Why if the 3 phase wye load with a connected source neutral lost a phase would there be current on the neutral? Why wouldn't the current just be L-L on the two remaining phases?
If any of the loads are line-to-neutral, only balancing all three lines' load currents can prevent neutral current. You'd have to lose the neutral for two, previously-line-to-neutral loads, to become simply two loads in series between two lines.
So if I did have a 3 phase wye load that had a neutral connected, and all phases were balanced, then why would there be no current on the neutral in this case?
Because (if the neutral connection was broken for this example) there would be no voltage difference between the source's neutral point and the loads' neutral point.
For an intact neutral to carry current, there would have to be a voltage difference between each end of that neutral if it were opened. The neutral carries current instead.
Why would all currents be balanced on the other phases when the impedance to the neutral is less? Is there an equation involving phase angles that shows this?
With three equal loads, the parts of wiring at the load that interconnect the individual loads will carry current, but the single conductor back to the source will not.
In a panel that happens to be evenly loaded among phases, the neutral bar will carry random currents between terminals, but the feeder neutral won't have nay current.
My OP is simply a theoretical question to help me understand, but in reality if I had a 3 phase load (heater etc..) that the OEM shows as having a neutral connected but I only have a 3-wire system, then can I still go aheand and connect this load without a neutral?
Yes, with the understanding that any change to the load's balanced condition will result in a voltage imbalance, possibly damaging parts of the load from over-voltage.
Obviously if all phases are balanced then there will be no issue, but would the issue of unbalance be a problem if neutral point of the load rose above zero volts?
Likely, if the loads were already at their voltage limit. It really depends on what happens to each phase's load, and the resulting line-to-(load-end-)neutral-point voltages.
