Short-circuit Electromagnetic Forces Research Articles

Numerical Investigations for Vibration and Deformation of Power Transformer Windings under Short-Circuit Condition

The analysis of the dynamic process of winding destabilization under sudden short-circuit conditions is of great importance to accurately assess the short-circuit resistance of power transformers. Based on magneto-solid coupling, an axisymmetric model of the transformer and a 3D multilayer model of the transformer considering the support components are established, respectively, and the short-circuit electromagnetic force (EF) is simulated by using the finite element method. It is concluded that the middle layer of the winding is subjected to the larger radial EF, while the axial EF has a greater effect on the layers at both ends. Moreover, the impression of the preload force, aging temperatures, and the area share of spacers on the vibration and deformation of windings are studied under short-circuit conditions. The overall distribution of plastic strain and residual stress in the winding is symmetrical, and the maximum values occur in the lower region of the middle of the winding. Finally, considering the material properties of disks and insulating components, the cumulative effect of plastic deformation under multiple successive short-circuit shocks is calculated. Compared with the traditional axisymmetric model of transformer, the three-dimensional multilayer model of the transformer established in this paper is more suitable for the actual winding structure and the obtained results are more accurate.

Short-Circuit Performance Analysis of a Distribution Transformer Using Coupled Field-Circuit Approach

The inability of power transformers to resist a short-circuit (SC) fault significantly impacts the safety of power systems. During SC faults, the leakage field undergoes significant distortion, resulting in large SC electromagnetic forces (EFs), which results in critical mechanical stresses. The finite element method (FEM) might be one of the best non-destructive numerical methods that enable designers to assess the transformer SC performance. Using the FEM, most SC performance analysis studies assume either the three-phase (LLL) or the single-phase-to-ground (LG) SC fault. Moreover, the existing studies use an excitation method that provides a high error rate due to the sensitivity of transient solvers. Furthermore, no considerable attention has been given to analyzing the influence of grounding the wye-connected windings on the SC performance. In this work, a non-linear-transient field-circuit coupled 3-D finite element model is created to analyze the SC performance of a delta-wye connected distribution transformer under various SC fault conditions. Results show that grounding the secondary windings significantly impacts the performance when a LG fault is applied. Except for the LG fault with wye configuration of the secondary windings, the windings SC current and EFs decay/rise over time with an exponential trend till reaching steady state.

Coupled Magnetic-Structural Modeling of Power Transformer for Axial Vibration Analysis Under Short-Circuit Condition

When an external short circuit occurs, the axial electromagnetic force increases dozens of times. Under the effect of the axial short-circuit electromagnetic force, the transformer windings vibrate violently. The spatial distribution of the disks is constantly changing during vibration, which can change the temporal and spatial distributions of the leakage magnetic field and the axial electromagnetic force. This process is called the strong coupling phenomenon of the structural field and the leakage magnetic field. In this article, a strong coupled magnetic-structural model is proposed by using the analysis method. The strong coupling equations, where the independent variables are the axial position of the disks, are obtained. The vibration process with strong coupling phenomenon considered can be obtained. The accuracy of the strong coupling model is verified by the iterative method. By comparing the results calculated by the strong coupling model with those calculated by the weak coupling model, the influence of the strong coupling phenomenon <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</b> the vibration process is obtained. Due to the influence of the strong coupling phenomenon, the winding vibration intensity increases and the maximum displacement of the disks can be doubled, which implied that the strong coupling phenomenon cannot be ignored when investigating the short-circuit strength of power transformers.

Research on Single-phase Power Supply in Short-circuit Test of Transformer on Magnetic-force Coupling Field

The short-circuit test is a test of the comprehensive technical ability of transformer manufacturing. The three-phase power supply is usually used for short-circuit test of transformer. To investigate the feasibility of using a single-phase power supply in the short-circuit test of transformer, in this paper, we modeled a 200 kVA power transformer in three dimensions, using the finite element method to calculate the short-circuit current and short-circuit electromagnetic force of the windings under different excitation modes when the three-phase short-circuit occurs in the low-voltage windings. Analyze and compare the short-circuit current and short-circuit electromagnetic force distribution characteristics of windings under different working conditions. The results show that when the three-phase short-circuit condition occurred in the low-voltage windings, regardless of the three-phase excitation or single-phase excitation exerted on the high-voltage windings, the short-circuit current and the short-circuit electromagnetic force of the voltage zero-crossing closing phase is basically the same. This proves that a single-phase power supply can be used instead of a three-phase power supply for short-circuit tests. the analysis result has certain reference significance for improving the short-circuit test of transformer.

Inductance Calculation of HTS Transformers with Multi-segment Windings Considering Insulation Constraints

High-temperature superconducting (HTS) transformers with multi-segment windings have been proposed in earlier literatures for the hysteresis loss reduction and short circuit electromagnetic force mitigation. The optimum distributive ratios for these multi-segment windings have been determined in earlier literatures. Asymmetrical seven segment winding with its optimum distributive ratio (k = 1/12) results in minimization of short circuit electromagnetic forces under normal tap and any adjusted tap. However, insulation design and leakage inductance calculation for the multi-segment winding of an HTS transformer have not been addressed in past literatures. Insulation design is one of the most crucial aspects in the transformer design, especially for high voltage power transformers. The analysis and optimization of the electric field distribution over the winding’s segments insulation in these HTS transformers provide the required dimensions for precise determination of the leakage inductances. In this paper, for the first time, winding insulation design and leakage inductance calculation of a 200 MVA, 230/20 kV HTS transformer with asymmetrical seven segment winding (and k of 1/12), are carried out. The analytical method besides a two-dimensional (2D) finite element method (FEM), through COMSOL Multiphysics software, is utilized for insulation design and calculation of leakage inductances of this transformer.

Calculation and Analysis of Mechanical Characteristics of Transformer Windings Under Short-Circuit Condition

Accurate calculation of short-circuit (SC) dynamic characteristics of power transformer windings is of great significance to the safety of transformers. A 110 kV power transformer model is established, and SC electromagnetic characteristics and dynamic characteristics of the transformer windings are obtained through magnetic-structural coupling analysis by the finite-element method, considering the nonlinear mechanical characteristics of spacers. The distribution of leakage magnetic field and electromagnetic force (EF) and dynamic stress and displacement of windings are calculated due to SC fault. The SC EF of windings decreases exponentially with time. The axial EF of the disks at both ends of the winding is larger, while the radial EF is smaller, compared with that of central disks. The variation law of winding stress and displacement is similar to dynamic EF. The stress and displacement at both ends of the winding are larger while that in the middle part is smaller. The maximum stress and displacement of the end of windings are nearly 60% and 90% higher than that of the middle part, respectively. The axial displacement is the major part of the total displacement. The analysis method can provide a reference for checking the SC strength of the transformer.

전기기기] 전력용 변압기 권선의 탭 조건에 따른 단락 전자력 계산에 관한 연구

This paper deals with short-circuit electromagnetic force of power transformer depending on tap condition. In order to reduce the analysis time, we used a 2-D axi-symmetric model. Firstly, in order to prove the 2-D axi-symmetric model, we calculated percent impedance and maximum value of leakage magnetic flux density by using analytical method and finite element method. Secondly, short-circuit currents are calculated by using a short-circuit equation. Finally, short-circuit electromagnetic forces produced by short-circuit currents are computed by finite element method. And the results has compared depending on tap condition. The results are expected to be useful in structure design of power transformer.

HTS Transformer Windings Design Using Distributive Ratios for Minimization of Short Circuit Forces

High-temperature superconducting (HTS) transformers have a promising feature in reduction of total weight, total size, and the losses of large-scale distribution transformers. However, the lower leakage reactance of HTS transformers results in a higher short-circuit fault currents and electromagnetic forces. Therefore, optimization of short-circuit electromagnetic forces is one of the crucial aspects in the design of HTS transformers. In this paper, a novel analytical method is proposed for determination of optimum distributive ratios resulting in minimization of these forces for asymmetrical multi-segment windings of an HTS transformer. Employing these distributive ratios, radial and axial components of short-circuit electromagnetic forces in an HTS transformer are significantly reduced. Two- and three-dimensional (2D and 3D) finite element method (FEM) simulations are employed to verify the analytical method results.

Double-Ladder Circuit Model of Transformer Winding for Frequency Response Analysis Considering Frequency-Dependent Losses

It is well known that power transformers inevitably suffer the impacts of short-circuit electromagnetic forces in service. For precise diagnosis investigation of winding mechanical deformation, this paper presents a double-ladder circuit model of transformer winding with lumped parameters for frequency response analysis. This advanced model includes the axial and radial ladder networks with regard to the winding disks and the eddy current paths of the magnetic core, respectively. In the radial ladder network, the nonlinear behavior of frequency-dependent parameters and core loss are considered. Relevant equivalent parameters in this double-ladder circuit model are calculated using the 3-D finite-element method. The energy balance method is applied to obtain the frequency-dependent inductances and resistances. In order to verify the effectiveness of this model, the frequency responses of voltage ratio at a wide frequency range from a few tens of hertz up to megahertz are simulated and measured.

Numerical Calculation of Short Circuit Electromagnetic Force in Isolated Phase Bus

Short circuit electromagnetic forces are one of the most important factors in design and operation of buses. 2D infinite element models are set up with ANSOFT for isolated phase buses, simulating with transient method and calculating short circuit electromagnetic force taking eddy effect and proximity effect into account. The result reveals that the maximum electromagnetic force under short circuit condition is a periodic function of current phase angle.

Analysis of Buckling Strength of Inner Windings in Transformers Under Radial Short-Circuit Forces

The buckling of conductors of inner windings in transformers is one of the major causes of their failures. It can occur when a large magnitude of radial short-circuit electromagnetic force acts on them. In this paper, initially, mechanical strains developed during winding processes and due to radial short-circuit forces have been determined. The two mechanical strains viz. the short-circuit induced strain and the winding process-induced strain are algebraically added to obtain their resulting strain. The stress corresponding to the resulting strain has been determined by using the Ramberg-Osgood stress-strain relation. The critical buckling stress has been calculated and compared with the resulting stress. The analytically obtained result of the strain induced in the winding conductor during its winding process has been verified using the finite-element method. A case study has been described in which the factor of safety against the buckling strength is determined.

Coupled Electromagnetic-Structural Analysis of the Spiraling Phenomenon in a Helical Winding of a Power Transformer

Spiraling of conductors in a helical winding of a transformer may lead to a catastrophic failure under the action of torsional short-circuit electromagnetic forces. Torsional forces are produced by the interaction of the axial component of the short-circuit current and the radial component of the leakage magnetic flux density. In this paper, 3-D magnetostatic analysis has been performed to determine the leakage magnetic-field distribution in a 130-MVA power transformer. Torsional electromagnetic forces are calculated from the analysis to determine circumferential displacements of conductors of its low-voltage helical winding. Furthermore, mechanical stress components are computed and a factor of safety is defined, which gives an indication as to whether the winding conductors are in the elastic or plastic zone. The numerical results thus obtained by the finite-element method are verified using the first principles from mechanics. The effect of looseness in the inner support structure on the von-Mises equivalent stress and, hence, on the factor of safety has been studied.

Calculation of short circuit electromagnetic forces in Dryformer using finite element method

Summary Dryformer is a new type of oil-free power transformers which its windings are made of high voltage cable. Calculation of electromagnetic forces acting upon windings under short circuit condition is an important stage in mechanical design of Dryformer. In this paper, 2D and 3D finite element models are utilized to analyze magnetic field and calculate short circuit forces upon Dryformer windings. The radial and axial forces upon high voltage and low voltage windings are investigated in 2D and 3D models, and the results are compared with each other. The results of this paper are very useful in mechanical design of Dryformer, where sufficient bracing must be provided to prevent winding being damaged. Copyright © 2013 John Wiley & Sons, Ltd.

Computation of Radial Electromagnetic Forces on Power Transformer LV Windings due to Short-Circuit Currents

The short-circuit electromagnetic force in radial direction induces critical mechanical stress on a power transformer. In this paper, the radial short-circuit forces which are exerted on transformer low voltage (LV) windings are investigated. Firstly, the mechanisms of leakage flux and short-circuit electromechanical forces in transformer coils are analyzed. Afterwards, based on IEC standards followed by short-circuit tests, calculations of radial short-circuit forces and evaluations of the ability to withstand short currents in LV windings are developed. The case studies and comparisons with improved measures show that the evaluation and calculation method is feasible and effective, and this method also offers three useful ways to strengthen the ability to withstand short-circuit currents for transformer windings.

Experimental Verification and Finite Element Analysis of Short-Circuit Electromagnetic Force for Dry-Type Transformer

The short-circuit force induces critical mechanical stress on a transformer. This paper deals with experimental verification and finite element analysis (FEA) for short-circuit force prediction of a 50 kVA dry-type transformer. We modeled high voltage (HV) winding into 20 sections and low voltage (LV) winding into 22 sections as similar as those windings of a model transformer. With this modeling technique, we could calculate electromagnetic forces acting on each section of the windings of a dry-type transformer under short-circuit condition. The magnetic vector potentials, magnetic flux densities, and electromagnetic forces due to short-circuit current are solved by FEA. The electromagnetic forces consisting of radial and axial directions depend both on short-circuit current and leakage flux density. These results were used as input source of sequential finite element method (FEM) to predict the resultant mechanical forces considering the structural characteristics such as stress distributions or deformations of windings, accurately. The obtained resultant mechanical forces in HV winding are compared with those of the experimental ones.

Eigenvalue Analysis for Investigation of Tilting of Transformer Winding Conductors Under Axial Short-Circuit Forces

The tilting phenomenon may lead to a catastrophic failure, such as an interturn fault in transformers, under the action of axial short-circuit electromagnetic forces. In this paper, first, a state-space approach has been used to determine the eigenvalues of various winding configurations used in practice by assuming a small value of tilt angle up to 10°. These eigenvalues decide the critical tilting forces and the natural frequencies of windings. The four cases involving disk, layer, helical windings (all these with strip conductor), and layer winding with continuously transposed cable conductor have been analyzed. Further, initial critical tilt angles are determined for various magnitudes of the axial force in a typical 5-MVA transformer.

Finite-Element Analysis of Short-Circuit Electromagnetic Force in Power Transformer

Transient electromagnetic forces in radial and axial directions induce critical mechanical stress on windings and transformers. In this paper, short-circuit electromagnetic forces that are exerted on transformer windings are investigated. A 3-D transformer model is considered to calculate the transient electromagnetic forces. The magnetic vector potential, magnetic flux density, and electromagnetic forces due to the short-circuit transient currents applied to the power transformer are analyzed by a coupled electromechanical finite-element method. The results obtained are compared with the analytical results and show good agreement. The numerical modeling technique dealt with in this paper is expected to be useful in the design of power transformers.

전자계-기계계 결합해석에 의한 건식변압기의 단락강도 예측

This paper deals with the coupled electromagnetic-mechanical field analysis for short-circuit electromagnetic force of the dry-type transformer. The short-circuit currents are calculated using external circuit in accordance with short-circuit test equipment. According to short-circuit current, the generated magnetic leakage flux density in dry-type transformer model is calculated by finite element method. The radially-directed electromagnetic forces in windings are calculated using electromagnetic field analysis and then axially-directed electromagnetic forces in windings are calculated using electromagnetic-mechanical field analysis. The calculated axially-directed electromagnetic forces in high voltage winding are compared to those of measured ones and showed good agreement with experimental results.

Transient Finite-Element Analysis of Short-Circuit Electromagnetic Forces in Isolated Phase Buses

Short-circuit electromagnetic forces have a vital role in the mechanical design of isolated phase buses. Electromagnetic forces in isolated phase buses under short-circuit conditions are analyzed in this article. These forces are calculated using the time-stepping finite-element method. The effects of system dimensions and material properties on the maximum value of forces and the time of its occurrence are investigated through extensive simulation. The concluding remarks are useful for the design and protection of the buses.

Three- and Two-Dimensional Finite-Element Computation of Inrush Current and Short-Circuit Electromagnetic Forces on Windings of a Three-Phase Core-Type Power Transformer

Although short-circuit current is frequently considered the major design fundamental for power transformers, experience with transformer failures shows that inrush currents that occur when transformers are energized can also cause serious damage. To investigate the resultant forces due to energizing power transformer windings, we modeled a three-phase, three-legged 66/11 kV, 40 MVA power transformer in two and three dimensions. We calculated electromechanical forces for short-circuit cases and also for inrush current through the windings, using the finite-element method. The results show that the forces exerted on the windings due to inrush current in many regions are larger than those due to short-circuit currents. Since the inrush current appears more frequently with a much longer duration compared to a short-current event, its harmful effects are worse than those of the short-circuit case.