Steinmetz equations for transformer core loss?

[cupoftea]

Hi,
Recently I was chatting to an SMPS consultant who asked me how I calculated the core loss in a Flyback SMPS core. I said I looked at the graphs of Watts/m^3 vs B…with lines added for various frequencys....and read off from there.
He told me this was wrong, and that I should use the Steinmetz equations…..well I agree, but no core datasheets give the Steinmetz coefficients….so how can we use Steinmetz?

 

[wwfeldman]

Steinmetz's equation - Wikipedia

en.wikipedia.org

as i read the wiki article, the Steinmetz equation applies to sinusoidal fluxes.
it also notes how the coefficients may derived from a hysteresis diagram, without details
and that they change with temperature.

there is a more complicated equations for non-sinusoidal fluxes.

if you talk to the SMPS consultant again, quiz him/her on the details

the last reference on the wiki page looks most promising
in the references, the doi link leads to

Calculation of losses in ferro- and ferrimagnetic materials based on the modified Steinmetz equation

This paper discusses the influence of nonsinusoidal flux-waveforms on the remagnetization losses in ferro- and ferrimagnetic materials of inductors, transformers and electrical machines used in power electronic applications. The nonsinusoidal changes of flux originate from driving these devices...

ieeexplore.ieee.org

 

[FvM]

You can only use data that is provided by the manufacturer. It's also known since long that classical Steinmetz method doesn't give good results for arbitrary waveforms and DC bias. I'd suggest design tools like Ferroxcube SFDT that calculate losses for arbitrary waveforms using state-of-the-art methods.

 

[byjuncal]

Using manufacturer plots for Power loss density vs Flux density for different frequencies you calculate the parameters used on the Steinmentz expression (k, a, b).
Regarding the case the current is not sinusoidal, that you can do is to use Furier to get the Flux magnitude for the fundamental and harmonics so you can apply Steinmentz in a more accurate way.

 

[Easy peasy]

core loss data published in data sheets is some what optimistic as they test on a small toroid with sinusoidal voltage excitation - testing the real coil in house with a simple push pull lash up ( low volts, low turns, no Cu loss ) to give the required Bpk and freq will give you real world figures for the heat in the core - more than you think.