Search Results (26)

Magnetically coupled resonant wireless power transmission (MCR-WPT) is an ideal solution for underwater wireless power transmission (UWPT). However, due to the conductivity of seawater, eddy current loss significantly reduces system transmission efficiency. This study develops an analytical estimation method to derive explicit expressions for eddy current loss and transmission efficiency, characterize their dependence on key parameters, and analyze the resonance frequency characteristics of the MCR-WPT system under different conductivities. The optimal resonant frequency and transmission efficiency improvement under variable-conductivity underwater environments are investigated. First, the coil model is simplified to its equivalent form. Based on the Biot–Savart law, the magnetic field is calculated by integral operations, and an analytical model of the eddy current loss is formulated. Consequently, the expression for the system transmission efficiency in seawater at different depths is derived, and a specific resonance frequency is identified at which the efficiency attains its maximum value. An underwater coil model is established using Ansys Maxwell finite element analysis (FEA), and the effects of electrical conductivity and resonance frequency on eddy current loss and system efficiency are analyzed. Finally, an underwater experimental platform is constructed. A freshwater solution and seawater solutions with varying electrical conductivities are prepared using artificial sea salt and pure water; frequency-sweeping experiments are then conducted. The experimental results are in good agreement with the theoretical analysis and simulations, thereby validating the accuracy of the proposed model. Full article

The paper analyzes the impact of low-frequency (50 Hz) electromagnetic fields (EMFs) generated by a 110 kV overhead power line (OHL) on the exposure of the population and workers, in the context of increasing transmission capacity through reconduction. For the worst-case operating scenario (N-1), the levels of the electric field (E) and magnetic induction (B) at 1.5 m above the ground are checked and compared to the limit values established by Recommendation 1999/519/EC for the public and by Romanian Government Decision no. 520/2016, which transposes Directive 2013/35/EU, for workers. The calculation method is based on the Biot–Savart law for the magnetic field and the Maxwell potential coefficient method for the electric field. Full article

The increasing deployment of shared transmission corridors for High-Voltage Alternating Current (HVAC) and High-Voltage Direct Current (HVDC) systems has intensified the need to evaluate electromagnetic compatibility in hybrid overhead line configurations. This study presents an analytical methodology to estimate the electric field magnitude and magnetic flux density generated by hybrid HVAC–HVDC transmission lines under steady-state operating conditions. The electric field is determined using the Maxwell potential matrix combined with the image method, while the magnetic field is obtained from a formulation based on the Biot–Savart law. Two representative case studies were analyzed with identical electrical operating conditions but different transverse conductor arrangements to evaluate the influence of geometry on the electromagnetic environment of the corridor. The results show that variations in the spatial configuration of the conductors produce noticeable changes in the location and magnitude of the electric and magnetic field maxima across the right-of-way. These findings demonstrate that conductor geometry plays a key role in the electromagnetic behavior of hybrid corridors and should be considered in the design and assessment of HVAC–HVDC transmission systems. Full article

This paper presents a roughness surface model for Lagrangian simulations that interacts with both temperature and vorticity fields. The chosen problem is the uniform flow around a rough circular cylinder heated with constant temperature under mixed convection. The methodology used is the Temperature Particles Method (TPM), in which both vorticity and temperature fields are discretized in particles to simulate the real flow in a purely Lagrangian form. The simulation is computationally extensive due to the application of the Biot–Savart law for the two fields and the calculation of buoyancy forces, which is alleviated by the use of parallel programming with OpenMP. The simulation of roughness effects for both fields is obtained using a Large Eddy Simulation (LES) model for vorticity, based on the second-order velocity structure function, which is correlated with the thermal diffusivity through the turbulent Prandtl number. In general, the results indicate that roughness increases the drag coefficient, while an increase in the Richardson number reduces this coefficient. Full article

Biopsy remains the gold standard for diagnosing lung cancer, with high-quality tissue samples being critical for accurate results. To improve puncture accuracy, reduce reliance on CT imaging, and minimize procedural complications, it is essential to address the challenges of tracking the biopsy needle’s trajectory and providing real-time positional guidance to physicians. In this study, we propose a tracking model based on a rectangular toroidal current distribution to determine the biopsy needle’s relative position within the electromagnetic tracking system. A printed circuit board (PCB) is used as the platform for generating the rectangular circulating magnetic field. An alternating electromagnetic field (~70 kHz) is modeled based on the Biot–Savart law. Induced voltages from multiple transmitting coils are processed using Fourier transform algorithms to separate frequencies, enabling the independent extraction of each coil’s signal. A least squares method is employed to solve the five-degree-of-freedom electromagnetic positioning equations for the receiving coils. The objective is to establish a precise and computationally efficient electromagnetic localization model for the biopsy needle. An experimental setup simulating lung biopsy procedures is implemented, utilizing the proposed rectangular toroidal current configuration. Results demonstrate an average localization error of less than 1.76 mm, validating the effectiveness of the system in addressing the challenges of real-time biopsy needle tracking. Full article

The anchor cables of slopes are affected by long-term environmental corrosion, geotechnical creep, and adverse weather, resulting in gradual loss of tensile force, which can lead to structural failure and subsequent safety accidents. The authors of this paper conducted research based on the magnetic induction density distribution characteristics of permanent magnets, including model derivation, theoretical simulation, and indoor experiments, aiming to propose a new anchor cable force monitoring technology with high sensitivity, strong applicability, and good stability. Based on the molecular circulation model and the Biot–Savart law, the analytical expression of the spatial magnetic field distribution of a rectangular permanent magnet was derived and, combined with the stress–strain relationship characteristics of anchor cables, a theoretical model for the relationship between anchor cable tensile force and magnetic induction density was established. MATLAB (R2018b) was used to simulate and analyze the spatial magnetic field distribution and the force–magnetism relationship. The analysis showed that the magnetic induction density along the central axis of the permanent magnet approximately exhibited a symmetrical quadratic curve distribution, and its value was significantly negatively correlated with the anchor cable force. Based on this, a new anchor cable force monitoring technology was proposed, and an indoor experimental platform was established. The indoor experimental studies further confirmed the negative correlation between force and magnetism (i.e., as the tensile force increases, the magnetic induction strength decreases, and as the tensile force decreases, the magnetic induction strength increases). The fitting results of the force–magnetism curve show that a quadratic function can better describe the correspondence between magnetic induction density and anchor cable force. Reproducibility analysis of the experimental data showed low dispersion in magnetic induction values under various design loads, along with good stability, validating the effectiveness and applicability of the proposed anchor cable force monitoring technology. Full article

This paper presents the development and principle of operation of resource-saving overcurrent protection, which is an alternative to traditional current protections. The experiments were used to study the electromagnetic field for the protection of electrical installations connected to the cells of complete switchgears, voltage 6–10 kV, without the use of conventional protections with metal-core current transformers. As is known, such current transformers (CTs) have significant weight and dimensional parameters and high price costs. The method of research is comparison of the developed protection with traditional current protections made using traditional measuring current transformers. The scientific novelty of this work consists of the developmental theory of the construction of protection for inductive coils based on the measurement of electromotive force values in different modes and points in the simulation of a three-phase short circuit inside the cell of the complete switchgear. The dependence of magnetic induction on the position of the inductive coil inside the cell has been found. It has been shown that the simplest formula of the Biot–Savart–Laplace law can be used to calculate them. This paper presents and describes the conducted experiments with their methodology. As a result of the industrial application of such protections, the act of implementation of the patent for the invention of an industrial enterprise is presented. The selection of settings of resource-saving protection is presented, as well as a feasibility study of the presented protection in comparison with conventional protection. This paper consists of the following sections: The Materials and Methods section describes the methodology used to achieve the purpose of the research. The Experiments section describes all the experiments conducted to achieve the purpose of the research. The Results section presents the results of the conducted experiments, an evaluation of the use of inductive coils in relay protection, an example of calculating the selection of the settings of parameters of resource-saving protection, a presentation of the patent for the invention, and a presentation of the feasibility study of the effectiveness of the considered resource-saving protection on inductive coils. The Conclusions section presents the result of this work, which is the creation of resource-saving protection on inductance coils. The References section presents a list of the sources used. Full article

This study introduces an innovative energy harvesting system designed for industrial applications such as fluid pipelines, air conditioning ducts, sewer systems, and subsea oil pipelines. The system integrates magneto-electric flow coupling and utilizes a dynamic vibration absorber (DVA) to mitigate the vibrations induced by fluid flow while simultaneously harvesting energy through magnetic dipole–dipole interactions in a vibration energy harvester (VEH). The theoretical models, based on Hamilton’s Principle and the Biot–Savart Law, were validated through comprehensive experiments. The results indicate the superior performance of the small-magnet system over the large-magnet system in both damping and power generation. The study analyzed the frequency response and energy conversion efficiency across different parameters, including the DVA mass, spring constant, and placement location. The experimental findings demonstrated significant vibration reduction and increased voltage output, validating the theoretical model. This research offers new avenues for energy harvesting systems in pipeline infrastructures, potentially enhancing energy efficiency and structural integrity. Full article

Construction of relay protections of electrical installations without the use of bulky metal- and insulation-intensive measuring current transformers (CTs) was repeatedly discussed at Conferences of the International Council on Large Electric Systems (CIGRE) as a challenge for the electric power industry. In the article, the authors present resource-saving reed switch current protection for 6–10-kV electrical installations connected to switchgear cells, which is an alternative to traditional protections. The scientific novelty of the work lies in (a) reed switch protection design on the basis of measuring the magnetic induction in different modes and at different points inside a cell, and we prove that inductance values are sufficient to detect phase short-circuits in electrical installations fed from this cell and derive the dependence of the induction on the position of an inductance coil inside the cell; (b) proven possibility of using the simplest formula of the Biot–Savart law for the calculations if the experimentally obtained coefficients are introduced into it; (c) development of a technique for calculating the parameters of the overcurrent protection based on reed switches. Experimental results are presented in graphical form and clearly show the points of EMS maxima and minima. Settings for resource-saving current protection are selected and a feasibility study of the effectiveness of resource-saving overcurrent protection is carried out. A technical and economical assessment of the efficiency of the suggested overcurrent protection is conducted. Full article

The problem of getting rid of expensive and metal-intensive current transformers has been declared by CIGRE as strategically important for the electric power industry. However, almost all traditional current protections receive information from measuring current transformers. In this work, a resource-saving reed switch overcurrent protection without current transformers is suggested, which can be used as an alternative to traditional current protections for 6–10 kV electrical installations connected to a switchgear cell. The protection is designed following the novel method we have developed based on inductance coils. Inductance coils measure the electromotive force under different operation modes of an electrical installation and at different points inside the switchgear cell it is connected to; the EMF values are recalculated in the values of magnetic induction, and reed switches are mounted instead of inductance coils at the points where the magnetic induction is maximal. Moreover, these values are sufficient to detect phase-to-phase short circuits in the electrical installation. The dependence of the induction value on the position of an inductance coil inside the cell is derived with the use of the simplest formula of the Biot–Savart law. The results can be used at large and small industrial enterprises, electric power stations, and substations of plants; they can be interesting for the scientific community because they help to solve the topical problem of the electric power industry. Full article

Using the analytic method based on the Biot–Savart law for the electromagnetic field, the distribution of the magnetic field of a ribbon busbar of finite length was determined. The analytical formulas describing the magnetic field in all areas of the considered ribbon busbars were obtained. The Mathematica program was used to visualize the solutions obtained. The Mathematica programme is a good and convenient tool for analytical measurements using the integration function and conversion of the analytical solutions, for the determination of field quantities, and for the graphical visualisation of the obtained final solutions. This allowed for quick field analysis to be conducted after changes were made in the geometrical or electrical parameters of the systems under examination. Full article

Electrolysis stands as a pivotal method for environmentally sustainable hydrogen production. However, the formation of gas bubbles during the electrolysis process poses significant challenges by impeding the electrochemical reactions, diminishing cell efficiency, and dramatically increasing energy consumption. Furthermore, the inherent difficulty in detecting these bubbles arises from the non-transparency of the wall of electrolysis cells. Additionally, these gas bubbles induce alterations in the conductivity of the electrolyte, leading to corresponding fluctuations in the magnetic flux density outside of the electrolysis cell, which can be measured by externally placed magnetic sensors. By solving the inverse problem of the Biot–Savart Law, we can estimate the conductivity distribution as well as the void fraction within the cell. In this work, we study different approaches to solve the inverse problem including Invertible Neural Networks (INNs) and Tikhonov regularization. Our experiments demonstrate that INNs are much more robust to solving the inverse problem than Tikhonov regularization when the level of noise in the magnetic flux density measurements is not known or changes over space and time. Full article

This paper presents a quasi-analytical method that allows the derivation of a rigorous series-form representation for the mutual inductance of two co-axial coil antennas located above an arbitrarily layered earth structure. Starting from Biot–Savart law, which gives the integral representation for the primary vector potential generated by the source coil, the potential reflected by the layered ground is derived, and the resulting total vector potential is then integrated along the external circumference of the receiving coil to give the mutual inductance of the two antennas. The obtained representation for the flux is then evaluated analytically through the usage of the Gegenbauer addition theorem once an accurate, rational approximation is used in place of the factor of the integrand that exhibits branch cuts. It is shown how the resulting explicit solution exhibits the same degree of accuracy as purely numerical approaches like the finite-difference time-domain (FDTD) method and conventional numerical quadrature schemes, while it is less time-demanding than the latter methods. Full article

There is a special concern for measuring and simulating low-frequency magnetic fields generated by underground power cables, particularly in human exposure studies. In the present study, an accurate 2D finite element model for computing magnetic fields generated by three-phase underground power cables with solid bonding is proposed. The model is developed in ANSYS Maxwell 2D low-frequency electromagnetic field simulation software for a typical 12/20 kV (medium-voltage) three-phase underground power cable in both trefoil and flat formations, but it can be adapted to any cable system. Model validation is achieved by analytical computations conducted with a software tool based on the Biot–Savart law and the superposition principle. RMS magnetic flux density profiles calculated at various heights above the ground with these two methods correlate very well. This is also true for induced shield currents. The application of the finite element model to multiple three-phase power cables laid together is also considered. Full article

A frequency-domain lifting-line solution algorithm for the prediction of the unsteady aerodynamics of wings is presented. The Biot–Savart law is applied to determine the normalwash generated by the wake vorticity distribution, whereas steady and unsteady airfoil theories (Glauert’s and Theodorsen’s, respectively) are used to evaluate the sectional aerodynamic loads, namely the lift and pitching moment. The wake vorticity released at the trailing edge derives from the bound circulation through the Kutta condition and is convected downstream with the velocity of the undisturbed flow. The local bound circulation is obtained by the application of the Kutta–Joukowski theorem, extended to unsteady flows. Assuming a bending and torsion wing, this paper provides the aerodynamic matrix of the transfer functions, relating the generalised aerodynamic loads to the Lagrangian coordinates of the elastic deformation. Its rational approximation yields a reduced-order state-space aerodynamic model suitable for an aeroelastic stability analysis and control purposes. The numerical investigation examines the influence of both the wake shed/trailed vorticity modelling and different approximations of the Kutta–Joukowski theorem for unsteady flows on the aerodynamic transfer functions given by the developed frequency-domain lifting-line solver. The accuracy of the solver is assessed by comparison with the predictions obtained by a three-dimensional boundary-element-method solver for potential flows. It is shown that, at least for the frequency range considered, regardless of the approximation of the Kutta–Joukowski theorem applied, the formulation based on the Theodorsen theory provides predictions that are in very good agreement with the results from the boundary element method for a slender wing. This agreement worsens as the wing aspect ratio decreases. A lower level of accuracy is obtained by the application of the sectional loads given by the Glauert theory. In this case, the predictions are more sensitive to the approximation used to express the Kutta–Joukowski theorem for unsteady flows. Full article