Equivalent Current Method Research Articles

Prediction of Electromagnetic Performance for IPMSM Based on Improved Analytical Model Considering Saturation Effects

Unlike surface-mounted permanent magnet synchronous motors (SPMSM), the rotor structure of interior permanent magnet synchronous motors (IPMSM) is irregular and relatively complex. This makes the analytical calculation for IPMSM quite complicated. Except for the use of some equivalent methods to make irregular permanent magnets (PMs) regular, existing subdomain models often cannot effectively and directly account for the complex rotor structure and cannot be easily applied to IPMSM. For this reason, an improved analytical model applicable to IPMSM is presented, studied, and developed in this article. First, a novel subdomain model division method is innovatively introduced. Complex rotor structure can be well accounted for. This not only facilitates the expression of vector potential and satisfies the establishment of subdomain model, but also recovers the original rotor topology to the maximum extent and effectively avoids many uncertainties and unreliability caused by over-equivalence. Afterwards, the magnetic equivalent circuit and equivalent surface current method are combined to fully consider the saturation effects of magnetic isolation bridges, rotor ribs, and cores. Model analysis accuracy is well guaranteed. Further, the precise subdomain method is investigated to achieve fast prediction of key electromagnetic performance. Both finite element analysis (FEA) and prototype experiment strongly highlight the validity of the improved analytical model. In addition, compared to FEA, the improved analytical model does not require tens of thousands of computation cells, which saves a lot of time and storage while ensuring the same prediction accuracy. This opens up unlimited possibilities for the design and optimization of IPMSM.

Characteristics Analysis of Novel Transverse Flux Linear Synchronous Motor for Maglev Transportation

The Maglev transportation mainly completes the propulsion, levitation and guidance functions, which generally require the application of linear motor. Based on this, a novel transverse flux linear synchronous motor is proposed in this paper which is integrated with propulsion, levitation and guidance. The whole structure and principle of the novel transverse flux linear synchronous motor are discussed. Then, the air gap magnetic flux density is calculated based on the equivalent current layer analysis method, and the propulsion and levitation are calculated with different operating times. Besides, the guidance force is calculated with different transverse displacements by using the Schwarz-Christoffel conformal mapping method. After the simulated of the finite element model, the analytical results of the forces are compared with the finite element method. Finally, all the calculated results of the propulsion, the levitation and the guidance are validated by an experimental prototype, which provide an electromagnetic theory analysis for electromagnetic suspension transportation that integrated with propulsion, levitation and guidance.

High-Frequency Oscillation Suppression Strategy for Flexible DC Transmission Systems Based on Additional Joint Damping

Flexible DC transmission systems experience negative damping characteristics in the high-frequency range due to the delay in the system control link. This can lead to interactions between the impedance of modular multilevel converters (MMCs) and AC transmission lines, resulting in high-frequency oscillation (HFO) issues. To resolve this problem, a simplified MMC control model was developed, taking into account the current inner loop control link. The Sobol method was employed to analyze the factors influencing the impedance characteristics of MMC. Additionally, a combined approach involving a virtual passive filtering method and an equivalent current sampling method was proposed to provide additional damping. The study compared and analyzed the impact of additional damping control on the impedance characteristics and system stability of MMCs. Lastly, a flexible direct current grid connection simulation model was constructed using PSCAD to validate the effectiveness of the proposed additional damping control strategy.

Hybrid analytical model for air‐gap magnetic field prediction of surface‐mounted permanent magnet motors with a quasi‐regular polygon rotor

AbstractIn this article, a hybrid analytical model for a quasi‐regular polygon rotor (QPR) is proposed. It mainly uses the subdomain method and conformal mapping to solve a non‐circular boundary in the QPR. Firstly, the subdomain method combined with an equivalent surface current method is used to calculate the air‐gap magnetic field considering a slotted stator with a circular rotor. Secondly, by segmenting the non‐circular boundary in the QPR, the complex relative air‐gap permeance of the QPR can be calculated using the conformal mapping. Thirdly, this complex relative air‐gap permeance modifies the air‐gap magnetic field calculated in the first step to obtain the actual magnetic field distributions. Consequently, no‐load and loaded air‐gap flux densities, back‐electromotive force and torque can be obtained. A 12‐pole/3‐phase permanent magnet motor is modelled using the proposed hybrid analytical model, which is validated by finite‐element analysis and experiment. This proposed hybrid analytical model presents a new way of processing the QPR. Its calculation speed is nearly 50 times faster than the finite‐element analysis, which is of great help to the initial design and optimisation of machines with QPRs.

A Novel Design of Permanent Magnets for the Air Gap Magnetic Field of Hollow-Cup Motor

Spacecraft motors are often driven with trapezoidal phase currents to achieve higher output torque. For hollow cup motors (HCM) driven by trapezoidal wave currents, parallel magnetised permanent magnet (PM) motors produce an air gap magnetic field (AMF) waveform which is significantly different from the trapezoidal wave, causing the motor to generate noise or vibration. The existing control optimisation method or structure improvement design method is difficult to directly apply to HCM due to its large gas gap. In this paper, according to the fundamental theory of a constant magnetic field, the AMF of HCM is analysed using the equivalent surface current method (ESCM) and its mathematical model is established. The analytical expression of the AMF is solved, and the influencing parameters of the AMF are clarified. The structural design of the HCM with eccentric PMs sintered with high-performance NdFeB is further improved. On this basis, a prototype motor is designed. Simulation results show that the structure can effectively increase the width of the flat section of the AMF and make the AMF close to an ideal trapezoidal wave (ITW). Experiments verify the correctness of the method.

Multiparameter Estimation of IPMSMs Using Core Loss Current Calculations in dq-Axis Equivalent Circuit Model

Accurate parameter estimation is critical for high-performance modeling and control of interior permanent magnet synchronous machines (IPMSMs). Core loss effects affect the accuracy of the parameter estimation, especially in high loading conditions with saturated cores. Existing research on parameter estimation considering core loss effects generally focuses on the core loss equivalent resistance estimation; however, they require either accurate core loss experimental data or finite element analysis (FEA) model. The core loss equivalent resistance is dependent on the loading conditions, harmonics, frequency, and temperature, which increases the difficulty of accurately estimating the resistance. This article firstly proposes a direct core loss equivalent current estimation method for multiparameter estimation purposes without estimating the core loss equivalent resistance. Based on the estimated core loss equivalent currents, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axis inductances equivalent currents are calculated to perform the multiparameter estimation. The proposed approach can improve the precision of the parameter estimation and the computation efficiency by calculating the core loss equivalent resistance currents without having the core loss data. The effectiveness of the proposed multiparameter estimation method is evaluated by comparing the calculated and measured torques of a laboratory 4.5 kW IPMSM in various operating conditions. The improved accuracy of the proposed method is verified by comparing it with two existing online parameter estimation methods and FEA-based offline parameter estimation results.

Theoretical modeling and analysis of a quasi-zero-stiffness vibration isolator equipped with extensible and axially magnetized negative stiffness modules

Quasi-zero-stiffness (QZS) isolation systems have demonstrated good performance in low-frequency vibration isolation fields. However, the existing QZS isolation systems with traditional negative stiffness elements cannot support high payloads under miniaturization and simplification. To give some beneficial insights into high loading capacity, optimized structure, and good vibration isolation performance, a novel axially magnetized negative stiffness module (MNSM) is proposed based on the concepts of modularity and expansibility. Concretely, an axially magnetized negative stiffness unit (MNSU) is designed as the fundamental building block of MNSM, and the proposed MNSM can be composed of different axially magnetized negative stiffness units (MNSUs) for diversified requirements. To effectively investigate the characteristics of the MNSU, a computationally high efficient equivalent surface current method is developed. As a result, two types of MNSUs with optimized parameters are achieved, and their design procedures are presented respectively. To verify the benefits of the MNSMs, the designed QZS isolator is theoretically modeled and solved with the average method and then verified through the Runge–Kutta method. Through analyzing the isolation systems with MNSMs under different nonlinearities and dynamic parameters, the results indicate that the proposed MNSMs can endow the QZS vibration isolator with a lower resonant frequency, a wider isolation frequency range, and a smaller transmissibility. Additionally, it is also demonstrated that there is an inverse relationship between the complexity of the MNSM structure and the sensitivity of the isolation system.

Research on Air Gap Magnetic Field Characteristics of Trapezoidal Halbach Permanent Magnet Linear Synchronous Motor Based on Improved Equivalent Surface Current Method

Accurate analysis of the air gap magnetic field is the focus of research in the field of precision permanent magnet linear synchronous motors. In this paper, the two-dimensional air gap magnetic field of a secondary trapezoidal Halbach permanent magnet array coreless permanent magnet linear synchronous motor (PMLSM) was taken as our research object. On the basis of the equivalent surface current method, we proposed an improved equivalent analytical algorithm with a trapezoidal side length unit. The equivalent analytical model of the magnetic induction vector of the two-dimensional air gap was established, and the air gap magnetic field of the trapezoidal Halbach array coreless PMLSM was calculated. At the same time, we analyzed the influence of the bottom angle α of a trapezoidal permanent magnet equivalent width coefficient αw, pole height coefficient αh, and air gap height coefficient αg on the amplitude (Bpeak) and total harmonic distortion (THDB) of the central magnetic field in the air gap. The results show that α and αw have a significant influence on the Bpeak and THDB of the central magnetic field air gap. With the synergy of α and αw, we identified the “flux convergence” effect, which makes the maximum range of Bpeak α &gt; 90° and αw &lt; 0.5. We also found the “equilateral” effect, which causes the minimum region of THDB to change linearly. The calculation results of the improved equivalent surface current analytical model established in this paper agree with those verified by the finite element method. The calculation is convenient, and the accuracy of the result is high. This research provides a new method for analyzing the air gap magnetic field of a permanent magnet with a nonrectangular cross-section and lays a theoretical foundation for optimizing the PMLSM pole model.

Electromagnetic Design and Analysis of Permanent Magnet Linear Synchronous Motor

Since permanent magnet linear synchronous motors are widely used in fatigue testing, in this paper, the thrust of a permanent magnet linear synchronous motor (PMLSM) is amplified more than 10 times by the method of resonance. Firstly, the air gap magnetic field is analyzed by the equivalent magnetization current method (EMC), the electromagnetic thrust is calculated, and the expression is given by the Maxwell tensor method. The vibration analysis of the whole machine is used to obtain the conditions under which the motor resonates. The dynamic and static characteristics of the motor are analyzed through finite element simulation, the results of the motor design are judged to be reasonable, and the theoretical calculation results are compared with the simulation results to verify the accuracy of the theoretical calculation. The accuracy of the simulation results is verified by static force experiments. Finally, the rated thrust of the motor was enlarged more than 10 times by resonance experiments.

A Novel 3-D Mathematical Modeling Method on the Magnetic Field in Nutation Magnetic Gear

Accurate prediction of the magnetic field is an essential guideline for permanent magnetic gear design and optimization. The existing magnetic field calculation methods are divided into 2-D and 3-D calculation methods. For coaxial magnetic gears, the calculation of a 2-D magnetic field can be employed to meet the design requirements. However, as a new spatial transmission mechanism, nutation magnetic gear relies on a 3-D magnetic field to transmit force and torque. Therefore, the 2-D magnetic field cannot meet the design requirements. Hence, it is necessary to accurately predict the 3-D magnetic field. In this article, an analytical mathematical model of the 3-D magnetic field of magnetic gears is established. To verify the accuracy of the model, the magnetic field generated by the same magnetic gear is predicted by the proposed model, finite element method, and equivalent current method. The results indicate that the 3-D magnetic field mathematical model proposed in this article can accurately predict a 3-D magnetic field, which is an essential guide for the research and optimization of magnetic gears.

Study on radar scattering characteristics of double S-shaped nozzles with different aspect ratio

To study the radar scattering characteristics of dual S-bend nozzles with different exit aspect ratios, the iterative physical optic method (IPO) method and equivalent edge currents method (EEC) method were combined to build a code that can be used to solve the electromagnetic scattering field of the nozzle. The reliability of the method has been verified by comparing the reference data. Then, the forward and back-forward IPO and ray tracing methods are used to reduce the calculation time. CFD method is used to calculate and analyse the influence of aspect ratio double S-shaped nozzle on aerodynamic performance. The thrust coefficient and the total pressure recovery coefficient of the double S-shaped nozzle will gradually decrease with the increase of the aspect ratio. the influence of the aspect ratio on the radar scattering characteristics of the dual S-shaped nozzle under the C-band was simulated by the IPO and the results were discussed.it is obtained that the RCS average value in the range of −40°~40° gradually decreases with the increase of the aspect ratio. Under the vertical polarization mode of the pitch detection plane, the average RCS of the AR6 model is 52.8% lower than that of the AR3 model, while it is reduced by 11.0% in the horizontal polarization mode, which has better stealth performance.

Static magnetic field analysis of hollow-cup motor model and bow-shaped permanent magnet design

The hollow-cup Permanent Magnet (PM) motors have the characteristics of low power consumption, and are widely used in the aerospace field. At present, the tile-shaped PMs used by hollow-cup PM motors have poor sinusoidal characteristics of the air gap magnetic flux density waveform, which will cause torque ripple. The existing method for improving the air gap magnetic flux density waveform is not very effective when applied to hollow cup, a special motor with no stator core and large air gap. A bow-shaped PMs structure is designed for the hollow-cup motor in this paper. First, the equivalent surface current method is used to calculate the analytical formula of the static magnetic field of the model. Then, the Finite Element (FE) method is used to calculate the static air gap flux density waveform of conventional tile-shaped PMs and bow-shaped PMs with different bow heights, and the corresponding harmonics and sine distortion are obtained by Fourier decomposition. The simulation results show that the bow-shaped PMs can effectively improve the sinusoidal characteristics of the static air gap flux density waveform. And the suitable bow height is determined. Finally, a prototype is made based on the suitable bow height for experiments, and compared with the analytical result and the FE result, and the accuracy and effectiveness of the bow-shaped PMs with the suitable bow height are verified.

Fast Power Density Assessment of 5G Mobile Handset Using Equivalent Currents Method

As the fifth-generation (5G) mobile communication is utilizing millimeter-wave (mmWave) frequency bands, electromagnetic field (EMF) exposure emitted from a 5G mmWave mobile handset should be evaluated and compliant with the relevant EMF exposure limits in terms of peak spatial-average incident power density (PD). In this work, a fast PD assessment method for a 5G mmWave mobile handset using the equivalent current (EQC) method is proposed. The EQC method utilizes the intermediate-field (IF) data collected by a spherical measurement system to reconstruct the EQCs over a reconstruction surface and then computes the PD in close proximity of the mobile handset with acceptable accuracy. The performance of the proposed method is evaluated using a mmWave mobile handset mock-up equipped with four quasi-Yagi antennas. The assessed PD results are compared with those computed using full-wave simulations and also those measured with a planar near-field (NF) scanning system. In addition, three influencing factors related to the accuracy of the EQC method, namely, the angular resolution, the phase error, and the handset position in the IF measurements, are also analyzed. The proposed method is a good candidate for fast PD assessment of EMF exposure compliance testing in the mmWave frequency range.

Measurements as Enhancement of Numerical Simulation for Antenna Placement on a Rotocraft

EM antenna performances in large and complex scenarios are often evaluated by Computational Electromagnetics (CEM) solvers based on the Domain Decomposition Technique (DDT), in which the radiating antennas are studied separately and then antennas are integrated as radiating sources in the numerical simulation of the entire scenario [1]. Such approach based on only simulations is commonly practiced during designing process and in general when a measurement of entire system cannot be done. Recently, an approach has been presented that combines simulations and measurements by exploiting the potentialities of both tools [2]-[3]. Due to the conclusiveness and high reliability of actual measured data, antenna measurements can be used as accurate radiation sources in numerical simulations. The usage of measured data to characterize the radiators, as well as including more realistic antenna data in the simulations, also helps to overcome the limitation that a full wave model of the antenna (or electrical and mechanical design) is not available due to intellectual property issues or when measuring the entire scenario is not feasible. The measured sources are based on the expansion of the measured field using equivalent current method [4], [5] and then are compatible with different commercial CEM solvers. This paper presents a case study of how measurements can enhance numerical simulations for electrically large structures with particular attention to antenna placement on a rotorcraft model using measured source for the antenna.

An Iterative Hybrid JMCFIE-MSIE-PO Method for Analyzing EM Scattering From Complex Target Above Rough Surface

An iterative hybrid method is proposed for analyzing the electromagnetic (EM) scattering from complex target above rough surface. First, the electric/magnetic current-combined field integral equation (JMCFIE) is formulated to calculate the EM scattering from the complex target combining conductor and multiple dielectric objects. Then, the single integral equation (SIE) method for multiple dielectric objects in the complex target (MSIE) is applied to reduce one-half of the unknowns in dielectric regions, and the hybrid JMCFIE-MSIE method is formulated. Afterward, physical optics (PO) approximation is employed for computing the EM scattering on the rough surface, and the iterative hybrid based on the combination of JMCFIE-MSIE and PO is derived for composite scattering from complex target above rough surface. Furthermore, the multilevel fast multipole algorithm is utilized to accelerate the matrix-vector multiplications in the computation process. The equivalent edge currents method is applied to meliorate the result. Finally, the validation and applicability of the proposed iterative solution are demonstrated by several numerical examples.

Brewster effect of super‐low altitude target above terrestrial environments using modified facet‐based weighted four‐path model

A modified facet-based weighted four-path model is presented to analyze the Brewster effect of super-low altitude target above terrestrial environments. In this approach, the facet-based weighted four-path model (FWFPM) is established to simulate the mutual interactions between the super-low altitude target and terrestrial environment. Gauss antenna radiation pattern is introduced to modify the FWFPM. The hybrid PO-MEC method is applied, where the physical optics (PO) is utilized to calculate the scattering field from each facet, and the method of equivalent currents (MEC) is used to compute the scattering field from the edge structure. The validation of the proposed method is verified by the example of a super-low altitude missile model above a rough surface. The Brewster effect of a super-low altitude aircraft above diverse terrestrial environments is studied. Moreover, the influences of relative permittivity, the roughness of environment, and the target's height on Brewster angle have been analyzed in detail to provide some useful conclusions.

Use of “virtual” antenna array methods for reduction of DO A estimation systematic error caused by the scattering of waves on mobile carrier body

Article shows that “virtual” antenna arrays can be used to effectively improve the DOA estimation accuracy of mobile direction finders. “Virtual” antenna arrays are the samples of the spatial field distribution calculated by approximation of the field near a three-dimensional scattering body that supports physical (“real”) antenna system. Signals from the outputs of the “real” array are used as input data for the approximation process. Information on the geometry and material properties of the medium is not required. This procedure can be based on the main provisions of electrodynamics (Kirchhoff-Huygens principle, the Lorenz lemma, method of equivalent currents and fields) or on the use of quasi-static approximation of the field based on the apparatus of the theory of analytic functions of a complex variable (the Cauchy integral and Laurent series). “Virtual” arrays can reduce the error caused by the carrier body without costly and labour-intensive calibration procedures.

Improved design of Lorentz force-type magnetic bearings for magnetically suspended gimballing flywheels

A Lorentz force-type magnetic bearing (LFMB) with good linearity is suitable for the high-precision deflection control of a magnetically suspended gimballing flywheel (MSGFW). In this paper, a novel LFMB with improved double magnetic circuits is presented. Inclined magnetization Halbach array permanent magnets (PMs) and trapezoidal PMs are utilized for improving the magnetic flux density. A mathematical model of the magnetic flux density is established based on the equivalent surface current method. To obtain the maximum magnetic flux density, the optimal magnetization angle is calculated, and the dimension parameters are optimized by the sequential quadratic programming method. A maximum magnetic flux density of 0.615 T is obtained, which is 7.9% larger than that of an LFMB with conventional double magnetic circuits. Based on simulation results, LFMB prototype magnetic flux density experiments are carried out. The results show that the magnetic flux density fluctuations of the two LFMB schemes are similar. The maximum magnetic flux density of 0.608 T is increased by 6.7% when compared with that of the LFMB with conventional double magnetic circuits at 0.57 T. The error between the simulation and the experiment is within 5%. This indicates that the LFMB with improved double magnetic circuits is promising when it comes to meet the agile maneuver requirements of the spacecraft.

Design and Analysis of Dual‐Magnet BLDCM for Momentum Wheel

To obtain the larger output torque and the higher stability speed accuracy, a novel dual‐magnet brushless DC motor is proposed, and its structure is introduced. The mathematical model is established by the equivalent surface current method, and the magnetic circuit is analyzed by finite element method. The radial and tangential air gap magnetic flux densities of the dual‐magnet scheme are larger and less than that of the ironless stator and the Halbach array schemes, respectively. The theoretical calculation and simulation results are verified by prototype experiments. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A Field Equivalence between Physical Optics and GO-Based Equivalent Current Methods for Scattering from Circular Conducting Cylinders

A Field Equivalence between Physical Optics and GO-Based Equivalent Current Methods for Scattering from Circular Conducting Cylinders