transformer - Can we remove the neutral wire?

If we have the connection shown below (star connection of the secondary part of a TX), the load per each phase is equivalent (balanced load), then the vector sum of I1, I2 and I3 is zero. In this case, I would like to ask if we can remove the neutral wire from the connection since no current will flow in it (theoretically at least)?

And if we can remove it, where is the return path (to form a closed circuit) for each phase current?

Answer

Since you have a 3-phase system, you can remove the neutral connector if the loads are actually going to remain same. In practice the loads often aren't going to be completely balanced and there will be some current going through the neutral conductor.

Do note that in traditional 3-phase systems, the phase difference between phases is 120 degrees. That in practice means that you'll always have at least one voltage source that will have negative voltage and serve as the return path for the system. Take a look at this simulation. The yellow squares represent the current and as you can see the return path is a voltage source and the voltage sources are short-circuited together on their other end so the return current goes from one voltage source to another.

Here is the simulation of what you posted and you said, no current goes through the neutral conductor. Do note that the simulation does show voltage at the conductor, but the voltage is with respect to ground and not with respect to the center point of the 3-phase voltage source.