How Do Eddy Current Losses in Transformer Cores Work?

[Physicist3]

Hi, I have been trying to understand eddy current loss in transformer cores but seem to have run into a bit of a misunderstanding with one of the books I have read, and I was wondering if someone could just clarify if I have got this all right.

starting with the beginning, if the magnetic flux varies sinusoidal, then the flux at one instant would be;

∅ = ∅_msin(ωt) (I have been told this should be done in degrees and not radians?)

value of induced emf in core at any time (t) =

[itex]\frac{d∅}{dt}[/itex] = ω∅_mcos(ωt)

Am I correct in saying that from this second equation, ωθ_m = E_m (Max induced EMF in core)?

If E_s = rms value of emf induced in core, this = [itex]\frac{1}{\sqrt{2}}[/itex]ω∅_m = [itex]\sqrt{2}[/itex]∏f∅_m = [itex]\sqrt{2}[/itex]∏f(AB_m)

Eddy current Power Losses = [itex]\frac{E_s²}{R_s}[/itex]
= [itex]\frac{2*∏²*f²*A²*B_m²}{R_s}[/itex]

The next bit is the section of the notes that seems to confuse me,

Eddy current Power Loss = P_E = K_E*f²*B_M², where K_E = Constant = 2*∏²*A²/R_s.

The book then says 'hence eddy current losses = α (f²*B_M²)

Does this mean that K_E is the same as α and eddy current power loss is the same as eddy current loss, or are these two different things? As far as I can see they appear the same but I just wanted to make sure from someone who has a bit more experience or knowledge of this.

thanks

 

[NascentOxygen]

value of induced emf in core at any time (t) =

[itex]\frac{d∅}{dt}[/itex] = ω∅_mcos(ωt)

Am I correct in saying that from this second equation, ωθ_m = E_m (Max induced EMF in core)?

That would be emf induced per turn in the winding around the core, I think.

The book then says 'hence eddy current losses = α (f²*B_M²)

Lose the equals sign. I think that should be a simple proportionality:

eddy current losses α (f²*B_M²)

 

[hisham.i]

Eddy current Power Loss = PE = KE*f2*BM2, where KE = Constant = 2*∏2*A2/Rs.

The book then says 'hence eddy current losses = α (f2*BM2)

Both are the same, eddy current losses means the power loss due to eddy current.

 

[jim hardy]

Try a search on Steinmetz - he figured it out by experiment late 1800's
some old textbooks are showing up online nowadays with first-hand explanation.

 

[alphy]

Hello,

It seems like you have a good understanding of the basics of eddy current loss in transformer cores. To answer your question, KE and α are not the same thing. KE is a constant that represents the specific material properties and geometry of the core. It is used in the equation for calculating eddy current power loss, which is the total amount of power lost due to eddy currents in the core.

On the other hand, α represents the proportionality constant between the eddy current power loss and the frequency and magnetic field strength. In other words, α tells us how much the eddy current power loss will increase with an increase in frequency and magnetic field strength. So, while KE is a constant specific to the core, α can vary depending on the operating conditions.

Therefore, eddy current power loss and eddy current loss are not the same thing. Eddy current power loss is the total amount of power lost due to eddy currents, while eddy current loss is the proportion of that power loss caused by eddy currents.

I hope this clarifies things for you. Keep up the good work in understanding eddy current loss in transformer cores!