That's plans for a low freq converter. The transformer would be impractically large. Normally you'd use a high freq transformer to make a HV DC supply then switch the DC supply back and forth to make AC output out of it.
Generally commercially made inverters are far cheaper than anything you could make, and more reliable too.
There's a lot more than simple schematics here too. At 1kw you're talking about running 80 amps through traces so busbars may be necessary. Getting the most out of a transformer at the best frequency, also a trick. In practice several transformers will be necessary.