... The other thing that can cause a difference/neutral current to flow

is if there's a difference in the power factor (read phase angle) between the two circuits. ...

I agree that even when the currents through L1 and L2 are equal in magnitude, if they are not 180° from each other then there will be a non-zero current through the neutral conductor.

Just to put this issue in a more familiar perspective, suppose we have two legs of a 120/208V wye that have equal resistive loads and with each drawing a current I

L. The load currents will be 120° apart, where one is effectively leading by θ=30° and one lagging by 30° relative to the 180° phase relationship needed for complete current cancellation. So each leg contributes sin(30°) x I

L = 0.5 I

L and the total neutral current is I

L (i.e, equal to the current in each phase).

Now using this line of reasoning we can determine the angle between two currents of I

L=20A in L1 and L2 that is necessary to get 7A in the neutral.

As above, we want sin(θ) x 20A = 7A /2 = 3.5A because each leg contributes half of the unbalanced current to the neutral, since the magnitudes of their currents are equal. Dividing both sides of this equation by 20A and taking the arcsin (inverse function of sin) we get θ = arcsin (3.5/20) = 10.08°. Therefore the currents in the two legs form a vector triangle with two 10.08° angles and with the legs 180° - 2 x 10.08 =159.8° apart. So 159.8° is the required angle between L1 and L2 currents of 20A to get 7A in the neutral.

Now using the example in post #47, if the load on one leg is resistive and the other either leads or lags by 2 x 10.08° = 20.16° then the currents will be at a 159.8° angle and the neutral current will be 7A. The power factor would be cos (20.16°) = 0.939. A 2HP motor might draw 20A at 120V at a reasonable load, and you would be lucky to get a power factor this good. But in this situation a better configuration would certainly be feeding the motor with 240V L1-L2 and using no neutral current.

So as was said before, the likelihood of the 7A being due to only P.F. is quite low in a residential environment but still possible.