By that I mean I know now what you want: "pure sine wave" grid tie inverter? - Because you already have the AC. Not as you said earlier to run your equipment,
For the sake of science; Yes you can! We have tried; It is a "waiting big big breakthrough", because it could be a single, few cents...
Pure sin wave is 100% analog; A PWM can steps to simulate; I am wondering how pure you have in mind. You may not be able to have a "pure" (analog) from a stable DC. However there is method to smooth out the steps.
Good luck.
Through our research we discover that an AC induction motor can act as a DC amplifier, as long as there is torque making it turns. Applying the process we are able to build RPM independent grid tie induction generator. Tested with variable US grid at consumer configuration.
Similar to PMA...