Single Phase Transformer Losses -- Hysteresis, Eddy Current Constants

[ZenSerpent]

Hi. My colleagues and I are doing a research on transformers (single-phase) and we stumbled across the following equations involving hysteresis and eddy current losses:

W_h = ηB_max^xfV
where W_h = hysteresis losses
η = Steinmetz hysteresis constant
B_max = maximum flux density
x = constant depending on material
f = frequency
V = volume of core

P_e = K_eB_max²f²t²
where P_e = eddy current losses
K_e = eddy current coefficient
B_max = maximum flux density
f = frequency
t = thickness of lamination

The question is: How do we find η, x, and K_e? Are there tables containing these values corresponding to the type of these materials?
We're math majors so assume that we don't have ample amount knowledge regarding the fields involved. We're planning to make a simulation software out of the mathematical model (at least) that may aid in making single-phase transformers. If possible however, we're planning to make an optimal mathematical model (optimization using partial derivatives, I think.) with minimal loss and from it we'll be able to determine the optimal length of windings and number of turns, optimal cross-sectional areas of these wires, optimal volume of core, optimal tongue width and dimensions of the core, and the optimal thickness and number of layers of the laminations using input values V_p, V_s, I₁, I₂, frequency, material type of core and wire, etc.

Thanks in advance and we promise to include anyone who may help us in the acknowledgment page of our thesis. :)

 

[jim hardy]

Here's an excellent old line magnetics company that still let's us use their library...

check this 'how to' article
http://www.mag-inc.com/design/design-guides/powder-core-loss-calculation

it looks like they use a similar equation of form PL/volume = C_onstant X B^b X F_requency^f
where C , b (exponent of flux B) and f(exponent of frequency are empirical and should be tabulated in their datasheets.

When you click curve fit equation tool
it takes you to another page with a link http://www.mag-inc.com/File%20Library/Product%20Literature/Powder%20Core%20Literature/2015-Magnetics-Powder-Core-Catalog.pdf .
a few pages into that one are curves for several materials that show the empirical constants

i'd see what you can glean from their datasheets

searching on keywords from that site will train your search engine

i'm no magnetics expert but, good luck guys

 

[ZenSerpent]

Thanks for the reply guys. Well, I have also seen sites where x = 1.6 as a default value (for Iron, I guess). I also tried searching the links for the said exponent but I didn't find any. And also, why did the formula that I posted has 1 as the exponent for f while the other equations I have seen on the said links are not equal to 1? Hehe... Seems confusing. [emoji28]

 

[jim hardy]

i saw several curves like this in the powder core catalog

C varies widely from around 40 to 500 but b's cluster around 2±15% and f's around 1.6±10%

now that's for powder cores
i didnt find stamped steel cores
their tape wound cores catalog has curves for several alloys but they didnt tabulate the curve fit constants for us
http://www.mag-inc.com/File%20Library/Product%20Literature/Strip%20Wound%20Core%20Literature/2016-Magnetics-Tape-Wound-Cores-Catalog.pdf

hope it helps you search further

old jim

 

[ZenSerpent]

Thanks a lot Jim. I now understand everything that you've been telling us. However, I think we'll prioritize laminated steel cores over powder cores since these powder cores do sound new to us and I'm not even sure if they are available here. I hope there are still websites dedicated to the steel ones.