Conductor Model Research Articles

Direct Estimation of Equivalent Bioelectric Sources Based on Huygens' Principle.

An estimation of the electric sources in the heart was conducted using a novel method, based on Huygens' Principle, aiming at a direct estimation of equivalent bioelectric sources over the heart's surface in real time. The main scope of this work was to establish a new, fast approach to the solution of the inverse electrocardiography problem. The study was based on recorded electrocardiograms (ECGs). Based on Huygens' Principle, measurements obtained from the surfaceof a patient's thorax were interpolated over the surface of the employed volume conductor model and considered as secondary Huygens' sources. These sources, being non-zero only over the surface under study, were employed to determine the weighting factors of the eigenfunctions' expansion, describing the generated voltage distribution over the whole conductor volume. With the availability of the potential distribution stemming from measurements, the electromagnetics reciprocity theorem is applied once again to yield the equivalent sources over the pericardium. The methodology is self-validated, since the surface potentials calculated from these equivalent sources are in very good agreement with ECG measurements. The ultimate aim of this effort is to create a tool providing the equivalent epicardial voltage or current sources in real time, i.e., during the ECG measurements with multiple electrodes.

Simulation of the magnetic field in residential buildings with built-in substations based on a two-phase multi-dipole model of a three-phase current conductor

Problem. Substations 10(6)/0.4 kV built into residential buildings create a magnetic field with magnetic flux density of more than 10 μT in nearby residential premises, which is a danger to the health of the population and makes the study of this magnetic field relevant for the development of methods for its protection. The main source of the substations external magnetic field is their low-voltage current conductor, the contribution of which to the total level of the magnetic field is more than 90 %. Multi-dipole mathematical models, which have a clear physical interpretation, are a promising method of modeling the substations magnetic field, which is important for the further development of methods of population protection. The purpose of the work is to modify the well-known multi-dipole model for calculation based on it with a limited error of the external magnetic field of current conductors of built-in substations that are close to residential buildings at a distance of up to one meter. Methodology. A modified two-phase multi-dipole mathematical model of the main source of the external magnetic field of substation – its three-phase low-voltage current conductors – is proposed, which, unlike the existing model, is based on a two- you to halve the distance to the area of calculation without increasing the error. Verification. An experimental verification of the modified two-phase multi-dipole model of the magnetic field of a three-phase 100 kVA transformer substation on its full-scale physical model was carried out, and the results of the experiment were presented, confirming the coincidence of the calculation and the experiment with a spread of no more than 7 %.

Analytical Method of Eddy-Current Field Induced by Moving Conductor in Gradient Magnetic Field

Electromagnetic field analyses of conductors moving in magnetic fields have been widely applied in scientific research and industrial production. In this paper, an equivalent model is proposed to solve the eddy-current field of an arbitrarily-shaped conductor moving in gradient magnetic field. As an example, the analytical model of a spherical conductor moving axially with air-core cylindrical coils is solved. First, the induced eddy-current density inside the conductor ball is derived by using the Ohm’s law of moving conductor. Next, the eddy current inside the conductor ball is equivalent to coaxial current-loops and regarded as excitation source in the newly established boundary-value problem. Then in experiments, the induced voltages of pick-up coil are in good agreement with the theoretical values, which can verify the analytical methods and results of this paper. Furthermore, the time-difference between the zero-crossing points of induced voltage curve is inversely proportional to the moving speed, and the amplitude of induced voltage is proportional to conductor conductivity. The analytical methods proposed in this paper can be used to solve the eddy-current fields induced by arbitrarily-shaped conductors moving in gradient magnetic fields directly, and do not need to calculate the governing equations and boundary conditions containing velocity terms.

Dynamic thermal line rating model of conductor based on prediction of meteorological parameters

This paper developed a new algorithm to predict dynamic thermal line rating to increase the capacity of transmission lines, which can enhance the capacity of wind power integrated to the grid and reduce the curtailment. The proposed dynamic thermal line rating prediction model was trained by analyzing historical meteorological data and conductor physical parameters, and used deep learning with parameters optimized by an optimized algorithm. The prediction accuracy of the model is verified by Mean Absolute Error, R2 and comparison with other models. The simulation results show that the proposed prediction model has a good performance. The suggested dynamic thermal line rating algorithm, which bears resemblance to the actual value, boosts the static thermal line rating by varying degrees of 23% to 75% at different instances throughout the sample. At the same time, this paper designs an optimal power flow economic dispatch objective function. By comparing the economic dispatch of the power grid calculated by adding static thermal line rating and the prediction models, the method proposed in this paper can effectively increase the amount of wind power integration and reduce power generation costs.

Influence of charges deposited on membranes of human hyperdirect pathway axons on depolarization during subthalamic deep brain stimulation

Objective. The motor hyperdirect pathway (HDP) is a key target in the treatment of Parkinson’s disease with deep brain stimulation (DBS). Biophysical models of HDP DBS have been used to explore the mechanisms of stimulation. Built upon finite element method volume conductor solutions, such models are limited by a resolution mismatch, where the volume conductor is modeled at the macro scale, while the neural elements are at the micro scale. New techniques are needed to better integrate volume conductor models with neuron models. Approach. We simulated subthalamic DBS of the human HDP using finely meshed axon models to calculate surface charge deposition on insulting membranes of nonmyelinated axons. We converted the corresponding double layer extracellular problem to a single layer problem and applied the well-conditioned charge-based boundary element fast multipole method (BEM-FMM) with unconstrained numerical spatial resolution. Commonly used simplified estimations of membrane depolarization were compared with more realistic solutions. Main result. Neither centerline potential nor estimates of axon recruitment were impacted by the estimation method used except at axon bifurcations and hemispherical terminations. Local estimates of axon polarization were often much higher at bifurcations and terminations than at any other place along the axon and terminal arbor. Local average estimates of terminal electric field are higher by 10%–20%. Significance. Biophysical models of action potential initiation in the HDP suggest that axon terminations are often the lowest threshold elements for activation. The results of this study reinforce that hypothesis and suggest that this phenomenon is even more pronounced than previously realized.

Curve Fitting Based Minimum Norm Estimation (CFB-MNE) for motor unit spatial localization using high density surface electromyogram signals

The purpose of the study is the real time spatial localization of single motor units using simulated Motor Unit Action Potential dictionary from a cylindrical muscle volume conductor model by means of a state-of-the-art curve fitting method. This Curve Fitting Based Minimum Norm Estimation (CFB-MNE) was made possible by using minimum norm estimation methods to solve an underdetermined inverse problem knowing produced HD-sEMG signals. Specific data extracted from the inverse problem of a pre-determined number of simulated motor units were used to create a 3D curve, which can be used as a fitting curve to anticipate the unknown location of motor units. Results show that the proposed algorithms succeeded in accurately localizing motor units with varying noise levels in a fast duration (less than 100 ms). From all the simulations, a mean root mean square error of maximum 1 mm was recorded for the localization of the depth (less than 1 mm) and a negligible error for the angular position (less than 1°). The proposed work is an innovative algorithm that aids in non-invasively localizing motor units within a muscle in real time. Further efforts are planned to manage MUAP superposition and type. Final applications are related to prosthetic control, rehabilitation guidance or aging monitoring.

Dynamic simulation of rail potential considering rail skin effect

The existing simulation of rail potential only considers the equivalent DC resistance and 1st-order RL circuit of a rail. However, the rail current contains a large number of harmonic components, which greatly affects the calculation of rail potential. To accurately calculate the rail potential, the rail is equivalent to a tubular conductor considering the skin effect. The improved equivalent circuit of reflux system is established by vector fitting method (VF), and the 8th-order foster equivalent circuit of rail is built. The dynamic simulation model considering multi-trains, multi-stations, and over voltage protection device (OVPD) actions is established. By measuring the actual internal impedance of the rail, the parameters of the equivalent tubular conductor model of the rail are fitted with the least square method. The maximum error between VF method and finite element simulation, field test results is 6.531%, and 7.271%, respectively. Compared with the equivalent of the 1st-order RL circuit and DC resistance, the rail potential results of the modified model are significantly improved, the rail potential is evaluated more accurately.

Evaluating the influence of anatomical accuracy and electrode positions on EEG forward solutions

Generating realistic volume conductor models for forward calculations in electroencephalography (EEG) is not trivial and several factors contribute to the accuracy of such models, two of which are its anatomical accuracy and the accuracy with which electrode positions are known. Here, we investigate effects of anatomical accuracy by comparing forward solutions from SimNIBS, a tool which allows state-of-the-art anatomical modeling, with well-established pipelines in MNE-Python and FieldTrip. We also compare different ways of specifying electrode locations when digitized positions are not available such as transformation of measured positions from standard space and transformation of a manufacturer layout.Substantial effects of anatomical accuracy were seen throughout the entire brain both in terms of field topography and magnitude with SimNIBS generally being more accurate than the pipelines in MNE-Python and FieldTrip. Topographic and magnitude effects were particularly pronounced for MNE-Python which uses a three-layer boundary element method (BEM) model. We attribute these mainly to the coarse representation of the anatomy used in this model, in particular differences in skull and cerebrospinal fluid (CSF). Effects of electrode specification method were evident in occipital and posterior areas when using a transformed manufacturer layout whereas transforming measured positions from standard space generally resulted in smaller errors.We suggest modeling the anatomy of the volume conductor as accurately possible and we hope to facilitate this by making it easy to export simulations from SimNIBS to MNE-Python and FieldTrip for further analysis. Likewise, if digitized electrode positions are not available, a set of measured positions on a standard head template may be preferable to those specified by the manufacturer.

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.

Electro-Thermal Modeling of One-Dimensional Conductors, Whiskers, and Wires Including Convection, and Considering Tin, Bismuth, Zinc and Indium

Electro-Thermal Modeling of One-Dimensional Conductors, Whiskers, and Wires Including Convection, and Considering Tin, Bismuth, Zinc and Indium

A Generalized Scalar Potential Integral Equation Formulation for the DC Analysis of Conductors

The electrostatic modeling of conductors is a fundamental challenge in various applications, including the prediction of parasitic effects in electrical interconnects, the design of biasing networks, and the modeling of biological, microelectromechanical, and sensing systems. The boundary element method (BEM) can be an effective simulation tool for these problems because it allows modeling three-dimensional objects with only a surface mesh. However, existing BEM formulations can be restrictive because they make assumptions specific to particular applications. For example, capacitance extraction formulations usually assume a constant electric scalar potential on the surface of each conductor and cannot be used to model a flowing current, nor to extract the resistance. When modeling steady currents, many existing techniques do not address mathematical challenges such as the null space associated with the operators representing the internal region of a conductor. We propose a more general BEM framework based on the electric scalar potential for modeling conductive objects in various scenarios in a unified manner. Restrictive application-specific assumptions are not made, and the aforementioned operator null space is handled in an intuitive and rigorous manner. Numerical examples drawn from diverse applications confirm the accuracy and generality of the proposed method.

Effects of head modeling errors on the spatial frequency representation of MEG

Objectives. We aim to investigate the effects of head model inaccuracies on signal and source reconstruction accuracies for various sensor array distances to the head. This allows for the assessment of the importance of head modeling for next-generation magnetoencephalography (MEG) sensors, optically-pumped magnetometers (OPM). Approach. A 1-shell boundary element method (BEM) spherical head model with 642 vertices of radius 9 cm and conductivity of 0.33 S m−1 was defined. The vertices were then randomly perturbed radially up to 2%, 4%, 6%, 8% and 10% of the radius. For each head perturbation case, the forward signal was calculated for dipolar sources located at 2 cm, 4 cm, 6 cm and 8 cm from the origin (center of the sphere), and for a 324 sensor array located at 10 cm to 15 cm from the origin. Equivalent current dipole (ECD) source localization was performed for each of these forward signals. The signal for each perturbed spherical head case was then analyzed in the spatial frequency domain, and the signal and ECD errors were quantified relative to the unperturbed case. Main results. In the noiseless and high signal-to-noise ratio (SNR) case of approximately ≥6 dB, inaccuracies in our spherical BEM head conductor models lead to increased signal and ECD inaccuracies when sensor arrays are placed closer to the head. This is true especially in the case of deep and superficial sources. In the noisy case however, the higher SNR for closer sensor arrays allows for an improved ECD fit and outweighs the effects of head geometry inaccuracies. Significance. OPMs may be placed directly on the head, as opposed to the more commonly used superconducting quantum interference device sensors which must be placed a few centimeters away from the head. OPMs thus allow for signals of higher spatial resolution to be captured, resulting in potentially more accurate source localizations. Our results suggest that an increased emphasis on accurate head modeling for OPMs may be necessary to fully realize its improved source localization potential.

3D finite-difference transient electromagnetic modeling with a whole-space initial field

A 3D finite-difference time-domain transient electromagnetic forward-modeling method with a whole-space initial field is proposed to improve forward efficiency and flexibility. The open-source software WFTEM3D is developed based on this method with two language versions: a FORTRAN code and a MATLAB code. First, the scheme calculates the whole-space initial field excited by magnetic dipole sources at an initial time after the current is switched off. Then, the scheme steps Maxwell’s equations in time using a staggered grid and a modified DuFort-Frankel method. Multiple magnetic dipole sources are superimposed to achieve the modeling for large loop configurations. The air is included into the grids and the Dirichlet boundary condition is used on the outer boundaries. The forward-modeling method has three advantages. First, the method can be used to simulate the whole-space model and the half-space model. Second, big mesh growth factors of 1.5–3 are allowed, which significantly improves the computational efficiency and facilitates the simulation of the multiscale model. Third, the approximate initial field can be calculated using a conductivity independent of the model, which facilitates the simulation of the nonflat topography model. These advantages are tested by examples. The model of a conductive brick in a half-space and the model of a complex conductor at a vertical contact are simulated. The run times are 0.48 and 9.72 s, respectively, on an ordinary computer with an Intel Core i7-6700 CPU, and the solutions are consistent with that presented in the literature. Examples of a multiscale model with three conductive bricks, a valley model, and a hill model are simulated, which further verify these advantages.

Analytical Modeling of Magnetic Air-Gap Field Distribution Due to Armature Reaction

The following paper presents an analytical study of the air-gap magnetic field distribution produced by the armature reaction of a linear machine. Based on the method of images, the magnetic field generated by a current carrying conductor inside the air-gap between two smooth infinitely permeable iron surfaces is modeled as a complex 2D function. The conductor model then becomes a current sheet model and horizontally oriented current sheets are used to model the magnetic field produced by the armature reaction for smooth ferromagnetic surfaces. Focus will be given to the study of the slot opening function in front of energized slots in comparison to the not energized ones of the classical theory pointing out some remarkable differences. Later, the model is extended to slotted geometries using a complex slotting function adapted for energized slots. At last, the Maxwell tensor expressed in complex formulation will be integrated to obtain the force components acting on the machine tooth tips, quantities that will be compared with FEM simulations in order to validate the proposed analytical model.

Bulk modulus of ionic conductors: A study based on a microscopic empirical model

The bond fluctuation model of ionic conductors suggests that the high ionic conductivity is related with the low structural stability of the materials. A physical quantity that is related with the structural stability is the bulk modulus. Some years ago, a microscopic empirical model of bulk modulus has been proposed. The model applied to diverse materials showed a good agreement with the experimental values. It is of considerable interest to verify if such a model works in materials that exhibit high ionic conduction at high temperatures. Our analysis indicates that the temperature dependence of the bulk modulus described by the model is weak when compared with the experimental values. The result indicates that considering merely the effect of thermal expansion is not sufficient to account for the temperature variation of the bulk modulus. In particular, it is shown that such a variation is large in ionic conductors. This observation is interesting from the materials design point of view, because, recent studies consider that the bulk modulus is an important quantity that controls the performance of solid electrolytes. A possible way to extend the model is discussed briefly.

DeeptDCS: Deep Learning-Based Estimation of Currents Induced During Transcranial Direct Current Stimulation.

Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique used to generate conduction currents in the head and disrupt brain functions. To rapidly evaluate the tDCS-induced current density in near real-time, this paper proposes a deep learning-based emulator, named DeeptDCS. The emulator leverages Attention U-net taking the volume conductor models (VCMs) of head tissues as inputs and outputting the three-dimensional current density distribution across the entire head. The electrode configurations are also incorporated into VCMs without increasing the number of input channels; this enables the straightforward incorporation of the non-parametric features of electrodes (e.g., thickness, shape, size, and position) in the training and testing of the proposed emulator. Attention U-net outperforms standard U-net and its other three variants (Residual U-net, Attention Residual U-net, and Multi-scale Residual U-net) in terms of accuracy. The generalization ability of DeeptDCS to non-trained electrode configurations can be greatly enhanced through fine-tuning the model. The computational time required by one emulation via DeeptDCS is a fraction of a second. DeeptDCS is at least two orders of magnitudes faster than a physics-based open-source simulator, while providing satisfactorily accurate results. The high computational efficiency permits the use of DeeptDCS in applications requiring its repetitive execution, such as uncertainty quantification and optimization studies of tDCS.

Computation of group-level electric field in lower limb motor area for different tDCS montages

ObjectiveTranscranial direct current stimulation (tDCS) injects a weak electric current into the brain via electrodes attached to the scalp to modulate cortical excitability. tDCS is used to rebalance brain activity between affected and unaffected hemispheres in rehabilitation. However, a systematic quantitative evaluation of tDCS montage is not reported for the lower limbs. In this study, we computationally investigated the generated electric field intensity, polarity, and co-stimulation of cortical areas for lower limb targeting using high-resolution head models. MethodsVolume conductor models have thus been employed to estimate the electric field in the brain. A total of 18 head models of healthy subjects were used to calculate the group-level electric fields generated from four montages of tDCS for modulation of lower limbs. ResultsC1-C2 montage delivered higher electric field intensities while reaching deeper regions of the lower-limb motor area. It produced a uniform polarization on the same hemisphere target with comparable intensities between hemispheres but with higher variability. ConclusionsProper montage selection allows reaching deeper regions of the lower-limb motor area with uniform polarization. SignificanceFirst systematic computational study providing support to tDCS experimental studies using montages for the lower limb while considering polarity factor for balancing brain activity.

Asynchronous axonal firing patterns evoked via continuous subthreshold kilohertz stimulation

Objective. Transcutaneous electrical stimulation of peripheral nerves is a common technique to assist or rehabilitate impaired muscle activation. However, conventional stimulation paradigms activate nerve fibers synchronously with action potentials time-locked with stimulation pulses. Such synchronous activation limits fine control of muscle force due to synchronized force twitches. Accordingly, we developed a subthreshold high-frequency stimulation waveform with the goal of activating axons asynchronously. Approach. We evaluated our waveform experimentally and through model simulations. During the experiment, we delivered continuous subthreshold pulses at frequencies of 16.67, 12.5, or 10 kHz transcutaneously to the median and ulnar nerves. We obtained high-density electromyographic (EMG) signals and fingertip forces to quantify the axonal activation patterns. We used a conventional 30 Hz stimulation waveform and the associated voluntary muscle activation for comparison. We modeled stimulation of biophysically realistic myelinated mammalian axons using a simplified volume conductor model to solve for extracellular electric potentials. We compared the firing properties under kHz and conventional 30 Hz stimulation. Main results. EMG activity evoked by kHz stimulation showed high entropy values similar to voluntary EMG activity, indicating asynchronous axon firing activity. In contrast, we observed low entropy values in EMG evoked by conventional 30 Hz stimulation. The muscle forces evoked by kHz stimulation also showed more stable force profiles across repeated trials compared with 30 Hz stimulation. Our simulation results provide direct evidence of asynchronous firing patterns across a population of axons in response to kHz frequency stimulation, while 30 Hz stimulation elicited synchronized time-locked responses across the population. Significance. We demonstrate that the continuous subthreshold high-frequency stimulation waveform can elicit asynchronous axon firing patterns, which can lead to finer control of muscle forces.

Prevention of Wildfires Using an AI-Based Open Conductor Fault Detection Method on Overhead Line

Overhead lines that are exposed to the outdoors are susceptible to faults such as open conductors on weak points and disconnection caused by external factors such as typhoons. Arcs that occur during disconnection generate energy at a high heat of over 10,000 °C, requiring swift fault shut-off. However, most conventional fault detection methods to protect electrical power systems detect an overcurrent; thus, they can only detect faults after the line is disconnected and the cross-section of the line that generates the arc discharge makes contact with another line or the ground, causing a high risk of fire. Furthermore, in the case of ground faults owing to the disconnection of overhead lines, the load and the grounding impedance are not parallel. Therefore, in the case of the fault current not exceeding the threshold or a high impedance fault due to the high grounding impedance of the surrounding environment, such as grass or trees, it is difficult to determine overhead line faults with conventional fault detection methods. To solve these issues, this paper proposes an AI-based open conductor fault detection method on overhead lines that can clear the fault before the falling open conductor line comes into contact with the ground’s surface so as to prevent fire. The falling time according to the height and span of the overhead line was calculated using a falling conductor model for the overhead line, to which the pendulum motion was applied. The optimal input data cycle that enables fault detection before a line–ground fault occurs was derived. For artificial intelligence learning to prevent wildfires, the voltage and current signals were collected through a total of 432 fault simulations and were wavelet-transformed with a deep neural network to verify the method. The proposed total scheme was simulated and verified with MATLAB.

The traction network design of the new three‐phase 3‐kV traction power supply system based on the limits of receiving‐end voltages and negative sequence voltage unbalance factor

AbstractThe characteristics of traction network (TN) of the three‐phase 3‐kV traction power supply system (TPSS) are: three‐phase conductors are flat layout (layout‐1, layout‐2); the material and cross‐section of conductors are ferromagnetic and irregular, respectively. So the phase impedance matrix (PIM) is unbalanced and the closed‐form formula for conductor impedance is hard to get. To address these issues, firstly, the PIM is derived, and the cause of unbalance is revealed. From the perspective of structure optimization, a new flat layout (layout‐3) and an equilateral triangle layout (layout‐4) is proposed. Then, to calculate the wideband frequency self‐ and mutual impedances of the special phase conductors, a frequency‐ and current‐dependent closed‐form formula based on 4‐parameters equivalent tubular conductor (ETC) model is proposed. Furthermore, an equivalent TN circuit model at 50 Hz is established to calculate the receiving‐end voltage and its negative sequence voltage unbalance factor (NSVUF). Finally, using these two indexes, the performances of the layout‐1 to 4 are evaluated and compared. The results show that the conductor spacing and power supply frequency affect the two indexes much while the dimension of the power supply rail (PSR) not; layout‐4 can completely balance the receiving‐end voltage and improve its magnitude which can enhance the power supply capability.