Net power absorbed and a tentative B vs H plot for an unloaded MOT

[haversin]

Following klugesmith's suggestion, I used a DI-149  data acquisition module to record a MOT primary voltage and current time histories. The secondary of the MOT was open. The DI-149 analog input specs are:  +- 10 volts full scale, 5000 samples per second for each channel (assuming two channels being recorded) and a ten bit ADC. One second of data was was recorded for 90v, 100v, 110v and 120v rms.

The setup.

Note: The MOT HV cap is not in the circuit. One terminal of this cap is being used as a connection point for the blade/push on
connectors.

Schematic.


Primary current.


The power absorbed by the MOT at time t is given by V(t)I(t) where V(t) and I(t) are the real voltage and current at time t. This term shows that the MOT alternatively absorbs and emits power. The time integral of V(t)I(t) over one period of the AC cycle (T) gives the net energy absorbed by the MOT in one T. Dividing the net energy by T then gives the net power absorbed.

Net power absorbed.


Magnetic flux density in the core is given by the time integral of voltage divided by the number of primary turns and cross sectional area of the core at the primary winding. There can also be a constant flux and flux density term in the core but this term is generally set to zero in making B vs H plots. In getting the value of the magnetizing field H, I assumed a constant H around a  intermediate closed path in the core. This is probably not very accurate, also the effects of the magnetic shunts were ignored.

A very tentative  B vs H plot.

[klugesmith]

Nice work and nice presentation!  Welcome to the fluxmetering club.   
Schematic diagram is much appreciated, and worth at least 1000 words.

How did you find the primary turns count?   
To render the chart with scale of B vs H, instead of whole primary winding volt-seconds vs amperes.

When numerically integrating the voltage channel values, did you need to put in a constant offset voltage to close the loop at then end of each AC cycle?

Do you know if your 2-channel data acquisiton takes samples simultaneously or alternately?  It wouldn't matter much at 5000 samples per second.

You could sense voltage (N * dF/dt) with the filament winding, instead of a resistive voltage divider.
Might not share 100% of the flux with primary winding.  But the measured voltage across primary includes an I * R term on top of N * dF/dt.   What happens if you subtract out the I * R component from your existing voltage data?

Applause for also getting true watts by averaging the V * I product.  The fact that it goes in different directions at different times is normal for inductive loads, like electric motors, with power factor less than unity.

[haversin]

Thanks klugesmith.

I counted 12 turns on the outer layer and counted 10 layers so assuming 12 turn per layer throughout I got 120 turns. I have been meaning to do a sanity check on this by wrapping say 10 turns around the primary winding (there's room to do this) and make a ac voltage comparison.

The B vs H curves represent just over one AC cycle (60z). The curves closed on themselves pretty well without changing the integration constant during the cycle. If you zoom in on lower left point of 110 v curve however you can see it didn't quite close. I had to shift each voltage curve to center them on B axis because of the different integration constants.

The two channels are multiplexed at 10 kHz so there is a 0.1 ms time difference . At 60 Hz this is only a 2 deg phase shift.

This MOT has no filament winding, It came from an old Amana Radarange oven which used a separate filament transformer. To make full use of the ten bit ADC range, I wanted the input voltages to the DI-149 to be close to full scale +- 10 volts at 120 v rms. The 23 to 1 resistive voltage divider was a simple way to do this.
One advantage of this setup is that the voltage across the primary is being measured after the IR voltage drop across the current sensing 0.5 ohm resistor so it is the actual voltage. The disadvantage is a minus sign must be applied to get the correct sign on the current. Of course in software this is no problem. There is the IR voltage drop of primary winding resistance but this is small.

Speaking of fluxmetering, I want to measure the flux density at the pole of a NIB magnet. Have you or anyone done this? If I'm reading wikipedia right it should be about 1.0 - 1.4 Tesla for sintered, and about 0.6 - 0.7 Tesla for bonded.