Effect of Width of Axial Supporting Spacers on the Buckling Strength of Transformer Inner Winding
TL;DR: In this article, the effect of the number of axial supporting spacers on the critical buckling stress of the inner winding of a transformer was investigated, and an algorithm has been given to calculate the critical bearing stress.
Abstract: During a short circuit, the transformer's inner winding, which is supported by the inner support structure, may fail due to the buckling phenomenon. This occurs due to the generation of large radially inward electromagnetic force on the inner winding. In the literature, the effect of the number of axial supporting spacers on the critical buckling stress is reported, but there is no investigation about the effect of their circumferential width on the value of the critical buckling stress. In this letter, the effect of the circumferential width of the axial supporting spacers on the value of critical buckling stress of the transformer inner winding has been investigated. An algorithm has been given to calculate the critical buckling stress of the inner winding. A case study has been taken from the published work, and by varying the width of the spacers, the factor of safety against buckling has been determined.
Citations
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TL;DR: In this article, the transformer's internal electromagnetic forces during the normal working and short-circuit conditions are investigated and finite element analysis is used to simulate the three phase transformer model and results are also verified by using the traditional analytical method.
Abstract: Transformer is one of the major components in the electrical power system. Safety and efficiency of the power system are also affected by the working of the power transformer. In this paper transformer's internal electromagnetic forces during the normal working and short-circuit conditions are investigated. Finite element analysis is used to simulate the three-phase transformer model and results are also verified by using the traditional analytical method. Axial and radial forces are calculated during the normal and short-circuit conditions. Transformer’s each high and low voltage windings are divided into 12 different parts. The main aim of dividing the transformer windings into different part is to investigate the radial and axial force into that particular part and to see where the radial and axial forces are higher.
6 citations
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TL;DR: In this article , the effects of varying the number of axial sticks and the proof stress of the conductor material on the value of critical stress on the inner winding of transformers have been investigated.
Abstract: The inner winding of transformers may get buckled under the short-circuit condition. To avoid the buckling of the inner winding, the critical stress at which buckling occurs should be more than the applied stress during a short-circuit event. The important parameters on which the critical buckling stress depends are the inner winding radial dimension, number and dimension of strands, distance between the two adjacent axial sticks, dimension of the axial sticks, proof stress of the conductor material, etc. In literature, for the given geometrical details of the inner winding, the variation of critical stress with the number of axial sticks and the value of proof stress of the conductor material are not reported. In this letter, the effects of varying the number of axial sticks and the proof stress of the conductor material on the value of critical stress of the inner winding have been investigated.
3 citations
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TL;DR: In this paper, the electromagnetic forces of the power transformer are calculated by using the finite element method with the help of two-dimensional models, and the main aim of this study is to investigate the radial and axial force of the displaced winding.
Abstract: The working of the electrical network mainly depends on the working of the power transformer. Several important factors of the electrical power system such as efficiency, safety, and total losses are also affected by the power transformer. One of the most important factors for the designing of the power transformer is electromagnetic forces. In this paper, electromagnetic forces of the power transformer are calculated by using the finite element method with the help of two-dimensional models. When the transformer's windings are in the original initial designing position, the current and electromagnetic forces of the routine and short-circuit circumstances are familiar to the transformer designers. However, the effect of the displacement of the transformer's windings on the electromagnetic forces is not well known to the transformer designers. In this work, electromagnetic forces during the non-displaced (normal conditions) and displaced windings of the transformer are examined by using finite element analysis. The main aim of this study is to investigate the radial and axial force of the displaced winding. Numerical results of the radial forces of the non-displaced windings are also compared with the analytical technique.
2 citations
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23 Oct 2022
TL;DR: In this paper , an analytical expression for the critical forced buckling stress of the transformer inner winding is given in which the winding section, between the three adjacent axial supporting spacers, has been modeled as a circular arch.
Abstract: The transformer inner winding conductors may fail due to buckling when an enormous compressive electromagnetic force is applied on them under the short-circuit situation. In literature, the analytical expression for the critical forced buckling stress of the transformer winding is given in which the winding section, between the three adjacent axial supporting spacers, has been modeled as a circular arch. In the model, the axial spacers are considered as a rigid body, but they may have some flexibility. In this paper, an investigation has been done, through case studies, to analyze the influence of the flexibility of the spacers on the critical stress of the inner winding.
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TL;DR: In this article , the equivalent support stiffness (ESS) analytical method is proposed to investigate the issues of support weakening and failure, which are affected mainly by assembly gaps and insulation shrinkage.
Abstract: Power transformers are inevitably subjected to external short circuit impact during their service period. The electromagnetic force generated by the fault current may cause winding destabilization and collapse. The radial buckling of the inner winding accounts for a considerable proportion. Based on the effective contact of the sticks, the traditional analytical methods ignore the manufacturing deviation and operation impact (MDOI) characterized by assembly gaps and insulation shrinkage. To address the limitation of the contact-constrained approach, this paper proposes the equivalent support stiffness (ESS) analytical method. The ESS method can investigate the issues of support weakening and failure, which are affected mainly by assembly gaps and insulation shrinkage. Further, two transformers are implemented in the short-circuit tests to demonstrate the feasibility of the ESS method. Among them, the assembly gaps are investigated by the first and second windings of the newly manufactured transformer, and the influence of insulation shrinkage is researched through a 30-year-old transformer. Furthermore, the application of the ESS method is expressed based on the tests and the simulations. The research presents quantitative references for transformer design and operational reliability assessment. The ESS method can be an improvement and supplement to traditional methods.
References
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TL;DR: In this article, Rabins' method for measuring the self-inductance of and mutual inductance between two-winding transformers was used to calculate the B-field forces.
Abstract: Introduction Historical Background Uses in Power Systems Core-Form and Shell-Form Transformers Stacked and Wound Core Construction Transformer Cooling Winding Types Insulation Structures Structural Elements Modern Trends Magnetism and Related Core Issues Basic Magnetism Hysteresis Magnetic Circuits Inrush Current Distinguishing Inrush from Fault Current Optimal Core Stacking Circuit Model of a Two-Winding Transformer with Core Circuit Model of the Core Two-Winding Transformer Circuit Model with Core Approximate Two-Winding Transformer Circuit Model without Core Vector Diagram of a Loaded Transformer with Core Per-Unit System Voltage Regulation Reactance and Leakage Reactance Calculations General Method for Determining Inductances and Mutual Inductances Two-Winding Leakage Reactance Formula Ideal Two-, Three-, and Multiwinding Transformers Leakage Reactance for Two-Winding Transformers Based on Circuit Parameters Leakage Reactances for Three-Winding Transformers Phasors, Three-Phase Connections, and Symmetrical Components Phasors Wye and Delta Three-Phase Connections Zig-Zag Connection Scott Connection Symmetrical Components Fault Current Analysis Fault Current Analysis on Three-Phase Systems Fault Currents for Transformers with Two Terminals per Phase Fault Currents for Transformers with Three Terminals per Phase Asymmetry Factor Phase-Shifting and Zig-Zag Transformers Basic Principles Squashed Delta Phase-Shifting Transformer Standard Delta Phase-Shifting Transformer Two-Core Phase-Shifting Transformer Regulation Effects Fault Current Analysis Zig-Zag Transformer Multi-terminal Three-Phase Transformer Model Theory Transformers with Winding Connections within a Phase Multiphase Transformers Generalizing the Model Regulation and Terminal Impedances Multiterminal Transformer Model for Balanced and Unbalanced Load Conditions Rabins' Method for Calculating Leakage Fields, Leakage Inductances, and Forces in Transformers Theory Rabins' Formula for Leakage Reactance Application of Rabins' Method to Calculate the Self-Inductance of and Mutual Inductance between Coil Sections Determining the B-Field Determination of Winding Forces Numerical Considerations Mechanical Design Force Calculations Stress Analysis Radial Buckling Strength Stress Distribution in a Composite Wire-Paper Winding Section Additional Mechanical Considerations Electric Field Calculations Simple Geometries Electric Field Calculations Using Conformal Mapping Finite Element Electric Field Calculations Capacitance Calculations Distributive Capacitance along a Winding or Disk Stein's Disk Capacitance Formula General Disk Capacitance Formula Coil Grounded at One End with Grounded Cylinders on Either Side Static Ring on One Side of Disk Terminal Disk without a Static Ring Capacitance Matrix Two Static Rings Static Ring Between the First Two Disks Winding Disk Capacitances with Wound-in Shields Multistart Winding Capacitance Voltage Breakdown and High-Voltage Design Principles of Voltage Breakdown Geometric Dependence of Transformer-Oil Breakdown Insulation Coordination Continuum Model of Winding Used to Obtain the Impulse-Voltage Distribution Lumped-Parameter Model for Transient Voltage Distribution Losses No-Load or Core Losses Load Losses Tank and Shield Losses Due to Nearby Busbars Tank Losses Associated with the Bushings Thermal Design Thermal Model of a Disk Coil with Directed Oil Flow Thermal Model for Coils without Directed Oil Flow Radiator Thermal Model Tank Cooling Oil Mixing in the Tank Time Dependence Pumped Flow Comparison with Test Results Determining m and n Exponents Loss of Life Calculation Cable and Lead Temperature Calculation Tank Wall Temperature Calculation Tieplate Temperature Core Steel Temperature Calculation Load Tap Changers General Description of Load Tap Changer Types of Regulation Principles of Operation Connection Schemes General Maintenance Miscellaneous Topics Setting the Impulse Test Generator to Achieve Close to Ideal Waveshapes Impulse or Lightning Strike on a Transformer through a Length of Cable Air Core Inductance Electrical Contacts References Index
147 citations
"Effect of Width of Axial Supporting..." refers background or methods in this paper
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06 Sep 2012
TL;DR: Transformer Engineering: Design, Technology, and Diagnostics, Second Edition as discussed by the authors helps to design better transformers, apply advanced numerical field computations more effectively, and tackle operational and maintenance issues.
Abstract: Transformer Engineering: Design, Technology, and Diagnostics, Second Edition helps you design better transformers, apply advanced numerical field computations more effectively, and tackle operational and maintenance issues. Building on the bestselling Transformer Engineering: Design and Practice, this greatly expanded second edition also emphasizes diagnostic aspects and transformer-system interactions.
What’s New in This Edition
Three new chapters on electromagnetic fields in transformers, transformer-system interactions and modeling, and monitoring and diagnostics
An extensively revised chapter on recent trends in transformer technology
An extensively updated chapter on short-circuit strength, including failure mechanisms and safety factors
A step-by-step procedure for designing a transformer
Updates throughout, reflecting advances in the field
A blend of theory and practice, this comprehensive book examines aspects of transformer engineering, from design to diagnostics. It thoroughly explains electromagnetic fields and the finite element method to help you solve practical problems related to transformers. Coverage includes important design challenges, such as eddy and stray loss evaluation and control, transient response, short-circuit withstand and strength, and insulation design. The authors also give pointers for further research. Students and engineers starting their careers will appreciate the sample design of a typical power transformer.
Presenting in-depth explanations, modern computational techniques, and emerging trends, this is a valuable reference for those working in the transformer industry, as well as for students and researchers. It offers guidance in optimizing and enhancing transformer design, manufacturing, and condition monitoring to meet the challenges of a highly competitive market.
119 citations
"Effect of Width of Axial Supporting..." refers methods in this paper
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TL;DR: In this paper, a finite-element analysis-based simulation model for CTCs is proposed and verified by the tests, and the final simulation model is based on a coupled analysis of magnetostatic force calculation and static structural deformation analysis.
Abstract: A test stand to evaluate the radial buckling strength of power transformer windings under the influence of electromagnetic forces is presented. The resulting conductor deformation can be measured in parallel to the sinusoidal test current. The proposed test results focus on the inception of forced buckling for continuously transposed conductors (CTCs), which are a special type of conductor often used in power transformer windings. In the literature, there barely exist calculations to the radial buckling withstand capability of CTCs. Therefore, a finite-element analysis-based simulation model for this kind of conductor is proposed and verified by the tests. For this verification, three different CTC types are used. The final simulation model is based on a coupled analysis of magnetostatic force calculation and static structural deformation analysis. It suitably reproduces the measurement results from the dynamic short-circuit tests. Furthermore, a standard formula describing radial buckling phenomena inside power transformers is adapted for use with CTCs.
25 citations
"Effect of Width of Axial Supporting..." refers background or methods in this paper
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