Short-circuit Forces Research Articles

Transfer Function Method to Diagnose Axial Displacement and Radial Deformation of Transformer Winding

Short circuit currents or forces during transport can cause mechanical displacements of transformer windings. The transfer function method is presented as a tool to detect these displacements. In order to be able to evaluate the measurements, the correlation between the characteristics of transfer functions and possible damages must be known. Axial displacement and radial deformation of transformer windings have been studied-in this research work using two test transformers. The primary winding of the first transformer for axial displacement has 31 double disk coils (1.3 MVA, 10 kV) and the secondary winding is a four-layer winding. The second transformer for the study of radial deformation has 30 double disk coils (1.2 MVA, 10 kV) as primary winding and a one-layer winding as secondary winding. The detailed mathematical models were developed for the test objects and a comparison was carried out between measured and calculated results. It is shown that this model can present the behavior of the transformer windings in the frequency domain in the case of sound and displaced conditions.

Instability of the continuously transposed cable under axial short-circuit forces in transformers

The axial instability of the winding conductor is one of the principal modes of mechanical failure in large power transformers. It is caused by axial compressive forces generated by the electromagnetic interaction of the short-circuit current and the radial leakage flux. It is a buckling type of mechanical instability that occurs under compression. Two possible modes of failure in the layer type coil wound with the continuously transposed cable are identified and analyzed in this paper. The critical design loads leading to instability of the individual strands as well as of the whole cable are separately derived. The actual instability threshold of the coil would be the lesser of the two critical loads. For the through-fault integrity of the transformer design, this threshold must be greater than the peak compressive force on the cable under the worst case short-circuit current.

Instability of the Machine-Transposed Cable under Axial Short-Circuit Forces in Large Power Transformers

The axial instability of the winding conductor is one of the principal modes of mechanical failure in large power transformers under axial compressive forces generated by the electromagnetic interaction of the short-circuit current and the radial leakage flux. It is a buckling type of mechanical instability that occurs under compression. Two possible modes of failure in the layer-type coil wound with the continuously transposed cable are identified and analyzed in this paper. The critical design loads leading to instability of the individual strands, as well as of the whole cable, are separately derived. The actual instability threshold of the coil would be the lesser of the two critical loads. For the through-fault integrity of the transformer design, this threshold must be greater than the peak compressive force on the cable under the worst-case short-circuit current.

Computation of inrush current forces on transformer windings

Inrush currents are frequently encountered during the switching process of transformers. The purpose of this paper is to present an investigation of forces that appear as a result of inrush currents. While both short circuit and inrush transformer situations might seem identical, they vary significantly from the core magnetization viewpoint. Three-dimensional computations have been carried out on a typical single-phase power transformer using the Hopfield neural network energy minimization technique. Results are given in the paper as well as comparison with short circuit forces.

Comparison of assumptions in computation of short circuit forces in transformers

This paper describes the modeling of shell type distribution transformers with varying degrees of complexity. Results from several types of studies are reported and used to evaluate the effectiveness of FEA methods for resolving the forces exerted on the coils of a single-phase shell form transformer. The sensitivity of these methods to the very small changes in configuration due to manufacturing tolerances or operation are investigated. Several types of analysis were performed and compared to determine the best approach for design or failure analysis.

Steady-state loss and short-circuit force analysis of a three-phase bus using a coupled finite element+circuit approach

The authors analyze a three-phase bus with steady-state and short-circuit currents using a coupled finite element+circuit analysis method that they had previously developed for rotating machines. The bus consists of nine copper conductors, three in parallel for each phase, in an aluminum duct. This technique is required because the distributions of the respective total phase currents among the parallel conductors are not known a priori. They present the results of both steady-state (frequency-domain) and transient (time-domain) calculations.

Loss and current distribution in foil windings of transformers

Detailed loss and current distributions in the foil-wound low-voltage winding of a 6 MVA power transformer using a finite-element analysis package are presented. The foil-winding eddy loss is estimated and its variation with clearance to yoke is examined. Plots of foil current and eddy-current density and loss-intensity distributions are shown and the magnitude and location of their maxima identified. These lead to the main finding that the foil-winding loss distribution is significantly nonuniform not only axially but also radially. This radial variation has been ignored in previous studies. This will have implications for the thermal performance which is outside the scope of the present study. Although the low-voltage foil winding is conventionally the inner winding, it is shown that making it an outside winding can result in a significant reduction in the maximum current density, loss intensity and the winding eddy loss as a percentage of the I/sup 2/R loss. The radial short-circuit forces on the outside foil winding, being tensile, could also be an advantage. The variation of foil eddy loss with foil thickness is examined.

Dynamic analysis of substation busbar structures

The usual method used to design substation busbar structures is to analyze the short circuit force loading with an equivalent static loading. However, it is shown here that the relatively slow response modes of the structure require that a dynamic analysis be performed for the higher frequency short circuit forces. Full scale test data is compared to simulation results obtained from a finite element model.

Application of global optimization strategies to the shape design of a transformer winding

In the paper the leakage field in a transformer, produced by windings of variable shape, is investigated. The two-dimensional axisymmetrical analysis of the magnetic field enables short-circuit forces on the two windings to be accurately evaluated. The design problem consists of improving the shape of the primary winding in order to minimize the total force exerted on it under short-circuit conditions. Numerical results achieved using evolution strategy are reported and discussed.

Numerical calculation of 3D eddy current field and short circuit electromagnetic force in large transformers

The improved T- Omega method is employed to calculate the three-dimensional transient eddy current field in large transformers, as well as the short-circuit electromagnetic forces acting on the transformer windings. The effects of the magnetic shielding and initial angles of currents are studied, and the nonuniform distribution of ampere-turn along the height of the windings is taken into account. Thus, a common software package is developed. Two different transformers are analyzed, and the computed results show agreement with measured ones.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

THE FEM ANALYSIS OF NONSYMETRICAL SHORT CIRCUIT FORCES AND FIELDS IN THE WINDOW OF CONVERTOR TRANSFORMER

The paper describes the simulation of a short circuit of one diode in a three‐phase convertor set connected to a 2 winding transformer. The forcing currents are computed with the circuit simulation method. The circuit — field model is solved with the finite‐element method. In the paper is presented the distribution of flux lines and values of short circuit forces (strains) solved during one period every 15 degrees in the window of the convertor transformer. This approach to dynamic phenomena using the method presented has not yet been applied to short circuit research in transformers.

Use of a modified Ussing chamber to monitor intestinal epithelial and smooth muscle functions

A technique that allows the simultaneous monitoring of epithelial and smooth muscle function was developed and used to study rat small intestine in vitro. A Ussing chamber was modified so that a strain gauge force transducer could be sewn to the serosal surface of an intestinal segment clamped in the chamber. The apparatus was used to monitor short-circuit current, potential difference, and resistance across the segment, and contractions of the longitudinal layer of the muscularis externa. Both spontaneous activity and responses to the application of carbachol were recorded. Carbachol applied to the serosal side induced dose-dependent increases in both short-circuit current and contractile force. The median effective doses of the two responses differed, with contractions being more sensitive to the drug. Carbachol applied to the mucosal side induced no changes in either epithelial or contractile activities. The ability of the serosal strain gauge transducer to monitor contractions faithfully was tested in an organ bath in which the gut segment was attached to an external force-displacement transducer. There was a close correlation between the dose-dependent increase in force in response to carbachol measured by the serosal transducer and that measured by the force-displacement transducer (r = 0.988). Thus our technique can be used to study simultaneously epithelial and smooth muscle functions of the intestine.

Short-circuit electromagnetic forces in three phase gas insulated systems with steel enclosure

In this paper, the short-circuit forces acting on the phase-conductors of arrangements with 3-phase steel enclosure, are examined. In the case of tubular conductors the forces result from the vector potentials calculated in the different arrangement areas. The potentials result as Fourier series ofn terms; their coefficients are determined from the numerical solution of a 10×n algebraic equations system. But in the case of filamentary conductors the corresponding system of equations consists of two independent systems, 4×n equations each, that can be analytically solved and lead to simpler relations for the forces. Parametric investigations showed that, for the praxis arrangements, the influence of the conductor radius on forces is very small and consequently the conductors may be considered as filamentary. The influence of the relative permeability, the conductivity and the thickness of the shell on the electromagnetic forces has also been examined.

Analysis of transient forces in metal clad generator buses

Transient short-circuit forces are analytically calculated in an arrangement of three parallel and coplanar busbars. Each is enclosed in a tubular, conducting, shell. Results can be used for the design of metal clad connection buses for large generators or similar uses. Shells made of aluminium with 10 mm thickness reduced the forces applied on the phase conductors by a factor of 20 or more as compared with arrangements without shells. Forces applied on a phase conductor and to the corresponding shell have same order of magnitude.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Numerical calculation of short circuit electromagnetic forces on the transformer winding

Based on expressions for transient three-phase short-circuit current, the formulas for radial and axial electromagnetic forces acting on transformer windings are derived. The short-circuit forces, include three components: DC component, fundamental-frequency component, and double-frequency component. Using a 17000-kVA transformer as a model, the 2-D leakage magnetic fields and forces with various phase angles are calculated by the finite-element method. The results are compared with design formulas. Numerical calculations show that the conventional design formulas used to calculate radial force can meet engineering needs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Mechanical short-circuit effects of single-core cables

A simple calculation model is presented that allows a determination of the permanent plastic deformation caused by short-circuit forces in plastic-insulated single-core cables. The accuracy of the model is sufficient for practical purposes. The model is verified by tests in a heavy-current laboratory. For rating, the mechanical short-circuit strength it is shown to be sufficient to adhere to a maximum permissible permanent displacement. For this calculation, only one material parameter, the yield point of the conductor material, is necessary.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Short-circuit electromagnetic forces in three-phase gas insulated systems with aluminium enclosure

In the paper, the short-circuit forces acting on three tubular conductors arranged in an equilateral triangle and constituting a 3-phase system enclosed by a cylindrical aluminium enclosure are examined. The relations for the time functions of the short-circuit forces are developed taking into account the transverse dimensions (diameter) of the conductors. The forces acting on such structures are compared with the forces on structures with filamentary conductors; it results that for usual structures the assumption of filamentary conductors causes a small error in the values of forces; for practical computations the simpler relations that concern forces on filamentary conductors can be used.

Erratum: Short-circuit electromagnetic forces in three-phase gas insulated systems with aluminium enclosure

Erratum: Short-circuit electromagnetic forces in three-phase gas insulated systems with aluminium enclosure

Experimental Verification of Three-Dimensional Analysis of Leakage Magnetic Fields in Large Power Transformers

In a previous paper by the first author, a three-dimensional analysis for the calculation of the leakage magnetic field in power transformers was presented. The experimental verification of this analysis is the subject of this paper. Extensive comparisons between calculated and measured values of flux densities in the winding of an experimental three-phase shell form transformer are presented. The results as well as the agreements and deviations obtained are discussed in light of the ultimate objective of accurate determination of various transformer performance parameters. The close agreements obtained verify the accuracy of the method of calculation as well as the validity of the experimental and measuring techniques. The results also demonstrate that accurate determination of losses, circulating currents, short circuit forces, impedance, shielding requirements and other performance parameters is possible only through three-dimensional calculations of the leakage magnetic field in the transformer.

Experimental Verification Of Three-Dimensional Analysis Of Leakage Magnetic Fields In Large Power Transformers

In a previous paper by the first author, a three-dimensional analysis for the calculation of the leakage magnetic field in power transformers was presented. The experimental verification of this analysis is the subject of this paper. Extensive comparisons between calculated and measured values of flux densities in the winding of an experimental three-phase shell form transformer are presented. The results as well as the agreements and deviations obtained are discussed in light of the ultimate objective of accurate determination of various transformer performance parameters. The close agreements obtained verify the accuracy of the method of calculation as well as the validity of the experimental and measuring techniques. The results also demonstrate that accurate determination of losses, circulating currents, short circuit forces, impedance, shielding requirements and other performance parameters is possible only through three-dimensional calculations of the leakage magnetic field in the transformer.