The combination of the A and C legs along with the grounded conductor of a high leg delta is electrically similar to a single phase center tapped service, and currents balance in the same way.
The rules for counting current carrying conductors are somewhat misleading. In almost _all_ cases the neutral of these circuits will carry _some_ current, and thus in reality is a conductor that carries current. In the circuit arrangements where you are not required to count the neutral as a CCC, however, if you evaluate the special case where the various _ungrounded_ conductors have balanced loading, you find no current on the neutral. (Again, you only get zero current on the neutral in specific cases, not in general.)
To calculate the current on the neutral in any given case, you need to use 'vector addition'.
As you know, the voltages and currents in AC electrical systems are constantly changing values. The current on the neutral is the sum of the various current flowing through all the legs feeding that neutral. If a constantly changing value is annoying, trying to sum up two or more constantly changing values to get a constantly changing result is even more annoying.
But a clever trick comes to our rescue. The first rule is that if you add two sine waves, of different amplitude and different phase, but of the _same_ frequency, then the result is also a sine wave, of the same frequency as the inputs. The amplitude and the phase will be different, but the frequency and the waveform stay the same. The second rule is that you can represent sine waves as vectors, by making the amplitude of the sine wave the length of the vector, and the phase of the sine wave the angle of the vector. With this representation, then the ordinary rules of vector addition apply; take two sine waves, represent them as vectors, add the vectors, and the vector that you get will correctly represent the sine wave that you would get if you tried to add the two sine waves together.
If you look at the voltage vectors representing two legs and the neutral of a three phase wye system (120/208V) you will see a 120 degree phase difference. The sum of two equal currents on the ungrounded legs will be be a third _equal_ current on the neutral leg.
Do the same with a conventional single phase service (120/240V) and you will see a 180 degree angle between the vectors (note, there is considerable discussion on the terminology of this point, save that for another thread!!!!). With equal loading on the ungrounded legs, when you do the vector addition you will get no current on the neutral.
Finally, if you do the same thing with A, C, and neutral of a delta high leg system, you will get no current on the neutral with equal loading on the ungrounded legs.
All of the above make certain assumptions: equal power factor on both legs, and no harmonics. If you don't have equal power factors, then the current phase angles won't match the voltage phase angles, and you will need to use different vector angles to get the correct sum; and if you have harmonics you no longer have simple sine waves, and need to use more complex representations of the current flow, and more complex techniques to do the addition.
-Jon
