Bert, if you are looking for info on the theory behind transformer based phase converters there used to be some good material out there on the commercially available models. They were made by a company called Ronk and were called the add-a-phase autotransformer phase converters.
I think the key to their ability to balance the load was using a transformer with multiple taps that could be configured to suit a particular load. I think they used to be used a lot for pumps and elevators in buildings that didn’t have 3 phase. I have a few of them in various sizes up to 10HP but I mostly just use VFDs now. It is hard to argue with the simplicity of the transformer type converters though.
I think the key to their ability to balance the load was using a transformer with multiple taps that could be configured to suit a particular load. I think they used to be used a lot for pumps and elevators in buildings that didn’t have 3 phase. I have a few of them in various sizes up to 10HP but I mostly just use VFDs now. It is hard to argue with the simplicity of the transformer type converters though.