About "leakage inductance"

Question

I'm a little confused about the transformer "leakage inductance" for days. Per this text book, it gives a schematic view of fluxes flow in the transformer:

It's apparent that the two leakage flux will create separate inductance on each side. And it give s equivalent circuit:

You see, there are two separate inductance on each side, that is, the primary leakage inductance and the secondary leakage inductance.

And we reflect all the load at secondary to the primary side, then get

All are easy to understand, there are two "leakage inductance", though you can reflect them to the same side, but in physics, there indeed are two "leakage inductanes".

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But in the app note from a leakage inductance tester, it says

Leakage inductance is an inductive component present in a transformer that results from the imperfect magnetic linking of one winding to another. Any magnetic flux that does not link the primary winding to the secondary winding acts as inductive impedance in series with the primary, therefore this “leakage inductance” is shown on a schematic diagram as an additional inductance before the primary of an ideal transformer.

And it gives,

Apparently, there is only one "leakage inductance" at one side in the figure above.

1. Which one this inductance conrrespond to in the text book above? The primary one only or the primary one add the reflected secondary one?
2. When it measure the "leakage inductance", it short the secondary. I wonder if it can short the secondary leakage out as below (Note: The R2 can't be shorted, it should always exist at the left side of the red line). If it can, then the measured leakage inductance from primary side will contain only the primary leakage; if it can NOT, then it will get the primary inductance added with the reflected secondary leakage, right?

Answer 1

Apparently, there is only one "leakage inductance" at one side in the figure above.

No, that is incorrect.

Every winding in a transformer does not couple 100% to each other winding and that is a fact. If some piece of text suggests that the leakage inductance is only attributable to one winding then that piece of text is at best misleading and, at worst blatantly wrong.

However, from the perspective of someone wishing to know how well two windings may couple then a single entity of leakage (a composite of both leakages) can be used to express that.

As for your 2nd question, you CANNOT short the secondary at the point you wish. This IS impossible - you can't take the equivalent circuit of the transformer and hack at it like that. The leakage measured is the composite leakage and this can be broken down into two components by using the turns ratio squared but even that is only an approximation; the magnetization inductance will alter the accuracy of this method slightly but, for all practical purposes, this method yields fairly accurate results.

Answer 2

First, imagine a core with one winding of N turns. If the winding carries has a voltage V across it, then the flux linked to it Must change at a rate V/N. Now, most (99%) of this flux increase happens through the core, but the rest circulates through the air. The flux (rate) through the air is the leakage component and can be modelled as a bulk leakage inductance.

Now on this core lets wind another coil, again with N turns. The core already has a flux caused by coil 1. Most of this flux passes though the second coil, generating an emf, but some of it "bypasses" this coil and passes through the air instead. This is modelled as the secondary leakage inductance. To simplify the circuit model it is possible to combine both inductances into one "lumped" inductor.

Answer 3

One can measure the leakage inductance on the primary or on the secondary. Both results reflect the total leakage adjusted by the turns ratio and summed up. That is all ok. Problems will show up if the parasitic capacitance of the winding at high frequencies become more dominant. Then you need to split the leakage inductance correctly to each side with its own parasitic components to get a useful model to reflect for example self resonances of the transformer correctly. Otherwise even the VOLTEC model will work for most applications.

Answer 4

It was explained long ago that separate leakage inductances (of a iron-core transformer) do not exist. In case of the cylindrical windings, the total Ls should be moved to the terminals of the inner winding.

Answer 5

For transformer, we ain't go only electrical way, but physical too

Transformer actions: 1) Current flows through primary winding 2) As a result, magnetic flux flows across the magnetic core 3) Magnetic flux causes current to secondary winding

All texts about leakage inductance refers to imperfect coupling or imperfect magnetic leakage

For primary leakage, it's obviously some electrical power doesn't coupled or linked to magnetic core and it causes power loss

But for magnetic core to secondary winding, imperfect linkage will have to be resulted in different way, say, core loss