Heating element testing - calculation

Question

I have a 3-phase, 30 kW, 480 V AC heating element.

I’m trying to utilize resistance as an aid for predictive failure.

Using Ohm’s law calculation 480 times 480 equals 230400. 230400 divided by 30000 W equals 7.68 Ω.

But when I measure the element it reads double that: 17.2 Ω.

Where am I making an error?

Answer 1

If this really is a three-phase heating element, there are two likely ways it could be connected (as well as some less-likely ones that I won't discuss). Image from the Wikipedia article Y-Δ transform, which you should also read:

Delta:

There is a 10 kW, 480 V coil connected between each pair of phases. Each coil's resistance is:

(480 V)²/10 kW = 23.04 Ω.

Measuring across any two terminals gives the parallel-series combination of (23.04 Ω+23.04 Ω)‖23.04 Ω = 15.36 Ω, exactly twice what you calculated.

Note: The symbol "‖" means "in parallel with". Please read one of the many online articles on calculating parallel resistances (example).

Wye (star):

There is a 10 kW heater from each phase to a common (neutral) connection. This neutral is not brought out of the heater because no current needs to flow through it in a balanced system. the voltage between any phase and the neutral is 480 V/√3 ≃ 277 V. Each heater's resistance is:

(277 V)²/10 kW = 7.68 Ω

Measuring across any two terminals gives the series combination of 7.68 Ω+7.68 Ω = 15.36 Ω, the same as above. (When only connecting two terminals, no current flows through the third coil so it has no impact on the measured resistance.)

Now, why did you measure 17.2 Ω? My guess is that it is due to manufacturing tolerances. Did you measure between all three possible combinations of terminals? Was there some variation?

The resistance of heating coils does tend to increase with temperature, but unless you measured this device while hot, this effect would not explain the discrepancy in resistance.