Check out @ timecode 4:00. The video shows a scope picture of a pure sine wave inverter, modified sine wave inverter and the grid.
The grid scope plot has the peaks chopped off with the modified sine wave inverter being the worst waveform of the 3.
The pure sine wave inverters that I have seen have a THD rating of @ 3% with the grid supposedly worse.
https://www.youtube.com/watch?v=1rxSapfp4Hs
Just to make sure no one on here gets confused:
Inverters are used from pure DC sources to create AC similarly to a regenerator. A regenerator is a different device. It has some extremely similar elements except differs in 2 key respects:
1. It has a power supply that pulls from grid AC, not a DC source.
2. It is generally designed for audio use or laboratory use depending on model.
The reason #2 matters a lot is that for inverters, the buyers don't usually care about THD and as long as it is reasonably functional, it sells. For the latter types, they care about this and are usually more attentive to THD.