Linear Conductors Research Articles

A Voltage Full-Waveform Reconstruction Method Based on Radiative Near-Field of Electric Field for the Hybrid DC Breaker of MMC-HVDC

The conventional current or voltage signal-based condition monitoring systems for DC high-voltage equipment have the disadvantages of huge volume, inconvenient operation, and low measurement bandwidth and sampling rate. To overcome these drawbacks, a simplified calculational model of the radiative near-field of the electric field in the circuit breaker valve hall is proposed. This model is based on the analytical model of the finite-length current-carrying linear ideal conductor and reveals the physical mechanism of non-invasive situational awareness based on the transient electric field of electrical devices. Predicated on this model, a reconstruction method for calculating the port transient voltage of the hybrid DC breaker is then established and verified by an artificial short-circuit test in an actual ±200 kV MMC-HVDC system. To the best of the author's knowledge, this is the first pilot short-circuit test in a full-scale MMC-HVDC system involving the hybrid DC breaker. Based on the testing data, the reconstructed and measured voltage show a relatively high degree of consistency both in time and frequency domain. The reconstructed voltage signals based on the radiation near-field not only expose the action time sequence of various electrical equipment with the response time of micro-second order, but also disclose the operation of the key devices and fault types for situational awareness in power system.

The Source-Stabilized Galerkin Formulation for Linear Moving Conductor Problems With Edge Elements

The Source-Stabilized Galerkin Formulation for Linear Moving Conductor Problems With Edge Elements

Biot–Savart-Based Design and Workbench Validation at 100 MHz of Transverse Field Surface RF Coils

Radiofrequency (RF) surface coils are extensively used as receivers in magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) systems thanks to their high signal-to-noise ratio (SNR). For specific magnetic resonance applications, the design of dedicated RF surface coils with a transverse (to the coil’s plane) RF magnetic field pattern can be necessary. Such transverse-field RF coils are constituted by several central linear (parallel or crossing) conductor elements connected by return current paths. Typically, the outer shape of such RF coils is circular or squared, although other geometries can be used. This paper describes the implementation and validation of a transverse-field RF surface coil simulator based on magnetostatic analysis, which permits the design and optimization of square butterfly and figure-of-eight RF coils with adjustable size and mutual distance between the central linear current elements. The simulation results, compared with the ones provided by a standard square loop RF coil, were validated with 100 MHz workbench measurements performed on three home-built prototypes. Finally, two novel quadrature RF coil structures designed by overlapping two orthogonal square butterfly and figure-of-eight RF coils were simulated and theoretically characterized. The RF coils described here should be suitable for a wide range of MRI/MRS preclinical/clinical applications, mainly at fields below 3 T.

Mathematical Model of the Unbalanced Monopole Feed. Part 2. Determination of Complex Capacitance of Normally Open Wire Antennas, Small with Respect to the Wavelength

A method for calculating the complex capacitance of small with respect to the wavelength, normally open antennas is proposed. Analytical expressions for determination of mutual potential coefficient of any two arbitrarily arranged linear conductors are obtained. The proposed technique can be useful in assessing the losses of normally open wire antennas placed in close proximity to the semiconductor surface, as well as in determination of their input resistance.

ОБҐРУНТУВАННЯ ВИБОРУ ФОРМИ ІНДУКТОРА ДЛЯ МАГНІТНО-ІМПУЛЬСНОЇ ОБРОБКИ ВЕЛИКОГАБАРИТНОГО ЗУБЧАСТОГО КОЛЕСА

Reducing products cost, and currently increasing the environmental friendliness of technological processes, is the main goal of machine-building production. Achieving these goals can be, in particular, due to the introduction of new processing methods. One of which is magnetic pulse processing(MPP). Using this method requires the use of special equipment, such as a magnetic inductor.The article proposes the use of a specially shaped inductor to strengthen the surface layer of the teeth of a large-sized gear wheel. The considered types of winding for the manufacture of a production coil of inductance from the point of view of the direct effect on the areas of the tooth with the greatest wear. Applying the Biot -Savart -Laplace law to calculate the magnetic fields of linear conductors, a detailed calculation of the inductor was carried out. It showed that the proposed design cannot provide strengthening over the entire plane of the contact spot of the tooth, where the greatest wear occurs during the operation of the wheel. When applying magnetic pulse processing, it is necessary to pay great attention to the shape and type of inductor winding. The type of winding and the turns arrangement of the inductor coil are also limited by the design of thepart. Special design restrictions are established where it is necessary to process internal cavities. Such cavities include the spaces between teeth of gear wheels.The article states that the magnetic field of the inductor, which has a parallel winding and covers a tooth, has the greatestforce on the edges of the tooth, and not on the area of the contact patch. It is also calculated that the magnetic field cannot exceed 1800 kA/m with the given parameters of the electric generator. Optimizing inductor shape and winding makes it possible to significantly reduce the requirements for generators while keeping the quality of the output at the same level.

A Stable Weighted Residual Finite Element Formulation for the Simulation of Linear Moving Conductor Problems

The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have numerical oscillations in the solution. To resolve this, the upwinding techniques, which are developed for the transport equation are borrowed and directly employed for the magnetic induction equation. In this work, an alternative weighted residual formulation is explored for the simulation of the linear moving conductor problems. The formulation is parameter-free and the stability of the formulation is analytically studied for the 1D version of the moving conductor problem. Then the rate of convergence and the accuracy are illustrated with the help of several test cases in 1D as well as 2D. Subsequently, the stability of the formulation is demonstrated with a 3D moving conductor simulation.

Wear Diagnostics of the Thrust Bearing of NK-33 Turbo-Pump Unit on the Basis of Single-Coil Eddy Current Sensors.

The problem of early wear diagnostics of the combined journal-and-thrust bearing of the turbo-pump unit (TPU) of the liquid-propellant rocket engine NK-33 is considered. A feature of the problem is the significant restriction on modifications of the power plant’s design. The original solution based on replacing the standard induction sensors of the turbo-pump rotational speed currently used in TPU by single-coil eddy current sensors (SCECS) with sensitive elements in the form of a segment of a linear conductor is proposed. The SCECS provide the monitoring of the axial displacement of the shaft in the thrust bearing, which characterizes the state of the unit and increases with the bearing wear. The function of the TPU shaft’s rotational speed measuring also remains. The article describes the proposed approach as well as a laboratory prototype of the system for early detection of the TPU thrust bearing’s wear. The results of the prototype research that confirm the feasibility of the proposed approach are analyzed.

Experimental Study of Mathematical Models of the Heating Defect Coefficient for the Heating-Cooling Cycles of an Electrical Connection

Reliable electrical connections are responsible for the trouble-free operation of entire systems where the load (electric stock) is roughly alternating. This circumstance makes it more complicated to identify the current state of the electrical connection during operation. During operation, the value of the transient resistance increases, as the tightening torque of the clamp dies is reduced (loosening) and the oxide films appear in sites of the wire and clamp joint. For the satisfactory condition, the value of the transient resistance should not exceed the value equal to the ohmic (linear) conductor resistance. Therefore, the aim of this work is the research study and comparison of the mathematical model to assess the state of the electrical connection under operational conditions that indirectly determines the actual value of the transient resistance.

Exact results for weakly nonlinear composites and implications for homogenization methods

Weakly nonlinear composite conductors are characterized by position-dependent dissipation potentials expressible as an additive composition of a quadratic potential and a nonquadratic potential weighted by a small parameter. This additive form carries over to the effective dissipation potential of the composite when expanded to first order in the small parameter. However, the first-order correction of this asymptotic expansion depends only on the zeroth-order values of the local fields, namely, the local fields within the perfectly linear composite conductor. This asymptotic expansion is exploited to derive the exact effective conductivity of a composite cylinder assemblage exhibiting weak nonlinearity of the power-law type (i.e., power law with exponent m=1+δ, such that |δ|≪1), and found to be identical (to first order in δ) to the corresponding asymptotic result for sequentially laminated composites of infinite rank. These exact results are used to assess the capabilities of more general nonlinear homogenization methods making use of the properties of optimally selected linear comparison composites.

Some remarks on the model of rigid heat conductor with memory: Unbounded heat relaxation function

The model of rigid linear heat conductor with memory is reconsidered focussing the interest on the heat relaxation function. Thus, the definitions of heat flux and thermal work are revised to understand where changes are required when the heat flux relaxation function $ k $ is assumed to be unbounded at the initial time $ t = 0 $. That is, it is represented by a regular integrable function, namely $ k\in L^1( \mathbb{R}^+) $, but its time derivative is not integrable, that is $ \dot k\notin L^1( \mathbb{R}^+) $. The study takes its origin in [2]: the heat conductor model described therein is modified in such a way to adapt it to the case of a heat flux relaxation function $ k $ which is unbounded at $ t = 0 $. Notably, also when these relaxed assumptions on $ k $ are introduced, whenever two different thermal states which correspond to the same heat flux are considered, then both states correspond also to the same thermal work. Accordingly, the notion of equivalence can be introduced, together with its physical relevance, both in the regular kernel case in [2] as well as in the singular kernel case analysed in the present investigation.

Mapping of equipotential surfaces using the free Quantum Geographic Information System software

Abstract In this work, we report the mapping of electrical equipotential lines (1D) and equipotential surfaces (3D) using the free Quantum Geographic information system (QGIS) software. For this purpose, experiments taking into account, four different electrical configurations were performed on physics classes of undergraduate students, using two conductors of opposite electrical charges for each experiment. For the first experiment two copper parallel linear conductors; for the second, a copper parallel linear conductor with a small circular ring acting as a point charge; for the third, two concentric circular ring and for the fourth one a semicircular ring with a small circular ring acting as point charge. The experimental data were treated and interpolated in the, open source, QGIS software, used in geoprocessing, to map the electrical equipotential planes and surfaces.

Deep Resistivity Structure of Basalt‐Covered Central Part of Paraná Basin, Brazil, From Joint 3‐D MT and GDS Data Imaging

AbstractThe deep structure beneath the basalt‐covered sediments of Paraná basin is not well understood. Magnetotelluric (MT) broadband (1,000 to 0.001 Hz) data recorded at 296 selected stations along three new survey lines were first inverted in three dimensions to reveal the local scale resistivity structure of the central part of the basin where there are three deep exploration wells with resistivity logs for model validation. The 3‐D MT inversion model correctly identified the resistive (>100 Ωm) flood basalts and postvolcanic cover layer, the underlying electrically conductive (~10 Ωm) sediments, and the highly resistive (>1,000 Ωm) crystalline basement at the well locations and provides a reliable average crustal resistivity structure consisting of ~20–24 km thick highly resistive upper crust and ~20 km thick conductive lower crust above a resistive mantle. Subsequent basin‐scale joint inversion of highest quality MT data sets (261 stations) and geomagnetic depth sounding array data imaged two prominent subparallel belts of N‐S and NNE‐SSW trending steep conductors in the deep crust and upper mantle, one located directly beneath the present‐day axis of thickest sedimentary deposits in the basin and another near the coastal location where dolerite dyke swarms intrude the outcropping Precambrian basement. Other roughly orthogonal bands (E‐W to NW‐SE) of linear crustal conductors radiate from these two main belts. The resulting networks of steep conductors at upper to midcrustal level seem to mark the fossil plumbing system of Paraná magmatic province and are interpreted as preexisting shear zones exploited by the voluminous Early Cretaceous magmatism in the region.

A function-driven characterization of printed conductors on PV cells

Nowadays the development in photovoltaic (PV) cells manufacturing requires increasingly sophisticated technologies, and in order to avoid efficiency losses in PV cell, printing techniques of the front contacts have to be well controlled. To this purpose, printed linear conductors (PLCs) on a PV standard cell are characterized by morphology- and resistance-based measurements, creating a well-calibrated test structure towards the development of an application-oriented material measure. It can be noticed that morphology and texture parameters determined by stylus and optical profilers are well in agreement, and the resistance calculated from the reconstructed cross-section area matches quite well the measured resistance of fingers. Uncertainties of about 14% to 17% are estimated for local measurements of morphology-based and measured resistance of finger segments up to 5 mm length. Fingers characterized by somewhat larger roughness/waviness values (, , ) show some local irregularities, which may degrade the electrical contact of the PV front surface.

Transmission Line Modeling of Scattering From a Linear Conductor Near the Surface of the Ground

Applied modeling of electromagnetic interactions with linear conductors is essential to advance near-earth sensing devices and integrated signal processing algorithms. This paper describes the development of a novel analytical transmission line (TL) model and its subsequent comparison with a method of moments simulation. The TL model predicts electromagnetic scattering by a linear conductor of finite length that is near lossy ground, here assumed to be a homogeneous conducting half-space. Our model uniquely combines the following: the effect of surface waves on the fields, the proximity of the air–ground interface on wave propagation along the conductor, orthogonal electric dipole exciter polarizations, and the role of an insulating layer on the conductor. It is shown that the TL approach is accurate and offers advantages such as fast computation time, physical insight into the scattering process, and potential for embedded signal processing.

DEVELOPMENT AND CREATION OF A LABORATORY MODEL OF AN INDUSTRIAL OVEN WITH MHD-STIRING FOR ALUMINUM AND ITS ALLOYS

In this work using physical models of an aluminum furnace bath, the mixing process of a liquid metal with a traveling magnetic field, which is created by a system of parallel linear conductors located under the bottom of the bath, is investigated. The flow velocity profiles and the dependence of the mixing rate on the force and frequency of the current in the inductor were obtained on a gallium model using a Doppler anemometer. In the experiment, a sharp decrease in the vertical temperature gradient in the bath was found when the threshold value of the mixing rate of the liquid metal was reached. With the help of mathematical modeling, the flow pattern, the evolution of the temperature field and the spread of the impurities in the bath of the physical model under MHD stirring are calculated. The results are compared with the results of the physical experiments.

3-D Integral Approach for Calculating Mutual Interactions Between Polygon-Shaped Massive Coils

The 3-D analytical calculations are proposed using Green’s function (integral approach) for determining magnetic flux densities, mutual inductances, or interaction energies and magnetic force components between different polygon-shaped coils with a rectangular cross section. The basic concept is the determination of the cited magnetic quantities from elementary linear conductors with arbitrary orientations in desired planes. The process is described by using the space transformation matrices of the different axes in which the conductors have previously been defined. The developed results are validated by comparison with those issued from 3-D finite-element methods (Flux 3-D Software). The calculated mutual inductances for some applications are also compared with realized experimental measures.

On Hashin–Shtrikman-type bounds for nonlinear conductors

For linear composite conductors, it is known that the celebrated Hashin–Shtrikman bounds can be recovered by the translation method. We investigate whether the same conclusion extends to nonlinear composites in two dimensions. To that purpose, we consider two-phase composites with perfectly conducting inclusions. In that case, explicit expressions of the various bounds considered can be obtained. The bounds provided by the translation method are compared with the nonlinear Hashin–Shtrikman-type bounds delivered by the Talbot–Willis (1985) [2] and the Ponte Castañeda (1991) [3] procedures.

Modified Rogowski coil for the detection of fast plane currents

Rogowski coils are used to diagnostic currents of cylindrical configuration, therefore they are known to have a toroidal geometry. Nowadays, also linear transmission lines can be developed to get planar beams. Therefore, linear Rogowski coil to detect current pulses inside the linear conductors are necessary. For large devices, the theory necessary to study the system is that of the transmission lines, especially if the pulse width is comparable to the propagating time of signal inside the detector. The device we developed is able to record pulses more than 80ns long with rise time near 500ps. The former depends on the inductance value, load impedance and resistance of the coil; while the second on the mechanical configuration of coil loops. Theoretically, the attenuation coefficient depends exclusively on the turn number of the coil, while experimentally it is found to depend also on the current distribution inside the line.

Internal inductance of a conductor of rectangular cross-section using the proper generalized decomposition

Purpose Rectangular conductors play an important role in planar transmission line structures, multiconductor transmission lines, in power transmission and distribution systems, LCL filters, transformers, industrial busbars, MEMs devices, among many others. The precise determination of the inductance of such conductors is necessary for their design and optimization, but no explicit solution for the AC resistance and internal inductances per-unit length of a linear conductor with a rectangular cross-section has been found, so numerical methods must be used. The purpose of this paper is to introduce the use of a novel numerical technique, the proper generalized decomposition (PGD), for the calculation of DC and AC internal inductances of rectangular conductors. Design/methodology/approach The PGD approach is used to obtain numerically the internal inductance of a conductor with circular cross-section and with rectangular cross-section, both under DC and AC conditions, using a separated representation of the magnetic vector potential in a 2D domain. The results are compared with the analytical and approximate expressions available in the technical literature, with an excellent concordance. Findings The PGD uses simple one-dimensional meshes, one per dimension, so the use of computational resources is very low, and the simulation speed is very high. Besides, the application of the PGD to conductors with rectangular cross-section is particularly advantageous, because rectangular shapes can be represented with a very few number of independent terms, which makes the code very simple and compact. Finally, a key advantage of the PGD is that some parameters of the numerical model can be considered as additional dimensions. In this paper, the frequency has been considered as an additional dimension, and the internal inductance of a rectangular conductor has been computed for the whole range of frequencies desired using a single numerical simulation. Research limitations/implications The proposed approach may be applied to the optimization of electrical conductors used in power systems, to solve EMC problems, to the evaluation of partial inductances of wires, etc. Nevertheless, it cannot be applied, as presented in this work, to 3D complex shapes, as, for example, an arrangement of layers of helically stranded wires. Originality/value The PGD is a promising new numerical procedure that has been applied successfully in different fields. In this paper, this novel technique is applied to find the DC and AC internal inductance of a conductor with rectangular cross-section, using very dense and large one-dimensional meshes. The proposed method requires very limited memory resources, is very fast, can be programmed using a very simple code, and gives the value of the AC inductance for a complete range of frequencies in a single simulation. The proposed approach can be extended to arbitrary conductor shapes and complex multiconductor lines to further exploit the advantages of the PGD.

Nonlinear ionic transport through microstructured solid electrolytes: homogenization estimates

We consider the transport of multiple ionic species by diffusion and migration through microstructured solid electrolytes in the presence of strong electric fields. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is heuristically deduced from a multi-scale convergence analysis of the relevant field equations. The resulting homogenized response involves an effective dissipation potential per species. Each potential is mathematically akin to that of a standard nonlinear heterogeneous conductor. A ‘linear-comparison’ homogenization technique is then used to generate estimates for these nonlinear potentials in terms of available estimates for corresponding linear conductors. By way of example, use is made of the Maxwell-Garnett and effective-medium linear approximations to generate estimates for two-phase systems with power-law dissipation. Explicit formulas are given for some limiting cases. In the case of threshold-type behavior, the estimates exhibit non-analytical dilute limits and seem to be consistent with fields localized in low energy paths.