Transformer reactance calculations with digital computers

Rabins, L.

doi:10.1109/tce.1956.6372526

Cited by 51 publications

(23 citation statements)

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“…via analytical formulae such as the ones described in [3]- [5]. The self and mutual inductances are calculated using the Rabin's Method [6], [4]. The inductances are modified including a common iron core flux to adapt the model to power frequencies (50/60 Hz), as shown in Appendix A.…”

Section: B Parameter Determinationmentioning

confidence: 99%

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Interfacing <formula formulatype="inline"><tex Notation="TeX">${\rm k}$</tex></formula>-Factor Based White-Box Transformer Models With Electromagnetic Transients Programs

Gustavsen

Portillo²

2014

IEEE Trans. Power Delivery

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White-box transformer models are used by transformer manufacturers during the dielectric design of windings. The models are often based on constant parameters (RLCG matrices) with the high-frequency losses accounted for by a scaling of the dc resistance ( -Factor). We show an efficient procedure for interfacing such models with Electromagnetic Transients Program (EMTP)-type circuit simulators via state equations and a Norton equivalent. The approach makes no approximations except for the discretization in the time domain. Diagonalization is utilized for achieving high computational efficiency. Proprietary information about internal voltages is optionally hidden from the user. Internal surge arresters are handled by the EMTP circuit solver by declaring their connection points as external nodes. The model interface includes automated initialization from 50/60-Hz initial conditions. The proposed interfacing capability permits manufacturers to apply their models in complete network simulations, and to share their models with users.

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Section: B Parameter Determinationmentioning

confidence: 99%

“…At each node, according to Kirchhoff law, we have for the total current flowing into each node (6) where is a specified current injection from ground into all nodes. Inserting (1), (2), and (5) in (6) gives (7a) while combining (3) and (4) gives (7b)…”

Section: State Equationsmentioning

confidence: 99%

Interfacing <formula formulatype="inline"><tex Notation="TeX">${\rm k}$</tex></formula>-Factor Based White-Box Transformer Models With Electromagnetic Transients Programs

Gustavsen

Portillo²

2014

IEEE Trans. Power Delivery

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“…Substituting (19) into (18), we obtain (20) Since the sine functions are orthogonal, we can equate corresponding coefficients on both sides of this equation. We obtain (21) The solution to (21) consists of a homogeneous solution and a particular solution (22) Thus, the solution (19) is given explicitly as (23) where are unknown constants that are determined by using boundary conditions. For regions I and III, the term is eliminated from (23) because the current density is zero inside these regions.…”

Section: A Calculation Of Vector Potentialmentioning

confidence: 99%

“…Using the separating variables and then applying the required constraints to the solutions for satisfying the boundary conditions, the vector potential in each region is obtained as a single series of sine and exponential components. This method is also an extension of the Rabins' method [21], [22] in planar coordinates and with different boundary conditions.…”

mentioning

confidence: 99%

New Methods for Computation of the Inductance Matrix of Transformer Windings for Very Fast Transients Studies

Eslamian

Vahidi

2012

IEEE Trans. Power Delivery

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To study very fast transients in transformers, computing the winding inductance matrix at very high frequencies (MHz) is required. The air-core approximation formulas cannot be used for this purpose because at very high frequencies the core behaves as a magnetic insulating wall and so the distribution of the magnetic field is quite different from that of air-core inductors. This paper presents new analytical methods for computing the winding inductance matrix at very high frequencies considering the presence of the core. A simple method, based on numerical integration of the vector potential functions, is described for the calculation of inductance outside the core window. For the region inside the core window, two different analytical solutions are developed and inductance formulas are extracted. The final expressions are simple and fast convergent. Comparisons with finite-element method simulations prove the high accuracy of the technique.

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“…The solutions are expressed in terms of infinite series. Boundary value problem has been used by Rabins [18] to compute the inductances of a transformer with a simplified geometry consisting of a core, coils, and yokes of infinite extent. In [19][20][21], the magnetic field distribution of circular coils located between two semi-infinite blocks of iron is given.…”

Section: Introductionmentioning

confidence: 99%

Inductance and Force Calculation for Axisymmetric Coil Systems Including an Iron Core of Finite Length

Lubin

Berger

Rezzoug

2012

PIER B

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Abstract-This paper presents new semi-analytical expressions to calculate the self-inductance and the electromagnetic force for a ferromagnetic cylinder of finite length placed inside a circular coil of rectangular cross section. The proposed analytical model is based on boundary value problems with Fourier analysis. Laplace's and Poisson's equations are solved in each region by using the separation of variables method. The boundary and continuity conditions between the different regions yield to the global solution. Moreover, the iron cylinder is assumed to be infinitely permeable. Magnetic field distribution, self-inductance and electromagnetic force obtained with the proposed analytical model are compared with those obtained from finite-element.

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Transformer reactance calculations with digital computers

Cited by 51 publications

References 0 publications

Interfacing <formula formulatype="inline"><tex Notation="TeX">${\rm k}$</tex></formula>-Factor Based White-Box Transformer Models With Electromagnetic Transients Programs

Interfacing <formula formulatype="inline"><tex Notation="TeX">${\rm k}$</tex></formula>-Factor Based White-Box Transformer Models With Electromagnetic Transients Programs

New Methods for Computation of the Inductance Matrix of Transformer Windings for Very Fast Transients Studies

Inductance and Force Calculation for Axisymmetric Coil Systems Including an Iron Core of Finite Length

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