Unbalancing of Power Transformer

Yes, it is possible. The way to do it is to make sure that the same load on the LV system downstream is present on each of the three phases. Then the neutral current will be zero. In practice, this can never be achieved as by their very nature, LV single phase loads come and go.

• When adding single phase loads to existing LV distribution boards, the tendency is for the electrician to start at the top-left in the absence of other instructions. In the UK, the chances are that this will be the red (pre-2006 terminology) or brown (post-2006 terminology) phase, so this phase will usually be more heavily loaded than the others. To balance the load, simply move some of these onto one of the other two phases.

Only local investigation can determine what is the correct thing to do, and how much of it.

How out of balance is the transformer output, what problems is it causing?

Only you can determine if the loads can be swapped between phases, we don't have access to your system.