Leakage Inductances of Transformers at Arbitrarily Located Windings

The article presents the calculation of the leakage inductance in power transformers. As a rule, the leakage flux in the transformer window is represented by the short-circuit inductance, which affects the short-circuit voltage, and this is a very important factor for power transformers. This inductance reflects the typical windings of power transformers well, but is insufficient for special transformers or in any case of the internal asymmetry of windings. This paper presents a methodology for calculations of the self- and mutual-leakage inductances for windings arbitrarily located in the air window. It is based on the 2D approach for analyzing the stray field in the air zone only, using discrete partial differential operators. That methodology is verified with the finite element method tested on real transformer data.

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On Simplified Calculations of Leakage Inductances of Power Transformers

Energies ◽

10.3390/en13184952 ◽

2020 ◽

Vol 13 (18) ◽

pp. 4952 ◽

Cited By ~ 1

Author(s):

Tadeusz Sobczyk ◽

Marcin Jaraczewski

Keyword(s):

Power Transformer ◽

Short Circuit ◽

Power Transformers ◽

Stray Field ◽

Good Representation ◽

The Finite Element Method ◽

Leakage Inductance ◽

Leakage Flux ◽

Calculation Results ◽

Discrete Differential Operator

This paper deals with the problem of the leakage inductance calculations in power transformers. Commonly, the leakage flux in the air zone is represented by short-circuit inductance, which determines the short-circuit voltage, which is a very important factor for power transformers. That inductance is a good representation of the typical power transformer windings, but it is insufficient for multi-winding ones. This paper presents simple formulae for self- and mutual leakage inductance calculations for an arbitrary pair of windings. It follows from a simple 1D approach to analyzing the stray field using a discrete differential operator, and it was verified by the finite element method (FEM) calculation results.

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Approximation of noisy data using multivariate splines and finite element methods

Journal of Algorithms & Computational Technology ◽

10.1177/17483026211008405 ◽

2021 ◽

Vol 15 ◽

pp. 174830262110084

Author(s):

Bishnu P Lamichhane ◽

Elizabeth Harris ◽

Quoc Thong Le Gia

Keyword(s):

Finite Element ◽

Differential Operators ◽

Impulsive Noise ◽

Noisy Data ◽

Multivariate Splines ◽

The Finite Element Method ◽

Data Smoothing ◽

Multivariate Spline ◽

Partial Differential Operators ◽

Mixture Of Gaussian

We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares functional. The penalties are based on partial differential operators, and are integrated using the finite element method. We compare three methods to two problems: to remove the mixture of Gaussian and impulsive noise from an image, and to recover a continuous function from a set of noisy observations.

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Leakage flux and force calculation on power transformer windings under short-circuit: 2D and 3D models based on the theory of images and the finite element method compared to measurements

IEEE Transactions on Magnetics ◽

10.1109/20.312690 ◽

1994 ◽

Vol 30 (5) ◽

pp. 3487-3490 ◽

Cited By ~ 30

Author(s):

A.G. Kladas ◽

M.P. Papadopoulos ◽

J.A. Tegopoulos

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Power Transformer ◽

Short Circuit ◽

3D Models ◽

The Finite Element Method ◽

Leakage Flux ◽

2D And 3D ◽

Force Calculation ◽

Element Method

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The Calder´on-Zygmund Theory I: Ellipticity

10.23943/princeton/9780691162515.003.0001 ◽

2017 ◽

Author(s):

Brian Street

Keyword(s):

Classical Theory ◽

Singular Integral ◽

Singular Integrals ◽

Differential Operators ◽

Integral Operators ◽

Singular Integral Operators ◽

Single Parameter ◽

Partial Differential ◽

Translation Invariant ◽

Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

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Magneto-Thermo-Structural Analysis of Power Transformers under Inrush and Short Circuit Conditions

Energies ◽

10.3390/en14113266 ◽

2021 ◽

Vol 14 (11) ◽

pp. 3266

Author(s):

Antonio Roniel Marques de Sousa ◽

Marcus Vinicius Alves Nunes ◽

Wellington da Silva Fonseca ◽

Ramon Cristian Fernandes Araujo ◽

Diorge de Souza Lima

Keyword(s):

Structural Analysis ◽

Electric Power ◽

Short Circuit ◽

Real Data ◽

Short Circuit Current ◽

Power Transformers ◽

Inrush Current ◽

Electric Power Supply ◽

Axial Forces ◽

Radial Forces

The main equipment responsible for connection and transmission of electric power from generating centers to consumers are power transformers. This type of equipment is subject to various types of faults that can affect its components, in some cases also compromising its operation and, consequently, the electric power supply. Thus, in this paper, electromagnetic, thermal, and structural analysis of power transformers was carried out with the objective of providing the operator with information on the ideal moment for performing predictive maintenance, avoiding unplanned shutdowns. For this, computational simulations were performed using the finite element method (FEM) and, from that, the different transformer operation ways, nominal currents, inrush current, and short-circuit current were analyzed. In this perspective, analyses of the effects that thermal expansion, axial forces, and radial forces exerted were carried out, contributing to possible defects in this type of equipment. As a study object, simulations were carried out on a 50 MVA single-phase transformer. It is important to emphasize that the simulations were validated with real data of measurements and with results presented in the current literature.

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