Talk:Leakage inductance/Archive 2

Archive 1

Archive 2

Archive 3

The concept of "ratio of magnetic flux = inductance ratio" is incorrect

I removed the following formula.

σ_P = Φ_P^σ/Φ_M = L_P^σ/L_M

σ_S = Φ_S^σ'/Φ_M = L_S^σ'/L_M

But, Jim1138 told me that it should be explain the reasons. So I stated as follows. The reason is that the Leakage factor is the ratio of the magnetic flux, but it is not the ratio of the inductance. The concept of "ratio of magnetic flux = inductance ratio" is incorrect. When the system current increases or decreases the mutual flux is proportional to the voltage across the mutual inductance and the leakage flux is proportional to the current in the secondary winding. Even if "coupling coefficient = mutual inductance / self inductance" is unchanged, the leakage flux changes greatly in proportion to the current flowing through the secondary winding, and the coupling factor value varies. Please look into this point again in detail. you should investigation into this point again in detail. 153.227.36.195 (talk) 08:20, 27 December 2016 (UTC)

I have to agree that there is something wrong with those equations. The ratio of the primary leakage flux to Mutual flux is a variable that depends on both primary and secondary currents, whereas the ratio of the inductance is a constant. But what is the meaning of σ_P if it is a variable depending currents that vary moment by moment? Constant314 (talk) 04:13, 28 December 2016 (UTC)

After more thought, the equation σ_P = Φ_P^σ/Φ_M = L_P^σ/L_M makes senses if it is measured with the secondary open circuited

and σ_S = Φ_S^σ'/Φ_M = L_S^σ'/L_M makes sense if it is measured with the primary open circuited.

Does it make sense that we just need to add some conditions tot he equations? Constant314 (talk) 06:59, 28 December 2016 (UTC)

If you discript the condition that "other windings is opened", it will be correct. In order to prevent the reader's misunderstanding, it is necessary to indicate at the same time that the flux ratio substantial changes when the secondary winding current is flowing in that case.153.227.36.195 (talk) 20:54, 30 December 2016 (UTC)

I'm of the opinion that the best way out of this conundrum is

σ_P = L_P^σ/L_M

σ_S = L_S^σ'/L_M

In other words, just drop the flux terms. I am convinced that the flux terms would apply under the condition that the other windings were open circuited and the flux terms themselves are RMS values or phasor amplitudes, but I don't have a reference to back it up. I have discussed this with the person that originally posted the material. He is sure that he accurately reflected what was in the reference(Hameyer, Kay (2001)), but there was probably some explanation that made it make sense. Unfortunately, the reference was an on line version of a very expensive book that is no longer on line or available where I can find it. So, the material is attributed to a book that is unavailable to anybody in the current discussion and I cannot even find it for sale.

So, at this point, I think we agree that the section is subject to multiple interpretations and is and will remain confusing unless it is clarified. However, we do not have access to the source reference to get that clarifiaction. I'm not sure that we even need the section. It doesn't make sense to me as is and I've designed signal transformers and flyback transformers from 60 Hz to 30 MHz (not all in one transformer). Maybe it makes sense to big equipment and big transformer designers who already know the material. I have several references on magnetics, rotating machines, transformers and power transmission. Leakage factor does not appear in any of them. Maybe it's a translated term from another language. Constant314 (talk) 22:19, 3 January 2017 (UTC)

Also note that i_M = i_P - i_S^' implies the primary and secondary have the same number of turns. Constant314 (talk) 02:54, 4 January 2017 (UTC)

Kay Hameyer's credentials FYI:

Kay Hameyer (Senior MIEEE, Fellow IET) received the M.Sc. degree in electrical engineering from the University of Hannover, Germany. He received the Ph.D. degree from University of Technology Berlin, Germany. After his university studies he worked with the Robert Bosch GmbH in Stuttgart, Germany, as a design engineer for permanent magnet servo motors and automotive board net components.

In 1988 he became a member of the staff at the University of Technology Berlin, Germany. From November to December 1992 he was a visiting professor at the COPPE Universidade Federal do Rio de Janeiro, Brazil, teaching electrical machine design. In the frame of collaboration with the TU Berlin, he was in June 1993 a visiting professor at the Universite de Batna, Algeria. Beginning in 1993 he was a scientific consultant working on several industrial projects. He was a guest professor at the University of Maribor in Slovenia, the Korean University of Technology (KUT) in South-Korea. Currently he is guest professor at the University of Southampton, UK in the department of electrical energy. 2004 Dr. Hameyer was awarded his Dr. habil. from the faculty of Electrical Engineering of the Technical University of Poznan in Poland and was awarded the title of Dr. h.c. from the faculty of Electrical Engineering of the Technical University of Cluj Napoca in Romania. Until February 2004 Dr. Hameyer was a full professor for Numerical Field Computations and Electrical Machines with the K.U.Leuven in Belgium. Currently Dr. Hameyer is the director of the Institute of Electrical Machines and holder of the chair Electromagnetic Energy Conversion of the RWTH Aachen University in Germany (http://www.iem.rwth-aachen.de/). Next to the directorship of the Institute of Electrical Machines, Dr. Hameyer is the dean of the faculty of electrical engineering and information technology of RWTH Aachen University. Currently he is elected member and evaluator of the German Research Foundation (DFG). In 2007 Dr. Hameyer and his group organized the 16th International Conference on the Computation of Electromagnetic Fields COMPUMAG 2007 in Aachen, Germany.

His research interests are numerical field computation, the design and control of electrical machines, in particular permanent magnet excited machines, induction machines and numerical optimisation strategies. Since several years Dr. Hameyer's work is concerned with the magnetic levitation for drive systems. Dr. Hameyer is author of more than 180 journal publications, more than 350 international conference publications and author of 4 books.

Dr. Hameyer is an elected member of the board of the International Compumag Society, member of the German VDE, a senior member of the IEEE, a Fellow of the IET and a founding member of the executive team of the IET Professional Network Electromagnetics.Cblambert (talk) 14:40, 4 January 2017 (UTC)

Knowlton's Standard Handbook for Electrical Engineers says in §8-67 The Leakage Factor. The total flux which passes through the yoke and enters the pole = Φ_m = Φ_a Φ_e and the ratio Φ_m/Φ_a and is greater than 1.Cblambert (talk) 15:01, 4 January 2017 (UTC)

Re Also note that iM = iP - iS' implies the primary and secondary have the same number of turns.: The S' means by definition secondary referred the primary, as detailed in various other Wikipedia articles include the Transformer article.Cblambert (talk) 15:56, 4 January 2017 (UTC)

The first 4 equations

σ_P = Φ_P^σ/Φ_M

σ_S = Φ_S^σ'/Φ_M

Φ_P = Φ_M Φ_P^σ = Φ_M Φ_PΦ_M = (1 σ_P)

Φ_S^' = Φ_M Φ_S^σ' = Φ_M Φ_SΦ_M = (1 σ_S)

are interrelated, which is why it not only makes no sense to remove the first 2 equations but shows the 3rd & 4th equation more fully expanded needed correction. The whole section, Refined leakage factor, hangs together seamlessly. The onus is on editors knowledgeable in the matter to show in detail why any one part of this section is not consistent with the end result and with the rest of this article. Cblambert (talk) 16:42, 4 January 2017 (UTC)

Hameyer's credentials are not being disputed. It's just that no one seems to be able to put their eyes on the source reference document. I appreciate you clarifying the meaning of iS'. Could you clarify whether the currents and fluxes are instantaneous values, RMS values, phasor values or phasor amplitudes? When I see currents written with lower case "i" I generally presume that means instantaneous (functions of time) values. Constant314 (talk) 21:50, 4 January 2017 (UTC)

I have sent Hameyer an e-mail asking for permission to get a copy of 2001 course notes document. My sense is that the flux equations are in general for steady-state frequency conditions (especially power frequency conditions) although the the flux linkage equations are generalized in terms of the derivative with respect to time, which is consistent with your sense that lc "i" is instantaneous. The key question as to the validity of Leakage factor being equal to the ratio of the inductance, would support the notion that the "i" is instantaneous for steady-state power frequency conditions with the end-result leakage factor derived from RMS flux equations.Cblambert (talk) 07:22, 5 January 2017 (UTC)

It is important to get to the bottom of this issue as is affect several interrelated articles including the Transformer, Induction motor, Circle diagram, Steinmetz equivalent circuit and other Wikipedia articles.Cblambert (talk) 07:28, 5 January 2017 (UTC)

The cause of the confusion was understood. The leakage factor is a term used for the core material, and it has not to be explained along with the leakage flux. And there was a cause to further deepen the confusion. The meaning of the leakage flux defined in the electromagnetics literature and the meaning of the "magnetic flux leaking from the core material" used in the explanation of the core material catalog are different. So it is wrong to explain the leakage factor in the secsion in the leakage inductance, and this explanation should be independent as a leakage factor of the core material.153.227.36.195 (talk) 17:42, 5 January 2017 (UTC)

So, is this article about "leakage flux" or "magnetic flux leaking from the core material"?Constant314 (talk) 18:11, 5 January 2017 (UTC)

This article is "Leakage inductance", is not it? This is a discussion of electromagnetism. Why is discussed about the "leakage factor" which is the term of core material?153.227.36.195 (talk) 19:19, 5 January 2017 (UTC)

Author of this talk section started saying that ratio of magnetic flux = inductance ratio" is incorrect and he now suddenly casts doubt on the whole article!? Is this discussion section grasping at straws? This article, Leakage inductance, has a long history which revolves around why it is that any magnetic device involves "Leaking inductance" which is imperfect as with any transformer or motor. The article has been used, and/or copied, extensively in/from corresponding Polish, Ukrainian, Japanese and other languages. Leakage inductance is used to explain in amazing simple terms the meaning of the coupling coefficient in terms of primary & secondary inductance, primary & secondary self-inductance, primary & secondary leakage inductance, magnetizing inductance, winding turns ratio and resistance and inductance referred to the primary. The leakage factor explains how it can be derived from also amazingly simple open-circuit and short-circuit tests. The leakage inductances can be used to derive a simplified equivalent circuit for magnetic devices. Leakage inductance provides the key to explaining many things about imperfect magnetic devices, which unavoidably requires dabbling in magnetic relationships. There is nothing wrong with magnetic relationships.Cblambert (talk) 22:42, 5 January 2017 (UTC)

It is correct that the magnetic flux ratio and the inductance ratio are not equal. Please refer to the following description.

leakage flux is proportional to the load current

So electromagnetically defined leakage flux is also zero when the load current is zero. However, the term "magnetic flux leaking from the core material" in the core material term is not zero. We need to be aware that terms which are similar to events of different meanings are used.153.227.36.195 (talk) 01:22, 6 January 2017 (UTC)

Dear 153.227.36.195, You have to show in detail what exactly you find is not supported in terms of sources by the article. It is not enough to point to a Google search with several book entries. If we all have a stomach for complex, tedious electro-magnetic relationships, we could always consider merging the Leakage inductance article into the Inductance article.Cblambert (talk) 02:57, 6 January 2017 (UTC)

By load current, do you mean secondary current? Constant314 (talk) 20:24, 6 January 2017 (UTC)

Yes it is. In the Electromagnetism, the leakage flux is proportional to the current of the secondary winding. This secondary winding current is the load current. There is a description in the document on the indicated link. The definition of leakage flux in a transformer described in the Electromagnetism is "The flux interlinks to the windings only one side and traverses paths not interlinks with other windings." So the leakage flux is zero, when the secondary winding current is zero.[1] But the definition of leakage flux in the Magnetism is "The magnetic flux which does not follow the special purpose path in a magnetic circuit."[2] There is no concept of load current here. So these two leakage fluxes are similar but different. The value of the formula also differs. If we made an article called The "Leakage flux", we have to describe these differences carefully. In some cases, the same technical term is used in different meanings in different fields of expertise. Leakage flux is a typical example of it. And the Electromagnetism and the Magnetism should not be confused. Cblambert said "in § 8-67 The Leakage Factor. The total flux which passes through the yoke". Here, total flux and yoke are the terms of the Magnetism. And the term leakage factor is the same. Here is the confusion between the Electromagnetism and the Magnetism. I found a literature very close to the description he seems to have quoted.[3] Here is yoke, total flux and leakage factor. If so then the leakage flux referred to here is that of magnetics, so it is different from that of a transformer. This is the cause of confusion. And there is one more problem. The following formula revived, is it correct?

σ_P = Φ_P^σ/Φ_M = L_P^σ/L_M

σ_S = Φ_S^σ'/Φ_M = L_S^σ'/L_M

The decisive thing is that the dimensions are different on the left and right sides of the equal sign.[4] The dimensions of the magnetic flux are as follows,

kg m² s^-2 A^-1

The dimension of the inductance is as follows,

kg m² s^-2 A^-2

If connect with equal sign, the notion of the electric current A is insufficient. Since this is a physical quantity, it can be objectively understand where there is a misunderstanding.153.227.36.195 (talk) 06:57, 8 January 2017 (UTC)

Maybe this is correct.

$\sigma _{P}={\frac {\phi _{P}^{\sigma }}{\phi _{M}}}={\frac {L_{P}^{\sigma }i_{P}}{L_{M}i_{M}}}$

$\sigma _{S}={\frac {\phi _{S}^{\sigma }}{\phi _{M}}}={\frac {L_{S}^{\sigma }i_{S}}{L_{M}i_{M}}}$

This is consistent with the description of the textbook and many literature. Besides, I think that it is reasonable that the dimensions on both sides of the equal sign match. If you can agree, it should be considered carefully and adopt this formula.153.227.36.195 (talk) 11:00, 8 January 2017 (UTC)

Maybe this is correct?! This is not serious discussion. Concrete, defendable, constructive proposals are needed.

This is consistent with the description of the textbook and many literature? Do you mean, This is consistent with descriptions of textbooks and the literature? If so, which description(s)? From which textbook(s)? In which literature?

This article starts from coupling factor in top section, progressing to leakage factor in the 2nd section in order to arrive at the equivalent circuit of a nonlinear transformer in 3rd section and refinement of leakage factor in 4th section. Both factors (coupling and leakage) are dimensionless as they are described in terms of the ratio of inductance and flux, so the zero-current argument invoked is meaningless. If there are any holes to pick in the article, they need to start at the top of the article, not at the end, as the whole article is clearly built with scientific logic from top to bottom.

This talk discussion definitely needs to stop grasping at straws.Cblambert (talk) 20:18, 8 January 2017 (UTC)

I find these two equations to be nonsense without further explanation

σ_P = Φ_P^σ/Φ_M = L_P^σ/L_M

σ_S = Φ_S^σ'/Φ_M = L_S^σ'/L_M

The right hand expression is clearly a constant. Φ_S^σ'/Φ_M clearly depends on both primary and secondary current. In particular, secondary current can be zero and thus Φ_S^σ' can be zero. This expression can be saved, if there is some condition can be put on the currents, such as the primary is driven by a voltage source at the transformer's rated vlotage and the the secondary is connected to a resistive load such that the transformer is delivering its fully rated secondary current. Further, there is the question as to whether Φ_M is an instantaneous, phasor or RMS quantity. I rather doubt that it is an instantaneous value because if it were, it could be instantaneously zero and the expression Φ_S^σ'/Φ_M would contain a divide by zero. Until these simple definitions are clarified, the rest of the section is hopelessly undecipherable. If we cannot clarify the meanings of these symbols then I think the entire section should be removed to the talk page until the symbols are clarified. Constant314 (talk) 21:01, 8 January 2017 (UTC)

Refined leakage factor

Magnetizing and leakage flux in a magnetic circuit

The nonideal transformer can be simplified as shown in third equivalent circuit, with secondary constants referred to the primary and without ideal transformer isolation, where,

i_M = i_P - i_S^' ------ (Eq.3.1)

i_M is magnetizing current excited by flux Φ_M that links both primary and secondary windings.

i_S^' is the secondary current referred to the primary side of the transformer.

Referring to the flux diagram at right, the winding-specific leakage ratio equations can be defined as follows,

σ_P = Φ_P^σ/Φ_M = L_P^σ/L_M ------ (Eq.3.2)

σ_S = Φ_S^σ'/Φ_M = L_S^σ'/L_M ------ (Eq.3.3)

Φ_P = Φ_M Φ_P^σ = Φ_M σ_PΦ_M = (1 σ_P)Φ_M ------ (Eq.3.4)

Φ_S^' = Φ_M Φ_S^σ' = Φ_M σ_SΦ_M = (1 σ_S)Φ_M ------ (Eq.3.5)

L_P = L_M L_P^σ = L_M σ_PL_M = (1 σ_P)L_M ------ (Eq.3.6)

L_S^' = L_M L_S^σ' = L_M σ_SL_M = (1 σ_S)L_M ------ (Eq.3.7),

where

• σ_P is primary leakage factor
• σ_S is secondary leakage factor
• Φ_M is mutual flux (main flux).
• Φ_P^σ is primary leakage flux.
• Φ_S^σ is secondary leakage flux.

The leakage ratio σ can thus be refined in terms of the interrelationship of above winding-specific inductance and leakage factor equations as follows:

$\sigma =1-{\frac {M^{2}}{L_{P}L_{S}}}=1-{\frac {a^{2}M^{2}}{L_{P}a^{2}L_{S}}}=1-{\frac {L_{M}^{2}}{L_{P}L_{S}^{\prime }}}=1-{\frac {1}{{\frac {L_{P}}{L_{M}}}.{\frac {L_{S}^{\prime }}{L_{M}}}}}=1-{\frac {1}{(1 \sigma _{P})(1 \sigma _{S})}}$ ------ (Eq.3.8).Cblambert (talk) 00:08, 9 January 2017 (UTC)Cblambert (talk) 20:24, 10 January 2017 (UTC)

I disagree completely with the previous discussion. Cblambert (talk) 00:23, 9 January 2017 (UTC)

I was thinking whether this problem could be solved or not. A hint was obtained from considerations of dimension. It is established the right and left sides of the equation under a limited electric current condition. So what is limited electric current condition? It is when the current values of the denominator and the molecule are equal. That is,

$\sigma _{P}={\frac {\phi _{P}^{\sigma }}{\phi _{M}}}={\frac {L_{P}^{\sigma }i_{P}}{L_{M}i_{M}}}$

$\sigma _{S}={\frac {\phi _{S}^{\sigma }}{\phi _{M}}}={\frac {L_{S}^{\sigma }i_{S}}{L_{M}i_{M}}}$

Although I delayed, the basis of the above formula is,[5]

$\phi =LI$

Here do the following,

$i_{P}=i_{M}$

${\frac {\phi _{P}^{\sigma }}{\phi _{M}}}={\frac {L_{P}^{\sigma }}{L_{M}}}$

Then,

$i_{M}=i_{P}-i_{S}$

That means,

$i_{S}=0$

So,

$\sigma _{S}=0$

This was initially suggested by Constant314. I also agree that. So, I think that such a limited conditions which related to the current are described somewhere in Hameyer.--153.227.36.195 (talk) 03:02, 10 January 2017 (UTC)

We can conjecture on the talk page, but for the article, we need the actual definitions and conditions from the reliable source. That being said, and strictly for the purpose of discourse, I note, that under normal conditions (primary driven by a voltage source, secondary load mostly resistive) that i_M lags i_S by almost 90 degrees. So how are we to take the meaning of i_S/i_M? Constant314 (talk) 21:50, 10 January 2017 (UTC)

This equal sign is not established when current flows through the secondary winding. In other words, it is only established under the condition that the secondary winding is open. At first, Cblambert brought the term and formula of the Magnetism which called the "Leakage factor" to the Leakage inductancethe of the Electromagnetism article. At first glance it seemed like a reckless challenge. However, under the limited conditions it is possible to match the equations of electromagnetism and magnetism. I am just trying to respect the intention of the writer as much as possible. But as you pointed out, there is no clear source yet.--153.227.36.195 (talk) 23:52, 10 January 2017 (UTC)

Definition of leakage inductance in other industrial fields

I found that there is a definition different from the definition of this article like Measuring Leakage Inductance or [6], To summarize them,

$L_{s/c}=a^{2}L_{\text{inductance of the short-circuit impedance}}$

I think that this should be annotated.

They are saiing that they define the inductance of the leakage impedance as leakage inductance or define the primary side conversion value of it as so. I think that we should need to suggest them for readers.--153.227.36.195 (talk) 20:11, 12 January 2017 (UTC)

The case for Hameyer's Refined leakage factor equations

The logic of Hameyer's Refined leakage factor equations can be recast along the follow lines:

a) We know from article's Eq. 2.1 & IEC IEV 131-12-41 that the coupling factor $k$ (a value that is dimensionless, fixed, finite, positive & less that 1) is given by the following:

$k=M/{\sqrt {L_{P}L_{S}}}$ ------ (Eq. 1).

b) We also know from article Eq. 2.7 & IEC IEV 131-12-42 that the leakage factor $\sigma$ can be derived in terms of coupling factor k to read as follows:

$\sigma =1-k^{2}=1-{\frac {M^{2}}{L_{P}L_{S}}}$ ------ (Eq. 2)

Note that $\sigma$ is therefore also a value that is dimensionless, fixed, finite, positive & less that 1.

c) Above Eq. 3.8 can therefore be given by the following:

c.1) by multiplying the ${\frac {M^{2}}{L_{P}L_{S}}}$ term by ${\frac {a^{2}}{a^{2}}}$, we get

$\sigma =1-k^{2}=1-{\frac {M^{2}}{L_{P}L_{S}}}=1-{\frac {a^{2}M^{2}}{L_{P}a^{2}L_{S}}}$ ------ (Eq. 3)

c.2) According to Eq. 2-8, $L_{M}=aM$, and given that by definition $a^{2}L_{S}=L_{S}^{\prime }$, we have:

$\sigma =1-k^{2}=1-{\frac {M^{2}}{L_{P}L_{S}}}=1-{\frac {a^{2}M^{2}}{L_{P}a^{2}L_{S}}}=1-{\frac {L_{M}^{2}}{L_{P}L_{S}^{\prime }}}$ ------ (Eq. 4)

c.3) By multiplying the ${\frac {L_{M}^{2}}{L_{P}L_{S}^{\prime }}}$ term by ${\frac {L_{M}.L_{M}}{L_{M}^{2}}}$, Eq. 3.8 becomes:

$\sigma =1-k^{2}=1-{\frac {M^{2}}{L_{P}L_{S}}}=1-{\frac {a^{2}M^{2}}{L_{P}a^{2}L_{S}}}=1-{\frac {L_{M}^{2}}{L_{P}L_{S}^{\prime }}}=1-{\frac {1}{{\frac {L_{P}}{L_{M}}}.{\frac {L_{S}^{\prime }}{L_{M}}}}}$ ------ (Eq. 5)

c.4) Expressed in terms of currents and inductances only, Eq. 3.1, Eq. 3.2, Eq. 3.3, Eq. 3.6 & Eq. 3.7 can be restated as follows:

i_M = i_P - i_S^' ------ (Eq.3.1)

σ_P = L_P^σ/L_M ------ (Eq.3.2)

σ_S = L_S^σ'/L_M ------ (Eq.3.3)

L_P = L_M L_P^σ = L_M σ_PL_M = (1 σ_P)L_M ------ (Eq.3.6)

L_S^' = L_M L_S^σ' = L_M σ_SL_M = (1 σ_S)L_M ------ (Eq.3.7)

such that, as Hameyer shows, above Eq. 3.8 is thus proven to be equal to:

$\sigma =1-k^{2}=1-{\frac {M^{2}}{L_{P}L_{S}}}=1-{\frac {a^{2}M^{2}}{L_{P}a^{2}L_{S}}}=1-{\frac {L_{M}^{2}}{L_{P}L_{S}^{\prime }}}=1-{\frac {1}{{\frac {L_{P}}{L_{M}}}.{\frac {L_{S}^{\prime }}{L_{M}}}}}=1-{\frac {1}{(1 \sigma _{P})(1 \sigma _{S})}}$ ------ (Eq.3.8)

c.5) Regarding development of Eq. 3.1 to Eq. 3.4 in terms of flux relationships, it is known that, far from being nonsense, σ_P = Φ_P^σ/Φ_M & σ_S = Φ_S^σ'/Φ_M must necessarily be values that are dimensionless, fixed, finite, positive & less that 1. Further, since in sinusoidal steady-state conditions and at rated primary voltage Φ_M (and magnetizing current) can be represented as a fixed non-zero phasor (or RMS) value, it follows that Φ_S^σ' (and current) must by definition be a fixed non-zero phasor (or RMS) value. Brenner and Javid show on pp. 591-593 that a transformer can be shown in additive and subtractive series connection of the two windings to be equal to:

Additive connection = $L_{ser}^{ }=L_{P}^{\sigma } L_{S}^{\sigma }-2M$ ------ (Eq. 5)

Subtractive connection = $L_{ser}^{-}=L_{P}^{\sigma } L_{S}^{\sigma } 2M$ ------ (Eq. 6)

such that winding inductances can be determined form the 3 equations:

$L_{ser}^{ }-L_{ser}^{-}=4M$ ------ (Eq. 7) and $L_{ser}^{ } L_{ser}^{-}=2*(L_{P}^{\sigma } L_{S}^{\sigma })$ ------ (Eq. 8) and $a={\sqrt {L_{P}/L_{S}}}$ ------ (Eq. 2.10).

c.6) The case for Hameyer's equations for the refined leakage factor is therefore conclusively proven and will be modified in this sense to restore the Refine leakage factor section of the Leakage inductance article.Cblambert (talk) 05:01, 11 January 2017 (UTC)

Since there are now no flux ratios or current ratios there is no longer a need to define them. I am satisfied with what you have now. The variables in Eq 3.1 don't seem to show up anywhere else. You might want to leave that out.Constant314 (talk) 05:28, 11 January 2017 (UTC)

Is σ in here the same as σ of this page [7]?

$\sigma ={\frac {\Phi _{t}}{\Phi _{g}}}$

--153.227.36.195 (talk) 10:33, 11 January 2017 (UTC)

I don't think so. That appears to be about flux at an intentional air gap. At a gap, some of the flux goes where you want it to go and some of it fringes around. That leakage factor is the ratio of the total flux to the flux that stays in the desired gap. Constant314 (talk) 18:45, 11 January 2017 (UTC)

I don't think so either. This article defines leakage factor in terms of the coupling factor per Eq. 1 and Eq. 2 above.Cblambert (talk) 21:57, 11 January 2017 (UTC)

I suggest that the flux and current relationships in flux diagram and in Eq. 3.1 to Eq. 3.8 all be maintained as it is important to the understanding of the Leakage inductance article to tie together the flux diagram Main_&_leakage_inductances.jpg to all the Hameyer equations.Cblambert (talk)

I have no problem with flux and current as long as they have a clear, sensible definition and conditions under which they apply are explicit. I would rather that those definitions and conditions come from the source, but if you can reconstruct them from memory and we can agree that they are clear and consistent then I will have no objection. I do object to using them without definition. If I look elsewhere, I may find the same symbols used in a similar situation but with a different meaning, as we have seen the use "leakage factor" with the same symbol used to mean something else. Constant314 (talk) 00:21, 12 January 2017 (UTC)

You have to be kidding. I would be interested in knowing about any such instances of different meaning for similaar situation because I have taken greats pains to other this. We are all in this together. Right?Cblambert (talk) 00

36, 12 January 2017 (UTC)

Then the meaning of σ here and the σ of the link shown by me will be different. Is that no problem? Then the meaning of σ here and the σ of the link shown by me will be different. Is that a problem? By the way, at in § 8-67 The Leakage Factor. The total flux which passes through the yoke", is it possible to see what was written about leakage factor? Also, the number of documents describing leakage inductance and leakage factor in the same field is extremely little. I tried searching for "search "leakage inductance leakage factor" but I can not find anything other than this page of Wikipedia and its quotations.--153.227.36.195 (talk) 02:01, 12 January 2017 (UTC)

I am not saying that the leakage factor you describe is wrong, but the leakage factor in this article is a very special definition and not general. So I recommend that you should add an annotation that the same term is used in other fields so that the reader will not misunderstand the leakage factor. At the same time, I found out that the leakage inductance has the same problem, did you know? For example, Measuring Leakage Inductance[8],To summarize,

$L_{s/c}=a^{2}L_{\text{inductance of the short-circuit impedance}}$

I think that this should also be annotated.--153.227.36.195 (talk) 20:11, 12 January 2017 (UTC)

For a reference, this definition is more general for the leakage factor and the leakage inductance.[9]--153.227.36.195 (talk) 20:59, 12 January 2017 (UTC)

What is the general definition of the leakage factor?

We also need to suggest readers about its general definition.--153.227.36.195 (talk) 20:11, 12 January 2017 (UTC)

"The magnetic leakage factor" for Magnetic materials and components [10] and "The inductive leakage factor" for the Circuit theory [11] are really the same thing? The symbol σ is described on one side and the symbol is not described on the other side. If they are different, it should be highlighted for readers.--153.227.36.195 (talk) 11:04, 13 January 2017 (UTC)

The essential problem with the Refined inductive leakage factor section remains

We still have these equations with no description about the conditions under which they apply.

σ_P = Φ_P^σ/Φ_M = L_P^σ/L_M ------ (Eq. 3.1)

σ_S = Φ_S^σ'/Φ_M = L_S^σ'/L_M ------ (Eq. 3.2)

It is obvious that they don't apply under all conditions. I believe that I can guess the conditions which is this: Eq. 3.1 applies when the primary is driven and the secondary is open. Under this condition, i_M = i_P which means Φ_P^σ and Φ_M are produced by the same current and their ratio is the same as L_P^σ/L_M. Eq. 3.2 applies when the secondary is driven and the primary is open circuited. I now consider this to be obvious. If the three of us agree that it is obvious, then lets put it in and be done. Constant314 (talk) 21:10, 13 January 2017 (UTC)

Exactly. Under those condition, those formula will be hold. I would like you to adopt it as a result of careful consideration.--153.227.36.195 (talk) 22:38, 13 January 2017 (UTC)

Anyway I studied valuable thing this time in here. I started by biting that formula in a short-temper without knowing the inductive leakage factor at all. I knew only the leakage factor which is the magnetic leakage factor. The outcome of this finding is the result of Cblambert's efforts and thanks for making many links to references. I had been barking like a wolf all the while. Please forgive me for many overstuffing behavior.--153.227.36.195 (talk) 23:08, 13 January 2017 (UTC)

Coupling factor and coupling coefficient

Although these two terms are very similar, I think that their relation may be follows,

${\text{Coupling factor}}=\left|{\text{Coupling coefficient}}\right|$

So the coupling coefficient is fit for the former (Eq. 2.1), but the coupling factor is fit for the latter (Eq. 2.1). Then, according to IEC IEV 131-12-41, the latter (Eq. 2.1) should be dscripted as follows,

$k=\left|M\right|/{\sqrt {L_{P}L_{S}}}$ --------------------- (Eq. 2.1)

--153.227.36.195 (talk) 04:46, 15 January 2017 (UTC)

First of all, let's read and examine Measuring Leakage Inductance[12] before the discussion. And how to obtain the coupling coefficient. [13]--153.227.36.195 (talk) 23:59, 16 January 2017 (UTC)

Old url for Hameyer

Old url for Hameyer is http://materialy.itc.pw.edu.pl/zpnis/electric_machines_I/ForStudents/Script_EMIHanneberger.pdf/ As in for Hameyer, Kay (2001). "Electrical Machine I: Basics, Design, Function, Operation" (PDF). RWTH Aachen University Institute of Electrical Machines. Retrieved 11 January 2013.page=133 in Induction motor.Cblambert (talk) 12:44, 17 January 2017 (UTC)

Refined inductive leakage factor derivation

The Refined inductive leakage factor derivation box below, taken verbatim from article, is obtained from basic principles, which happens to agreed with Haymeyer (and with Constant314). The onus is on others to disprove this derivation.

Refined inductive leakage factor derivation

a. Per Eq. 2.1 & IEC IEV 131-12-41 inductive coupling factor k is given by

$k=\left|M\right|/{\sqrt {L_{P}L_{S}}}$ --------------------- (Eq. 2.1)

b. Per Eq. 2.7 & IEC IEV 131-12-42 Inductive leakage factor $\sigma$ is given by

$\sigma =1-k^{2}=1-{\frac {M^{2}}{L_{P}L_{S}}}$ ------ (Eq. 2.7) & (Eq. 3.7a)

c. ${\frac {M^{2}}{L_{P}L_{S}}}$ multiplied by ${\frac {a^{2}}{a^{2}}}$ gives

$\sigma =1-{\frac {a^{2}M^{2}}{L_{P}a^{2}L_{S}}}$ ----------------- (Eq. 3.7b)

d. Per Eq. 2-8 & knowing that $a^{2}L_{S}=L_{S}^{\prime }$

$\sigma =1-{\frac {L_{M}^{2}}{L_{P}L_{S}^{\prime }}}$ ---------------------- (Eq. 3.7c)

e. ${\frac {L_{M}^{2}}{L_{P}L_{S}^{\prime }}}$ multiplied by ${\frac {L_{M}.L_{M}}{L_{M}^{2}}}$ gives

$\sigma =1-{\frac {1}{{\frac {L_{P}}{L_{M}}}.{\frac {L_{S}^{\prime }}{L_{M}}}}}$ ------------------ (Eq. 3.7d)

f. Per Eq. 2.14, Eq. 3.1, Eq. 3.2, Eq. 3.5 & Eq. 3.6

$\sigma =1-{\frac {1}{(1 \sigma _{P})(1 \sigma _{S})}}$ --- (Eq.3.7e)

All equations in this article assume steady-state constant-frequency waveform conditions the k & $\sigma$ values of which are dimensionless, fixed, finite & positive but less that 1.

Cblambert (talk) 17:18, 17 January 2017 (UTC)

My only objection is that σ_P and σ_S are elsewhere set equal to the ratios of inadequately defined fluxes. Constant314 (talk) 21:05, 17 January 2017 (UTC)

Do you have a proposal on how to close this gap? One of us could always invest US$15 to get, through IEEE Explore, MIT-Press's Self- and Mutual Inductance, which conveniently covers the following topics: The Coupled-Circuit Equations, Coefficient of Coupling and Leakage Coefficient, Measurement of the Parameters, Leakage Inductance, Equivalent Circuits for Two-Winding Transformers, Summary, Problems.Cblambert (talk) 00:37, 18 January 2017 (UTC)

I have added a citation-footnote reading: ' U. of Colorado - Magnetics, slide 32: It can be seen by inspection that, for steady-state sinusoidal waveform conditions applied to a real, linear transformer, σP is equal to the leakage-to-magnetizing ratios of both inductances and fluxes. With both U. of Colorado and Hameyer agreeing, I think the onus is indeed on others to disprove the derivation.Cblambert (talk) 05:48, 18 January 2017 (UTC)

The Voltech document is about measuring L_P^σ L_S^σ' under the conditions of a short circuited secondary. The article is about how to correct the measurement in the case where the short circuit is not quite a perfect short circuit. It says nothing about fluxes and nothing about the ratio of leakage flux to magnitizing flux. There is nothing apparent about flux ratios on the U of Colorado slide. As draw on slide 32, magnetizing flux is a function of both primary current and secondary current and therefor Φ_P^σ/Φ_M and Φ_S^σ'/Φ_M are not constants. For example I can make Φ_S^σ'/Φ_M = 0 by open circuiting the secondary. My proposal for fixing this is to remove all reference to Φ_P^σ, Φ_M and Φ_S^σ' in equations 3.1 and 3.2 and delete equations 3.3 and 3.4 until we get a source that defines the fluxes. The rest of the math deals with constants that are independent of the fluxes and the final result and all the intermediate steps are unchanged. Constant314 (talk) 17:38, 18 January 2017 (UTC)

If Cblambert needs formula for deriving (Eq. 1.4) I will write it.--153.227.36.195 (talk) 19:31, 18 January 2017 (UTC)

Re Voltech: I know exactly what Voltech is doing, but the document does say as that in a perfect world leakage inductance is as quoted. Voltech is invoked here because sentence used to refer to open-circuit conditions only and circuiting is a good approximation in transformer of a certain rating.Cblambert (talk) 01:37, 19 January 2017 (UTC)

Re flux, the fluxes are shown in Eq. 3.1 & Eq. 3.2 as a ratio, which does not vary.Cblambert (talk) 01:37, 19 January 2017 (UTC)

Hameyer pp. 28-29, eq. 3-31 thru eq. 3-36 is for now until disproved a valid reference.Cblambert (talk) 01:37, 19 January 2017 (UTC)

Re U. of Colorado: I have deleted the footnote.Cblambert (talk) 01:43, 19 January 2017 (UTC)

Re former Eq. 1.4, any equation needs to be consistent with the rest of the article in terms of notations, and otherwise melding seamlessly and logically. Any eq. should be excluded from in 1st sub-section as it deals with the k diagram.Cblambert (talk) 02:10, 19 January 2017 (UTC)

You have not adopt no matter how I show many sources. The term Leakage inductance is not just for Magnetism persons. Also it should be considered the leakage inductance for Electromagnetism persons and Electronics engineers. If you are an engineer, you would think how to obtain those specific values if you wanted to use those values for applications not only in theoretical. I already showed one of the derivative methods.[| formula (22)] And I show another way to derive even more easily those values as follows,

In the figure on the right, short-circuit the secondary winding and find the short-circuited inductance value of the primary side.

$L_{sc}^{pri}=L_{P}(1-k) {\frac {1}{{\frac {1}{kL_{P}}} {\frac {1}{L_{P}(1-k)}}}}=L_{P}-kL_{P} {\frac {1}{\frac {L_{P}-kL_{P} kL_{P}}{kL_{P}^{2}-k^{2}L_{P}^{2}}}}=L_{P}-kL_{P} {\frac {kL_{P}^{2}-k^{2}L_{P}^{2}}{L_{P}}}$

$=L_{P}-kL_{P} kL_{P}-k^{2}L_{P}=L_{P}-k^{2}L_{P}=L_{P}(1-k^{2})$

${\frac {L_{sc}^{pri}}{L_{P}}}=1-k^{2}$

$k^{2}=1-{\frac {L_{sc}^{pri}}{L_{P}}}$

$k={\sqrt {1-{\frac {L_{sc}^{pri}}{L_{P}}}}}$

$k={\sqrt {1-{\frac {L_{sc}^{pri}}{L_{oc}^{pri}}}}}$

This result is consistent with the source which I showed.--153.227.36.195 (talk) 02:47, 19 January 2017 (UTC)

Thanks. This may well be the case (I need to take time to check this). The point that there already exists a good simple solution including in terms of a drawings. Adding an alternative solution adds to the confusion, which is evidently quite complex to deal with now. A compelling reason is needed to warrant adding this extra complexity. I make no different in principle between magnetism, electromagnetism & electronics. There used to be a section of Leakage inductance in practice which someone went missing. I will restore it.Cblambert (talk) 04:31, 19 January 2017 (UTC)

Need for explicit IEC explanation endnote

Endnote is felt necessary due to counter repeated recently expressed view by some that IEC is "an industry association".Cblambert (talk) 17:48, 21 February 2017 (UTC)

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