Re: @2nd AC :-) re "same frequency"
"a crude approximation of a sine wave will do - just look at nearly all the cheap inverters used in cars and vans."
Yes but the ones used in cars and vans are not grid-tied inverters. The ones used in cars and vans can only be used **instead of**, not **as well as**, the One True Grid. The difference matters.
Suppose the grid is running at 50.000000 Hz and your proposed inverter is running at 50.01 Hz.
Suppose that at some point in time the grid input and the inverter output are in sync: same voltage output at the same instant in time. That's handy really, given that the two outputs are paralleled (that's what makes it a grid tied inverter, as used in solar PV or whatever, rather than a cheapo standalone job).
Suppose that some seconds pass. Now, your theory says the two can be at different frequencies. If (as you suggest) the frequencies are different, then the instantaneous values of the grid input and the inverter output are no longer the same voltage, even though they are both feeding the same piece of wire. In fact according to your theory there will come a point in time when one output will be (say) 120V+ and one will be 120V-. Do you see a problem there yet?
So, how do we stop them getting out of sync like that? We design the grid tied inverter so that its instantaneous output follows the instantaneous voltage fed in from the grid. In other words:
THE GRID AND THE INVERTER HAVE TO BE THE SAME FREQUENCY. EXACTLY.
Are folk getting the message yet?