Parallel Conductors Research Articles

2D versus 3D-Like Electrical Behavior of MXene Thin Films: Insights from Weak Localization in the Role of Thickness, Interflake Coupling and Defects.

MXenes stand out from other 2D materials because they combine very good electrical conductivity with hydrophilicity, allowing cost-effective processing as thin films. Therefore, there is a high fundamental interest in unraveling the electronic transport mechanisms at stake in multilayers of the most conducting MXene, Ti3C2Tx. Although weak localization (WL) has been proposed as the dominating low-temperature (LT) transport mechanism in Ti3C2Tx thin films, there have been few attempts to model it quantitatively. In this work, the role of important structural parameters - thickness, interflake coupling, defects - on the dimensionality of the LT transport mechanisms in spin-coated Ti3C2Tx thin films is investigated through LT and magnetic field dependent resistivity measurements. A dimensional crossover from 2D to 3D WL is clearly evidenced when the film thickness exceeds the dephasing length lϕ, estimated here in the 50-100 nm range. 2D WL can be restored by weakening the coupling between adjacent flakes, the intrinsic thickness of which is lower than lϕ, hence acting as parallel 2D conductors. Alternatively, lϕ can be reduced down to the 10 nm range by defects. These results clearly emphasize the ability of WL quantitative study to give deep insights in the physics of electron transport in MXene thinfilms.

Current Sharing Among Three-Strand Parallel Conductors Composed of REBCO Tapes in Three-Phase Armature Coil Conditions

Current Sharing Among Three-Strand Parallel Conductors Composed of REBCO Tapes in Three-Phase Armature Coil Conditions

Solution of the internal and external problems of electrodynamics for a symmetrical vibrator with a reflector made of parallel straight conductors

Background. The work is aimed at the development and research of rigorous methods for calculating multi-element emitting and re-emitting structures, consisting mainly of the same type of elements, as well as studying the physical processes occurring in them. An iterative approach to solving the internal problem is proposed, which allows minimizing the cost of computer time and computer memory. Aim. In this work, using the proposed approach, we solve the internal and external problems of electrodynamics for a symmetrical vibrator with a reflector made of parallel straight conductors. The convergence of the iterative process is studied, the currents on the elements of the structure, its input resistance and radiation characteristics are calculated. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). The solution of the internal problem within the framework of the method of moments is reduced to solving a SLAE with a block matrix. Results. A mathematical model of a radiating structure is proposed, which is a symmetrical vibrator with a reflector made of parallel straight conductors. The internal and external problems of electrodynamics are formulated and solved for given parameter values. An effective algorithm for calculating the block matrix of SLAEs is proposed. Recommendations are given for the selection of systems of projection functions within the framework of the method of moments. The convergence of the iterative process for solving an internal problem of electrodynamics has been studied. The input resistance of the structure and the basic characteristics of its radiation are determined. Conclusion. A rational choice of systems of projection functions, based on the properties of the structure and its constituent elements, makes it possible to significantly reduce the size of the SLAE matrix and, accordingly, reduce computational costs. Taking into account the properties of the structure and its constituent elements also makes it possible to construct effective algorithms for calculating the SLAE matrix. It is shown that the convergence of the iterative process may be absent near resonant frequencies, therefore, when solving the internal problem, a combined approach should be used, which involves the use of both rigorous and approximate methods for solving SLAEs. At non-resonant frequencies, the iterative approach demonstrates its effectiveness. It is concluded that for such structures it is advisable to distinguish between resonant and non-resonant operating modes. In the non-resonant mode, the current functions have a fairly smooth dependence on frequency; in the resonant mode, these dependences become quite sharp and difficult to predict. In this regard, the task of developing an iterative approach to solving the internal problem of electrodynamics in resonant operating modes seems relevant.

Calculation on Current Distributions among Transposed Three- and Six-parallel Conductors in Superconducting Armature Coils for Superconducting Synchronous Motors

Abstract The armature coil of the superconducting synchronous motor for electric aircraft requires a current of 1,000 A or more. However, a single superconducting tape at liquid nitrogen temperatures is insufficient for this operating current. Therefore, the armature coil should be composed of multi-strand parallel conductors. If the coil is constructed from parallel conductors, the inductance balance between the parallel conductors will be collapsed, so the current distributions will be non-uniform. As a solution for this issue, the uniform current distribution can be achieved by the transposition technique that changes the order in which tapes are stacked. Our previous research has developed the transposition method for the 2 n -strand parallel conductors (n = 1, 2, 3, and so on). However, some of the superconducting synchronous motors are actually designed using a number of parallel conductors other than 2 n . This study focused on the three- and the six-strand parallel conductors. We analytically clarified the unique transposition configuration for the three-strand parallel conductors that achieves uniform current distribution, and the transposition configuration for the six-strand parallel conductors by combining the transposition configuration for the three- and two-strand parallel conductors. As a result, the current distribution ratio became less than ±5% when the number of turns of the double pancake coil was a multiple of six by applying the transposition.

Analysis of the thermal effect of two external parallel printed circuit board conductors set on a metal base and operating in a space vacuum on each other

Background. The need to analyze the thermal effect of two external parallel conductors is due to an increase in the density of the conductive pattern. For printed circuit boards set on a metal base and operating in the vacuum of space, this need is aggravated by the weakness of the issue's development. 
 Aim. Analysis of the mutual influence of two external parallel printed circuit board conductors set on a metal base and operating in a space vacuum on each other to identify the dependence of their temperature on the distance between them and determine the distance at which this dependence practically disappears.
 Methods. To achieve the purpose, a finite element method calculation implemented in the ANSYS program, the Steady-State Thermal module, was used. Three multilayer printed circuit boards were calculated: 4-layer, 6-layer, 8-layer. The temperature coefficient of resistance was taken into account separately, by recalculation.
 Results. Graphs of the dependence of overheating (the difference between the temperature of the printed conductor and the metal base) on the distance between the printed conductors were constructed. The approximation of the obtained results is carried out. According to the approximated dependencies, the minimum values of the distances between printed conductors are found, at which the cross influence of printed conductors practically disappears. As the thickness of the printed circuit board increases, this distance increases.
 Conclusion. The results obtained can help to assess the influence of neighboring printed conductors in the design of the boards of the onboard equipment of spacecraft.

One Hundred and Fifty Years of Skin Effect

In 1873, J.C. Maxwell derived relations for current density and current in a solitary long cylindrical conductor supplied with variable current. According to Maxwell, the current density in a conductor increases towards the conductor surface. This phenomenon is called the skin effect. The skin effect affects in particular the inductance of a line formed by one or several long parallel conductors. A number of papers have been published regarding the skin effect and its effect on inductance. Another phenomenon, closely related to the skin effect, is the proximity effect, which refers to the dependence of the current density in a conductor on the proximity of other conductors through which a time-variable current is flowing. Many published papers deal with the calculation of current density in two conductors, using the method for calculating current density in a solitary conductor. All the phenomena given above can be analysed and quantitatively described based on the knowledge of current density in conductors, and therefore the method for calculating current density in a group of conductors is of fundamental significance. It follows from the analysis performed that the skin effect is not a general characteristic of current density in long conductors, except for in the solitary conductor. This conclusion affects the knowledge of the phenomena associated with the skin effect.

Influence of the Skin and Proximity Effects on the Thermal Field in a System of Two Parallel Round Conductors

This paper presents a semi-analytical method for determining the distribution of the thermal field in a system of two parallel round conductors, taking into account the skin and proximity effects. The method of a suitably constructed Green’s function was applied to find an analytical expression for the eigenfunctions describing the temperature distributions. In turn, the relevant integrals, which cannot be determined analytically, were calculated numerically. The foundation of the method is the knowledge of the current density distribution in the conductors. As a result, the steady-state distribution of the temperature field in the conductors for various parameter values can be determined. The obtained numerical results were positively verified using the finite element method. Using the developed method, the share of skin and proximity effects in the temperature rise and steady-state current rating was evaluated. Closed analytical formulas were obtained for the AC case with the skin effect taken into account. When the skin depth is smaller than the wire radius, the skin effect has quite a large impact on the conductor temperature. The impact of the proximity effect is much smaller but clearly noticeable when the distance between the wires is smaller than five times the wire radius. In addition, the influence of the value of the heat transfer coefficient on the thermal field of the conductors was also examined.

Multiconductor Cell Analysis of AC High Speed Railway Lines

The aim of this paper is the application of Multiconductor Cell Analysis to a very special case of a multiconductor system, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., the AC high-speed railway system, with 14 parallel conductors. The present matrix approach allows representing both the single elements and the entire railway system also including the high voltage three-phase supply network. The algorithm allows computing all the steady-state regime electrical quantities (voltages, currents and power) of each section: in particular, the ground return current, responsible for electromagnetic interferences, can be derived by the knowledge of all the circulating currents. It is also possible to evaluate the electric unbalance impact on the supply three-phase power system given by the railway system. Eventually, two different scenarios are presented, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., a maximum allowable high-speed line power request and a contact-wire to rail short circuit.

Basic Concept for Uniform Current Distribution in Parallel Conductors by Introducing a Small Number of Transpositions in REBCO Armature Coils

We propose the concept of uniform current between groups (CUCG) in superconducting armature coils composed of two or more strands of transposed parallel conductors. We validate the proposed concept by measuring the current distributions in several double pancake test coils comprising two and four parallel conductors using Rogowski coils by applying AC signals of varying frequencies and amplitudes. Accordingly, uniform transport currents across four strands were confirmed. The proposed concept produced uniform current distributions across four groups of parallel conductors with a small number of transpositions. This work paves the way for developing armature coils composed of more than eight strands in parallel conductors by introducing a small number of transpositions based on CUCG.

Current Distribution of Armature Coils Combining Two Different Sizes of REBCO Racetrack Double Pancakes

We are currently developing superconducting electric propulsion armature coils which utilize REBa2Cu3Oy (REBCO) strands. To implement the REBCO coils in aircraft, the voltage must be reduced for safety concerns by using high-current capacity. Parallel conductors can be used to expand the current capacity, but the current cannot flow equally through each strand owing to the slight difference in inductance. We have investigated transposed parallel conductors which can almost equalize the inductance of each conductor. Conversely, the distributed windings for the armature coils can improve the magnetic field waveform and transform it into a sine wave by reducing the distortion of the magnetic flux density about the rotating magnetic field. However, it is difficult to implement a distributed armature winding using the REBCO strands since it is tape-shaped and difficult to twist. Therefore, we propose a distributed armature winding which combines two types of racetrack double pancakes. Each double pancake comprises two-strand insulated REBCO superconducting parallel conductors transposed inside the pancake for current equalization. In this study, we perform an experimental demonstration of the current equalization based on the transposition of the distributed armature winding. We made coils with two-strand as a simplified, but the actual coils were needed more 10 strand parallel conductors. In future works, we will manufacture transposed parallel conductor coils using much more strands and measure the current distribution. Additionally, this study measured the current distribution with only the stater. Thus, we will combine the rotor and measure the magnetic field distribution of the rotating magnetic field in the armature.

Current Sharing Among Transposed Three-Parallel REBa2Cu3O y Tapes in Single-Phase Armature Coils

To realize a large current capacity in REBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_y</i> superconducting coils, we have proposed a cabling design for the transposed multi-strand parallel conductors. This cabling design is also useful for a superconducting armature coil in a fully superconducting rotating machine system. Very recently, we developed an analytical method based on simple modeling, to roughly calculate the current distributions among the continuous strands in rotating machine conditions. In this manuscript, the current distributions predicted by the analytical method were compared with the measured values. Further, to understand the complex current distribution property for the three-strand parallel conductors, the turn number dependence of the current distribution with various transposition combinations was investigated. The current branches were measured under liquid nitrogen temperature of 77.3 K by Rogowski coils by applying AC transport current. The analytical method described the complex current distribution of the strands well, especially the coil with a large number of turns.

A Comprehensive Investigation of Winding Eddy and Circulating Current Losses of Stator Iron Coreless PMBLDC Motors

A method is proposed to comprehensively study the eddy and circulating current losses of stator winding wound by multiple parallel strands, to further improve the power density of stator iron coreless permanent magnet brushless DC (PMBLDC) motors. Analytical models of the eddy and circulating current losses in stator winding are deduced firstly to explicitly express the influencing factors of these two losses. As is shown, these factors are mutually contradicting. While the eddy current loss can be greatly reduced by using multiple parallel conductor strands, the circulating current loss will be extensively increased. The factors influencing these two winding losses, such as the strand diameter, magnetization types, and rotating speed, are investigated. A prototype of stator iron coreless PMBLDC motor without an inner rotor core is manufactured and tested to validate the theory. The experimental results of winding eddy and circulating current losses with different combinations of strand diameters and parallel numbers agree well with the theoretical results.

Two-Wire Power Line Microwave Communication Using Low-Loss Modes

A closed-form solution for the common and differential modal currents induced on a pair of infinitely long parallel conductors by a source, field coupled to a power line, is derived. For lossy conductors, the current consists of a continuous spectrum of radiation modes and (for the common mode) a modified low-loss Sommerfeld–Goubau (SG) mode and (for the differential mode) a quasi-TEM mode. This model is used to investigate the influence of a parallel conductor on microwave power line communication systems. When the complete current spectrum is used, it is shown that the SG mode is not the primary reason why low-loss communication is possible on power lines for distances on the order of 100 m. Nevertheless, and consistent with previous research, microwave communication using power lines has advantages over free space communication, and for typical parameters, the performance of these systems can be enhanced if the power line contains more than one conductor.

Spontaneous Symmetry‐Breaking of Nonequilibrium Steady–States Caused by Nonlinear Electrical Transport

AbstractNegative differential resistance (NDR) in certain materials has been attributed to spontaneous emergence of symmetry‐breaking electrical current density localization from a previously homogeneous distribution, which is postulated to occur due to the nonequilibrium thermodynamic force of minimization of entropy production. However, this phenomenon has not been quantitatively predicted based on intrinsic material properties and an applied electrical stimulus. Herein an instability criterion is derived for localization of current density and temperature from a thermal fluctuation in a parallel conductor model of a thin film that is subject to Newton's law of cooling. The conditions for steady–state electro‐thermal localization is predicted, verifying a decrease in entropy production upon localization. Electro‐thermal localization accompanied by a decrease of entropy production is confirmed in a multiphysics simulation of current flow in a thin film. The instability criterion predicts conditions for spontaneous current density localization, relating symmetry breaking fundamentally to dynamical instability via Local Activity theory.

The Full-Analytical Model of AC Loss for Hollow Copper Winding in Medium Frequency Transformer

Hollow copper windings used in medium frequency transformers can not only reduce losses, but also improve heat dissipation efficiency by passing coolant through the center of the conductor. In this paper, the high-frequency AC loss of the hollow copper winding of the transformer is modeled. By decomposing the rectangular hollow copper winding with complex structure into three parallel solid copper conductor regions with regular structure, the boundary field strength and current distribution of each region are accurately solved. The effect of filling rate on loss is also considered and then an accurate analytical model of AC loss of hollow copper winding is obtained. The maximum calculation error is less than 9.8%. Simulation and experiment verify the accuracy and versatility of the model.

Development and assessment of simplified analytical method for current distribution among REBa2Cu3O y parallel conductors in armature windings for fully superconducting rotating machines

Fully superconducting rotating machines employing REBa2Cu3O y (REBCO, RE = rare earth elements or Y) superconducting armature and field coils, are particularly interesting for aircraft applications, owing to their high output power density (kW kg−1). To achieve high current capability in superconducting coils, we have proposed a cabling design for transposed multi-strand parallel conductors. In the parallel conductor design, the REBCO strands are insulated from each other, except for both terminal ends, and transposed during the winding process to achieve uniform current distribution by cancellation of interlinkage magnetic flux between the strands. In this study, a simplified analytical method considering inductances was developed based on Laplace’s equation in cylindrical coordinates to roughly calculate the current distributions of multi-strands under armature coil conditions. The validity of the analytical method was investigated through current distribution measurements of the sample coils wound with two-strand parallel conductors. Consequently, the analytical method was validated with approximately 10% deviation under the experimental coil conditions. To establish a more accurate analysis method, certain improvements are needed.

Study on the Interference Law of AC Transmission Lines on the Cathodic Protection Potential of Long-Distance Transmission Pipelines

Through inductive coupling, AC transmission lines can generate large amounts of voltage to buried oil and gas pipelines in areas with common corridors, posing a threat to the cathodic protection effect of pipelines. Therefore, this paper investigates the effect of AC transmission lines on the cathodic protection of long-distance pipelines through inductive coupling. COMSOL Multiphysics finite element simulation software is used to calculate the distribution of cathodic protection potential of long-distance pipelines under different voltage levels, parallel spacing, conductor-to-ground height, conductor arrangement and pipeline burial depth for normal operation of AC transmission lines. Comparison and analysis of the AC transmission line on the pipeline cathodic protection potential interference law is conducted. The results show that: 1. AC transmission lines cause serious electromagnetic interference with the pipeline cathodic protection system, which will cause the pipeline cathodic protection potential to shift out of the effective protection area. 2. The maximum value of the induced voltage of the pipeline will appear at the two ends of the pipeline, and the induced voltage of the pipeline in the middle position is 0. 3. The shift of the pipeline cathodic protection potential increases with the increase of voltage level and decreases with the increase of parallel spacing, conductor height and burial depth. The pipeline cathodic protection potential shift is highest when the wires are arranged horizontally and lowest when they are arranged in an umbrella shape.

THE DEFINITION OF AMPERE IS CONFUSING

: SI unit of ampere is defined by means of magnetic force between two parallel conductors through which current flows. However, no mention is made of electric force in the opposite direction, which also exists between conductors. For that reason the existing definition is confusing for students, because it leads them to assume that by means of it ampere is also practically realized in laboratory. An analysis of forces shows that under certain conditions the electric force is much smaller than the magnetic force, but that fact still changes the physical picture of the propounded definition. The electric force can be compensated, which should be stated in textbooks when it comes to the definition of ampere, or else mention that ampere is practically realized by the current balance.

Abnormal Seebeck Effect in Vertically Stacked 2D/2D PtSe2 /PtSe2 Homostructure.

When a thermoelectric (TE) material is deposited with a secondary TE material, the total Seebeck coefficient of the stacked layer is generally represented by a parallel conductor model. Accordingly, when TE material layers of the same thickness are stacked vertically, the total Seebeck coefficient in the transverse direction may change in a single layer. Here, an abnormal Seebeck effect in a stacked two-dimensional (2D) PtSe2 /PtSe2 homostructure film, i.e., an extra in-plane Seebeck voltage is produced by wet-transfer stacking at the interface between the PtSe2 layers under a transverse temperature gradient is reported. This abnormal Seebeck effect is referred to as the interfacial Seebeck effect in stacked PtSe2 /PtSe2 homostructures. This effect is attributed to the carrier-interface interaction, and has independent characteristics in relation to carrier concentration. It is confirmed that the in-plane Seebeck coefficient increases as the number of stacked PtSe2 layers increase and observed a high Seebeck coefficient exceeding ≈188 µV K-1 at 300 K in a four-layer-stacked PtSe2 /PtSe2 homostructure.

Parallel strips coupled split ring resonators for a desktop wireless charging system overcoming irregular route restrictions

In order to achieve efficient long-distance wireless charging and avoid the influence of irregularity of the transmission path, a desktop wireless power transmission (DWPT) implementation method based on parallel-strips-coupled split ring resonators (PSSRR) was proposed in this paper. In the DWPT system, the power was transmitted from the transmitting coil (Tx) to the receiving coil (Rx) through the magnetic resonance coupling and guiding of the PSSRR. The PSSRR consisted of two split ring resonators (SRRs), the dielectric disk above each SRR and two parallel conductor strips for the SRRs’ connection. The SRR and the dielectric disk can realize effective mutual conversion between magnetic field and propagating mode through near field magnetic resonance coupling. The parallel conductor strips were applied to achieve efficient power transmission in the first-ordered mode. The transmission characteristics of the DWPT systems with coplanar or non-coplanar bent paths were analyzed. The simulated and experimental results verified the feasibility and robustness of the DWPT system. Under the plane bent path, the transmission efficiency of the proposed DWPT system can reach 76 % at a transmission distance of 1900 mm. The proposed method provided a solution for long distance WPT through required irregular path or multi-path. The system still had the problem that partial intermediate connection was needed and surrounding metal or high permittivity materials affected the transmission characteristics. Further research can be carried out from these two aspects.