How can I calculate core losses given only frequency?

[jrp051680]

I cannot seem to figure this out. I know total core losses at 120Hz and 60Hz are 100w and 32w respectively for some unknown constant ac voltage. I can't seem to figure out how to go about finding core losses at other frequencies or separating eddy and hysteresis losses. Can anybody shed some light on this for me?

 

[The Electrician]

I used the search terms: "core losses" steinmetz

and found this paper: http://people.clarkson.edu/~pillayp/c28.pdf

The paper and its references should help you.

 

[jrp051680]

Thanks for the reply. The problem I am having is that I don't know the max flux density B_m or what the core material is to be able to calculate K_e, K_h or n. There has to be a simple answer to this that I must be overlooking and its driving me crazy. Thanks for the link.

 

[uart]

Is this a real world problem or an exercise (book problem)? I'd try the following approach for a somewhat simplistic (as in my not be completely accurate for a real world problem) solution.

The eddy current loss component is usually modeled as proportional to $B^2 f^2$ and the hysteresis loss component as proportional to $B^{1.6} f^1$. Here however the B^1.6 term is only a fairly rough approximation and different materials may use a slightly different constant (to 1.6) there. In any case, if we take the above relationships as correct then we can find a fairly simple solution.

$$P_L = k_1 B^2 f^2 + k_2 B^{1.6} f^1$$

It's also approximately true that at constant voltage the flux will be inversely proportional to frequency.

So,

$$P_L(n) = k_1 \left( \frac{B_1}{n} \right)^2 (n f_1)^2 +k_2 \left( \frac{B_1}{n} \right)^{1.6} (n f_1)^2$$

You don't know B but you do know that for a given voltage that B_1 is a constant so you can lump it (and f_1) with the constants k1 and k2 to get the above into a simple function of "n" (and of course the two lumped constants that you can determine from your two data points).