The calculation of the magnetic field of rectangular conductors in a closed slot, and its application to the reactance of transformer windings

Billig, E.

doi:10.1049/pi-4.1951.0007

Cited by 12 publications

(11 citation statements)

References 1 publication

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“…Applying the image method to conductors inside a winding window would theoretically create an infinity of image conductors. This is because the mirror effect of image method not only duplicates the current sources, but also the material interfaces [11]. It creates mirrored version of magnetic mirrors.…”

Section: ) Conductors Inside a Winding Windowmentioning

confidence: 99%

“…A similar approach has been established in [11]. However, a preferential direction was supposed to take into account the infinity of conductors.…”

Section: ) Conductors Inside a Winding Windowmentioning

confidence: 99%

“…A practical way to represent the increase of losses with the frequency is to use factors quantifying this increase compared to DC losses. In this paper, skin factor defined in (11) and proximity factor defined in (12) will be used.…”

Section: ) Core-type and Shell-type Leakage Inductancementioning

confidence: 99%

“…It should be noted that skin effect losses Pskin are directly related to the current I flowing inside the considered conductor and this is why it makes sense to define skin factor in (11). However, proximity effect losses Pprox are indirectly related to the current I.…”

Section: ) Core-type and Shell-type Leakage Inductancementioning

confidence: 99%

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Semi-Analytical Methods for Calculation of Leakage Inductance and Frequency-Dependent Resistance of Windings in Transformers

Fouineau¹,

Raulet²,

Lefebvre³

et al. 2018

IEEE Trans. Magn.

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Leakage inductance and frequency-dependent resistance of windings are key parameters for the design of magnetic devices. This report focuses on analytical or semi-analytical calculation techniques to be integrated into a medium frequency transformer optimization process. To this extend, a review of currently most used method to calculate inductance and resistance of windings transformer is established. Based on this review, new calculation methods are developed. Magnetic field cartography is evaluated on the basis of two-dimensional structures thanks to a combination of Ampère's law and image method. From this magnetic field map, leakage inductance can be calculated. The obtained accuracy with this method is equivalent to three-dimensional finite element modeling. For frequency-dependent resistance evaluation, new methods based on two-dimensional or one-dimensional approach are compared to finite element modeling and reviewed models. An analysis of behavior of each model is done, showing that newly developed models are more suitable in the case of medium frequency transformer design in terms of accuracy, robustness and calculation time. This work could be useful to magnetic devices designers because newly developed models could easily be adapted to various geometries, such as toroidal structures or even inductors.

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Section: ) Conductors Inside a Winding Windowmentioning

confidence: 99%

“…A similar approach has been established in [11]. However, a preferential direction was supposed to take into account the infinity of conductors.…”

Section: ) Conductors Inside a Winding Windowmentioning

confidence: 99%

Section: ) Core-type and Shell-type Leakage Inductancementioning

confidence: 99%

Section: ) Core-type and Shell-type Leakage Inductancementioning

confidence: 99%

See 2 more Smart Citations

Semi-Analytical Methods for Calculation of Leakage Inductance and Frequency-Dependent Resistance of Windings in Transformers

Fouineau¹,

Raulet²,

Lefebvre³

et al. 2018

IEEE Trans. Magn.

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show abstract

“…Unfortunately, Hague's discussion is not free from error and contains some claims for the method which cannot be sustained. The work is also mentioned by Bewley 2 and by Billig, 3 who praises its sound theoretical basis and suggests that, in this respect, it is superior to other methods. There is an extended account in Hague, in 1929," called these papers 'a complete treatise', and his praise would have been even more justified if he had had access to Roth's later work.…”

Section: Introductionmentioning

confidence: 93%

Roth's method for the solution of boundary-value problems in electrical engineering

Hammond

1967

Proc. Inst. Electr. Eng. UK

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Between the years 1927 and 1938 the French engineer E. Roth developed a powerful method for the solution of boundary-value problems in electrical engineering. He applied the method to problems in heat conduction and magnetic-field problems in electrical machines and transformers, although the application of the method is not necessarily limited to such devices. In spite of its possibilities, the method has been omitted from the standard treatises on electromagnetic problems, because there are certain difficulties associated with it. The paper gives a critical account of the method, listing both advantages and disadvantages and relating these to the physical and mathematical basis of Roth's work. List of symbols A = magnetic vector potential B-magnetic flux density H = magnetic field strength / = current density V = electric scalar potential V* = magnetic scalar potential a, b, c, d, e,f = slot dimensions m, n = parameters C m n = coefficient x, y = rectangular coordinates X = function of x only Y = function of y only J

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Effective resistance and reactance of a rectangular conductor placed in a semi-closed slot

Swann¹,

Salmon²

1963

Proc. Inst. Electr. Eng. UK

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The calculation of the magnetic field of rectangular conductors in a closed slot, and its application to the reactance of transformer windings

Cited by 12 publications

References 1 publication

Semi-Analytical Methods for Calculation of Leakage Inductance and Frequency-Dependent Resistance of Windings in Transformers

Semi-Analytical Methods for Calculation of Leakage Inductance and Frequency-Dependent Resistance of Windings in Transformers

Roth's method for the solution of boundary-value problems in electrical engineering

Effective resistance and reactance of a rectangular conductor placed in a semi-closed slot

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