Inverters that convert DC into AC are pretty commonplace, some cars even have standard AC receptacles in them for you to plug in your favorite appliance. However, there’s a particular type of inverter called a grid tie inverter that allows you not only to make AC, but also inject it back through an AC outlet to power other devices in conjunction with the normal AC service. Why? Maybe you want to use your own generator or solar power. In some cases, the power company will pay you if you produce more power than you consume. Maybe you just want to know you can do it. That seems to be the motivation behind [fotherby’s] build, which is quite substantial.
The setup only handles about 60 watts, but it does all the functions you need: DC to AC conversion as well as phase and voltage matching. Actually, just converting DC to AC is almost trivial if you don’t care about the waveform. But in this case, you do care that you can create an AC signal to match the one already on the line.