An (AFAIK) unsolved conundrum

Ideal? 100% of power in appears as power out. Solved. Ed

The OP wanted some way of measuring the power by only looking at the transformer core, not the input or output terminals.

Hint: Although the flux is (mostly) a function of voltage, the MMF (ampere turns) integrated around the closed path of the core can tell you something, particularly if the primary and secondary windings are separated.

Agree, but how does one know the MMF without measuring the current through one of the windings? I think the OP wants to just look at the magnetic parameters in the core, half-way between the primary and secondary windings, and be able to monitor the amount of power flowing.

The flux levels don't change much with the amount of load on the secondary, yet the amount of power flowing through the core from primary to secondary does. The trick is defining the amount of energy *flow* through the core.

daestrom

If you could measure E and H at all points on a surface surrounding either the primary or the secondary winding, I guess you could calculate a value for power crossing the surface (along the lines of Poynting). So, if you had many sensors distributed in a surface like arrangement, you might be able to calculate an estimate of the power transfer. Right?

Maybe. But how about a method that looks only at the core section between the windings. I think that's what the OP had in mind.

Think about creating a magnetic flux leakage path of a known but high reluctance bypassing the secondary windings with a Hall effect sensor in it. The flux through the bypass should be proportional to the MMF between these two points. The reluctance needs to be high enough so that the flux bypassing the secondary is small compared to the secondary winding flux.

Speaking of leakage flux, I guess we're considering practical transformers, at least to some extent, and dropping the 'ideal' transformer. I imagine this is still in the spirit of the question.

With your measurement, would you get an indication of winding current? Is there more you could derive?

If it turns out that most energy transfer in a transformer is transferred through the core (which seems likely but it's only an assumption) then I guess sensing E and H in a single 'slice' of the core between windings might be sufficient.

Your suggestion sounds a lot more implement-able so far.

Later,

The setup I described measures winding current.

One could also throw a turn around any section of the core and measure voltage. Multiply the two and get power. Both measurements could be made on a section of the core lying between the primary and secondary windings, satisfying the OPs request to measure power transferred only using measurements made of the core.