnector, so we have periods during the day that we can be paid to take power from the grid to store it .....
T1 Terry