An autotransformer can be used for step-up, step-down and split phase output balancing purposes. While the step-up and step-down functions are fairly straightforward, split phase output balancing may require some more attention.
Consider for example a 30A 120/240V split phase supply. The supply could be the grid, a generator or two stacked inverters. Some of the loads connected are 240V, others are 120V. On each 120V leg the load should not exceed 30A.
The problem is that as soon as 120V loads are connected, the two legs will show a different current. This is because the 120V loads on the two legs will never be balanced. A 120V 1200W hairdryer, for example, will draw 10A from one leg. A 120V clothes washer could even draw in excess of 20A from one leg. Between the two legs the difference in current, or current unbalance, will therefore often be 20A or more. This means that the 30A supply will not be used up to its full potential. By the time one leg draws 30A, the other leg may be drawing no more than 10A, and increasing the 240V load, for example, will result in an overload of one leg while the other leg still has spare capacity.
Theoretically, the total power that can be drawn from a 30A 120/240V supply is 30 x 240 = 7,2kVA. In case of 20A unbalance, the practical maximum will be 30 x 120 + 10 x120 = 4,8kVA, or 67% of the theoretical maximum.
The solution is an autotransformer.