Transformer Core Loss and Hysterisis Losses.

[IrVen]

I would like to know why the core loss resistance and magnetizing reactance is parallel to the primary voltage in the transformer equivalent circuit?

 

[edison123]

Because they are not load dependent.

 

[dpc]

Think about it. The excitation current through the primary winding. Even if the secondary winding was completely removed, the excitation current would still flow.

 

[electricpete]

The magnetizing branch is actually downstream of the primary leakage reactance and then in parallel with the secondary circuit. But since leakage reactance is fairly small, the distinction is not particularly important and to a first approximation as stated above the magnetizing branch current is constant wrt load. And the reasoning above certainly explains why can't put it in series with the load.... then we'd have no excitation if no load... just doens't match reality.

Another way to look at it is to go back to the derivation of the Tee equivalent circuit representation of coupled linear magnetic circuits. That is given on pages 1-7 of Krause's "Analysis of Electrical Machinery" here:

http://media.wiley.com/product_data/excerpt/6X/04711432/047114326X.pdf

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[jghrist]

Maybe the question is why are they in parallel instead of why are they not in series with the load.

This is just for convenience in calculating the equivalent impedance elements. You could have a resistance in series with a reactance and be equally valid. The parallel combination is the Thevenin equivalent of the series combination.

 

[electricpete]

It is certainly a valid model to replace the primary leakage reactance, magnetizing reactance (and core loss resistance element if present) with it's Thevinin equivalent. There are several situations where this is a more convenient representation. But in that model there is no component which we call the "magnetizing reactance" which was specifically referred to in the original post.

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[electricpete]

Corrected to add bolded portion:

It is certainly a valid model to replace the primary leakage reactance, magnetizing reactance (and core loss resistance element if present) and supply voltage source with it's Thevinin equivalent

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[electricpete]

At any rate, it was probably good to mention as jghrist did that there are other representations.

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[electricpete]

The Tee model (leakage reactances and magnetizing reactance) has a close tie to the physical picture of the fluxes. The magnetizing reactance is associated with flux that links both windings and the leakage reactance is associated with the flux that links one winding but not the other.Typically the magnetizing reactance is much larger than the leakage reactance. If you temporarily imagine the leakage reactance is 0 (all flux linked by both windings), you can get a simple picture of the operation of the transformer.First wind the primary winding onto a single phase core and energize it. It will draw a magnetizing current which is the voltage divided by the magnetizing reactance. The rate of change of flux (times the number of turns) exactly balances the applied voltage. Now wind a secondary winding on top of the primary open circuited. Since it links the same flux as the primary, you can see a voltage will appear on the secondary which is equal to rate of change of flux times secondary turns. Since both primary and secondary satisfy Vk =Nk * dPhi/dt with same flux, we have Vk~Nk. V2 = V1 * N2/N1.If you connect a load to the secondary a current will be drawn from the secondary. However the total rate of change of flux must still balance the primary applied voltage, so the primary will contribute additional load component of current whose amp-turns will exactly cancel the amp-turns drawn by the secondary circuit load.

You can see the transformer primary supplies a constant excitation current, plus a current equal (after turns trnasformation) to the secondeary current. So naturally these branches are parallel.

All of the above has neglected the leakage reactance which is a small effect, but certainly necessary to predict the load-dependent voltage droop accross the transformer. Does not change the logic which led us to place the excitation and secondary branches in parallel fed from the primary.

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[jghrist]

I think I messed up when I used the term Thevenin equivalent. I meant only that you can have a series impedance equivalent to the parallel impedance as the magnetizing branch. The parallel impedance model is easier to calculate because the no-load loss is V²/R, making it easy to calculate the parallel resistance element if you know the no-load losses.