Now, that's revealing something! Skirting the issue doesn't help here.

BTW, let's go back to school.

Here's what you failed to consider/know:

Voltage out of each phase equals the internal transformed values minus the voltage drops on the coils. The correct assumption is that those voltage are displaced 120 degrees apart. Lemme show why Mr. Winders' equation is correct:

Vab = V1 - ia.Za

Vbc = V2 - ib.Zb, and

Vca = V3 - ic.Zc

[V1] = [V2] = [V3], all displaced by 120 degrees from each other

Taking the KVL around the loop:

(240/0 - ia.Za) + (240/-120 - ib.Zb) + (240/120 - ic.Zc) = 0

Since the voltages are of the same magnitude, the only differences are their respective angles, when summed up, they zero out!

(240/0 + 240/-120 + 240/120) - ia.Za - ib.Zb - ic.Zc = 0 -----> 0 -ia.Za - ib.Zb - ic.Zc = 0

So, you are left with:

-ia.Za - ib.Zb - ic.Zc = 0

substituting the ratios defined earlier as w and x:

-ia.Za - w.ib.Za - x.ic.Za = 0

Dividing by -Za:

ia + w.ib + x.ic = 0. -----> IMHO, this equation defines the relationship of the phase currents inside the transformer bank!