For my take on this, please consider a model system consisting of two _single_ phase generators sharing a common shaft, with some way of adjusting the phase angle between the outputs of the generators. The details are not important, the key features are:

1) shared shaft

2) matched output voltage (for our example, call it 120V)

3) matched excitation (perhaps these are permanent magnet rotors)

4) ability to adjust phase angle

5) the two coils are placed electrically in series.

6) the common shaft is connected to a constant speed prime mover (to run the generators)

7) we have a way of measuring the mechanical output of the prime mover

8) the series output of the two generators is connected to a variable resistive load, which we adjust for our tests

It is pretty clear that by appropriate adjustment of the relative phasing of these two generators, we can get any voltage between 0 and 240V.

Let us start with the phase angles adjusted to give 240V, and let us adjust the resistive load for a current of 100A. The load is consuming 24000W. Each generator is producing 12000VA and 12000W. The losses in each generator are those associated with producing 100A of output. The mechanical input to the generator set is the sum of the 24000W output and the losses in the generator set.

Now adjust the phase angles so that the output is very low, say 1V. Each generator is still producing 120V, but the phase angles have been adjusted so that the voltage of one 'bucks' the voltage of the other, leaving a net output of 1V. Adjust the resistive load for a current of 100A. Now the load is only consuming 100W. But each generator is still producing 120V, and still carrying 100A. Each generator is still producing 12000VA, and the losses in each generator are still those associated with producing 100A. Yet the electrical output of the _system_ is vastly reduced. Where does it go?

As gar mentions above, you need to consider power factor. What is the phase angle of the current with respect to the voltage. I am not going to go into the derivation, but in the system described above, the phase angle of the two generators is about 179.5 degrees, and the phase angle of the current flowing through each generator about 89.75 degrees out of phase of the voltage. (I'll leave it as an exercise to figure out 'leading' or 'lagging' and where

When you have a power factor in a single frequency AC system, the voltage is not in phase with the current, and for part of the cycle the power flow gets reversed. In the example above, each generator sees 12000VA, with most of this 'apparent power' circulating back and forth between the two generators.

In this example the mechanical input to the generator is the sum of 100W of output and the losses in the generator set. Since the hugely poor power factor means that each generator still has the losses associated with 12000VA (perhaps 400 - 1600W of loss), you can see that having this power factor does impact the efficiency of the generator system. But you have not 'thrown away' the full 11900W of input; you have just 'thrown away' the _losses_ associated with having 100A of current flowing through 240V of coils, when you only have an output of 1V.

Getting back to the original question: if you have a wye system consisting of 120V coils, and you connect a 100A single phase resistive load across two of the terminals, then you have 12000VA being delivered by each coil, but only 20800W being delivered to the load. Even though there is a resistive load, and the current through the resistor is exactly in phase with the line-line voltage, each coil experiences a power factor because the current is _not_ in phase with the line-neutral voltage.

A similar power factor issue is seen in delta transformers. Consider a single phase resistive load connected between terminals A and B of a delta secondary. Some of the current for this load will be supplied by the A-B coil, but some of the current will be supplied by the C-A and B-C coils operating in series. (If you prefer, consider a load connected across the open side of an open delta source....) The current through the C-A and B-C coils will not be in phase with the voltage produced by these coils. The net result is that you see a power factor on each of these other coils, even with a pure resistive load.

The answer in both of these cases is to balance the three phase loading. With a balanced three phase resistive load connected to a three phase source (either wye or delta), the current flowing through the coils will be in phase with the voltage produced by the coils, and you don't 'lose' VA.

Hope this helps.

-Jon