Mutual Inductance (Two coils connected in parallel to source)

[jake.davidoff]

Hi,

I recently performed a stator core loop test and am now in the process of capturing the setup and results in a report.

A short explanation of the test setup and execution:

A cable is wrapped around the core and energized, which induces a magnetic flux through the core. The core consists of many thin laminations that are all grounded from the back. If there exists any shorts between the laminations, the flux through the core will induce a current though the loop that is created by the shorted laminations. This area will heat up and will be detectable by thermal instrumentation.

My problem:

I am trying to determine the inductance of our system. Due to ampacity restrictions with our cables, we connect two coils in parallel from our source. This allows for only half the current to be pushed through each cable while achieving the same magnetic flux (same volts per turn). This has been done for years in our company but no one has documented any calculations to support the method.

My initial intuition told me that if one of the two coils was removed, the current draw from the source should be half. If looking at an electric circuit with two independent inductors connected in parallel, this would be correct. However, after conducting a small scale experiment, it was found that the current draw from the source stayed constant when one coil was removed.

I am assuming this is due to mutual inductance of the coupled coils; however, I am not sure how to pursue the calculation.

Note: The volts per turn stayed constant when one of the parallel coils was removed so the magnetic flux stayed constant, as expected.

Any insight would be greatly appreciated.

Thanks!
Jake

 

[marcusl]

Are you using an AC source?

 

[jake.davidoff]

Yes, AC source

 

[marcusl]

With air core coils, the AC current and flux density would approximately halve when one coil is removed. The "approximately" part--the deviation from 1/2--would be the amount due to mutual inductance. A magnetic core would behave similarly for small fields where the permeability is constant.

Since you find no change in operation between one or both coils, it is likely that you have thoroughly saturated your magnetic core with just the first coil. That is, the coil's H field is sufficient to drive the material well onto the wings of the iron's hysteresis curve where its incremental permeability is one. In this situation the core magnetization is unchanged when driven harder with the second coil. You probably don't need that second coil at all.

 

[jake.davidoff]

Thank you for your response. I have looked into the derivation of mutual inductance and now understand where the factor of approx 1/2 comes from. After doing some preliminary calculations, it seems as though that same factor will make the current draw from the source constant in the two cases, which corresponds to my experimental findings.

I also see what you are saying regarding saturation. I am assuming this only applies to the flux achieved and not the current.

Please correct me if I am incorrect in the above statements.

Thanks again