Conductor Cross-section Research Articles

Analysis of Proximity Consequences of Coil Windings in Electromagnetic Forming

Multiturn coils are required for manufacturing sheet metal parts with varying depths and special geometrical features using electromagnetic forming (EMF). Due to close coil turns, the physical phenomena of the proximity effect and Lorentz forces between the parallel coil windings are observed. This work attempts to investigate the mechanical consequences of these phenomena using numerical and experimental methods. A numerical model was developed in LS-DYNA. It was validated using experimental post-mortem strain and laser-based velocity measurements after and during the experiments, respectively. It was observed that the proximity effect in the parallel conductors led to current density localization at the closest or furthest ends of the conductor cross-section and high local curvature of the formed sheet. Further analysis of the forces between two coil windings explained the departure from the “inverse-distance” rule observed in the literature. Finally, some measures to prevent or reduce undesired coil deformation are provided.

Reactive power compensation in the railway electrical traction system, using synchronous machines controlled by SCADA

This article brings forward a solution for compensating the reactive power of the railway electrical traction system. Using the V-characteristics of the synchronous machine, reactive power can be produced or absorbed from the power supply network, keeping the power factor at a value as close to 1 as possible. Given that the load consumed by the railway electrical traction system is variable, it is necessary to be able to promptly correct the power factor. The SCADA system will change the synchronous machine’s operating characteristics relative as a function of the angle between the voltage and the current that are set at a given time by the consumers (electrical locomotives) passing through the railway section. By compensating the reactive power, the amount of active power supplied to the electrical network of the railway traction system is increased, without the need to modify the cross-section of the electrical conductors.

Simulation and Analysis of Radial Temperature for Aluminum Conductor Steel Reinforced with 1250mm2 Large Cross-Section

In order to meet the growing demand for electricity, the construction of UHVDC project has vigorously carried out. With the improvement of voltage level, the cross-section of conductor also increases. For large cross-section conductor, the number of steel and aluminum single wires and layers of the conductor are large, and the internal structure is very complex. It has been proved that there is a temperature difference in the radial direction of the conductor due to the contact heat transfer between steel and aluminum based on previous studies. However, most studies are focused on normal conductors, not large cross-section conductors. Therefore, in this paper, the geometric model and temperature calculation model for 1250mm2 large cross-section ACSR conductor, which is widely used in UHVDC, were established. Simulation of conductor temperature distribution was carried out, and the influence of wind velocity, environment temperature and current on radial temperature difference was analyzed. The results show that, with the increase of wind velocity and the decrease of current, the radial temperature difference of conductor decreases gradually, while the environment temperature has little influence on the radial temperature difference.

Designing a low-mass, high-current modal filter for the spacecraft power bus

The paper presents the results of a quasi-static simulation of a modal filter with a reduced cross-section of conductors that are conducting a significant current. Time characteristics in differential and common modes are considered. The dependence of the attenuation coefficient on the thickness of the conductors is shown.

Measurements of self-field and voltage for the REBCO stacked tapes assembled in rigid structure (STARS) conductor at 77 K

The measurements of self-fields and voltages for the stacked tapes assembled in rigid structure (STARS) conductor were carried out when the conductor immersed in liquid nitrogen was energized. In the measurements, a 3 m straight line shaped STARS conductor, which is composed of 45 REBCO tapes (15 tapes × 3 rows) embedded in a copper stabilizer, was used as a conductor sample. The measurement results indicate that the ramp rate at the conductor excitation and the one-time thermal cycle of the conductor do not affect the self-fields but the voltages.The current center position in the conductor cross-section during the conductor excitation was analyzed from the measurement results of the self-fields. The current center position always maintains the same position in the middle of the cross-section during the excitation. The analysis indicates that the current distribution of the STARS conductor is stable during the excitation. In addition, two-dimensional magnetic field calculations were conducted using the various models for the cross-sectional configuration of the STARS conductor. As a result, the calculation results agree with the measurement results regarding the self-fields.

Technical and Economic Model of the Conductor Cross-Section for Active-Adaptive Electrical Networks

Technical and Economic Model of the Conductor Cross-Section for Active-Adaptive Electrical Networks

Modeling Quench Propagation in the ENEA HTS Cable-In-Conduit Conductor

The quench protection in high-temperature superconducting (HTS) magnets is a well-known issue. Therefore, it is fundamental to have reliable models available for the analysis of the quench propagation in such magnets. The quench propagation in an ENEA HTS cable-in-conduit conductor, developed for fusion applications with the particular reference to an insert for the central solenoid of the Italian Divertor Tokamak Test (DTT) facility, is analyzed here with a new 1-D multiregional thermal-hydraulic and electric model, based on dedicated preliminary analyses and experimental and numerical characterization of the conductor. It is shown that large temperature differences arise in the conductor cross section during the quench propagation. The model is then applied to parametrically assess the effects of delay and fast current-discharge times on the conductor peak temperature, to avoid damaging the HTS. The parametric study shows that both the delay and current discharge time should stay below 0.5 s, to keep the peak temperature below 150 K.

Analysis of AC Loss Contributions From Different Layers of HTS Tapes Using the A−V Formulation Model

This article presents a numerical model based on the definition of the scalar and vector potentials to calculate the ac losses generated in a high-temperature superconductor coated conductor tape by an ac transport current and by an ac external magnetic field applied with a generic orientation. The material characteristics of the different layers of a reference tape are included in the model equations, which allow analyzing the differences between a model including only the superconducting layer or all layers of the coated conductor. The model is applied to study the dependence of ac losses on the amplitude of the transport current and magnetic field (applied individually or combined) and their frequency. The numerical results are compared with analytical formulations, with a second numerical model based on the H -formulation, and with experimental results. The conditions at which the contribution of the nonsuperconducting layers to the total ac losses of the tape become relevant are analyzed. In particular, the dependence of losses on the frequency of the ac external magnetic field applied at different orientations, is investigated. The current density distribution computed on the conductor cross-section is used to explain the trend of the calculated losses.

Time Hardening Model for Large Cross Section Conductor Based on Creep Experiments Analysis Under Different Temperature

The increased cross section of overhead conductors can obviously improve the power transmission capacity. Whereas its large creep elongation may make the design works be more difficult. In this paper, time hardening model was proposed to analyze the creep properties of the large cross section conductor. To perform such analysis, the creep tests of the typical large cross section conductor JL1/G2A-1250/100-84/19 under different temperature conditions were carried out. Then the time hardening models excluding and including temperature coefficient were deduced respectively. The results showed that the calculation based on the time hardening model were well agreed with the results of laboratory tests and field observation. What is more, the accuracy of the time hardening model in this paper is higher than the fitting model. Finally, the section integration model was discussed based on the nonsynchronous stringing process so as to provide a new method for calculating the creep value of large cross section conductors.

Development of standard cable cross-sections of rural electrical networks

For the optimal development of electric networks, not only the optimal choice of the network element parameter from the existing standard scale (parametric series) of sizes is important, but also the optimization of standard scales of equipment sizes or checking their optimality. The method of economic intervals explores the existing parametric series of standard cross-sections of 10 kV cable cores and establishes that the existing series does not satisfy the conditions for optimizing the use of cable lines in rural areas. Since cable lines have not yet found wide distribution in rural areas, there are conditions not only to verify the optimality of the existing scale of cable conductor cross-sections but also to establish an optimal scale of 10 kV cable conductor cross-sections, intended for the construction of cable power transmission lines in rural areas (if the existing scale does not meet optimality conditions). For rural distribution electric networks, the initial and final sections in a parametric series (25 and 120 mm2) are determined and the optimal for rural areas parametric series of cable cross-sections of 10 kV (25; 50; 120 mm2) is recommended.

Numerical Analysis and Experimental Verification of Eigenfrequencies of Overhead ACSR Conductor

<span lang="EN-GB">This contribution deals with the modal analysis of ACSR conductor using the finite element method (FEM) and experimental measurements of eigenfrequencies. In numerical experiments for the modelling of the conductor the material properties of the chosen conductor cross-section are homogenized by the </span><span lang="EN-US">Representative</span><span lang="EN-GB"> Volume Element (RVE) method. The spatial modal analysis of the power line is carried out by means of our new 3D FGM beam finite element and by standard beam finite element of the commercial software ANSYS. Experimental measurements are also carried out for verification of the numerical calculation accuracy.</span>

Analysis on the contact force behaviors among strands of CICC conductor cross section

International Thermonuclear Experimental Reactor (ITER) hopes to achieve controllable thermonuclear fusion by constraining the motion of high temperature plasma by a strong magnetic field which is generated by superconducting magnets wound by the cable-in-conduit conductors (CICCs). The CICC structure is complex, usually with thousands of NbTi/Cu or Nb3Sn/Cu twisted in four or five stages. It operates in a complex environment of extremely low temperature, high current and strong magnetic field. The electromagnetic force generated by the superconducting material will cause deformation, reduce its characteristic parameters and bring hidden trouble to the safety of the device. Traditional studies on the contact force of the cross-section strand of CICC mostly adopt non-actual object photoelastic model in the experiment, and numerically adopt discrete element method (DEM) without particle deformation. However, it is difficult to give the contact force of the cross-section strand closer to the real working condition. In this experiment, the deformation characteristics were calculated between strands of the prototype of CICC by spraying speckle on the cross-section and using digital image correlation (DIC). Theoretically, taking the strand deformation obtained by DIC as the input parameter of granular element method (GEM), the distribution characteristics of the contact force of the CICC conductor under the action of transverse pressure are calculated, and the size and direction of the contact force chain are statistically analyzed.

Inductance Formula for Rectangular Planar Spiral Inductors with Rectangular Conductor Cross Section

In modern technology, inductors are often shaped in the form of planar spiral coils, as in radio frequency integrated circuits (RFIC’s), 13.56 MHz radio frequency identification (RFID), near field communication (NFC), telemetry, and wireless charging devices, where the coils must be designed to a specified inductance. In many cases, the direct current (DC) inductance is a good approximation. Some approximate formulae for the DC inductance of planar spiral coils with rectangular conductor cross section are known from the literature. They can simplify coil design considerably. But they are almost exclusively limited to square coils.
 This paper derives a formula for rectangular planar spiral coils with an aspect ratio not exceeding a value between 2.5 and 4.0, depending on the number of turns, and having a cross-sectional aspect ratio of height to width not exceeding unity. It is valid for any dimension and inductance range.
 The formula lowers the overall maximum error from hitherto 28 % down to 5.6 %. For specific application areas like RFIC’s and RFID antennas, it is possible to reduce the domain of definition, with the result that the formula lowers the maximum error from so far 18 % down to 2.6 %. This was tested systematically on close to 140000 coil designs of exactly known inductance. To reduce the number of dimensions of the parameter space, dimensionless parameters are introduced. The formula was also tested against measurements taken on 16 RFID antennas manufactured as PCB’s.
 The derivation is based on the idea of treating the conductor segments of all turns as if they were parallel conductors of a single-turn coil. It allows the inductance to be calculated with the help of mean distances between two arbitrary points anywhere within the total cross section of the coil. This leads to compound mean distances that are composed of two types of elementary ones, firstly, between a single rectangle and itself, and secondly, between two displaced congruent rectangles. For these elementary mean distances, exact expressions are derived. Those for the arithmetic mean distance (AMD) and one for the arithmetic mean square distance (AMSD) seem to be new.
 The paper lists the source code of a MATLAB® function to implement the formula on a computer, together with numerical examples. Further, the code for solving a coil design problem with constraints as it arises in practical engineering is presented, and an example problem is solved.

Electrodynamic Parameters of a Coaxial Cable at Bipolar Pulses Propagation

All-in-interworking technology, based on IEEE 802.3 standard, was mainly developed for the separable media cabling and data transmission speed increase. Although the high-speed networking is already provided by a fiber optic cable, coaxial guides are in demand for similar applications. Time-domain analysis is undertaken to estimate electrodynamic states of inner and outer guiding conductors at periodic bipolar pulses propagation on a coaxial cable. An electric current density distribution on the cross-section of the inner conductor is obtained from a solution of Maxwell equations under periodic boundary conditions that are prescribed by a product of two functions. The first one is introduced implicitly for a profile of surface current density in the axial direction, while the other determines this profile transient states. As for shielding braid, which is the cable outer conductor, its current density distribution is derived from an analysis of field harmonics that penetrate into conductive subsurface layers under similar boundary conditions. It is also shown that prescribed implicative boundary conditions for both conductors allow to obtain, at least under auxiliary assumption, some completed formulae useful to the estimation of the pulses duration admissible decrease at their transmission on the coaxial cable. The paper contains some comparative and numerical results as well

A short-time physics problem in superconductivity: Stability against quench

This paper investigates the stability problem of superconductors against quench. Numerical Finite Element simulations are applied to calculate the distribution of transient temperature, critical current density and transport current in the conductor cross-section under a disturbance, here flux flow losses. Contrary to standard stability models, the focus of the paper is on situations very close to the superconducting/normal conducting phase transition. The obtained results demonstrate it is not realistic, even in thin films, to assume uniform conductor temperature under a disturbance. A method is suggested on how to predict the time and position of a quench when it is expected to occur in the conductor cross-section. Quench starts locally. Application of a microscopic stability model allows to describe continuous, not abrupt but very fast break-down of transport current in situations close to the phase transition.

Electrical properties of medium voltage electricity distribution networks

An increasing amount of low carbon technologies (LCT) such as solar photovoltaic, wind turbines and electric vehicles are being connected at medium and low voltage levels to electric power networks. To support high-level decision-making processes, the impacts of the LCTs on large numbers of different types (e.g., rural, suburban, urban) of distribution networks need to be fully understood and quantified. However, detailed modeling of large numbers of real-world networks is challenging for two reasons. First, access to real-world network data is limited, and second, cleaning the data requires a significant amount of time, even before modeling of the networks. This paper offers a novel systematic methodology aimed at identifying and quantifying the key electrical properties of medium-voltage level distribution networks. The methodology allows for characterizing different types (e.g., suburban, urban) of distribution networks and obtaining 'depth' dependent electrical properties of the models of the networks. Two key sets of (electrical) data were used for the study. The first set was installed capacities of distribution substations; and the second set was the conductor cross sections of the distribution lines. In the graph models of real-world networks, 'nodes' represent the distribution sub­stations, switchgears, busbars and consumers locations of the network. 'Links/edges' stand for the connections between the nodes through distribution lines. The results of the investigation of the real-world networks showed that, the substation capacities and the conductor cross sections could characterize the electrical properties of suburban and urban type distribution networks. The resulted probability density functions (PDF) of the electrical properties of suburban and urban type distribution networks have the potential to be directly used in generating realistic distribution network models.

The Method of Unambiguous Determination of the Design Electrical Load According to the Heating Condition

A problem of checking conductors for heating condition in power supply systems in case of random electrical load is considered. A probabilistic model of current is used. The current is considered as a random process with a normal distribution law. It is shown that the existing practice of determining the design load from a ten-minute heating time constant does not provide a reliable solution. It is proposed to use the curve of the effective inertial current versus the heating time constant. Methods to obtain this dependence with a random electrical load are identified. The exact solution is found at the intersection of this curve with the curve of the long-term permissible conductor load versus the heating time constant. The calculations took into account that the scale of standard cross-sections of conductors is discrete. Errors of existing method are evaluated with example of random electrical load with exponential correlation function. It is shown that the error in determining the design electric load and the error in selecting the cross-section of the conductors are different.

Optimal Design Method to Improve the Magnetic Field Distribution of Multiple Square Coil Systems

Power electronic equipment regulated by the International Thermonuclear Experimental Reactor (ITER) organization must be tested in a relevant steady-state magnetic field immunity test, and the test area is generally required to be a cube shape. For this reason, a multiple square coil system structure is used. In this article, a Taylor expansion and an optimization program are used to determine the optimal parameters of a coil system with different groups. For a three-coil system, the effects of the conductor cross-section, conductor spacing, helical structure, and conductor connection on the magnetic field uniformity are analyzed. A clear understanding of the influence degree of the error helps design an actual coil system. ITER organization is currently conducting research on magnetic field generator for electronic devices in large scientific devices. The design method proposed in this article can reduce the design difficulty and provide theoretical support.

Analytical model for large deflection bending of helically stranded electrical wires

An analytical model is presented to calculate the elasto-plastic bending response of electrical wires subjected to large deflections. Electrical wires are defined as helically wound conductors enclosed in polymer insulation. For modeling purposes, the conductor layout in a wire’s cross section is estimated using a packing algorithm. Euler-Bernoulli beam theory describes the overall wire bending behavior; the conductors’ stick-slip behavior is modeled based on Coulomb’s friction law. In the plastic region, the conductors are modeled as laminated composite beams. A cantilever bending setup is used to characterize the force displacement response of wires with different diameters, number of conductors, beam lengths, and conductor cross sections. The model parameters are calibrated to ensure that the force-displacement calculations are within the 95% confidence interval of the test data.

Two-Dimensional Periodic Dual-Polarized Over Wave Region Antenna Array

The two-dimensional periodic dual-polarized antenna array in the form of a nonuniform multiconductor line of square cross-section conductors is proposed and studied. Using the approximate theory, matching characteristics of the two-conductor line with three different laws of impedance variation are studied and the optimum law is found. Electrodynamic modeling of an infinite two-dimensional periodic array of these elements is carried out using the finite element method at different scanning modes. Using a numerical experiment, the possibility of implementing the over wave region matching mode is demonstrated for arrays of 144 (12 × 12) and 576 (24 × 24) elements: for the array of 576 elements, the working bandwidth in the cophased mode was 1 : 34; when scanning in the sector of 90°, more than 1 : 15.