Air-gap Flux Density Harmonics Research Articles

Analysis of MW-Level Offshore Wind Turbine Generators with Dual Star–Delta Fractional-Slot Windings

This paper investigates the use of fractional-slot concentrated windings (FSCWs) in large-scale (MW level) offshore wind generators. It focuses specifically on a power rating of 3 MW and uses an existing direct-drive synchronous PM machine (DD-SPM) with 480s/160p and dual three-phase integer-slot winding (ISW) as a baseline. A multiple of the common 12s/10p FSCW machine is used that matches the electrical frequency of the ISW machine, yielding a 192s/160p dual three-phase machine. The hybrid star–delta connection has grown increasingly popular owing to its unique harmonic cancellation properties, which can help reduce rotor and PM eddy current losses in FSCW machines. In this paper, two dual three-phase star–delta-wound machines are scaled to 3 MW and included in the investigation. Specifically, a 384s/160p dual three-phase and dual star–delta winding machine, which is a multiplication of the 24s/10p machine, and a 192s/176p dual three-phase and dual star–delta winding machine, which is a multiplication of the 24s/22p machine, are used. These machines are investigated using finite element analysis (FEA) and compared on the basis of their air-gap flux density harmonics, open-circuit electro-motive force (EMF), torque performance, and losses and power. It is found that the proposed 384s/160p dual star–delta winding machine has the best electromagnetic performance of all, with a stator power that is 1.2% greater than that of the baseline ISW machine. However, this machine has a coil pitch of 2 and so loses the manufacturing and fault-tolerant advantage of having concentrated windings. If concentrated windings are desired, then the proposed 192s/176p dual star–delta winding machine is the best choice, with the stator power only 2.6% less than that of the baseline ISW machine, but unfortunately still has significant rotor and PM eddy current losses.

Analysis and Comparison of Even-Order Back EMF Harmonics of Fractional-Slot Concentrated-Winding Consequent Pole Permanent Magnet Vernier Machines

Fractional-slot concentrated-winding (FSCW) consequent pole (CP) permanent magnet vernier (PMV) machines have received increasing attention due to their less magnet consumption but larger torque capability. However, the PM magnetomotive force (MMF) distribution is asymmetric in the CP structure. Thus, even-order air-gap flux density and back-electromotive force (back-EMF) harmonics are generated, which increases torque ripples. In this paper, to eliminate the even-order back-EMF harmonics and the resulting torque ripples, a comprehensive investigation on even-order flux density and back-EMF harmonics of five-phase FSCW CP PMV machines was presented, and then the general design rules without even-order back-EMF harmonics were summarized. Firstly, considering single- and double-layer windings, the effects of slot/pole number combination and flux modulator distribution on even-order flux density and back-EMF harmonics were analyzed. Secondly, the optimal slot/pole number combinations were selected, and then the rules for eliminating even-order back-EMF harmonics of CP PMV machines were summarized. As an extension, it was revealed that the harmonic elimination mechanism of CP PMV machines is applicable to CP-Halbach PMV machines. According to the summarized general design rules, the five-phase CP and CP-Halbach PMV machines with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> =20/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_r</i> =21/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_f</i> =10 were proposed. Their detailed performance has been comparatively analyzed and then the optimal one was selected for prototyping. Both finite element analysis (FEA) and experiments were carried out to validate theoretical analyses.

Comparative Analysis of Novel Asymmetric Consequent-Pole and Conventional Flux Reversal Permanent Magnet Machines

Torque density is a critical performance index for flux reversal permanent magnet (FRPM) machines. In this paper, a novel asymmetric consequent-pole (ACP) FRPM machine with alternate teeth wound is proposed. Different from the conventional consequent-pole FRPM machine with uniform “Fe/N-Fe/N-Fe/N” structure, the proposed ACP FRPM machine adopts “Fe/N/Fe-N-Fe/N/Fe” topology. With the novel topology, torque capability of the proposed machine is significantly improved due to the newly produced lower working harmonics of air-gap flux density. The operating principle of the proposed ACP FRPM machine is analyzed based on the magnetomotive force (MMF)-permeance model with variable winding factors and validated by finite element analysis (FEA). The effects of geometric parameters such as magnet, main tooth-tip and rotor tooth width on average torque and torque ripple are also investigated. Finally, a prototype has been manufactured to validate the theoretical results. With experimental test results, it is demonstrated that the proposed topology can achieve 109.1% higher back EMF and 55.7% higher torque density despite the stator current is reduced by 25.4% compared with the conventional consequent-pole FRPM machines.

Development of a Novel Radial-Flux Machine With Enhanced Torque Profile Employing Quasi-Cylindrical PM Pattern

This article presents a novel radial-flux surface-mounted PM (SPM) machine with quasi-cylindrical pole pattern (QCPP). With the proposed configuration, the cogging torque and torque ripple of surface-mounted machines could be greatly decreased due to the adoption of large eccentric distance and the reduction of high-order airgap flux density harmonics. Moreover, the increase of fundamental flux component helps to improve torque generation well. Additionally, the magnet poles are semi-embedded into the rotor, and thus the sleeve in conventional SPM machines is no longer necessary, which helps to reduce the airgap size and improve the torque output further. Besides, the quasi-cylindrical magnet could offer lower rotor eddy loss and higher anti-demagnetization capability than conventional radial and eccentric pole patterns. Studies have been conducted on the novel structure to validate its advantages. Firstly, the topological structure and working principle of the QCPP machine are presented. Then, the influence of the QCPP structural parameters on the torque performance is investigated. Next, an electrical machine with quasi-cylindrical pole pattern is designed. Subsequently, the electromagnetic characteristics, such as flux density distribution, back EMF, average torque, cogging torque, torque ripple, eddy loss in sleeve, rotor stress and anti-demagnetization capability, of the proposed machine are analyzed and compared with those of conventional SPM machine with eccentric magnetic poles and skewing slots. Finally, one research prototype is developed, and experiments are carried out to evaluate the design concept and performance of the proposed QCPP machine.

Saturable Voltage-Behind-Reactance Models of Induction Machines Including Air-Gap Flux Harmonics

Accurate and numerically efficient models of induction machines are of critical importance for reliable analysis and simulation of large-scale power systems. Specifically, modeling magnetic saturation that causes air-gap flux harmonics, which can significantly affect machine dynamics, has been the focus of many research efforts. In this paper, two voltage-behind-reactance (VBR) models are proposed for induction machines which formulate the air-gap flux harmonics caused by the main flux saturation. Specifically, the proposed constant-parameter VBR (CPVBR) model can be conveniently interfaced with the external network using constant <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RL</i> branches and controlled voltage sources. The numerical performance of the two proposed VBR models is validated and benchmarked against the state-of-the-art models of induction machines with saturation and air-gap flux harmonics. It is shown that the proposed models offer superior numerical performance (i.e., higher accuracy and simulation speed) compared to the existing models, which would be beneficial for offline and/or real-time simulations of power systems.

Investigation of Air-Gap Field Modulation Effect in Spoke-Type PM Machines

In this article, the air-gap field modulation effects (AFMEs) in spoke-type permanent magnet (STPM) machines with concentrated winding are investigated and revealed by quantifying the torque contributions of the various air-gap flux density harmonics. Due to the relatively stronger flux concentrated effect, the STPM structure exhibits greater resulting air-gap field harmonics for torque generation. In order to provide an in-depth understanding of their torque generation mechanism, the contributed torque components of the various air-gap field working harmonics are quantified by employing the Maxwell stress tensor (MST) approach. It identifies a fact that the abundant air-gap flux density harmonics have participated in torque production in the STPM machine. As a consequence, the field-modulated harmonics contributed a nonnegligible torque component, and hence, a pronounced AFME can be obtained in the STPM machine. Besides, the influences of the key dimension parameters, including split ratio, stator slot opening ratio, rotor PM thickness, and length, on AFEM for torque performance of the STPM machines are evaluated by the finite-element (FE) method. Finally, the reliability and effectiveness of theoretical analysis and FE simulation are verified by experiments on an STPM machine prototype.

Design and Optimization a New Spoke-Type Flux-Modulation Machine With Inverted T-Shape Permanent Magnets

This paper takes a new spoke-type flux-modulation (STFM) machine with inverted T-shape permanent magnets as the research object and proposes a multi-objective optimization design method based on air-gap flux density harmonics to improve the torque and torque ripple. The key of the proposed method is to optimize the overall torque performance by improving the contribution of main air-gap harmonics to torque and torque ripple. The working harmonic expression of the machine is firstly obtained based on the magnetomotive force (MMF) -permeance model due to the new rotor structure make the working harmonics are different from the existing flux-modulation PM machine. Then, the torques generated by the 11th and 31st air-gap harmonics and the torque ripple generated by the 29th air-gap harmonics are taken as sub-objectives. Furthermore, the response surface analysis (RSM) and the barebones multi-objective particle swarm optimization (BB_MOPSO) algorithm are combined to optimize three sub-objectives. The overall torque and torque ripple are improved due to the optimization of three sub-objectives. Moreover, the 20-slot/11-pole pair traditional model is used as a benchmark to verify the performance of the investigated machine. Finally, a prototype is manufactured and tested to verify the correctness of the theoretical analysis.

Development of a Comprehensive Analytical Model of Induction Motor Under Stator Interturn Faults Incorporating Rotor Slot Harmonics

The objective of this article isto developa comprehensive mathematical model of a three-phase induction motor to facilitate stator interturn (SIT) fault related study. A detailed analytical model that includes accurate inductance modeling considering rotor slot harmonics (RSH) under healthy as well as SIT faults is described. The proposed model is developed analytically in a step-by-step manner incorporating the features of RSH. A detailed but simplified analysis considering both magnetomotive force harmonics and air-gap flux harmonics has been presented. An asymmetric model is proposed, including SIT faults, in a single phase of the induction motor in the next stage of the modeling. The effect of saturation has also been considered in the model. The proposed model is validated by comparing the simulation results in transient, steady state, and frequency domain with the experimental results. Comparison shows a high degree of correlation with the results of the actual motor. The contributions of this work are justified by comparing the proposed model with the existing models. This article also shows that a frequency signature related to RSH present in the line current is capable of characterizing the SIT faults.

Quantitative Analysis of Electromagnetic Forces by Decoupling Air-Gap Field Modulation and Force Modulation in Rotor-Permanent-Magnet Machines

This article proposes a quantitative analysis model for the electromagnetic forces in rotor-permanent-magnet (rotor-PM) machines, decoupling the air-gap field modulation and the force modulation. First, a unified analytical model of the equivalent concentrated forces (ECFs) is deduced based on the air-gap flux density (AFD) harmonics. Second, the air-gap field modulation and the force modulation are decoupled by the ECF coefficient. Then, to determine the contributions of the modulated AFD harmonics, a quantitative analytical method is proposed. On this basis, the vibration performance of a 12-slot/10-pole (12s/10p) interior PM machine is investigated considering the modulation effect. The results reveal that the influences of rotation speed, PM-excited field, and armature field on the vibration can be clearly represented by the proposed method. Finally, the modal test and the acceleration measurement are conducted to validate the analysis.

Mechanism of Torque Ripple Generation by Time and Space Harmonic Magnetic Fields in Permanent Magnet Synchronous Motors

The mechanism of torque ripple generation by time and space harmonic magnetic fields in permanent magnet synchronous motors is investigated to obtain advanced motor designs. The general expression between the torque ripples and harmonic air-gap flux densities in the motor is derived by using Maxwell stress tensor. Both the numerical and experimental verifications of this expression are carried out. By using this expression, the difference of the torque ripple generation between the surface and interior permanent magnet synchronous motors are discussed. Based on these investigations, the shape of the rotor surface of an interior permanent magnet motor is optimized. It is clarified that specific harmonic components of thetorque ripples in interior permanent magnet synchronous motors can be reduced to be nearly zero by optimizing the rotor surface shape.

Reduced Order Modeling Based on Multiport Cauer Ladder Network for Space Harmonics of Air-Gap Flux Density in Cage Induction Motor

This study investigated an efficient procedure for developing an accurate behavioral model of a cage induction motor (IM) based on the multiport Cauer ladder network (CLN). The CLN method was applied to a cage IM with semi-closed rotor slots as a model order reduction (MOR) technique, and a method for selecting the appropriate space harmonics (SHs) included in the air-gap flux density, which is necessary for a multiport CLN method for induction machines, was discussed. Then, the developed approach was applied to the transient analysis of the cage IM coupled with a control system, and its effectiveness in terms of computational accuracy and cost was investigated.

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.

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.

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.

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.

Minimization of Cogging Torque for V-Type IPMSM by the Asymmetric Auxiliary Slots on the Rotor

The interaction between the permanent magnets and the armature teeth of the PMSM generates cogging torque. It causes vibration and noise. Therefore, this paper establishes the analytical formula of the cogging torque of the motor with auxiliary slots on the surface of the rotor. It shows that reasonable slots can weaken the cogging torque. But it&#x2019;s essential to determine whether the air-gap flux density harmonics will increase appreciably by slotting. A V-type IPMSM with 8-pole, 48-slot is modeled to analyze the cogging torque. Two new rotor slot shapes&#x2014;inwardly biased slots and outwardly biased slots&#x2014;are proposed and researched to reduce the cogging torque of the V-type IPMSM. And they are compared with the traditional symmetrical auxiliary slots. Research shows that the inwardly biased slots and the symmetric auxiliary slots can obtain a better effect on the cogging torque than the outwardly biased slots. By the symmetrical auxiliary slots, the cogging torque is weakened by 75.88%, but the torque ripple increases from 22.36% to 29.60%. By the inwardly biased slots, the cogging torque is weakened by 75.64%, and the torque ripple drops from 22.36% to 12.95%. The inwardly biased slots could successfully suppress the torque ripple.

Optimization and Improvement of Advanced Nonoverlapping Induction Machines for EVs/HEVs

This paper presents a comprehensive design optimization and performance improvement guidelines for induction machines (IMs) having advanced nonoverlapping windings (ANWs). The effectiveness of various optimization approaches, such as individual optimization and single- and multi-objective global optimization using the Genetic Algorithm (GA), has been studied. To minimize the potential drawbacks of high bar copper loss, high torque ripple, and low power at high speed due to high magnet-motive force (MMF) harmonics of nonoverlapping windings (NWs), two different performance improvement approaches have been utilized: (a) to redesign the rotor structure to reduce the parasitic effects such as torque ripple and additional bar copper losses due to air-gap flux density harmonics; (b) to increase the stack length to improve the torque at the constant-power region. It has been revealed that the proposed ANW IMs with bridges in their rotor openings, particularly with u-shaped bridges, show better performance in terms of torque ripple, bar copper loss, and bar current density. By using the proposed design method, an advanced IM (AIM) can achieve a 5.3% higher efficiency with ~34% shorter total axial length, compared to its conventional IM (CIM) counterpart with integer-slot distributed windings (ISDWs). A time-stepping 2-D finite element analysis (FEA) based nonlinear magnetic field solution program has been employed to perform all the parametric analyses, optimizations, and evaluate the optimal solutions and improved designs. Moreover, in order to show the reliability of the FEA predictions performed in this study, the FEA predictions of globally optimized CIM are validated by experimental measurements.

Permanent magnet shape optimization method for PMSM air gap flux density harmonics reduction

This paper proposed a permanent magnet optimization method to suppress the air gap flux density harmonic of permanent magnet synchronous motor (PMSM). The method corrected the effective air gap length of the motor, calculated the magnetization length of the permanent in the case of parallel magnetization, and took the influence of the permanent magnet relative permeability into consideration. Based on these works, for a given sinusoidal air gap flux density waveform, the corresponding structural parameters can be calculated, so as to achieve the optimization of the permanent magnet. By using this method to optimize the shape of the magnet, the fundamental wave of the air gap flux density can be retained to the greatest extent, so as to eliminate harmonics and maintain the output capacity at the same time. The feasibility and accuracy of the method have been verified by finite element analysis (FEA) and prototype machine experiment. This method is simple and time-saving, and has a satisfactory accuracy, which provides a reference method for permanent magnet optimization of PMSM.

Torque ripple optimization for synchronous reluctance motors based on a virtual permanent magnet harmonic machine model

The torque ripple is affected by both the stator and the rotor magnetic field harmonics. In synchronous reluctance motors (SynRM), there are only rotor permeance harmonics existing on the rotor side for the absence of the rotor windings. Since the asymmetric rotor flux barriers are widely applied in the SynRM rotor, it is difficult to calculate the rotor permeance accurately by the analytical method. In this article, the effects of the rotor permeance harmonics on the air-gap magnetic field are studied by a virtual permanent magnet harmonic machine (VPMHM), which is a finite-element (FE) based magnetostatic analysis model. The air-gap flux density harmonics produced by the SynRM rotor are extracted from the VPMHM model and used as the intermediate variables for the torque ripple optimization. The proposed method does not need to solve the transient process of motor motion. Hence, the time of the optimization process can be significantly shortened. Finally, a full electric cycle is simulated by dynamic FE simulation, and the torque ripple is proved to be effectively reduced.

Design and Analysis of a Novel Axial-Radial Flux Permanent Magnet Machine with Halbach-Array Permanent Magnets

Electric machines with high torque density are needed in many applications, such as electric vehicles, electric robotics, electric ships, electric aircraft, etc. and they can avoid planetary gears thus reducing manufacturing costs. This paper presents a novel axial-radial flux permanent magnet (ARFPM) machine with high torque density. The proposed ARFPM machine integrates both axial-flux and radial-flux machine topologies in a compact space, which effectively improves the copper utilization of the machine. First, the radial rotor can balance the large axial forces on axial rotors and prevent them from deforming due to the forces. On the other hand, the machine adopts Halbach-array permanent magnets (PMs) on the rotors to suppress air-gap flux density harmonics. Also, the Halbach-array PMs can reduce the total attracted force on axial rotors. The operational principle of the ARFPM machine was investigated and analyzed. Then, 3D finite-element analysis (FEA) was conducted to show the merits of the ARFPM machine. Demonstration results with different parameters are compared to obtain an optimal structure. These indicated that the proposed ARFPM machine with Halbach-array PMs can achieve a more sinusoidal back electromotive force (EMF). In addition, a comparative analysis was conducted for the proposed ARFPM machine. The machine was compared with a conventional axial-flux permanent magnet (AFPM) machine and a radial-flux permanent magnet (RFPM) machine based on the same dimensions. This showed that the proposed ARFPM machine had the highest torque density and relatively small torque ripple.