Calculation Of Magnetic Field Research Articles

Calculation of magnetic field and eddy current loss in end clamping ring of 300MVA synchronous condenser based on a novel semi‐analytical method

AbstractIt is very important to consider the eddy current reaction of the metal structure in large electric machines, which has a direct impact on the calculation results of induced current and loss. In order to solve the problem that the complex end leakage magnetic field is difficult to calculate directly, a new semi‐analytical method (NSM) considering the eddy current reaction is proposed. Firstly, the corresponding relationship between the external magnetic field and the global magnetic field of the clamping ring in two simple calculation models is obtained by the 3‐D finite element method. Then, the external magnetic field of the clamping ring in a 300MVA synchronous condenser under rated operating conditions is calculated, and the global magnetic field of the clamping ring is determined based on the obtained corresponding relationship. The eddy current density and eddy current loss of the clamping ring are calculated using the external magnetic field and the global magnetic field respectively. Finally, the calculation results were compared with the 3‐D finite element results, which verified the importance of the global magnetic field and the accuracy of the NSM.

Multi-functional sensor based on photonic crystal fiber using plasmonic material and magnetic fluid.

A unique highly sensitive photonic crystal fiber, to the best of our knowledge, is investigated based on plasmonic material and magnetic fluid (MF) for the simultaneous measurement of temperature and magnetic field sensor. The designed sensor is explored by tracing the different parameters such as birefringence, coupling length, power spectrum, and the peak wavelength of the transmission intensity. The magnetic field and temperature computation are attained simultaneously by examining the linear fitting curve and the movement of transmission peaks. The obtained sensitivity for temperature is 7.1nm/°C with an exposure range of 25°C to 100°C. In contrast, the magnetic field sensitivity is 12nm/Oe with a detection range of 160-200Oe. In addition, the resolutions are -1.245∘ C and 5.53Oe for temperature and magnetic field, respectively. Our inspected sensor is used to detect extremely low and high values of magnetic fields. The investigated structure is presented with simplification, compactness, easy implementation, and high sensitivity, which is expected to be a good foundation for the advancement of optical sensing devices in the future applications of industries, security, small grids, and environmental systems.

Electric and magnetic field calculation software in transmission lines

<span lang="EN-US">There is an interest in the biological effects of exposure to low-frequency electromagnetic fields issued by transmission lines on animals and humans. The fields generated by the lines are relevant for the design and operation of power systems. The study of the electric and magnetic fields in the transmission networks implemented commercial simulators bases on the finite element method. These commercial simulators are characterized by accuracy and high hardware and software requirements. This work presents CEM-LT, a tool that accurately precisely the electric and magnetic field in the transmission lines, with simple and intuitive handling and low processing times, making it ideal for being implemented together with optimization methods. The electric and magnetic field in the servant area for two case studies is analyzed to evaluate the accuracy and processing times. The level of accuracy is characterized by comparing the results with COMSOL obtaining errors of less than 2.4%. The case study with the highest computational requirement achieved a processing time of 3,027 seconds.</span>

Vacuum arc characteristics of an AMF–TMF composite contact with fixed AMF contacts under different opening velocities

The objective of this paper is to determine the vacuum arc characteristics of a novel axial magnetic field (AMF)–transverse magnetic field (TMF) composite contact under different opening velocities. The AMF–TMF composite contact consists of a pair of outer fixed AMF contacts and a pair of inner movable TMF contacts. Drawn arc experiments were carried out in an L–C discharging circuit with this composite contact system to observe the differences in the arc development process under different opening velocities. The opening velocity of the inner movable contact was set to 1.3, 1.8, and 2.3 m/s. The arc current was up to 20 kA rms. In the experiments, the arc behavior was recorded using a high-speed camera. The arc current of each contact and the arc voltage were measured. Then the arc characteristics, including the arc current transfer characteristics, diffused arc duration, and mental droplet distribution before zero current, were quantitatively analyzed. Furthermore, magnetic field calculation was carried out to explain why the arc characteristics are different under different opening velocities. Experimental results show that with an increase in the opening velocity from 1.3 to 2.3 m/s, the diffused arc duration before zero current increases from 1.05 to 1.75 ms when the cathode is on the fixed side and increases from 1.30 to 1.90 ms when the anode is on the fixed side. In addition, the quantity of mental droplets between contacts before zero current is less with high opening velocity. It indicates stronger short-current breaking capacity under higher opening velocity. From the simulation results, it can be seen that during the arcing period, more current transfers to the fixed AMF contact under higher opening velocity and generates a stronger AMF. It could explain the earlier diffusion of the vacuum arc column under higher opening velocity.

Calculation Method of Ship’s External Magnetic Field Based on Neural Network

In view of the difficulties in the calculation of the external magnetic field in the closed-loop degaussing of the ship, this paper analyzes the relationship between the internal and external magnetic field of the ship, and builds a neural network model accordingly to realize the calculating model between internal and external magnetic field. Aiming at the problem of insufficient training set, a data augmentation method based on the linear nature of the induced magnetic field is proposed. By using this method to expand the training set, the training speed and accuracy of the model can be improved. Through experimental verification of the steel double-layer shell model, the proposed magnetic field estimation method can accurately predict the external magnetic anomaly when the induced magnetic field and the fixed magnetic field are changed. This method not only has the advantages of fast calculation speed and high real-time performance, but also solves the long-standing problem that the fixed magnetic field changes are difficult to predict.

Analysis and Calculation of the Three-Dimensional Air-Gap Magnetic Field and Electromagnetic Torque of a Multishaft Ring-Plate Magnet Gear

A kind of multishaft ring-plate magnet gear (MRMG) structure is proposed. Because an MRMG has the characteristics of an eccentric permanent magnet gear with a small aspect ratio and large magnetic leakage at the end, there is a large deviation when using traditional 2-D FEM or an analytical method to analyze and calculate field and torque values for an MRMG. In this article, a 3-D mathematical analytical model of the MRMG eccentric air-gap magnetic field and electromagnetic torque is established, which is suitable for computer modeling. First, based on the cylindrical coordinate system of the inner and outer permanent magnet rings, the 3-D analytical models of the air-gap magnetic field of the inner and outer permanent magnet rings are established, respectively, by using the vector magnetic potential method. Then, by analyzing the position relationship between the inner and outer permanent magnet rings and their superposition angles, the radial and tangential air-gap magnetic fields of the inner and outer permanent magnet rings are superimposed according to their included angles, and a 3-D analytical model of the air-gap magnetic field and the electromagnetic torque of an MRMG is established. Because all the calculations are magnetic field integrals along the axial length of the MRMG, the magnetic field’s end effect is included in the established model, and the calculated results are more accurate than those of a 2-D FEM and analytical method (error >13%). A 3-D FEM and static loading experiment show that the model has a good accuracy (error < 2%) with the measured results and finite-element analysis, but the calculation speed of the model is faster than that of the 3-D FEM, which not only greatly shortens the calculation time but is also suitable for computer programming and is easily used to perform the MRMG analysis and optimization of different MRMG structural parameters.

Magnetic field analysis of a hybrid excitation multi-degree-of-freedom spherical motor.

A hybrid excitation multi-degree-of-freedom spherical motor (HE-MDOFSM) is designed, which can achieve MDOF motion by cooperatively controlling the excitation current in 12 sets of stator windings. The designed motor has the advantages of high power density and a large motion range. In addition, because the designed motor has an irregular three-dimensional (3D) structure, it is difficult to perform dynamic magnetic field calculations with existing methods. To solve this problem, we propose a modified 3D dynamic magnetic equivalent circuit (3DD-MEC). The proposed method establishes a node network according to the structural edge features of the motor core and the permanent magnet and calculates the reluctance of the connecting branch based on the differential principle. Moreover, a connection strategy of air-gap nodes in 3D space is formulated, and the magnetic saturation characteristics of the iron core are reflected by an iterative calculation of magnetic permeability. Using the 3DD-MEC method, the 3D dynamic magnetic field information of the HE-MDOFSM can be quickly and accurately calculated. Finally, the reliability of the method is verified by simulation and experiment, which provides a reference for improving the design optimization efficiency of HE-MDOFSM.

High-performance permanent magnet array design by a fast genetic algorithm (GA)-based optimization for low-field portable MRI

Lightweight and compact permanent magnet arrays (PMAs) are suitable for portable dedicated magnetic resonance imaging (MRI). It is worth exploring different PMA design possibilities and optimization methods with an adequate balance between weight, size, and performance, in addition to Halbach arrays and C-shaped/H-shaped magnets which are widely used. In this paper, the design and optimization of a sparse high-performance inward-outward ring-pair PMA consisting of magnet cuboids is presented for portable imaging of the brain. The design is lightweight (151kg) and compact (inner bore diameter: 270mm, outer diameter: 616mm, length: 480mm, 5-Gauss range: 1840×1840×2340mm3). The optimization framework is based on the genetic algorithm with a consideration of both field properties and simulated image quality. The resulting PMA design has an average field strength of 101.5 mT and a field pattern with a built-in linear readout gradient. Subtracting the best fit to the linear gradient target resulted in a residual deviation from the target field of 0.76mT and an average linear regression coefficient of 0.85 to the linear gradient. The required radiofrequency bandwidth is 6.9% within a field of view (FoV) with a diameter of 200mm and a length of 125mm. It has a magnetic field generation efficiency of 0.67mT/kg, which is high among the sparse PMAs that were designed for an FoV with a diameter of 200mm. The field can be used to supply gradients in one direction working with gradient coils in the other two directions, or can be rotated to encode signals for imaging with axial slice selection. The encoding capability of the designed PMA was examined through the simulated reconstructed images. The force experienced by each magnet in the design was calculated, and the feasibility of a physical implementation was confirmed. The design can offer an increased field strength, and thus, an increased signal-to-noise ratio. It has a longitudinal field direction that allows the application of technologies developed for solenoidal magnets. This proposed design can be a promising alternative to supplying the main and gradient fields in combination for dedicated portable MRI. Lastly, the design is resulted from a fast genetic algorithm-based optimization in which fast magnetic field calculation was applied and high design flexibility was feasible. Within optimization iterations, image quality metrics were used for the encoding field of a magnet configuration to guide the design of the magnet array.

Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning

Electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) can be modeled using partial differential equations (PDEs). Using state-of-the-art finite-element methods (FEM), it often takes tens of seconds to solve the PDEs for computing a high-resolution E-field, hampering the wide application of the E-field modeling in practice and research. To improve the E-field modeling's computational efficiency, we developed a self-supervised deep learning (DL) method to compute precise TMS E-fields. Given a head model and the primary E-field generated by TMS coils, a DL model was built to generate a E-field by minimizing a loss function that measures how well the generated E-field fits the governing PDE. The DL model was trained in a self-supervised manner, which does not require any external supervision. We evaluated the DL model using both a simulated sphere head model and realistic head models of 125 individuals and compared the accuracy and computational speed of the DL model with a state-of-the-art FEM. In realistic head models, the DL model obtained accurate E-fields that were significantly correlated with the FEM solutions. The DL model could obtain precise E-fields within seconds for whole head models at a high spatial resolution, faster than the FEM. The DL model built for the simulated sphere head model also obtained an accurate E-field whose average difference from the analytical E-fields was 0.0054, comparable to the FEM solution. These results demonstrated that the self-supervised DL method could obtain precise E-fields comparable to the FEM solutions with improved computational speed.

Investigation on torque ripple minimization in switched reluctance motor by using different techniques associated with TSF taking into account of magnetic saturation effects

In this work, three control techniques of minimization of torque ripple in SRM are proposed and compared to the classical control technic names as Hysteresis control proposed in [1]. The principle of these methods is based on the Torque Sharing Function (TSF) fixing the reference torque in each phase. In the literature review, the classical method used in the reduction of torque ripples in SRM is the TSF-Hysteresis Controller (TSF-H). The first proposed method is the TSF-Predictive control (TSF-P), here the objective is to find the voltage to be applied to the machine minimizing the error of the current through a prediction algorithm on the supply current. The second proposed method is the sliding mode control (TSF-SMC-PSO) whose parameters are optimized by the particle swarm algorithm (PSO). Finally, the third proposed method is the sliding mode controller whose parameters are optimized by fuzzy logic controller (TSF-SMFC). The finite element method (FEM) through the magnetic field calculation software FEMM was used to calculate the flux and torque in static system and to take into account magnetic saturation circuit of the SRM. The results obtained show that the TSF-SMC-PSO control methods have better performance compared to the other proposed methods mentioned above.

Nonlinear Semianalytical Model for Axial Flux Permanent-Magnet Machine

In this article, we propose a novel nonlinear semianalytical model (AM) for the magnetic field calculation of electric machines. The nonlinear properties and local saturation effect of the iron part are taken into consideration in Cartesian coordinates, which is the main contribution of the proposed model. Thus, high accuracy of electromagnetic field results can be obtained with the low computational time cost. The model is developed based on the harmonic modeling technique by solving Maxwell's equations. The detailed theoretical derivations, which use the complex Fourier series and the Cauchy product, are presented. To verify the proposed model, an axial flux permanent-magnet (PM) machine is selected to be investigated. Both finite-element model and experimental results agree well with that of the proposed model. Moreover, the nonlinear AM has potential application for other types of PM electrical motor in Cartesian coordinates, such as flat PM linear machines.

Simulation of plasma transport in MPS-LD linear plasma device by using BOUT++

A linear plasma device (LPD) module based on the 2D transport module under the BOUT++ framework is developed in this paper to simulate plasma transport in the LPD. The LPD module includes three parts, i.e. magnetic field calculation, simulation mesh generation and plasma transport setup. The magnetic field is calculated with the circular current loop using the location and current information of each coil. The mesh generation code can produce a simulation mesh for LPD by employing the magnetic field. The plasma transport model is based on the reduced Braginskii equations, which consist of the continuity equation, momentum equation, and energy equation. The fluid neutral model is applied for neutral particle simulation. Deuterium (D) and helium (He) ions and atoms can be simulated by the model. The first attempt to simulate plasma transport in the new LPD, called multiple plasma simulation linear plasma device (MPS-LD), is presented using the developed model. The D plasma transport in the MPS-LD is simulated and benchmarked against the two-point model, showing the validation of the BOUT++ simulation. The effects of radial transport on the heat load to the target are studied, which illustrates the significant impact of the radial diffusivities and on the plasma. Moreover, the He impurity injection process during the discharge is studied with emphasis on plasma–impurity interactions. The simulation results show that He injection can reduce the plasma energy load to the target significantly, and the efficiency depends on the He source density and injection velocity. The present work provides an alternative and flexible simulation tool for plasma transport in LPDs.

Green and recyclable demolition of steel reinforced concrete: Application and calculation model of induction heating demolition technology

In steel-reinforced concrete (SRC) structures, it is difficult to separate or recycle steel and concrete using traditional demolition methods, which create a large amount of construction waste. A green and recyclable technology for demolishing SRC structures by induction heating (IH) is proposed in this study. The magnetic field calculation model of the rectangular coil used in IH demolition (IHD) is deduced and verified using COMSOL software. This calculation model can reduce the workload of magnetic field modelling and provide guidance for IHD scheme development. In addition, IH experiments are conducted on five section steels of different sizes. Furthermore, IHD experiments are performed on five SRC specimens that incorporated the five section steels. The temperature distribution and rise laws of the IHD are obtained. The feasibility of the IHD is verified. Under the IHD experimental conditions, the section steels and concrete are separated within approximately 15 min, and the critical expansion difference is approximately 1.85 mm. The applicability of the calculation model in the coil design and IH scheme is verified. The proposed IHD is expected to provide new ideas for reducing and recycling the amount of construction waste generated from the demolition of SRC structures.

Magnetic Field Calculation in Axial Flux Permanent Magnet Motor With Rotor Eccentricity

In this article, a novel magnetic field calculation approach that considers the static inclined eccentricity of axial flux permanent magnet (AFPM) machine is presented. The equivalent remanence of permanent magnet (PM) is introduced and calculated, in which the air-gap length can be regarded as uniform. Then, the analytical model based on harmonic subdomain technology can be used directly. The magnetic field distribution (MFD) and electromagnetic performance under eccentric state are calculated and compared. The effectiveness of the proposed method is verified both by the finite element (FE) model and experimental results. The main contribution of this article is to provide a simple and accurate method for the calculation of the eccentric magnetic field of the PM motor, not limited to the AFPM.

Axially Symmetric Source Field Penetration Through a Circular Aperture in a Thin Impedance Plate

The field penetration through a circular aperture in an infinite plane with a nonzero surface impedance excited by an axially symmetric source is analytically investigated. The problem is formulated in terms of an original dual-integral-equation approach and solved through the method of moments in the Hankel spectral domain. The proposed formulation is applied to the calculation of the axial magnetic field when the source is a current loop of finite radius coaxial with the aperture and it is shown that it is possible to separate the contributions of the aperture and of the nonzero impedance plate to the transmitted field. In the case of low frequencies and small apertures, closed-form expressions are also derived. Moreover, the approach is also applied to the case of a perfectly conducting plane giving rise to results that coincide with those recently presented in the literature. Finally, the accuracy of the proposed approach is validated through full-wave calculations.

Turbogenerator Electromagnetic Analysis with Changing Reactive Load

Comparative numerical analysis of electromagnetic processes in the end zone of powerful turbogenerators has been carried out at changes in reactive load from rated duty to underexcitation, as well as performance parameters of static overload that determine the stability of synchronous operation of turbogenerators in the power system. It was demonstrated that the representation of magnetic field sources and calculation results in the form of rotating waves allows simplifying and speeding up the solution of threedimensional electromagnetic problems in the turbogenerator end zone. Using a previously developed calculation method, the electromagnetic fields and processes in over- and underexcitation modes, in particular, peculiarities of shielding in turbogenerators are studied. It was established that the added losses and electrodynamic forces in underexcitation modes acting on the outermost core packages, pressure plate, and stator shield increased by 1.5–3.0 times, resulting in accelerated aging of the turbogenerator end zone. An appropriate margin shall be provided in the cooling system and the structural design of the turbogenerator end zone. Static overload capacity in nominal conditions is determined by the ratio of maximum power to rated power. An analytical functional relationship between static overload capacity and load conditions was established. It was demonstrated that when switching to the underexcitation mode while maintaining the active load due to a decrease in the excitation current and maximum power, the static overload factor decreases to unity, that there is virtually no static stability margin of the turbogenerator in this mode. Calculations were made for turbogenerators with a capacity of 200–1111 MVA. It is recommended to limit the operation of turbogenerators in underexcitation modes and to use specialized compensators more extensively.

Determination of Electric and Magnetic Field Calculation Uncertainty in the Vicinity of Overhead Transmission Lines

This paper presents a new approach for uncertainty determination of the electric field intensity and magnetic flux density calculation in the vicinity of overhead transmission lines. The proposed method is based on the law of propagation of uncertainty as defined in the Guide to the expression of Uncertainty in Measurement. A mathematical model is developed for determining the electric field intensity and magnetic flux density calculation uncertainty based on the Charge simulation method and method based on Biot – Savart law, respectively. The verification of the proposed method was performed by estimating the uncertainty of the electric field and magnetic flux density calculations for four single circuit and two double circuit high-voltage overhead transmission lines. The analysis of the obtained results demonstrates that the proposed method can be successfully used to determine the uncertainty of electric field intensity and magnetic flux density calculations in the vicinity of overhead transmission lines.

MuFinder: A program to determine and analyse muon stopping sites

Significant progress has recently been made in calculating muon stopping sites using density functional theory. The technique aims to address two of the most common criticisms of the muon-spin spectroscopy (μ+SR) technique, namely, where in the sample does the muon stop, and what is its effect on its local environment. We have designed and developed a program called MuFinder that enables users to carry out these calculations through a simple graphical user interface (GUI). The procedure for calculating muon sites by generating initial muon positions, relaxing the structures, and then clustering and analysing the resulting candidate sites, can be done entirely within the GUI. The local magnetic field at the muon site can also be computed, allowing the connection between the muon sites obtained and experiment to be made. MuFinder will make these computations significantly more accessible to non-experts and help to establish muon site calculations as a routine part of μ+SR experiments. Program summaryProgram Title: MuFinderCPC Library link to program files:https://doi.org/10.17632/pwwt7p9hv8.1Developer's repository link:https://gitlab.com/BenHuddart/mufinderLicensing provisions: GPLv3Programming language: PythonNature of problem: To automate the process of calculating muon stopping sites using density functional theory, thereby making these calculations accessible to non-experts.Solution method: A Python-based graphical user interface (GUI) through which users can calculate muon stopping sites using the structural relaxation method. The program makes use of newly-developed algorithms for generating candidate initial muon positions and for clustering muon positions obtained from the structural relaxations. Analysis of the muon sites, including calculation of the local dipolar magnetic field, is also possible within the GUI.

Magnetic field computer interface based on Cartesian robot for practical demonstration of Ampere’s law in precollege courses

Basic science courses, such as physics, are fundamental to precollege studies. For instance, in different engineering applications, electricity and magnetism require comprehending subjects such as electrical circuits and power electronics. However, abstract concepts such as electric or magnetic fields are often difficult to explain without visual tools. Computer programs designed for learning physics fundamentals are useful in this area because they allow the visualization, interaction and reinforcement of main concepts in a better way than using only blackboard. In this work, an interactive MATLAB based program to visualize a magnetic field in 3D was presented. The measurements were sampled by a computer-controlled Cartesian robot with a Hall effect sensor. The magnetic field was generated by an energized electromagnet to show the relationship between electricity and magnetism. The designed graphical user interface aims to stimulate interest in electromagnetism in precollege students.

Accurate Calculation of Magnetic Field of Same-Pole and Same-Slot Surface-Mounted Three-Phase Permanent Magnet Synchronous Motor

This article presents a new type of surface-mounted three-phase permanent magnet synchronous motor with the same number of poles and slots which has obvious advantages in cogging torque. Since the same-pole and same-slot three-phase permanent magnet motor has three or more slot types and the slots are not evenly distributed on the circumference, this article adopts an accurate subdomain model that considers the position and slot width of each slot separately to perform an analytical calculation of the magnetic field. The motor is divided into three subdomains and modeled by Maxwell’s equations, and the magnetic scalar vector equation satisfied by each subdomain is solved by the method of separation of variables. A 24-pole 24-slot three-phase permanent magnet motor consisting of 13-pole 12-slot and 11-pole 12-slot is used to verify the correctness of the proposed analytical computational model. Compared with the finite element analysis, the proposed analytical model shows high accuracy in the calculations of the magnetic flux density of the three subdomains.