Magnetic Circuit Model Research Articles

An approach to solving the effect of background in fluidized bed on electromagnetic tomography

As a non-invasive measurement technique, electromagnetic tomography (EMT) system based on tunneling magneto resistance (TMR) can detect the distribution of medium in the gas–liquid–solid fluidized bed by the difference of permeability. The distribution of medium in the three-phase fluidized bed is not uniform, and the solid clusters and bubble clusters are formed in the background of the gas–liquid–solid mixture. Since the effect of the background in the pipe of the fluidized bed on the boundary measurement data of the TMR-EMT system is much greater, it is difficult to detect solid clusters and bubble clusters when the image is reconstructed directly using the boundary measurement data. In order to improve the detection of clusters by the TMR-EMT system, a method to weaken the effect of the background is proposed. The equivalent magnetic circuit model is used to estimate the background permeability. Then the magnetic dipole theory and demagnetization effect theory are utilized to establish a simple background compensation model based on the estimated background permeability. Using the compensation model, the effect of the background is weakened from the boundary measurement data and the cluster distribution information is highlighted. Simulation and experimental results demonstrate the effectiveness of the proposed method.

Analysis of low saliency ratio and torque characteristics of the fractional slot concentrated winding surface mounted motors

In recent years, fractional slot concentrated winding permanent magnet synchronous motors (FSCW PMSMs) have become a hotspot in the research field. Due to the unique inductance characteristics of the FSCW PMSM, a fast and accurate calculation of the d/q-axis inductance and saliency ratio is necessary. In this paper, a method is proposed to calculate the d/q-axis reactance of the FSCW SPMSM, which constructs the equivalent magnetic circuit model of the d/q-axis armature reaction flux separately, and the saliency ratio characteristics of the FSCW SPMSM were demonstrated. In addition, to meet the high requirements of the modern industries, especially in servo systems, accurate consideration of the effect of stator resistance on torque and electromagnetic performance is important and more applicable. According to the relationship between the vector parameter, the explicit expression of the d/q-axis currents that consider the stator resistance is obtained, and the prediction of load angle at maximum electromagnetic torque is achieved. Then, combined with the finite element method, the influence mechanism of stator resistance on the motor steady-state performance is revealed. Finally, the experimental data are compared with the calculation data, and the correctness of the models and analysis was verified.

A novel stress concentration inspection method for marine oil and gas pipeline based on UNSM

Stress concentration of marine oil and gas pipelines can lead to deformation and cracks, laying out great hidden dangers for safe operation. This paper proposes a novel in-line inspection method for stress concentration based on UNSM (unsaturated magnetization) for oil and gas pipelines. Firstly, the stress concentration inspection mechanism with UNSM is analyzed, and the equivalent magnetic circuit model of the inspection probe is derived. Secondly, the response signal features of axial, radial and complex stresses were investigated parametrically by numerical simulation. Then, quantitative tensile stress inspection was carried out with the UNSM inspection probe. Finally, the pipeline stress state is continuously scanned by the self-developed defect dynamic scanning experimental system. The results show that the UNSM inspection probe can effectively detect the abnormal stress of the pipeline. Meanwhile, the axial tensile, radial compressive stress and complex stress increase the axial permeability of the pipeline, resulting in a negative correlation of characteristic signals. Besides, the signal feature shows the "basin" distribution and decreases gradually with the increase of the lift-off. The above research provides a reference for developing in-line inspection equipment for the abnormal stress of marine pipelines.

The effect of excitation current on radial electromagnetic force wave of tangential magnetizing parallel structure hybrid excitation synchronous motor

To study the influence of the magnitude of the excitation current on the radial electromagnetic force wave of the tangential magnetizing parallel structure hybrid excitation synchronous motor (TMPS-HESM) under different working conditions. Firstly, the basic structure of the motor and the rotor magnetic circuit model is introduced. Secondly, considering the influence of excitation current, the Maxwell stress tensor method is used to analyze the radial electromagnetic force wave of the motor and the source, frequency and order of the radial electromagnetic force wave that has a great influence on the electromagnetic vibration of the motor are qualitatively obtained. Then, the three-dimensional finite element method is used to calculate the variation law of the radial electromagnetic force wave when different excitation currents are applied under no-load and load conditions, revealing that the DC excitation will increase the amplitude of the radial electromagnetic force wave of a specific order. Meanwhile, the influence of load torque variation on the radial electromagnetic force wave is discussed, and it is found that the (2f, 8) and (6f, 24) order electromagnetic force waves are greatly affected by the armature reaction. The work provides a theoretical basis for further suppressing the electromagnetic vibration of this type of hybrid excitation motor.

Magnetic Field Analysis and Development of Disk Axial–Radial Hybrid Excitation Generator for Range Extenders in Extended-Range Electric Vehicles

Magnetic Field Analysis and Development of Disk Axial–Radial Hybrid Excitation Generator for Range Extenders in Extended-Range Electric Vehicles

General 2-D Analytical Framework for No-Load Analysis of Interior Permanent Magnet Machines

Solving two-dimensional (2-D) Maxwell’s equations in interior permanent magnet (IPM) motors is fairly complex due to the asymmetrical geometry of rotor magnets in the cylindrical coordinate system. This paper presents a general imaging solution to enable the 2-D open-circuit modeling of the family of IPM machines. Interior magnets are replaced/modeled with (i) virtual magnets on the surface of the rotor body (mapping interior magnets to the surface of the rotor body), and (ii) virtual volume current on the surface of the rotor body. The specifications of the virtual magnet (i.e., the remnant flux density) and the virtual volume current (i.e., current density level) are determined via magnetic circuit model. Next, the 2-D flux distribution of the transformed machines are calculated by solving 2-D Maxwell’s equations and considering relevant boundary conditions. Meanwhile, the effect of stator slots on flux profile is accounted by injecting proper amount of surface magnetizing current on the stator bore. Analytical results are supported via finite element method (FEM) and a series of experimental measurements.

Analytical Prediction of D- and Q-Axes Inductance for Dual Three-Phase Surface-Mounted Permanent Magnet Motor Accounting for Eccentric Pole and Tooth Saturation

This paper presents an analytical model to calculate the d- and q-axis Inductance of dual three-phase surface-mounted permanent magnet motor accounting for eccentric pole and tooth saturation. The novel method combines the advantages of the subdomain model and lumped parameter magnetic circuit model. This motor is divided into several subdomains. And the eccentric pole is further subdivided into multiple symmetrical regions. Based on the Poisson’s and Laplace’s equations, the subdomain model is established. The reluctance of the tooth and the tip is calculated by the subdomain model and lumped parameter magnetic circuit model. According to the relationship between the tooth reluctance, tip reluctance and the corresponding air-gap reluctance, the equivalent air-gap magnetic density coefficient is obtained. Based on the coefficient, the new air-gap magnetic density and tooth magnetic density are solved. For the solution of saturation, this paper compares the density of two adjacent solutions until the error between the two is very small. Based on the iterative calculation, the d- and q-axis inductance is obtained. The finite element method and experiment are employed to validate the analytical model.

Modeling and Simulation of a Planar Permanent Magnet On-Chip Power Inductor

The on-chip integration of a power inductor together with other power converter components of small sizes and high-saturation currents, while maintaining a desired or high inductance value, is here pursued. The use of soft magnetic cores increases inductance density but results in a reduced saturation current. This article presents a 3D physical model and a magnetic circuit model for an integrated on-chip power inductor (OPI) to double the saturation current using permanent magnet (PM) material. A ~50 nH, 7.5 A spiral permanent magnet on-chip power inductor (PMOI) is here designed, and a 3D physical model is then developed and simulated using the ANSYS®/Maxwell® software package (version 2017.1). The 3D physical model simulation results agree with the presented magnetic circuit model, and show that in the example PMOI design, the addition of the PM increases the saturation current of the OPI from 4 A to 7.5 A, while the size and inductance value remain unchanged.

An accurate calculation method for inductor air gap length in high power DC–DC converters

High-power inductors are fundamental components in high-power DC–DC converters, with their performance being a crucial metric of converter efficiency. This paper presents an in-depth analysis of a novel calculation method for the air gap length in such inductors. Taking into account the effects of air gap diffusion and the winding magnetic field, an expression for the air gap diffusion radius is derived, focusing on a distributed air gap structure. Furthermore, models for calculating the air gap and winding reluctance are developed, grounded in electromagnetic field theory. An equivalent magnetic circuit model, formulated based on Kirchhoff's second law, facilitates the proposed method for air gap length calculation. This study also involves the development of 3D models for both discrete and decoupled integrated inductors. The comparison between simulation outcomes and calculated air gap lengths indicates a maximum error of less than 8%, with the minimum error being as low as − 0.79%. Compared with traditional methods, the calculation method proposed in this paper has significant advantages. Additionally, the discrepancy between calculated values and experimental measurements is found to be 1.11%. These results validate the accuracy and applicability of the theoretical analysis and calculation method, underscoring their significance in the design and optimization of high-power DC–DC converters.

Calculation and Analysis of an Integrated Motor–MB Magnetic Circuit Model

Calculation and Analysis of an Integrated Motor–MB Magnetic Circuit Model

Modeling of Coupled Electric and Magnetic Circuits in Electromagnetic Suspension Vehicles

Modeling of Coupled Electric and Magnetic Circuits in Electromagnetic Suspension Vehicles

Magnetic Equivalent Circuit Model for a Two Degree-of-Freedom Rotary-Linear Machine with Transverse Flux Structure

Magnetic Equivalent Circuit Model for a Two Degree-of-Freedom Rotary-Linear Machine with Transverse Flux Structure

Distributed Magnetic Equivalent Circuit Modelling of Synchronous Machines

Distributed Magnetic Equivalent Circuit Modelling of Synchronous Machines

Distributed Modeling of Isolated Active Magnetic Bearings Considering Magnetic Leakage and Material Nonlinearity

In order to expand the application field of magnetic bearings, this article studies a novel radially isolated active magnetic bearing (IAMB) system in which the stator and the rotor are separated by a layer of metal isolation sleeve. Aimed at the shortcomings of existing modeling methods, a distributed magnetic circuit model (DMCM) was proposed based on the magnetic field segmentation theory for IAMBs. Considering material nonlinearity and leakage flux, the flux distributions of the isolation sleeve and air gap are calculated accurately. Finally, the 3D finite element model (3D FEM) and experimental platform were built to verify the feasibility of the IAMB and the correctness of the DMCM.

A Novel Separated Hybrid-Magnetic-Circuit Variable Flux Memory Machine

Aiming at the problems of the existing hybrid-magnetic-circuit variable flux memory machine (HMC-VFMM), such as weak flux regulation (FR) capability and low efficiency in high-speed region, etc., this article proposes a novel separated HMC-VFMM (SHMC-VFMM), which innovatively arranges a series magnetic circuit on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -axis and a parallel magnetic circuit on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis. The SHMC design can simultaneously reduce the PMs fluxes through low-coercive-force PMs configured on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -axis and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis, which will improve the FR capability. The magnetic saturation is alleviated by reducing the usage of high-coercive-force PMs, which further broadens the FR range. The proposed design also simplifies the rotor mechanical structure, thereby improving the rotor design flexibility. Firstly, the topological evolution process and the working principle of the proposed machine are interpreted in in succession. Then, the mechanism of further expanding the FR range of the proposed machine is revealed by comparing its equivalent magnetic circuit model with that of the existing machine. Subsequently, the electromagnetic characteristics of the two compared machines are analyzed by using the finite element method, which validates the performance advantages of the proposed machine. Finally, an SHMC-VFMM prototype is manufactured and measured to verify the superiority of the proposed SHMC design.

Study of the decoupling magnetic integrated high‐frequency transformer for DC/DC converter

AbstractThe isolated DC/DC converter plays an irreplaceable role in the development of the DC microgrid. However, the multiple discrete high‐frequency transformers occupy considerable volume in power converters due to the connection of multiple isolated converters. In order to reduce the number of discrete transformers and increase the power density as well as the reliability of the power converter, a three‐port isolated DC/DC converter with a decoupling magnetic integrated high‐frequency transformer (DMIHFT) is proposed for the DC microgrid in this paper. The semiconductor count of the proposed converter is reduced by combining one DAB converter and two LLC converters. Three discrete transformers are integrated into a single common core, and magnetic decoupling is achieved among each transformer by rational design at the same time. In addition, the magnetic circuit model derivation process of the proposed DMIHFT and the operation principles of the converter are described in detail. The design guidance of the proposed DMIHFT is present. And then, a 15 kW/20 kHz DMIHFT is designed based on the design guideline, and the simulation is carried out. Finally, a 15 kW/20 kHz DMIHFT prototype is fabricated, and the effectiveness of the proposed DMIHFT is verified by experimental results.

A 2D hybrid analytical electromagnetic model of the dual‐stator axial‐field flux‐switching permanent magnet motor

AbstractThe two‐dimensional (2D) analytical model for the calculation of the components of the flux density distribution in the air gap in a dual‐stator axial‐field flux‐switching permanent magnet (PM) motor (DSAFFSPM) is presented. The novelties of this study are deriving a 2D hybrid analytical model and replacing the rotor teeth with some surface currents for the calculation of air‐gap magnetic flux density for the first time in the DSAFFSPM motor. The 2D analytical model for DSAFFSPMs is more challenging due to the doubly salient structure and inner PM of the stator. 1D analytical interior PMs are first transferred to the bore of the stator body using the magnetic equivalent circuit model (MEC). Next, the effects of the rotor teeth are taken into consideration by injecting virtual surface currents for 2D analytical model. Applying boundary conditions and solving the Laplace/Poisson equations, the vertical and tangential flux components of the flux density distribution in the air‐gap DSAFFSPM motor are computed. The verification of the proposed method and the obtained results are validated by the 3D finite element method.

A reluctance-based electromagnetic transient model for the Sen Transformer with inter-turn fault

In order to analyze the electromagnetic characteristics of the Sen Transformer (ST) in the event of an inter-turn fault (ITF), an electromagnetic transient model of the ST with ITF based on reluctance is proposed in this paper. Firstly, the magnetic equivalent circuit model of the ST with ITF is established based on the magnetic coupling relationship among the internal windings of the ST with ITF. Secondly, the electrical analytical model for the current in each winding of the ST with ITF is derived from the electrical connection established the ST with ITF and the external system. Finally, the electromagnetic transient model of the ST with ITF can be obtained by combining the magnetic equivalent circuit model with the electrical analytical model. The J-A hysteresis model is employed for representing the saturation characteristics of the iron core and the hysteresis effects. Meanwhile, an energy method is used to calculate the leakage reluctance between the windings. Three case studies have been conducted with the assistance of MATLAB and ANSYS/Maxwell. The results of the analytical calculations are compared with the time-domain simulation to verify the validity of the model. Furthermore, the growth of the current in the fault phase is significant after an ITF occurs in the ST, while the growths of the currents in the non-fault phases are very small. Moreover, the effects of the number of fault turns and the fault location on the current in the ST with ITF are further analyzed.

A Discrete Coupled Multiphase Interleaved LLC Converter With Symmetrical Components Analysis

This paper proposes a coupling structure and a generalized analysis approach for multi-phase interleaved LLC converters that applies to all odd phases that can simultaneously improve the current balancing in all interleaved phases. Firstly, a discrete coupled inductor array (DCIArray) structure is proposed, and its magnetic circuit model is analyzed in detail; then, the generalized symmetrical component theory is introduced to decouple the inductance matrix to the sequence impedance, with expansion to all odd-phase LLC converters, and then the sequence impedance, coupling coefficient, components tolerance impacts, and extended voltage gain with control architecture are discussed under the corresponding models; Finally, the recommended design for three-phase and five-phase DCIArray was discussed. Experiments based on both three-phase and five-phase prototypes have proved that the proposed scheme has excellent current sharing in almost all frequency ranges.

Modified magnetic equivalent circuit of double‐stator single‐rotor axial flux permanent magnet machine considering stator radial‐end flux‐leakage

AbstractA modified non‐linear magnetic equivalent circuit (MEC) model is presented for double‐stator single‐rotor axial flux permanent magnet (AFPM) (DSSR‐AFPM) machine considering stator radial‐end flux‐leakage, which is severer under a heavier load. Compared to the conventional MEC model for DSSR‐AFPM machine, the proposed model can predict the electromagnetic performance more accurately when the machine operates under a heavy load. The proposed MEC model is verified by the finite element analysis (FEA) on a 24‐slot/20‐pole DSSR‐AFPM machine. The comparison results show that the relative error between the proposed MEC model and FEA is &lt;4% for back electromotive force and &lt;5% for average electromagnetic torque, respectively. Specifically, the relative error of the average torque for the modified MEC model is 4.92% at 28.30 Arms/mm2 slot current density, which is lower than the conventional MEC model, that is, 7.75%.