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:(adsbygoogle = window.adsbygoogle || []).push({});

W_{h}= ηB_{max}^{x}fV

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_{e}B_{max}^{2}f^{2}t^{2}

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}, I_{1}, I_{2}, frequency, material type of core and wire, etc.

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Single Phase Transformer Losses -- Hysteresis, Eddy Current Constants

**Physics Forums | Science Articles, Homework Help, Discussion**