Transient Electromagnetic Field Research Articles

An Exact Solution of the Fractional Transient Electromagnetic Field Inside an Atmospheric Duct

The objective of this paper is to find the exact solution of the fractional electromagnetic (EM) equation within an atmospheric duct (dielectric medium) of the transient EM field caused by a vertical magnetic dipole and discuss the results in both fractional D-dimensional space and integer space. The novelty of this work is the exact solution of the fractional EM equation in terms of Bessel and Mittage-Leffler functions based on Caputo fractional derivative order α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} and the Laplacian operator in D -dimensional fractional space. Using the separation of variables method, the resulting magnetic field can be controlled by D=α1+α2+α3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=\\alpha _1+\\alpha _2+\\alpha _3$$\\end{document} and alpha as spatial and time fractional parameters, respectively. The transient magnetic field behaviour inside the duct is plotted through some of figures depending on fractional parameters D and α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}. The classical integer results in usual space are recovered from fractional solution at D=α=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=\\alpha =1$$\\end{document}. The main results highlighted are that spatial frequencies grow at a faster rate during EM wave propagation; thus, the amplitude of the propagated wave in integer space is greater than that in fractional space. Increasing the fractional parameters D and α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} simultaneously increases the amplitude of the EM wave and can be used to control the power and energy of the EM wave.

Measurement of electrical conductivity of human tissue: A feasibility study of a novel time-domain approach

A straightforward, non-invasive experimental approach to the extraction of electrical conductivity of human tissue using the transient electromagnetic field coupling between two loop antennas is presented. The main objective of this initial study is to demonstrate the feasibility of the new time-domain (TD) methodology. The designed loop antennas and the experimental setup with its instrumentation are described. The presented results show that the proposed method is capable of obtaining accurate values of the electrical conductivity of human tissue.

Transient Electromagnetic Field Response Analysis Considering Dam Boundary Conditions

Abstract The transient electromagnetic (TEM) method has outstanding advantages in detecting depth and response information and can be used to detect anomalies hidden deep inside dams. However, the current data analysis method based on geological exploration is inapplicable to the interpretation of dam detection data, the main reason being the lack of consideration of the influence of dam boundary conditions on the diffusion of the TEM field. In this work, by establishing a numerical model of a dam for TEM detection, the effects of the dam slope ratio, upstream water body, overburden, and other dam boundary conditions on the TEM field were studied. The results showed that the slope ratio made the propagating TEM field to exhibit a constraining behavior, and a negative deviation could be seen in the attenuation curve, indicating a false high-resistance anomaly. The upstream water body distorted the diffusion of the electromagnetic field, and the low-resistance covering layer caused a low-retardation retention phenomenon in the magnetic field, leading to a positive deviation in the attenuation curve, indicating a false low-resistance anomaly. The influence of the boundary conditions was present throughout the entire observation window in which the detection was performed, and the sensitivity of the magnetic field to these boundary conditions was significantly higher than that of the change rate of the magnetic field. With the increase in the observation time, the main influencing factors were the slope ratio, overburden layer, and upstream water body.

Everlasting interaction: Polarization summation without a Landau pole

We propose an external field approach to evaluating effective action allowing the interaction to act everywhere at all times (everlasting). Requiring that the asymptotic gauge fields are always interacting, we implement displacement fields encoding polarization corrections into the derivation of effective action. The result is a novel polarization summation for one-cut reducible loop diagrams, which can be applied to two cases: transient quasiconstant electromagnetic fields and everlasting interactions. In the first case, a perturbative expansion of our result recovers the Schwinger-Dyson reducible diagram series with a Landau pole. The everlasting summation evaluated in nonperturbative fashion removes the Landau pole, providing a new avenue for modeling strongly interacting theories. Published by the American Physical Society 2024

Experimental Study of Electromagnetic Interference from Concentrated Discharge Channels within the Soil to Adjacent Directly Buried Cables during Lightning Current Inflow to the Ground

Independent lightning rods are often installed in substation grounding systems for lightning protection. The concentrated discharge channel formed when a lightning current flows to the ground through a grounding electrode will cause electromagnetic interference to the directly buried secondary cable. And the three-dimensional structure of the discharge channel will affect the transient electromagnetic field distribution, thereby affecting the electromagnetic transients on cable shields. In order to explore the influence of soil discharge phenomena on the electromagnetic interference of the directly buried secondary cable, in this paper, we carried out experiments on cables in two different grounding modes, single-ended and double-ended grounding, and captured image of soil discharge channels. The results show that the cable grounding mode will affect the coupling mode that causes the shielding layer current. The relative spatial position of the soil discharge channel and the cable has a significant impact on the magnitude of the shielding layer current under both grounding modes. The water content and salt content of the soil also have different degrees of influence on the coupling current of the shielding layer in different grounding modes.

The damping factor improved the algorithm in semi-airborne transient electromagnetic modelling based on accelerated FDTD

3D modelling plays a crucial role in analysing semi-airborne transient electromagnetic fields, how to accurately and efficiently calculate electromagnetic response has become a significant issue. In this paper, a damping factor improved algorithm of the accelerated finite difference time domain (AFDTD) is proposed for semi-airborne transient electromagnetic modelling. Differing from the previous research, we introduce a novel function to redefine the damping factor, allowing for adaptive adjustment and enhancing calculation accuracy within the finite difference time domain (FDTD) iterative process. To verify the effectiveness of our approach, we conduct tests using homogeneous half-space models, which demonstrate that the improved damping factor significantly enhances calculation accuracy without a notable reduction in efficiency. Furthermore, we apply our improvement to typical conductivity models and polarisable conductivity models, and the results indicate that our approach achieves high accuracy in accelerated semi-airborne transient electromagnetic modelling.

Recovering induced polarization effects from 1-D coupled inversion of transient electromagnetic data

SUMMARY Induced polarization (IP) effects can significantly affect and superimpose the inductive earth response, leading to heavily distorted data and, if overlooked, false geological interpretation. In this paper, we implemented the Levenberg–Marquardt (LM) and very fast simulated annealing (VFSA) algorithms to recover IP effects from central loop transient electromagnetic (TEM) data. To incorporate the IP effect in the TEM response, we used the Cole–Cole parametrization, maximum phase angle (MPA), maximum imaginary conductivity (MIC) and Jeffrey transform of Cole–Cole parameters. The result of 1-D forward calculation and inversion of synthetic TEM data revealed that the Cole–Cole parametrization is more robust and reliable than MPA, MIC and Jeffrey transform, and that the synthetic data were well fitted and IP parameters well recovered using this model. However, the incorporation of the IP effect leads to a highly nonlinear and non-unique inverse problem which requires an accurate starting model, especially for LM inversion. To evaluate the performance of our algorithm using field data, we carried out a 1-D inversion of TEM data acquired along a profile that traverses a waste site located near Cologne, Germany. Furthermore, to obtain a priori information and validate the result of TEM data modelling, we conducted an electrical resistivity tomography (ERT) and time-domain IP (TDIP) survey along the TEM profile. A 2-D inversion was used to retrieve the Cole–Cole parameters as input for TEM interpretation. By including the IP information, the TEM field data can be explained quantitively, and a consistent and improved interpretation of the waste body is achieved.

Prediction of plasma path and analysis of axial fracturing properties in rock fragmentation by high-voltage pulsed discharge (RHPD)

Rock fragmentation by high-voltage pulsed discharge (RHPD) is widely utilized in resource recovery and energy extraction due to its low energy consumption and high efficiency. However, observing the plasma development process during RHPD presents challenges, and the frequency dependence of dielectric properties further complicates plasma path prediction and the analysis of fracturing properties in the axial direction of the plasma. To address these issues, we analyzed the development properties of plasma within rocks and established a segmented breakdown criterion that considered the propagation velocity of plasma. Additionally, utilizing a transient electromagnetic field model and a particle flow model (PFM), we established a multi-physics field model and proposed a predictive method for the plasma path in a rock–liquid combination environment. This allows for the quantification of the velocity, potential, and length of the plasma. Furthermore, we computed the time response of shock waves and analyzed the loading mechanism of shock waves. Based on the spatial distribution of plasma, the PFM was applied to simulate the fracturing properties of rocks under shock wave loading. Finally, we established a comprehensive experimental platform for RHPD and conducted three-dimensional reconstructions of the fractured area to validate the accuracy of plasma path prediction methods and fracturing properties analysis. This study significantly advances plasma development theory and provides insights for optimizing rock fragmentation efficiency.

3-D forward modeling of shale gas fracturing dynamic monitoring using the borehole-to-ground transient electromagnetic method

The borehole-ground transient electromagnetic method enhances the detection range and resolution by placing the transmitter electrode within the borehole, allowing for close-proximity excitation of subsurface targets and compensating for the shortcomings of traditional ground-based methods. Utilizing an unstructured vector finite element method combined with a second-order backward Euler variable time-stepping difference scheme and the MUMPS solver, we have achieved three-dimensional forward modeling simulation of the transient electromagnetic field for a borehole-ground electric source. Based on the validation of its accuracy, we analyzed the effectiveness of this method for dynamic monitoring of shale gas reservoir fracturing. Through forward modeling, we examined the characteristics of the radial electric field response during shale gas reservoir fracturing monitoring and evaluated the effectiveness of the borehole-ground TEM method in dynamic monitoring of shale gas reservoirs. The research results indicate that this method can meet the requirements for reservoir fracturing dynamic monitoring and has a promising application prospect.

Transient electromagnetic perspective technology in the ultra-long coal mining face

The ultra-long coal mining face has the advantages of high recovery efficiency and low production cost; however, the widening of the coal face poses the difficulty of detecting the hidden geological bodies inside the coal face, and using conventional geophysical methods gives rise to imprecise detection results. Therefore, this paper proposes a transient electromagnetic perspective technology based on the conventional mining transient electromagnetic method. A long rectangular loop is used as the transmitting source in one coal mining tunnel of the coal mining face, and it is received in the opposite coal mining tunnel. This method is characterized by a long detection distance and high construction efficiency. Firstly, the paper used numerical simulation to investigate the spread of the transient electromagnetic field from the long rectangular loop source in both a uniform full-space model and a full-space laminated model. This showed the transient electromagnetic field propagation law and the effect of the coal seam thickness. Then, we analyzed the transient electromagnetic perspective signal characteristics of typical geological structures and gave the all-time apparent resistivity calculation method. Conclusively, the feasibility of this method is ultimately confirmed by the analysis of the measured data. Also, the research results provide a new technological approach to detecting hidden geological structures in the ultra-long coal mining faces.

Electromagnetic Vibration and Noise Analysis of Linear Phase-Shifting Transformer

The advantages of adjustable angle phase-shifting and great expansibility make the linear phase-shifting transformer a novel type of power conversion device with a wide range of potential applications. However, during the procedure, there is a lot of noise. For the purposes of transformer design and vibration and noise reduction, it is crucial to investigate its electromagnetic vibration and noise. In this paper, the radial electromagnetic force wave considering the influence of the end effect as the source of the noise of the linear phase-shifting transformer was deduced and calculated. Based on this, the spectrum and space–time properties of the radial electromagnetic force waves were simulated and verified. Additionally, a finite element model was created using the Ansys Workbench 2022R1 platform to study the electromagnetic vibration and noise of the linear phase-shifting transformer. A joint simulation of the electromagnetic, structural, and sound fields was then performed. First, the transformer’s natural frequency was determined by modal analysis. After that, the transformer’s structure and the results of the transient electromagnetic field computation were combined and a harmonic response analysis was conducted to determine the vibration acceleration spectrum. Finally, in order to solve the sound pressure field, the transformer’s boundary vibration acceleration was coupled to the air domain. Furthermore, an analysis was conducted to determine the noise distribution surrounding the linear phase-shifting transformer. The joint simulation findings demonstrate that the linear phase-shifting transformer’s resonance, which produces larger electromagnetic vibration and noise, is indeed caused by the radial electromagnetic force. Simultaneously, the impact of the LPST core’s fixed components on the electromagnetic vibration and noise of the core was examined.

Sensitivity analysis of inverted model parameters from transient electromagnetic measurements affected by induced polarization effects

We investigate the application of the distance-based global sensitivity analysis (DGSA) to evaluate the sensitivity of electrical model parameters obtained from transient electromagnetic (TEM) data including induced polarization (IP) effects. We propose novel open-source forward modeling and inversion routines for single-loop TEM data including IP effects with the maximum phase angle model to model the frequency dependence of the complex resistivity. In a first step, we evaluate the accuracy of our forward modeling and inversion routines using numerical studies, where the actual variations of layer thicknesses and resistivities, as well as the frequency dependence of the complex resistivity is known. In a second step, we extend our investigation to field data and apply our approach to three distinct case studies in layered media: 1) a confined aquifer corresponding to conductive non-polarizable media, 2) a graphite deposit corresponding to highly conductive and polarizable anomalies in a resistive host rock and 3) an ice glacier corresponding to highly resistive polarizable media. Our DGSA results reveal that standard depth of investigation (DOI) approaches may overestimate the true sensitivity of the model obtained from the inversion. TEM data collected in conductive layered media without IP effects show reduced sensitivity above the predicted DOI. The case studies in polarizable media demonstrate that the maximum phase angle is more influential on the TEM model response than the relaxation time and dispersion coefficient. Our DGSA results for polarizable media reveal that TEM field data collected at the graphite deposit and at the ice glacier are sensitive to the geometry of the polarizable layer.

Influence of stator and rotor core material definition method on no‐load electromagnetic field calculation results for tubular hydrogenerator

AbstractIn this letter, the effects of various material definition approaches for stator and rotor cores on the no‐load electromagnetic field calculations of a 34 MW tubular hydrogenerator are investigated, utilizing the transient motion electromagnetic field time‐step finite element (FE) method. The findings indicate that employing a linear simplified definition for the stator core material maintains high accuracy and rationality in the calculation results of the no‐load electromagnetic field and voltage waveform while offering substantially greater computational efficiency than the non‐linear definition method. Conversely, using a linear simplified definition for the magnetic pole core material of the rotor significantly increases the error margin in the results, rendering them unacceptable.

Ultra‐Fast Pulsed Discharge Preparation of Coordinatively Unsaturated Asymmetric Copper Single‐Atom Catalysts for CO2 Reduction

AbstractSingle‐atom catalysts possess great potential for applications in electrochemical carbon dioxide reduction reactions. Recently, the fast and low‐cost preparation of highly efficient single‐atom catalysts remains a challenge. Herein, a high‐density current generated by pulsed discharge is employed for the formation of graphene aerogel anchored Cu single atom catalysts perfectly. The Cu atoms decomposed by Cu(NO3)2•xH2O are fixed on graphene under the local transient high temperature and intense electromagnetic field. The activity and selectivity of formic acid are correlated with the coordinatively unsaturated Cu─N1O1 moieties, reaching an optimal Faradaic efficiency (93.7%) at −0.9 V versus a reversible hydrogen electrode (RHE). In situ characterizations reveal that the asymmetric Cu─N/O structure in a pinched state displays better catalytic activity in CO2RR. Density functional theory results indicate that the Cu─N1O1 sites regulate the adsorption configuration of intermediates and lower the energy barrier for the hydrogenation of *OCHO species, thereby promoting CO2‐to‐HCOOH conversion.

Turn-Off Current and TEM Field Based on Distributed Capacitance Model of Multiple Coils in Helicopter Transient Electromagnetic System

For compensating the primary field coupling from the transmitting coil and the sensing coil, the bucking coil is often used to achieve pure secondary field for the helicopter transient electromagnetic (HTEM) system. Traditionally, the distributed capacitance of the bucking coil and the transmitting coil is ignored and pay few attentions to study it. In fact, it has very important influence on the turn-off current of the transmitter and the transient electromagnetic (TEM) field of the system. In this paper, a novel distributed capacitance model of the HTEM coils is theoretically established at the first time, its effects on the turn-off current and the TEM field are analyzed in detail. It finds that the turn-off current in the transmitting coil and the bucking coil are not equal caused by the distributed capacitance although they are connected in series. The field experiments are completed and proved that the measured TEM fields agree very well with the simulated results based on the distributed capacitance model. This is very helpful to optimize the early-time TEM field and promote the shallow TEM data interpretation capability for the HTEM surveying.

Research on Transient Electromagnetic Field and Eddy Current Losses Reduction in End of Large-Capacity Synchronous Condenser During UHVDC System Faults

Research on Transient Electromagnetic Field and Eddy Current Losses Reduction in End of Large-Capacity Synchronous Condenser During UHVDC System Faults

Research on Torque Ripple and Influencing Factors of Hydro-Generator

Background: The safe and stable operation of large-capacity hydro-generators is of great significance to the power grid. However, due to the armature reaction and the stator slots of the hydroelectric generator, the torque ripple of the generator is usually large. Long time running under the condition of large torque ripple will cause damage to the generator components and even threaten the safety of the power grid. Objective: To study the factors affecting the torque ripple of the hydro-generator and reduce the torque ripple. Methods: A 24 MW bulb tubular hydro generator is taken as an example, a two-dimensional transient electromagnetic field model was established, and the correctness of the model was verified by experiments. The causes of armature reaction and cogging effect on motor torque are analyzed. The effects of these two factors on torque ripple are studied respectively. The torque ripple under different working conditions is calculated, and the main factors causing and increasing torque ripple during normal operation of hydro generator are determined. Results: The torque ripple increases approximately linearly with the increase of the 7th and 11th harmonic contents, while it increases nonlinearly with the increase of the 5th harmonic contents. When the excitation current increases from 720 A to 960 A, the torque ripple is increased by 11.4kN•m. In addition, when the excitation current increases from 720A to 840A (Rated excitation current of the generator is 840A), the torque ripple increases greatly, the torque ripple increases by 6.6kN•m. When the excitation current exceeds the rated excitation current, due to the influence of magnetic saturation, the increasing extent of torque ripple gradually decreases. When the excitation current increases from 840A to 960A, the torque ripple increases only by 4.8kN•m. Conclusion: Due to the armature reaction, the harmonic magnetic potential will be generated in the generator, which will affect its torque ripple. The torque ripple of the generator will increase obviously with the increase of harmonic content. When the generator is in no-load operation, the slot effect is the main cause of the torque ripple. In the actual operation of the generator, it usually needs to adjust the excitation current to make the generator meet the requirements of various working conditions.

3D forward modeling and response characteristics of low-resistivity overburden of the CFS-PML absorbing boundary for ground-well transient electromagnetic method

This study used the stable and convergent Dufort-Frankel method to differentially discretize the diffusion equation of the ground-well transient electromagnetic secondary field. The absorption boundary condition of complex frequency-shifted perfectly matched layer (CFS-PML) was used for truncation so that the low-frequency electromagnetic wave can be better absorbed at the model boundary. A typical three-dimensional (3D) homogeneous half-space model was established and a low-resistivity cube model was analyzed under the half-space condition. The response patterns and drivers of the low-resistivity cube model were discussed under the influence of a low-resistivity overburden. The absorption boundary conditions of CFS-PML significantly affected the low-frequency electromagnetic waves. For a low-resistivity cube around the borehole, its response curve exhibited a single-peak, and the extreme point of the curve corresponded to the center of the low-resistivity body. When the low-resistivity cube was directly below the borehole, the response curve showed three extreme values (two high and one low), with the low corresponding to the center of the low-resistivity body. The total field response of the low-resistivity overburden was stronger than that of the uniform half-space model due to the low-resistivity shielding effect of electromagnetic waves. When the receiving-transmitting distance gradually increased, the effect of the low-resistivity overburden was gradually weakened, and the response of the low-resistivity cube was strengthened. It was affected by the ratio of the overburden resistivity to the resistivity of the low-resistivity body.

Influence of Magnetic Screen Material on Leakage Magnetic Field and Losses in the End Zone of Turbine Generator Based on Double Iterative Method

The overheating problem of the end components affects the safe and stable operation of the turbine generator. The magnetic screen layer can improve effectively the distribution of leakage magnetic field in the end zone. Taking the nonlinearity of the core material, rotor rotation, and the complex structure into consideration, mathematical model of nonlinear transient electromagnetic field is established in the end zone of 1407MVA turbine generator. The influence of different materials of magnetic screen layer on the end leakage magnetic field is studied based on double iterative method. Current density distribution of screen plate and finger plate are determined. The losses of the end components are obtained under the different materials of magnetic screen layer, which are used as heat sources in the three-dimensional fluid-solid coupled heat transfer model. Complex fluid flow and temperature distribution of the end components are obtained in the end zone of the turbine generator. The calculation results are verified by experiments.

Analysis of leakage flux, losses, and temperature in large synchronous generator end zone under the multi‐layer screen thickness based on novel iterative method

AbstractThe multi‐layer screen is the key component in the large synchronous generator end zone. The leakage flux, losses, and temperature of end components are significantly affected by the thickness of multi‐layer screen in the synchronous generator. To investigate the influence of multi‐layer screen thickness on the end leakage flux, losses, and temperature in the synchronous generator end zone, 1407MVA nuclear power synchronous generator is studied. Three‐dimensional transient electromagnetic field model of synchronous generator end zone is established. Three‐dimensional transient electromagnetic field in the end zone of 1407MVA synchronous generator with the multi‐layer screen is calculated based on the novel iterative method. The flux density of end components is compared and studied in the end zone under the variation of multi‐layer screen thickness. Influence of the different thicknesses of multi‐layer screen on the losses of the shield plate, screen, finger plate, and stator end core is researched. The losses of end components obtained from 3D end electromagnetic field calculation are applied to the end zone as the heat source in the three‐dimensional fluid and thermal coupled field. The temperature distribution of the end components is determined. The accuracy of the calculated results is validated by the experimental values.