Harmonic Flux Research Articles

Analysis of alternating flux density harmonics inside the rotor of a 1 MW high-speed interior permanent magnet synchronous machine used for flywheel energy storage systems

With the popularization of renewable distributed energy generation in the power grid, flywheel energy storage systems (FESS) with fast response and high power density are gradually becoming popular for achieving fast frequency modulation. Generally, the rotor of high-speed permanent magnet synchronous machine (HSPMSM) used for FESS rotates in a vacuum to reduce air friction loss, which concurrently makes it difficult to dissipate heat in the rotor. For reducing rotor iron loss and preventing demagnetization of the PM due to high temperature, effective measures need to be applied. In this study, a 1 MW 10,500 r/min high-speed interior PMSM (HSIPMSM) is proposed for an FESS. As rotor iron loss is caused by alternating flux density harmonics (FDH) inside the rotor, the causes and characteristics of alternating FDHs are analyzed. Then, the finite element analysis (FEA) is combined with two-dimensional fast Fourier transform (2D-FFT) to obtain the alternating frequencies and amplitude variation trends of alternating FDHs in the designed rotor. The analytical results indicate that the amplitudes of alternating FDHs on the PM surface are effectively reduced due to bypass of the rotor core at the outside of the PM to alternating FDHs, which helps to restrain the rotor iron loss from the source. This provides a design idea for mitigating the high temperature of high-power high-speed PM rotors.

Finite Control Set Model Predictive Field-Oriented Control For Three-Phase Induction Motor Drives

Field-oriented control is one of the well-established vector control strategies for induction motor drives. However, its cascaded structure and requirement of a modulator for constant switching frequency operations makes it complex and computationally expensive. Model predictive control (MPC) is a novel control strategy used for AC motor drives. In this paper, a finite control set model predictive control (FCS-MPC) based field-oriented control (FOC) is presented. The Finite control set model predictive field-oriented control (FCS-MPFOC) utilizes a cost function that quantifies the error between the reference and anticipated current values for all the potential voltage vectors of the voltage source inverter. The voltage vector that generates the lowest value of the cost function is directly implemented on the inverter to produce the drive voltage. The efficiency of the proposed method is authenticated by using a three-phase induction motor, fed via a two-level three-phase voltage source inverter in the MATLAB/Simulink environment under various speeds, load torque, and model parameter mismatch situations. In order to authenticate the performance of the proposed strategy, it is compared with traditional model predictive torque control. Simulation results show that the proposed method performed significantly well in total current harmonic distortion, flux and torque ripples, switching frequency, and parameter variations.

PMSM Torque Ripple Minimization Based on Novel Low Carrier Ratio PWM Technique

Harmonic injection is commonly used in permanent magnet synchronous motor torque ripple minimization (TRM) of electric vehicle. Traditional inverter switching frequency limits TRM application at high speed due to harmonic modulation accuracy and inverter loss. To achieve TRM in the whole speed range and reduce inverter loss, a novel online calculated low carrier ratio pulsewidth modulation (LCRPWM) is proposed in this article. The carrier ratio determining regular according to the injected harmonics is established first. The relationship between injected harmonics and LCRPWM switching angle is revealed and a set of nonlinear equations is established. Thus, the problem is transformed from solving nonlinear equations into optimization by establishing a cost function. The analytical solutions of nonlinear equations are obtained, which avoids iterative operation and plunging into local minimum. Therefore, the switch angle solution method is suitable for online calculation. The LCRPWM is verified in simulation compared with the traditional regularly sampled space vector PWM, which achieves better results in voltage harmonic injection and flux tracking at a much lower switching frequency. At last, the LCRPWM is used in a test bench experiment that shows good TRM effects. The influence of sideband harmonics on torque ripple is analyzed.

Modeling of Magnetic Fields in Deformed Air Gaps of Salient Pole Synchronous Machines

Large low-speed drives are designed with a high number of pole pairs, annular and magnetically saturated at rated operation. Large bore diameters tend to unwanted deformations of circular air gap (AG) circumference due to magnetic forces or gravitational forces. The electromagnetic computation with changing geometrical conditions therefore poses a cumbersome non-linear field problem due to its high amount of degrees of freedom. For an accurate predictive model of machine acoustics and vibrations, the study of these topological impacts on the magnetic AG field is indispensable. Particularly when considering an arbitrary AG deformation, related to additional spatial flux harmonics, the computational chain of the finite element method (FEM) involves adaptations at each stage (pre- and post-processing). The proposed modeling approach is universal and reduces the computational effort significantly using finite element (FE) solutions of symmetrical machine parts with varying AG widths. 2-D FE simulations are performed to study the impact of deformations. The results of the approach are compared with FE solutions of a complete 2-D model with an exemplary deformation for validation. The aim of this work is to study both magnetic AG fields and forces efficiently in an exemplary high-pole wind turbine generator with a deformed AG topology by interpolating and assembling appropriately partial model solutions.

A New Spoke PM Motor with ECC ASPs to Reduce Flux Density Harmonics

This paper proposes new eccentric (ECC) auxiliary salient poles (ASPs) applied in spoke permanent-magnet (PM) motors. These ECC ASPs optimize flux density harmonics and further reduce torque pulsation. Then, the optimization procedure is proposed to reveal the relationship between the ECC method and ASP, and optimization steps are reduced. Firstly, the design of the ECC ASPs is based on the stairs, which are equivalent to sinusoidal flux density. Second, the expressions of offset length for maximum air gap, pole arc angle, and thickness ratio are revealed. Through theoretical analysis and the finite element method (FEM), the proposed ECC ASPs can generate low torque pulsation and improve sound and vibration features.

Intense isolated attosecond pulses from two-color few-cycle laser driven relativistic surface plasma

Ultrafast plasma dynamics play a pivotal role in the relativistic high harmonic generation, a phenomenon that can give rise to intense light fields of attosecond duration. Controlling such plasma dynamics holds key to optimize the relevant sub-cycle processes in the high-intensity regime. Here, we demonstrate that the optimal coherent combination of two intense ultrashort pulses centered at two-colors (fundamental frequency, omega and second harmonic, 2omega) can lead to an optimal shape in relativistic intensity driver field that yields such an extraordinarily sensitive control. Conducting a series of two-dimensional (2D) relativistic particle-in-cell (PIC) simulations carried out for currently achievable laser parameters and realistic experimental conditions, we demonstrate that an appropriate combination of omega -2omega along with a precise delay control can lead to more than three times enhancement in the resulting high harmonic flux. Finally, the two-color multi-cycle field synthesized with appropriate delay and polarization can all-optically suppress several attosecond bursts while favourably allowing one burst to occur, leading to the generation of intense isolated attosecond pulses without the need of any sophisticated gating techniques.

Magnet Eddy Current Loss and Thermal Analysis of a Dual-Permanent-Magnet-Excited Machines

This article investigates the eddy current loss mechanism of a dual-permanent-magnet-excited machines (DPMM). Based on the flux modulation effect, abundant harmonics are induced in the air gap of DPMM. The harmonics of air-gap flux density due to rotor permanent magnets (PMs), stator PMs, and armature reaction are investigated qualitatively and separately. Then, the orders, frequency, and rotation speed of the harmonics are deduced theoretically. The harmonics that contribute to the eddy current losses are deduced accordingly. Finally, the loss distribution of the proposed DPMM is estimated through simulation and the thermal field of the proposed motor is analyzed. A prototype is fabricated to validate the analysis. Temperature rise of both stator and rotor PMs under rated load condition is measured through experiment.

Common-Mode Voltage Mitigation of Dual T-Type Inverter Drives Using Fast MPC Approach

This article proposes an intensive study for common-mode voltage (CMV) elimination/reduction in a five-level dual T-type multilevel converter (MLC) drive. An advanced and fast model predictive control (MPC) approach is developed for CMV reduction (CMVR) and CMV elimination based on the preselection of the switching states (SS). In addition, the proposed approach considers the torque control and the capacitor balancing of the proposed drive as essential aspects of MLC drives. A detailed study of the impact of the converter SS on the CMV is presented. The main features of the proposed MPC approach are reducing the complexity of the cost-function, the tuning burden of the weighting factors, and the computation time by more than 80% compared to conventional MPC techniques. A hardware implementation based on Silicon Carbide T-type MLC is built. The experimental results demonstrate the effectiveness of the proposed MPC approach to mitigate/eliminate the CMV along with achieving the torque command and balancing the dc-link capacitors. Unlike conventional CMVR techniques, the proposed approach reduces the CMV by 75% of its normal values without jeopardizing the harmonic contents, drive efficiency, and flux as well as torque ripples.

Analysis and Reduction Methods of Cogging Torque in Dual PM Vernier Machines With Unevenly Distributed Split Teeth

This article investigates the source and reduction methods of cogging torque in dual PM Vernier machines (DPVMs), especially for the ones with unevenly distributed split teeth (UDST). At first, the increase of no-load back electromotive force in DPVMs with UDST is illustrated through the analysis of airgap working flux harmonics. The reason for largely increased cogging torque of DPVMs with UDST is then analyzed, and main flux harmonics that contribute to cogging torque are identified. To reduce cogging torque and torque ripple, several effective methods are introduced in this article, which are mainly based on the reduction or offset of corresponding airgap flux harmonics. The cogging torque reduction effects and torque performances of these methods are compared. Among them, newly proposed N/S-parts offset method is proved to be superior to other methods in DPVMs. A new DPVM prototype with UDST and N/S-parts offset structure is built and tested. Experimental results show that through the N/S-parts offset method, cogging torque of the machine is largely decreased from 9 to 0.3 N·m, which validates the analysis and simulation results.

A Flux−Linkage Torque Ripple Suppression Method of Dual−Series FPMSMs Decoupling Control Based on Dual−Frequency Vector Modulation

A novel cross−series connection of two five−phase permanent magnet synchronous motors (FPMSM) supplied by single inverter can halve the number of required power units and current sensors. This, along with a decoupling control strategy for FPMSMs in series based on an improved dual−frequency vector modulation (DFV−SVPWM) and a flux−linkage torque ripple suppression method with current compensation are proposed in this paper, each of which have great significance for multi−unit industrial equipment. The third harmonic flux−linkage will produce torque ripple in the FPMSM in series, which has an adverse effect on accuracy. In this paper, a synchronous decoupling mathematical model of dual−series FPMSM with harmonic flux−linkage is established to analyze the decoupling relationship between torque and current. In addition, an enhanced DFV−SVPWM with higher modulation ratio is proposed for the decoupling control of double motors in series. Furthermore, based on the torque influence of two series−connected motors by harmonic flux−linkage and the decoupling control with improved DFV−SVPWM, a torque ripple compensation method with current compensation is proposed, which can effectively suppress the torque ripple of FPMSM with harmonic flux−linkage and not affect the other. The correctness and superiority of the scheme are verified by simulation and experiment in this paper.

Design and Optimization of a High-Torque-Density Low-Torque-Ripple Vernier Machine Using Ferrite Magnets for Direct-Drive Applications

In recent years, Vernier permanent magnet machines (VPMs) have gained much interest in academia. However, due to the large leakage flux, the power factor of Vernier machines is too low to be applied in real industry. In this article, a novel split-tooth, concentrated-winding Vernier machine using ferrite magnets is proposed for high-torque, low-speed direct-drive applications in home appliance industry. It uses consequent-pole magnets in the rotor, as well as additional assisted magnets in the stator teeth, in order to reduce the leakage flux and boost the torque density. A systematic way of reducing the torque ripple from 40% to 4% is proposed by carefully choosing the right combination of stator/rotor pole-pair numbers. A comprehensive design optimization is conducted to achieve the optimal performance. Finally, the ac loading is carefully reduced to meet the torque, saturation, power factor and space requirements. The test results of a prototyped machine show that the proposed design can achieve 34% more torque and 20% less loss with a reasonable power factor of 0.63, compared with an optimized PM synchronous machine under the same volume. It is found that the significant torque boost is attributed to the multiple working harmonics of the air-gap flux density.

Investigation of the electromagnetic characteristics and operating performance of a bidirectional PM excited machine

This paper presents a study of bidirectional permanent magnet excited machine (BPMEM) based on the study of field-modulation permanent magnetic gear machine (FPGM). The BPMEM structure includes the installation of consequent-pole permanent magnets (PMs) on both the stator and rotor sides of the FPGM so that the stator and rotor can be bidirectionally excited to increase the working airgap flux density amplitude, reduce the flux leakage between poles, and increase the torque density. Therefore, the paper first analysis the influence of different airgap structures and PM arrangements on the airgap flux density and studies the winding slot–pole combination and the resulting working flux density harmonics to analyse the electromagnetic torque generation mechanism. By using the finite element analysis (FEA), the quantitative analysis and comparison of the FPGM, slot-wedge-less FPGM (SWL-FPGM), consequent-pole FPGM (CP-FPGM) and BPMEM verify the superiority of BPMEM in improving electromagnetic torque. In addition, the paper also studies the key performance of BPMEM’s overload capacity, power factor and flux-weakening capability. Finally, no-load and independent load experiments are carried out on the FPGM prototype to verify the correctness of the FEA model and analysis method of the machine in this paper.

Analysis of the operation principle for tubular flux-switching permanent magnet linear machine

PurposeThis study aims to unveil the generation mechanism of the thrust force in a tubular flux-switching permanent magnet (PM) linear (TFSPML) machine; the operation principle of the TFSPML machine is analyzed.Design/methodology/approachFirst, the air-gap flux density harmonic characteristics excited by PMs and armature windings are investigated and summarized based on a simple magnetomotive force (MMF)-permeance model. Then, the air-gap field modulation theory is applied in analyzing the air-gap flux density harmonics that contribute to the electromagnetic force. In addition, a simple method for separating the end force of the TFSPML machine is proposed, which is a significant foundation for the comprehensive analysis of this type of machine. As a result, the operation principle of the TFSPML machine is thoroughly revealed.FindingsThe analysis shows that the average electromagnetic force is mainly contributed by the air-gap dominant harmonics, and the thrust force ripple is mainly caused by the end force.Originality/valueIn this paper, the operation principle of the TFSPML machine is analyzed from the perspective of air-gap field modulation.

On-Line Detection of Demagnetization for Permanent Magnet Synchronous Motor via Flux Observer

Demagnetization in permanent magnet synchronous motor (PMSM), caused by high temperature or inverse magnetic field, may increase loss and torque ripple, and even degrade the system stability in severe cases. On-line detection can identify the incipient demagnetization of permanent magnets (PMs), as well as providing reference for subsequent fault-tolerant control, so as to avoid further demagnetization. Therefore, an on-line demagnetization detection method is proposed in this paper by using flux observer. First, an observer is established in the three-phase stationary reference frame by taking the stator currents and the amplitudes of the fundamental and harmonic components of flux as state variables. Then, three demagnetization indexes are presented to evaluate the properties of PMs based on the observed flux information. The proposed method can directly track the amplitude of harmonic flux and evaluate the severity of the demagnetization more comprehensively. Simulation and experimental results demonstrate the effectiveness of the proposed method.

Effect of Pole Shaping on Torque Characteristics of Consequent Pole PM Machines

Consequent pole (CP) permanent magnet (PM) machines offer scope for reducing the quantity of PM material and hence cost compared to more conventional PM machine topologies of the same rating. In this type of machine, the rotor pole arc is usually optimized to realize the largest output torque with pole shaping methods used to reduce torque ripple. However, such approaches tend to be limited by constraints imposed on the pole shapes. It is a common practice to adopt similar PM and iron pole shapes, an approach that does not fully account for the different characteristics of PM and iron poles in CPPM machines, often leading to large even order harmonics in the airgap flux density. This article proposes a shaping method with a variable rotor profile and pole arc span being established by means of optimization by Genetic Algorithm. It is demonstrated that for a fixed quantity of PM material, different PM and iron pole shapes in combination with optimal PM and iron pole arc spans are essential for ensuring both maximum output torque and lower torque ripple when the due account is taken of flux leakage. It also demonstrates that since the flux density in the region under a PM pole is governed by the magnetic potential produced by magnets while it is governed by magnetic reluctance under iron pole, different PM pole and iron pole shapes are necessary to reduce the even-order harmonics in a CPPM machine and consequently to reduce torque ripple. The performances of optimized and more conventional CP machines are compared by finite-element method on 12-slot/8-pole prototype motors.

Design and Optimization of the Low-Frequency Metasurface Shield for Wireless Power Transfer System

This article presents an optimized kilohertz (kHz) shielding metasurface (MTS) for wireless power transfer (WPT) system. Recently, the working frequencies of reported MTSs are concentrated in the megahertz range, which limits its application in low-frequency WPT system. Accordingly, the model of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times 3$ </tex-math></inline-formula> matrix MTS shield (M-MTSS) with resonance frequencies of 65 and 190 kHz is proposed to eliminate the influence of fundamental (85 kHz) and harmonic (255 kHz) leakage magnetic flux density on the human body, respectively. A circuit model is established to consider all coupling of the system structure. Meanwhile, an exhaustive fitting analysis is carried out on the electromagnetic parameters of the application model. The winding of the M-MTSS is optimized to achieve a tradeoff between the efficiency and the magnetic field. Moreover, the calculated magnetic flux density distribution and the principle of the M-MTSS are illustrated. Finally, a test platform is set up to evaluate the performance of suppressing the emission of magnetic flux density. The experimental results showed that the magnetic flux of the fundamental and harmonic is reduced in the entire plane. These results verify the feasibility of the proposed method.

Design, Analysis, and Optimization of Permanent Magnet Vernier Machines Considering Rotor Losses

The purpose of this paper is the design, analysis, and optimization of a new structure of a permanent magnet vernier machine (PMVM) with a high torque density and low rotor losses. First, the modulation principle and topology of this PMVM is introduced. Then, its average torque and rotor loss are enhanced and reduced by optimizing the flux modulation poles distribution. For the sake of further reducing the rotor losses on the premise of maintaining the torque density, the contribution of the air gap flux density harmonics to the rotor loss is analyzed. Then, a new topological structure of a rotor with a flux barrier is introduced to reduce the rotor losses due to the decrease of each harmful harmonic. Through the analysis of the structure of the PMVM with the flux barrier, the influence of the parameters on the performance is built. After that, a multi-objective optimization algorithm is used to optimize the PMVM so as to obtain the optimal performance. Moreover, the electromagnetic performance comparison between the newly proposed machine and the original one is presented to indicate that lower rotor losses can be obtained by the proposed machine when the torque is ensured. Finally, a prototype of proposed PMVM is built and further tested to verify the validities of the theoretical and finite-element analyses.

Calculation of Magnetic Flux Density Harmonics in the Vicinity of Overhead Lines

This paper considers the method for the calculation of magnetic flux density in the vicinity of overhead distribution lines which takes into account the higher current harmonics. This method is based on the Biot–Savart law and the complex image method. The considered method calculates the values of the magnetic flux density for each harmonic component of the current separately at all points of interest (usually lateral profile). In this way, it is possible to determine the contributions of individual harmonic components of the current intensity to the total value of magnetic flux density. Based on the contributions of individual harmonic components, the total (resultant) value of the magnetic flux density at points of interest is determined. Validation of the computational method is carried out by comparison of the results obtained by the considered calculation method with measurement results. Furthermore, the application of the calculation method was demonstrated by calculating magnetic flux density harmonics in the vicinity of two overhead distribution lines of typical phase conductor arrangements.

Sub-50 fs pulses at 2050 nm from a picosecond Ho:YLF laser using a two-stage Kagome-fiber-based compressor

The high-energy few-cycle mid-infrared laser pulse beyond 2 μm is of immense importance for attosecond science and strong-field physics. However, the limited gain bandwidth of laser crystals such as Ho:YLF and Ho:YAG allows the generation of picosecond (ps) long pulses and, hence, makes it challenging to generate few-cycle pulse at 2 μm without utilizing an optical parametric chirped-pulse amplifier (OPCPA). Moreover, the exclusive use of the near-infrared wavelength has limited the generation of wavelengths beyond 4 μm (OPCPA). Furthermore, high harmonic generation (HHG) conversion efficiency reduces dramatically when driven by a long-wavelength laser. Novel schemes such as multi-color HHG have been proposed to enhance the harmonic flux. Therefore, it is highly desirable to generate few-cycle to femtosecond pulses from a 2 μm laser for driving these experiments. Here, we utilize two-stage nonlinear spectral broadening and pulse compression based on the Kagome-type hollow-core photonic crystal fiber (HC-PCF) to compress few-ps pulses to sub-50 fs from a Ho:YLF amplifier at 2 μm at 1 kHz repetition rate. We demonstrate both experimentally and numerically the compression of 3.3 ps at 140 μJ pulses to 48 fs at 11 μJ with focal intensity reaching 10 13 W / cm 2 . Thereby, this system can be used for driving HHG in solids at 2 μm. In the first stage, the pulses are spectrally broadened in Kagome fiber and compressed in a silicon-based prism compressor to 285 fs at a pulse energy of 90 μJ. In the second stage, the 285 fs pulse is self-compressed in air-filled HC-PCF. With fine-tuning of the group delay dispersion (GDD) externally in a 3 mm window, a compressed pulse of 48 fs is achieved. This leads to a 70-fold compression of the ps pulses at 2050 nm. We further used the sub-50 fs laser pulses to generate white light by focusing the pulse into a thin medium of YAG.

Torque ripple attenuation of PMSM using improved robust two-degree-of-freedom controller via extended sliding mode parameter observer

Torque ripple caused by flux harmonics, nonlinearity of inverter and current measurements decreases the accuracy of the servo control system, which limits the application of permanent magnet synchronous motor (PMSM) with high precision requirement. To reduce torque ripple, this paper proposes an improved robust two-degree-of-freedom controller (IR-2DOFC) based on an extended sliding-mode parameter observer (ESMPO) for a PMSM. The IR-2DOFC is constructed around the 2DOFC with iterative learning control (ILC) and a series-connecting structure, which not only suppresses unmodeled disturbances and periodic components, but also attenuates the negative impact of ILC on the dynamic response. Meanwhile, to improve the robust stability of the IR-2DOFC, ESMPO identifies the mechanical parameters so that they can be employed to further establish the IR-2DOFC parameters. Additionally, the observed disturbances can be regarded as a feed-forward compensation component to the IR-2DOFC, which enhances the disturbance-rejection performance. Simulations and experiments show that the IR-2DOFC with ESMPO has an improved dynamic response performance, which exhibits better robustness with respect to internal and external load disturbances and harmonics torque compared with proportional–integral (PI) and PI-ILC controllers.