What is likely to happen, if anything, if I try and export to the grid and import from the grid simultaneously?

Yes, I was wondering more if it was likely to cause an issue or whether it would just net off - I.e pull 3.4kW from the grid. 

Theoretically - yes. Nothing should fail as long as both are wired and protected to handle the currents as they occur individually. Grid battery storage does the same thing. Don't think the battery gets "empty" tho.  

Your electricity cost must be absolutely outrageous if you save money using battery storage and only connecting utility grid at night , unless you omitted having daytime solar charging system. Your car does have a plug, so there is control when you charge it up. 

 Andrew J While this sounds like a great plan, the payback won't be worth the effort.  I believe the car charging is separate from the battery storage.  You have a 6 hour window to charge your battery storage system.  How much capacity do you have?  Subtract the energy that you will use to defer buying electricity at the higher (15p) rate during the day.  The remainder is what you have the potential to make 8p per kWh.  If you have 2 kWh per day excess, you make 16p per day, less then 60£ in a year.

There's a lot of ifs and buts here. I assume that the output of the house battery is via an inverter which will change the current from DC to AC.The AC from the inverter will need to be a sine wave synchronised to the incoming mains supply before exporting anything at all to the grid. This is not easy, in fact it sounds like a nightmare waiting to happen. I have a vision of high-speed switches and big thyristors in my mind struggling to get out and run away.

Is the car an EV, or is it a regular car with a 12v battery under the bonnet, charged by a dynamo or alternator depending on it's age? If the latter then all you need is an ordinary 12v DC battery charger plugged into the mains via a time switch. An EV is probably a lot more complicated and the requirements will be different for every make and model of EV.

I implore you to take the advice of a specialist before doing any of the above.

As I say, I don’t have control over when the car charges, it is a schedule set by my utility company based on some algorithm they have otherwise I would just schedule accordingly. The 16kW house battery is just part of the overall system. 

But I’m interested in my question: I think the outcome will be either a net pull from the grid, or the battery just won’t discharge. 

It’s not a plan and I’m not trying to make money but that’s not really relevant to my question. Just trying to work out what may happen as my alternative is to try and manually manage things. 

As long as your grid tie point is behind the meter, you are correct that you will consume what you feed into the system and just draw the balance.

If your grid tie point is separate or ahead of the meter, your inverter needs to be capable of Export - which based upon your original post, I read it to be true.

good point, I'd assumed the wattmeter is the point of entry from the grid. I also assumed the inverter is regenerative, but that may not be a supported feature  :-)  

Does the battery system/inverter support regenerative pumpback ? 

first I live across the pond so I will ask the first question: what is, and how is the 'grid' paying you??

this is rather important as my grid pays me per Kw at the same price they charge me. So it work out nice ie. if I draw 3 Kw and generate 5 Kw they pay for 3 Kw only. When i move into my new digs I bringing in 3 phase for the shop, etc. I take 2 legs for 220/110 and that where the switch  will be since they are looking at total load on the 3 phase any I generate on the back end gets credit. 

I don't have times, or high/load times so I don't worry about it but you might have to. do you have different rates for different time of the day / night?

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