So, with that being the case we would have to consider how much voltage is dropped at the center of a 240 V circuit from each phase of the circuit, and that would be 120 V
Are you saying that you have a 120/240 3W system that is not grounded (in violation of 250.20(B) unless allowed in 250.22)? Regardless the greatest voltage between two conductors would be 240V so a 120/240 breaker is not allowed.
