The Poynting Vector and the New Theory of a Transformer. Part 11. Three-Phase Three-Core Transformers without a Neutral Wire

A topological equivalent circuit for a three-phase three-core transformer reflecting the spatial structure of its magnetic system is developed. Owing to this approach, it became possible to represent the magnetic fluxes of the magnetic circuit’s all main sections and the apertures for each of three phases directly in the circuit in the absence of the windings’ neutral wires. The circuit is constructed by stitching together the anatomical circuit models of single-phase transformers obtained in the previous parts with taking into account the relationships between the fluxes at the junctions of the phase zones in iron. Its validity is confirmed by the rigor nature of the physical and mathematical relations for idealized transformers with infinite magnetic permeability of iron and simplified magnetic field patterns, which corresponds to the generally accepted approach with neglecting the magnetization currents. The difference lies in the fact that the developed model takes into account the heterogeneity of magnetization in different parts of the magnetic circuit with allocating more than 30 sections in the iron and apertures. The transition to the model of a real three-core transformer is carried out by adding four nonlinear transverse magnetization branches in each extreme phase zone and eight branches in the central phase zone to the idealized equivalent circuit. It is shown that in cases of winding connections without neutral wires, there is no flux of the Poynting vector in interphase zones in any unbalanced mode. In this case, the problems connected with the occurrence of fluxes exceeding the no-load fluxes under the conditions of symmetric and asymmetric short circuits, as well as the occurrence of buckling fluxes in these modes in the region outside the transformer iron, are solved.

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Voltages Induced in Overhead Ground-Wire Cable as Risk Factor. Part 1

Safety in Technosphere ◽

10.12737/19021 ◽

2016 ◽

Vol 5 (1) ◽

pp. 28-40 ◽

Cited By ~ 1

Author(s):

Токарский ◽

A. Tokarskiy ◽

Рубцова ◽

Nina Rubtsova ◽

Рябченко ◽

...

Keyword(s):

Risk Factor ◽

Single Phase ◽

Interval Length ◽

Maximum Permissible Level ◽

Overhead Transmission Line ◽

Spark Gap ◽

Three Phase ◽

Electric And Magnetic Fields ◽

Short Circuits ◽

Selection Of

To ensure the staff safety under hot-line overhead transmission line (OTL) maintenance, as well as overhead ground-wire cable (OGWC) insulation integrity maintaining, by the example of three-phase 750 kV OTL has been presented an algorithm for calculation of voltages and electromotive forces (EMF) induced in this line’s OGWC by electric and magnetic fields (EF and MF) generated by OTL phases’ voltages and currents. Algorithms for calculation of line-to-earth voltages distribution along grounded at one end OGWC’ intervals have been given. It has been shown that the voltage induced at OGWC by EF of 750 kV OTL is much less than the voltage induced by this OTL’s MF. For single-phase short circuits modes has been presented an algorithm for selection of grounded at one end OGWC’ interval length by condition of respecting of voltage’s maximum permissible level on a spark gap shunting OGWC’s insulator set.

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Open-Loop Single-Phase Space State Model and Equivalent Circuit of a Non-Conventional Three-Phase Inverter

Electronics ◽

10.3390/electronics9050744 ◽

2020 ◽

Vol 9 (5) ◽

pp. 744

Author(s):

Vinícius Melo ◽

Alexandre Melo ◽

Walbermark Santos ◽

Jussara Fardin ◽

Lucas Encarnação

Keyword(s):

Equivalent Circuit ◽

Direct Current ◽

Single Phase ◽

Green Energy ◽

State Model ◽

Phase Inverter ◽

Three Phase ◽

Space State ◽

Phase Models ◽

Three Phase Inverter

Recently, many non-conventional three-phase inverters, topologies for green energy source grid-connection systems, and electric drives have been proposed. Simplifying the inverter circuit is crucial to analyze and solve their models in order to design them. The main goal of the study is centered on obtaining a single-phase equivalent circuit and space state model from non-conventional three-phase inverters based on bidirectional direct current–direct current (DC–DC) Buck-Boost topology using isolated gate bipolar transistors (IGBT). From just one phase of the three-phase inverter, the single-phase equivalent circuit was obtained by means of Kirchhoff’s laws. The equivalent circuit operation steps were presented in order to obtain the space state model. Finally, the equivalent circuit was simulated, and experimental results with a 200 W three-phase inverter feeding a resistive, inductive, and capacitive loads were performed to confirm the theoretical and simulation analyses. The results show the state space dynamic behavior variables of single-phase and three-phase models are quite similar. Therefore, it can be concluded that the proposed circuit can be used with property to represent equivalent single-phase models of non-conventional three-phase inverters.

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The Economic Operation of Common Coupling Groups of Distribution Transformer

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.521.288 ◽

2014 ◽

Vol 521 ◽

pp. 288-291

Author(s):

Yu Sheng Quan ◽

Xin Zhao ◽

Hua Gui Chen ◽

En Ze Zhou

Keyword(s):

Single Phase ◽

Short Circuit ◽

Phase System ◽

Distribution Transformer ◽

Three Phase ◽

Unbalanced Load ◽

Transformer Coupling ◽

The Difference ◽

Short Circuit Fault ◽

Better Than

Based on the method of symmetrical components of D, 11 and Y, o distribution transformer coupling two different effects of different magnetic circuit coupled to the three-phase system with a system-generated analysis and comparison. Analysis of the difference between the two groups of different connections on the transformer structure. Described in the single-phase short circuit fault clearing, 3n harmonic current suppression and affordability aspects of single-phase unbalanced load, D, ll coupling transformers are significantly better than Y,0 coupling transformer. This has necessarily important for the study of energy loss reduction.

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Calculation approach of reluctance in the magnetic circuit of transformer employed to convert into equivalent electric circuit

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering ◽

10.1108/compel-12-2017-0552 ◽

2018 ◽

Vol 37 (5) ◽

pp. 1668-1677 ◽

Cited By ~ 2

Author(s):

Yingying Wang ◽

Jiansheng Yuan

Keyword(s):

Magnetic Field ◽

Single Phase ◽

Magnetic Circuit ◽

Electric Circuit ◽

Inrush Current ◽

Equivalent Electric Circuit ◽

Content Type ◽

Three Phase ◽

Simulation Results ◽

Peak Value

Purpose The theoretical method of converting the magnetic circuit into an electric circuit is mature, but the way to determine the inductances in the electric circuit is not reliable, especially for the core working in saturation status, and it is impossible to determine the inductances by the transformer terminal measurements, as the measurement information is not enough to determine a number of inductances. This paper aims to propose an approach of calculating the reluctances. Design/methodology/approach In this paper, an approach of calculating the reluctances is proposed based on the numerical simulation of magnetic field in transformer with different values of current excitation. The reluctance of a core segment or air region as a branch of magnetic circuit is obtained by the magnetic energy and magnetic flux. By this way, all the reluctances as function of flux can be determined, and then the inductances can be determined. The reluctances and equivalent electric circuit of three-phase integrative transformer is determined, and its validation is proved in the paper. Findings The single phase example shows that the proposed method has a good performances on analysis of the inrush current in deep saturation. The peak value of the inrush current derived from the proposed approach matches well with the results obtained by coupled circuit-FEM analysis, and the difference is about 4.8 per cent. For studies on dual models of single phase transformers, the leakage inductances have important effects on the peak value of the inrush current. The reluctances of three-phase transformer are calculated, and the equivalent circuit simulation results are slightly smaller than the coupled circuit-FEM simulation results. Originality/value Approach of calculating the reluctances based on the numerical simulation of magnetic field in transformer is proposed. The magnetic core and air space are divided into several segments, and the reluctance for each segment is calculated based on the energy in the region and the flux of the cross-sectional area. By applying various excitation currents, all the reluctances as function of flux can be determined, and then all the non-linear inductances including the non-linear leakage inductances are obtained. The proposed approach is reliable to determine a number of inductances in the dual electric circuit, especially for deep saturation status.

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Once again about the indivisibility of the scattered inductance of the transformer

Electrical Engineering and Power Engineering ◽

10.15588/1607-6761-2021-1-1 ◽

2021 ◽

pp. 8-17

Author(s):

S.E. Zіrka ◽

Y.I. Moroz ◽

C.M. Arturi

Keyword(s):

Equivalent Circuit ◽

Physical Meaning ◽

Magnetic Circuit ◽

Finite Thickness ◽

Equivalent Circuits ◽

Leakage Inductance ◽

The Core ◽

Inrush Currents ◽

Radial Thickness ◽

Short Circuits

Purpose. The purpose of the article is to show the inadequacy of the traditional T-shaped equivalent circuit for modeling transformer operations with saturated core. The aim is to point out the unreasonableness of the separation of the transformer leakage inductance into components. The aim is also to explain the need to apply the П-shaped transformer equivalent circuits to transformers with two and three windings with finite radial thickness. Methodology. Analysis of magnetic fields in the transformer window and simulation of transient processes in equivalent circuits of the transformer using a preprocessor ATPDraw to the program ATP. Findings. The unfoundedness of the well-known T-shaped transformer equivalent circuit is shown. Differences in the processes in the core legs and yokes when transformer is connected to the network and during short circuits of the windings are noted. Equivalent circuits of a transformer with two and three windings of finite thickness are proposed, reproducing these differences. Originality. The absence of physical meaning in dividing the transformer leakage inductance into components is stated. The advantages of the П-shaped equivalent circuit are shown when calculating inrush currents accompanying the transformer switching to the network on its inner and outer windings. Practical value. We show theoretical insolvency and practical unsuitability of the Т-shaped equivalent circuit for studying transformer operations accompanied by saturation of the magnetic circuit. Advantages of the П-shaped equivalent circuit are clarified.

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New equivalent circuit of three-phase three-limb transformer based on magnetic circuit characteristics

2011 International Conference on Advanced Power System Automation and Protection ◽

10.1109/apap.2011.6180643 ◽

2011 ◽

Author(s):

JiaLe Suonan ◽

Liqiang Xu ◽

ZaiBin Jiao

Keyword(s):

Equivalent Circuit ◽

Magnetic Circuit ◽

Three Phase

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TEM investigations of surface residual stress relaxation in A12O3 and Al2O3-SiC nanocomposite

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100170876 ◽

1994 ◽

Vol 52 ◽

pp. 628-629

Author(s):

J. Fang ◽

H. M. Chan ◽

M. P. Harmer

Keyword(s):

Residual Stress ◽

Single Phase ◽

Stress Relief ◽

Stress Recovery ◽

Surface Residual Stress ◽

Microscopic Mechanism ◽

Sic Particles ◽

Annealing Procedure ◽

The Difference ◽

Nano Size

It was Niihara et al. who first discovered that the fracture strength of Al2O3 can be increased by incorporating as little as 5 vol.% of nano-size SiC particles (>1000 MPa), and that the strength would be improved further by a simple annealing procedure (>1500 MPa). This discovery has stimulated intense interest on Al2O3/SiC nanocomposites. Recent indentation studies by Fang et al. have shown that residual stress relief was more difficult in the nanocomposite than in pure Al2O3. In the present work, TEM was employed to investigate the microscopic mechanism(s) for the difference in the residual stress recovery in these two materials.Bulk samples of hot-pressed single phase Al2O3, and Al2O3 containing 5 vol.% 0.15 μm SiC particles were simultaneously polished with 15 μm diamond compound. Each sample was cut into two pieces, one of which was subsequently annealed at 1300° for 2 hours in flowing argon. Disks of 3 mm in diameter were cut from bulk samples.

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