Space Harmonics Research Articles

Optimized design of a fault-tolerant 12-slot/10-pole six-phase surface permanent magnet motor with asymmetrical winding configuration for electric vehicles

This paper presents a comprehensive methodology for optimizing the design of a 12-slot/10-pole permanent magnet (PM) motor with a six-phase winding configuration tailored for electric vehicles (EVs). The design aims to enhance motor performance under both healthy and fault conditions. While the single neutral configuration offers superior torque during faults, it also introduces zero sequence currents and additional space harmonics, which can lead to increased torque ripple that is difficult to control. This study addresses these challenges through innovative machine design optimization. The optimization process begins with sizing equations to establish an initial design. K-means clustering techniques are then employed to identify distinct loading points that accurately represent the full EV driving cycle, effectively minimizing computational power requirements. Following this, the Full Range Minimum Loss (FRML) strategy is applied to determine optimal current profiles across these loading points, significantly reducing copper losses. Finally, a multi-objective optimization approach is utilized to minimize torque ripple, enhance average torque, and optimize machine losses. The results demonstrate substantial improvements in torque and reduced ripple, validated through experiments conducted with a 2 kW lab-scale motor. This integrated approach not only ensures a robust and efficient motor design but also enhances fault tolerance, making it well-suited for advanced EV applications.

A composite microstrip line and leaky wave antenna structure with self-diplexing characteristic

A novel structure is proposed for the dual-band self-diplexing integration of microstrip line and leaky wave antenna (LWA). Through introducing a mode selective transmission line (MSTL) to the antenna, the autonomous transition between transmission modes at varying operating frequencies is thus achieved. At the high-frequency band, such proposed antenna in the quasi-TE10 mode, the periodic slots, and patches are used as LWA. Meanwhile, at the low-frequency band, the baseband signal with quasi-TEM mode can be transmitted effectively. These experimental results demonstrate that this design strategy benefits the realization of transmission with an insertion loss of less than 3 dB below 5.5 GHz. Furthermore, this antenna enables continuous beam scanning of −1 space harmonics from 10.5 to 15.5 GHz, with a beam direction sweeping from −75° to + 54°. This study innovatively employs MSTL structure to solve the problem of radio frequency (RF) and baseband links operating independently in traditional communication systems. It provides a promising solution for multi-functional integrated applications in future wireless communications.

Direct Torque Control of a Dual Star Induction Generator Based on a Modified Space Vector PWM Under Fault Conditions

Recent studies have shown that electrical systems in wind power conversion are subject to a 67% failure rate, and conventional three-phase generators are considered to be the most sensitive to these faults. Induction generator current harmonics are a major source of torque ripples causing acoustic noise and vibrations. These ripples can progressively increase under faulty operating conditions. In six-phase machines, there is appearance of high harmonic currents in the air gap as space harmonics. Power electronic converters are also subject to faults, the most common being Short-Circuit (SC) and Open-Circuit (OC) faults. SC faults cause large peaks in the line currents, which trigger the protection devices, resulting in a complete shutdown of the production system. OC faults, on the other hand, cause imbalances in the phases, but the system remains in operation.Direct Torque Control (DTC) based on Space Vector Modulation (SVM) at constant switching frequency is an effective solution to tackle induction generator current harmonics. This paper proposes a DTC combined with a Proportional Integral Fuzzy Logic Controller (PIFLC) optimized by Particle Swarm Optimization (PSO) in order to overcome the problems of torque ripples. Furthermore, using Vector Space Decomposition (VSD) and the Modified Space Vector Pulse Width Modulation (MSVPWM) strategy, a significant reduction of harmonics in the air-gap can be achieved.Simulations were carried out under MATLAB/Simulink, and the results obtained demonstrate the superiority of the proposed DTC-PIFLC-PSO controller in terms of robustness against wind speed variations and under faulty switch conditions in the power converter of the Dual Star Induction Generator (DSIG) generator. In addition, a comparative study with the classical PI controller is presented to show the effectiveness of the DTC-PIFLC-PSO controller against faults with a significant reduction in the Total Harmonic Distortion (THD) during both faulty and non-faulty conditions.

A triple 3-phase fault-tolerant fractional slot concentric winding interior permanent-magnet machine with low space harmonics

A triple 3-phase fault-tolerant fractional slot concentric winding interior permanent-magnet machine with low space harmonics

Advanced modeling and control of wind conversion systems based on hybrid generators using fractional order controllers

AbstractThe focus of this study is on modeling and management of a Wind Energy Conversion System (WECS) based on a Hybrid Excitation Synchronous Generator (HESG). Using a wind simulator, two controllers, CRONE and H∞, are evaluated for Maximum Power Point Tracking (MPPT) and optimal rotation speed. The results show the CRONE controller's higher tracking capability, and robustness tests investigate the influence of parametric uncertainty. Space harmonic effects, commutation effects, and turbine shaft flexibility are all addressed in the sophisticated models. The introduction of Fractional Order Proportional‐Integral (FOPI) control for MPPT is a game changer. Although fractional calculus‐based accuracy and robustness are uncommon in WECS, they show promise for emissions reduction and increased energy efficiency. This work validates a dependable control approach inside an isolated HESG‐based WECS's power‐maximizing range. Extensive investigation of the parameters impacting FOPI control efficiency yields useful insights for effective MPPT control. A variable‐speed wind turbine (WT) is linked to a HESG through a multiplier, with a controller controlling generator coil excitation voltages and a rectifier connecting the WECS to a load. A thorough 3 kW HESG electrical model that includes generator space harmonics and converter commutation effects is among the contributions. For HESG‐based WECS stability, frequency analysis finds important resonant and anti‐resonant frequencies. These issues are addressed by a FOPI control technique, which ensures system stability and performance. The necessity of exact frequency analysis in HESG‐based WECS is highlighted by a step‐by‐step controller parameter tuning approach.

Design and Comparative Analysis of Axial Flux Permanent Magnet Vernier Motors

This paper analytically investigates both the air gap flux density and the generated power of an Axial Flux Permanent Magnet Vernier Motor (AFPMVM). The AFPMVM has the same operational principle as a magnetic gear. It operates using space harmonics of the air gap flux density due to the magneto-motive force (MMF) and air gap permeance. This paper also examines the effect of various combinations of the rotor magnet pole pairs, stator slots, and winding pole numbers on the power factor and power density using the 3-D finite element method (3D-FEM). It is observed that, although having a higher pole ratio results in low cogging torque and high power density, it makes the machine length longer and has a lower power factor. Therefore, by employing the high pole ratios, the main advantage of the axial flux machines, i.e. having a shorter length, is sacrificed.

Space Harmonics Effects on Performances of Linear Induction Motors: Modelization and Characterization

This article presents the impact analysis of space harmonics’ presence on a single-sided three-phase linear induction motor, along with a comprehensive parametric investigation. The presence of space harmonics often reduces the linear induction motor’s performance. The electromagnetic phenomena are governed by Maxwell’s equations. The chosen mathematical model uses a 2D formulation with magnetic vector potential. The model implementation is performed using the finite element method on the free Gmsh-GetDP platform. The electromagnetic thrust is calculated in the current excitation case using two numerical models of the finite element method with and without term-generating space harmonics in order to highlight their effect. The adaptation to voltage supply operation is obtained via equivalent electric circuits through the calculation of the operational impedance. The choice of the machine’s parameters by the designer in order to enhance its performance or reduce energy consumption is a difficult task. The analysis and the determination of the dependence of the parameters and the performance are necessary. The main objectives of this study are to determine this dependency and to analyze the space harmonic impact of the linear induction motor’s parameters on its performances. A comparative exploration of space harmonics’ presence using two numerical models (single and multiharmonics) and an assessment of the parametric effect of space harmonics’ presence on various machine characteristics such as thrust, efficiency, and power factor have been carried out. The motor’s characteristics (i.e., thrust, efficiency, and power factor) strongly depend on parameters such as the pole pair number and conductivity. Improving the operation and maximizing the performance of such a machine for a given specification requires the use of optimization algorithms. Motor characteristics (thrust, efficiency, and power factor) are highly dependent on parameters such as the number of pole pairs and conductivity.

An Endfire Periodic Leaky Wave Antenna With Wideband and High-Gain Capability by Manipulating Its Higher-Order Space Harmonics

An Endfire Periodic Leaky Wave Antenna With Wideband and High-Gain Capability by Manipulating Its Higher-Order Space Harmonics

Clustering Optimization of IPMSM for Electric Vehicles: Considering Inverter Control Strategy

The actual performance of driving motors in the electric vehicle (EV) powertrain depends not only on the electromagnetic design of the motor itself but also on the driving condition of the vehicle. The traditional motor optimization method at the rated point is difficult to deal with because of the mismatch between its high-efficiency area and the actual operation area. This paper systematically proposes an optimal design method for driving motors for EVs, considering the driving conditions and control strategy to improve motor efficiency and passengers’ riding comfort. It uses cluster analysis to identify representative points and related energy weights to consider motors’ comprehensive performance in different driving cycles. Three typical operation conditions are selected to implement the proposed optimization process. In the design process, by using the sensitivity analysis method, the significance of the structural parameters is effectively evaluated. Moreover, the semianalytical efficiency model and torque model of permanent magnet driving motors based on finite element analysis results are deduced to consider the influence of magnetic saturation, space harmonics, and cross-coupling between d-axis and q-axis magnetic fields. Based on the driving system demands of an A0 class pure EV, the whole optimization design is divided into four steps and three scales, including the motor scale, control scale, and system scale. By using the multi-objective optimization method, Pareto optimality of motor efficiency and torque ripple is achieved under the city driving cycle and highway driving cycle. Compared to the optimization only at the rated condition, the proportion of motor sweet region increased about 1.25 times and 3.5 times by the proposed system-scale optimization under two driving cycles, respectively. Finally, the effectiveness of the proposed optimization method is verified by the prototype experiments.

High-Scanning-Rate and Wide-Scanning-Angle Leaky-Wave Antenna Based on Double-Layer Slow-Wave Structure

In this letter, a leaky-wave antenna (LWA) based on double-layer (DL) slow-wave structure, possessing high scanning rate and wide scanning angle features is investigated. The DL unit structure consists of a top layer structure with cross-shaped unit and a bottom layer structure with slot-shaped unit. The DL units realize the property of controlling the cut-off frequency and slope of dispersion curves independently by independently changing the unit slow-wave property of top and bottom layers. The radiation of LWA is achieved by triangularly modulating the cross-shaped units of top layer. Due to the existence of the slot-shaped units of bottom layer, strong slow-wave property is introduced to increase the growth rate of period phase shift, thus achieving high scanning rate. Meanwhile, the n = −2 space harmonic (SH) of the LWA is separated from the fast-wave region of n = −1 SH, thus enlarging scanning angle in forward quadrant. A prototype of the proposed LWA is fabricated and measured. The LWA can achieve a wide scanning angle from −68 ° to +74 ° in a narrow frequency band of 9 to 10.75 GHz.

Tunable Multibeam Periodic Leaky-Wave Antenna Based on Radiation of Multiple Space Harmonics

This letter proposes a tunable multi-beam periodic leaky-wave antenna (LWA) based on radiation of multiple space harmonics. The LWA is composed of a microstrip transmission line and a set of stubs. When the main transmission line is loaded with one / two / multiple groups of periodic stubs, one / two / multiple <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n = - 1$</tex-math></inline-formula> space harmonics that are in the radiation region can be obtained, which are superpositioned to generate one / two / multiple beams. By adjusting the connections between the stubs and the line with switch diodes, the number of beams and the radiation directions can be reconfigured at a fixed frequency. The working mechanism of the tunable multi-beam antenna is investigated. A prototype of tunable dual-beam LWA is fabricated and measured. The measurement results show that two beams can be generated and can be reconfigured independently at a fixed frequency, with maximum gains of 7.93 dBi and 5.48 dBi, respectively.

Robust Control for Torque Minimization in Wind Hybrid Generators: An H∞ Approach

This study focuses on implementing a wind turbine emulator based on a permanent magnet synchronous machine with excitation auxiliary windings and thoroughly investigates the space harmonics created by this innovative topology in MATLAB/Simulink. A Hybrid Generator (HG) is a robust generator that does not have slip rings or brushes in its structure. Furthermore, the flux of the hybrid generator HG may be easily adjusted as it is created by direct current excitation coils and permanent magnets. Unfortunately, the space harmonic rate in the HG is relatively high. In other words, the mechanical vibrations caused by the electromagnetic torque ripple threaten the drive train’s behaviour and, ultimately, the wind turbine’s lifespan. This study describes two methods for decreasing the ripple in electromagnetic torque. Both circuit architecture and robust H∞ control techniques are considered. After simulating the two approaches, a list of requirements is provided for the maximum allowable amplitude of the inductance and the flux harmonics.

Saturation-Induced Variable-Flux Characteristics in a 12-Slot 10-Pole Concentrated Winding Permanent-Magnet Motor

This paper proposes a stator core design to achieve variable-flux characteristics enhanced by magnetic saturation in fractional-slot concentrated winding (FSCW) permanent-magnet (PM) motors without additional excitation systems, complicated structures, or active controls. Magnetic saturation induced at suitable locations can enhance variable-flux characteristics because the PM flux linkage is variable with the magnetic saturation in cores. In distributed winding configurations, magnetic saturation is induced symmetrically for each rotor pole by the fundamental that is dominant in the spatial distribution of the air-gap flux density. The magnetic saturation at each rotor pole can enhance variable-flux characteristics. In FSCW configurations, magnetic saturation is not induced symmetrically for each rotor pole because of several dominant space harmonics. The magnetic saturation at several rotor poles cannot enhance variable-flux characteristics. In the proposed design, the stator core has thin tooth tips for inducing magnetic saturation. The magnetic saturation in the stator core achieves the variable-flux characteristics that are effective for expanding the operating region or decreasing electromotive force and increasing torque. The efficacy of the proposed design is determined by estimating motor performance through a finite element method analysis and demonstrating the actual motor performance of a prototype.

Modal Projection for Quasi-Homogeneous Anisotropic Turbulence

This article, or essay, addresses the anisotropic structure and the dynamics of quasi-homogeneous, incompressible turbulence. Modal projection and expansions in terms of spherical harmonics in three-dimensional Fourier space are in line with a seminal study by Jack Herring, around the so-called Craya–Herring frame of reference, with a large review of the related approaches to date. The research part is focused on structure and dynamics of rotating sheared turbulence, including a description of both directional and polarization anisotropy with a minimal number of modes. Effort is made to generalize expansions in terms of scalar spherical harmonics (SSHs) to vector spherical harmonics (VSHs). Looking at stochastic fields, for possibly intermittent vector fields, some directions are explored to reconcile modal projection, firstly used for smooth vector fields, and multifractal approaches for internal intermittency but far beyond scalar correlations, such as structure functions. In order to illustrate turbulence from Earth to planets, stars, and galaxies, applications to geophysics and astrophysics are touched upon, with generalization to coupled vector fields (for kinetic, magnetic, and potential energies), possibly dominated by waves (Coriolis, gravity, and Alfvén).

Miniaturized Metamaterial-Inspired Travelling Wave Tube for S Band

A miniaturized traveling wave tube (TWT) was studied by proposing a novel metamaterial (MTM) slow wave structure (SWS). The dispersion results show that n = −1 space harmonic of the fundamental mode exhibits the “forward” wave properties, which is the foundation of the MTM-inspired TWT. Meanwhile, the interaction impedance for mode 2 of the novel MTM SWS can be sharply decreased by introducing four blend edges to weaken the corresponding longitudinal electric field. Also, two coaxial couplers are presented to input/output the signals. The transmission results show that the reflection is as low as −15 dB from 2.90 GHz to 3 GHz, which ensures the amplified signal can be effectively outputted. The MTM-inspired TWT exhibits miniaturized superiority for its compact high frequency structure including the MTM SWS and the coaxial couplers. Especially, for the high-frequency structure, the transverse and longitudinal sizes are ~λ/5 and ~3λ, respectively (λ is the free-space wavelength at the operating frequencies). The simulation of the beam wave interaction shows that the proposed MTM-inspired TWT yields output powers of kW levels from 2.90 GHz to 3 GHz, with a gain of 23.5–25.8 dB and electronic efficiency of 14–22% when the beam current is 0.5 A and the beam voltage is 13 kV. The results indicate that the gain per wavelength is as high as 8.5 dB in the operating bands. The simulation results confirm that it is possible to weaken the backward wave oscillation from the higher mode in the miniaturized MTM-inspired TWT.

Wide-Angle Beam-Scanning Leaky-Wave Antenna Array Based on Hole Array SSPPs

In this letter, a leaky-wave antenna (LWA) array based on hole array spoof surface plasmon polaritons (SSPPs) is proposed, which can realize wide frequency beam scanning angle. By etching periodic hole arrays on the upper metal of the defective ground structure, the SSPP structure is formed and the frequency scanning beam is generated by using its higher-order radiation mode characteristics. The radiation mechanisms of the design are explained by using the dispersion relationship, electric field distributions, and space harmonics. The LWA array is fed by a 1 to 4 power divider and achieves good impedance matching within 6-16 GHz bandwidth. The average peak gain value of the proposed LWA antenna array is about 16.86 dBi and the frequency beam scanning range is 91°. The antenna array has the characteristics of easy fabrication, low cost, and high gain performance, which provides a new design concept for wide-scanning-angle LWA Array and can meet the demand of high gain requirements in radar and other related fields.

Design of a Modular In-Wheel Motor With High Fault-Tolerant Performance and Low MMF Space Harmonic

In-wheel motors, as the core power component of electric vehicles, not only require high power density, but also high reliability and fault-tolerant (FT) capability. This paper proposes a modular permanent magnet (PM) in-wheel motor, and design to receive the high FT performance and low MMF space harmonic. First, according to the working mechanism and main faulty types of the modular FT motor, the corresponding FT control strategies are given, and the slot-pole combination with high FT performance for the modular motor is developed. Second, the electromagnetic characteristics of the modular in-wheel motor are investigated. The relationship between the FT performance and the inductance parameters is linked through the magnetic coupling coefficient. The design requirement for the inductance of this kind of motors is proposed. Third, the torque performance of the motor is studied, and the factors affecting torque performance during fault and FT operations are revealed. Finally, a prototype with slot-pole combination of 24S16P and four modules is produced, and the electromagnetic characteristics of the motor under FT operations are verified by experiments.

Estimation of Stator Vibration in DFIM Under Various Types of Rotor Excitation

Variable speed power generation using Doubly Fed Induction Machine requires an adjustable frequency supply at the rotor terminals which can be achieved using power converters. Ideally, a variable frequency sinusoidal voltage should be applied, but it is not possible without the help of power converters. For a typical 250 MW DFIM with a speed variation of -10.73% to +8.33%, excitation power of 25 MW at 3.3kV and 11600 Amps is required. With this much high rotor current at low fundamental rotor frequency (3.75 Hz) electromagnetic forces in the air gap contain harmonic force components. Also, any time harmonic of radial force density in the rotor will be induced in the stator as a distinct time harmonic, modified by the influence of space harmonics in DFIM with regular three phase integral slot winding on both stator and rotor and vice versa. So, if the frequency and order of electromagnetic force components conflicts with mode shape and natural frequencies of the machine stator strong magnification in vibration will occur or more severely develops mechanical resonance. The stator vibration of electrical machine is generated by the electromagnetic forces acting on the surface of the stator tooths. This paper analyzes stator vibration for 250 MW DFIM in multiphysics simulation with its rotor winding excited through pure sinusoidal excitation at fundamental rotor frequency of 3.75 Hz and with two-Level voltage source converter at 3.75 Hz fundamental rotor frequency. Hardware results with supported multiphysics simulation on a laboratory prototype of 2.2 kW rating DFIM.

Torque Ripple Generation Mechanism of Induction Motors by Time and Space Harmonic Fields

In this article, we investigate the generation mechanism of torque ripples in induction motors by using theoretical expression of torque ripples and finite element analysis, to obtain useful information of motor designs. By analyzing the time and space harmonics included in the air-gap flux densities, it is revealed that the torque ripple generation mechanism of induction motors is quite different from that of synchronous motors. The proper stator/rotor slot combinations to reduce the torque ripple is also clarified.

Insert Misalignment Studies of a Coaxial-Cavity Gyrotron—Full-Wave Approach

Insert misalignment studies are carried out for a coaxial-cavity gyrotron with triangular corrugations on the insert wall using the full-wave approach, space harmonics method (SHM). By applying electromagnetic boundary conditions, dispersion relation is derived for a coaxial-cavity with misaligned insert. Misalignment of the insert caused by axial displacement as well as tilting of the insert axis from the outer resonator axis are taken into consideration in the study. As the electromagnetic fields in the interaction space vary with the insert misalignment, due to this the mathematical formulations of the beam-coupling coefficient, wall losses, RF interaction efficiency, and output power are modified. For a 2-MW, 220-GHz gyrotron, the insert misalignment studies are carried out using the proposed full-wave model with the help of our in-house code Gyrotron Design Suite. For validation, the results obtained using the SHM approach are compared with that of the surface impedance model (SIM) approach. In addition, comparison studies between SIM and SHM approaches are performed for the practically developed 170-GHz, 2-MW coaxial-cavity gyrotron with both triangular and rectangular corrugations in the insert.