Air-gap Flux Density Harmonics Research Articles

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.

Induction Machine Modeling Considering Magnetizing Flux Saturation With Air-Gap Harmonics

Accurate and computationally-efficient models of induction machines (IMs) are essential for many simulation programs and analysis of power systems transients. Conventionally, when modeling magnetic saturation in the classical qd models, only the fundamental component of magnetizing flux is considered. To represent the saturation air-gap flux harmonics, fairly complicated phase-domain and/or implicit models have been proposed in the prior literature. In this paper, a new explicit two-axis IM model is developed to include the air-gap harmonics caused by magnetic saturation. The new model is validated by experimental measurements and simulations in various steady state and transient scenarios, and is shown to provide accurate results while being simple to implement.

Quantitative Identification of Airgap Flux Density Harmonics Contributing to Back EMF in Dual-Permanent-Magnet-Excited Machine

Due to the bidirectional field modulated effect, the dual-permanent-magnet-excited (DPME) machine relies on the countless airgap flux density harmonics with specific pole-pair numbers (PPNs) to produce stable torque or effective back-EMF. Regarding the generation of back-EMF, there is no doubt that the flux density harmonics which make a negative contribution will reduce the performance of DPME machine. However, to the best of our knowledge, there is very little research on the identification of field harmonics which play a negative role in the generation of back-EMF. In this paper, the partial-analytical-method (PAM) is proposed to quantitatively identify the field harmonics. Firstly, the PAM is described in detail, and the ratio of contribution (RoC) is defined to assess the contribution of field harmonics to back-EMF. Then the PAM is applied to a 12/10 DPME machine. The identification results show that two of the five types of field harmonics, i.e., Type-II and Type-V, make a negative contribution to back-EMF, the RoCs of which are -2.94% and -4.32%, respectively. In these two types of harmonics, the ones with PPN=22 are mainly responsible for the negative contribution to back-EMF, which needs attention at the outset of the design.

Quantitative Analysis of Back-EMF of a Dual-Permanent-Magnet-Excited Machine: Alert to Flux Density Harmonics Which Make a Negative Contribution to Back-EMF

Recently, the dual-permanent-magnet-excited (DPME) machine has attracted growing attention due to its high torque density. Due to the bidirectional field modulated effect (BFME), airgap flux density harmonics (AFDHs) are more complex and abundant than traditional permanent magnet synchronous machines (PMSMs). Moreover, the back-electromotive force (EMF) generated by AFDHs is also complex. Unfortunately, only a few papers qualitatively analyze back-EMF. The qualitative analysis for back-EMF can reveal some important conclusions; for example, only AFDHs meeting specific pole pair numbers (PPNs) can generate back-EMF. However, it may also ignore some details and valuable findings. In this paper, a purely analytical magnetomotive force (MMF) permeance model (PAMPM) for a DPME machine is built to quantitatively analyze the back-EMF. The PAMPM does not require a numerical method, such as conformal transformation. With the PAMPM, AFDHs that contribute to the generation of back-EMF can be recognized and quantified. Interestingly, AFDHs with m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> =np <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> cause PM flux-linkage to have a dc bias, and not all AFDHs play a positive role in the generation of back-EMF. The main recognition results are as follows: 1) the S-II and R-II types of AFDHs in a 12/10 DPME machine overall make a negative contribution to the generation of back-EMF; and 2) AFDHs with PPN=22 in the two types mainly cause a negative contribution. To further verify the above results, 2D finite element simulation and experimental tests of a prototype machine are also conducted.

Optimization Design of Power Factor for an In-Wheel Vernier PM Machine From the Perspective of Air-Gap Harmonic Modulation

In this article, an optimization design method of power factor is proposed for vernier permanent magnet (VPM) machine, in which the key is to analyze and investigate the power factor from the perspective of air-gap flux harmonic modulation. To improve the design efficiency, air-gap harmonics are analyzed and serve as the crucial bridge between power factor and machine geometry. It is noted that, during the operation of the VPM machine, more attention is required for the power factor of low-speed operation area. Based on the popular new European driving cycle of the electric vehicles, three low-speed driving conditions are chosen for the optimization design. For the systematic investigation, a V-shape VPM machine is selected as an optimization example. In order to evaluate conveniently, the comprehensive power factor is defined and sensitive air-gap flux harmonics of different conditions are selected as the optimization objectives, for improving the power factor characteristics in low-speed conditions. In addition, power factor and machine performances are evaluated to validate the proposed method. Finally, the prototype machine is built and tested. Both the simulation and experimental results reveal the feasibility and effectiveness of the proposed method and investigated VPM machine.

A Sinusoidal Current Control Strategy Based on Harmonic Voltage Injection for Harmonic Loss Reduction of PMSMs With Non-Sinusoidal Back-EMF

In permanent magnet synchronous machine design, a limited number of stator and rotor slots distorts the air-gap flux distribution and its effective length. It causes machine parameters to vary with the rotor position. The rotor flux linkage harmonics introduce nonsinusoidal back-EMF, which causes current harmonics when conventional PI current controller is adopted. Those machines suffer from high-frequency torque ripple due to air-gap flux harmonics in low-speed region. However, in high-speed region, where the torque ripple is filtered out by the mechanical system, the torque ripple may be disregarded. In this case, torque-ripple suppression methods and the associated harmonic current components generate losses. Therefore, a sinusoidal current control is required to reduce the undesired harmonic losses. In this manner, this article focuses on the sinusoidal current control strategy based on harmonic voltage injection, which requires knowledge of rotor magnet flux linkage harmonics. This article also proposes both off- and on-line schemes for the identification of rotor magnet flux linkage harmonics. These methods do not require any proprietary machine design details such as the shape of stator or rotor for finite element analysis. Commonly used PI plus resonant controller is also designed and its disadvantages in terms of speed-dependent gain and stability, in comparison to the proposed scheme, are highlighted. Finally, experimental results are presented to compare the proposed scheme with the conventional method at different operating conditions.

Mitigating the Torque Ripple in Electric Traction Using Proportional Integral Resonant Controller

There is increasing popularity of using permanent magnet (PM) machines in vehicle propulsion systems. Due to the pre-excitation of PM, the machines could offer higher efficiency and torque density. However, their inherent torque ripple could be problematic for electric vehicles (EVs) due to low damping of torsional vibration which may affect passenger comfort. This can prohibit the use of PM machines to improve vehicle energy efficiency. This paper presents the application of resonant control (RC) to suppress the impact of the PM torque ripple, which aims to reduce the vibration of a vehicle. A prototype PM machine and driveline have been fitted to a light-duty off-road vehicle. Firstly, the drivetrain frequency response was analyzed. The main source of the vibration is identified as the 24th harmonic torque ripple of the 12-slot/8-pole PM machine, which originates from the cogging torque and air-gap flux harmonics. The vibration becomes more severe when the torque ripple frequency is close to the natural frequency of the drivetrain. Then, the RC in conjunction with PI controller (PIR) was introduced to be used at the outer speed loop, so that an accurate current reference signal can be generated for the inverter to mitigate the speed ripple. When compared to the conventional Proportional-Integral (PI) controller, PIR controller has demonstrated over 80% reduction in speed ripple, even when the torque ripple frequency is close to the natural frequency of the vehicle.

Design of a Large Capacity Line-Start Permanent Magnet Synchronous Motor Equipped With Hybrid Salient Rotor

This article presents a successful design of a three-phase large capacity line-start permanent magnet synchro nous motor (LSPMSM) developed for industrial applications. A hybrid rotor containing both slotted solid steels and cage bars is included in the designed LSPMSM to enhance the motor starting and synchronizing abilities. A salient rotor periphery making air-gap length, which maximizes at the quadrature axis and minimizes at the direct axis, is employed to reduce the harmonics of air-gap flux density and motor losses. The implementation of a genetic algorithm coupled with a neural network optimizes the rotor-periphery saliency ratio and other crucial dimensions for further performance improvement. Finite-element analyses highlight the advantages of the designed LSPMSM by comparing its performance indexes with those of a conventional cage-rotor LSPMSM. The effectiveness of the designed motor is validated by a series of prototype tests.

Self-Excited Synchronous Machine Using Airgap Harmonics

This article introduces a self-excitation technology for field wound synchronous machines (FWSMs) to eliminate conventional components required by brushless and brushed static excitation systems. This technology is based on the utilization of pre-existing airgap flux harmonics, so no exciter or brush is required. The energy of these airgap harmonics at the slotting frequency is captured using rotor-mounted harvesting coils. A power electronic converter is then used to rectify the induced harvesting coil voltage and regulate the field winding current of the FWSM. Simulation results are presented showing the efficacy of the proposed method for a prototype FWSM under various loading conditions. For demonstration, a full-scale 5.4-MVA synchronous generator is used for design and validation.

Analysis of Double-Layer Permanent-Magnet Flux Reversal Machines With Different Permanent Magnet Arrangements in Stator

This article presents two novel double-layer permanent-magnet flux reversal (PMFR) machines to improve the torque capability, namely Machine A and Machine B. Both the Machine A and Machine B are designed as the consequent-pole PMFR machines. The rotors of two machines are identical, which adopt Halbach array permanent-magnet (PM) in the rotor slot to guide the flux into the rotor teeth to reduce the leakage flux. However, the PM relative positions of two PMFR machines on the adjacent stator teeth are different, which result in different pole numbers of air-gap flux density. The operation principles and performances of two machines are introduced and compared in this article. In addition, the air gap fields of two machines by PM magnetomotive force (MMF) are analyzed and the contribution of the dominant air-gap flux density harmonics to torque is revealed.

Harmonic Currents Injection Strategy With Optimal Air Gap Flux Distribution for Multiphase Induction Machine

The proposed technique focuses on the nonsinusoidal power supply control strategy aiming to obtain the optimal air gap flux density distribution. The electrical constraints for the alignment between rotated fundamental and harmonic air gap flux are illustrated in detail. The supporting simulation is performed to analyze the misaligned angles between fundamental and harmonic air gap flux for the traditional methods. Different from traditional flux-oriented methods, the improved algorithm for harmonic currents injection is designed based on rotor flux orientated control in fundamental plane and air gap flux orientated control in harmonic planes. The synchronous and aligned control of the fundamental and harmonic air gap flux is achieved regardless of load condition. The experimental verification is implemented based on a multiphase driving platform using a seven-phase induction machine as prototype. Various scenarios are provided for the proposed control strategy comparing with the traditional ones in terms of induced electromotive force waveforms, harmonic currents, and advance angles of air gap flux. The simulated and experimental results validate the theoretical assumption and the effectiveness of the proposed method.

Analysis and design of 18‐slot/10‐pole six‐phase fault‐tolerant permanent magnet synchronous motor for electric vehicles

This study analyses a double Y shaft 30° winding for six-phase fault-tolerant permanent magnet synchronous motors and introduces a novel modular 18-slot stator topology used in high-performance electric vehicles with unequal teeth width and unequal slot size. The new topology adopts double-layer winding in the same phase and single-layer winding in the adjacent phase. Additionally, two new pole/slot combinations for the six-phase motor, 18-slot/10-pole and 18-slot/14-pole, are proposed by analysing the air-gap flux harmonics that are produced by the stator winding. In addition, the optimal design of the 18-slot/10-pole motor is determined by using the average torque and the torque ripple as indexes. The motor can run continuously in the range of 0–4 times the rated speed with a one-time short-circuit current, a high isolation capability in the different phases and a high efficiency. The final parameters and performance of the 18-slot/10-pole motor are provided.

Comparative analysis of spoke‐type, consequent‐pole and hybrid‐pole permanent magnet machines

In recent years, consequent-pole permanent magnet (CPM) machines draw much attention due to their high utilisation ratio of permanent magnet (PM) material. However, they have some disadvantages, such as the even-order harmonics of airgap flux density, which may cause asymmetric phase back-EMF and the increase of torque ripple. In this study, a novel hybrid-pole PM (HPM) machine is proposed, in which the rotor combines consequent-pole and spoke-type PM rotors. The working principle of the proposed HPM machine is analysed based on the equivalent magnetic circuit, and validated by the finite-element method. Then, the electromagnetic performance of the HPM machine is compared with those of the existing CPM and spoke-type PM machines. It is shown that the HPM machine obtains similar average torque, PM utilisation ratio, torque ripple and efficiency to the spoke-type PM machine, whilst it has a higher PM utilisation ratio and much lower torque ripple than the conventional CPM machines. Finally, these analyses are validated by the tested results of a 9-slot/6-pole HPM machine.

Rotor Pole Design of Radial Flux Magnetic Gear for Reduction of Flux Density Harmonics and Cogging Torque

This article focuses on a novel design of rotor topology for an interior permanent magnet superconductive radial flux magnetic gear to achieve sinusoidal air-gap flux density and lower cogging torque. The method is based on optimization of buried magnet's pole shape in a radial flux structure, modified by using a pulsewidth modulation technique and variable air-gap length applying the supershape formula on the iron core of the inner rotor. The unsatisfied harmonic contents of the air-gap flux density can be reduced with this technique while the main harmonic component and average torque can be maintained or enhanced. The key idea is to set the distribution of the air-gap flux density by segmenting the pole shoe into several elementary blocks and predetermined grooves based on a special curve. Superconductor bulks are placed between pole pieces of modulator ring to improve the flux-modulation effect and decrease cogging torque percentage. The computation of the block sizes and effects of variation of supershape formula parameters are performed by solving a constrained optimization problem. Results show that the radial air-gap flux density harmonics are eliminated, leading to almost sinusoidal air-gap flux density and lower level of cogging torque.

Multiphase PM Machines With Halbach Array Considering Third Harmonic Flux Density

For the five-phase permanent magnet (PM) machines with conventional Halbach array rotor, although the third harmonic current is injected into the phase current, the torque density hardly increases due to the absence of the third harmonic air gap flux density. Hence, a Halbach array considering third harmonic air gap flux density is proposed in this paper, and the topology is described and compared with the conventional Halbach array. The magnetizing angle of the proposed Halbach array and the stator teeth width are optimized based on the nonlinear programing method. The electromagnetic performances of the five-phase PM machines with the proposed Halbach array, including open-circuit flux density, back electromotive force, flux density under the rated load, cogging torque, average torque, torque ripple, loss, and efficiency, are compared with the PM machine with conventional Halbach array by finite-element method. It is demonstrated that the torque density and efficiency of the PM machine with the proposed Halbach array are higher than that of the PM machine with conventional Halbach array. Finally, the five-phase 10-slot/8-pole PM machines with proposed Halbach array is manufactured and tested to verify the analysis.

A Novel Spoke-Type PM Machine Employing Asymmetric Modular Consequent-Pole Rotor

This paper proposes a novel spoke-type permanent magnet (PM) machine, which adopts asymmetric modular consequent-pole (AMCP) rotor to enhance the effective PM flux due to the increased flux-focusing effect and reduced leakage flux and to improve the flux-weakening capability due to the increased d -axis inductance. Moreover, the pole-shaping method based on three sectional arcs is proposed to suppress the harmonics of airgap flux density. Since the rotor structure is relatively complex, the finite-element analysis together with multiobjective genetic algorithm is adopted to optimize this design. Furthermore, the electromagnetic performance of the spoke-type PM machine with the proposed AMCP rotor (Spoke-AMCP), including the open-circuit airgap flux density, phase back electromotive force, torque, PM utilization ratio, efficiency, and flux-weakening capability, are compared with two conventional spoke-type PM machines with evenly distributed and alternate flux barriers (Spoke1 and Spoke2) and consequent-pole spoke-type PM machine (Spoke-CP). It is demonstrated that the Spoke-AMCP machine obtains the largest output torque and PM utilization ratio, lowest torque ripple and similar efficiency compared to Spoke1, Spoke2 and Spoke-CP machines. Moreover, although the Spoke-AMCP machine has the largest PM flux linkage, it has slightly better flux-weakening capability than the Spoke1 and Spoke2 machines. Finally, a 12-slot/10-pole Spoke-AMCP machine is built and tested to verify the analyses.

Analysis of Back-EMF in Flux-Reversal Permanent Magnet Machines by Air Gap Field Modulation Theory

In this paper, the back-electromotive force (back-EMF) characteristics of the flux-reversal permanent magnet (FRPM) machines with different magnetization methods and winding layouts are analyzed and synthesized based on the magneto motive force (MMF)-permeance model. The air gap field modulation theory is utilized to investigate the permanent magnet-MMF harmonics and open-circuit air gap flux density harmonics that make a contribution to back-EMF as well as its harmonics. Based on this analysis, the specific harmonic of back-EMF can be reduced by suppressing the corresponding PM-MMF harmonic. Besides, the influence of rotor pole number on back-EMF is also studied. It is found that with the aid of this modulation theory, the reasonable magnetization method, winding layout, and rotor pole number can be obtained to improve the back-EMF characteristics of an FRPM machine with an arbitrary slot/pole combination. Furthermore, prototype machines are manufactured and tested to verify the analytical predictions.

Design of a High-Speed Solid-Rotor Induction Machine With an Asymmetric Winding and Suppression of the Current Unbalance by Special Coil Arrangements

High-speed solid-rotor induction machines (IMs) suffer from higher rotor eddy-current losses (as a result of the air-gap flux density harmonics) more than any other type of high-speed machines because of the solid-rotor steel. A double-layer short-pitch asymmetric winding arrangement with prefabricated coils is proposed in this paper to mitigate the solid-rotor losses and enable easier assembly. However, the asymmetric winding also brings some current unbalance because of three-phase asymmetric stator inductances, especially the winding leakage inductances. Current unbalance can cause harmful effects for both the machine and supply, e.g., torque ripples, unbalanced magnetic pulls, and unbalanced thermal loads of the supply network and supply power electronics. Additionally, a three-phase unbalanced current can cause an extra source of electromagnetic emission to the environment, which can be harmful to surrounding electronics and can cause extra eddy-current losses in surrounding solid surfaces (e.g., a metal terminal box). To mitigate the current unbalance, two methods are compared in this paper. The first method is a slight increase of the stator slot height and placing of the coil sides at the top or bottom within the slot height for different phases. The stator slot height is optimized based on the 2-D finite-element method (FEM) to achieve the best solution for mitigation of the current unbalance. The other method is based on the results of the first method, and the coil side position for a specific phase is further adjusted. Unlike conventional methods of mitigating the current unbalance by power electronics, the proposed method suppresses the current unbalance solely by adjusting the machine design, which avoids extra investments for power electronics devices. In addition, the machine control strategy remains unchanged compared with the traditional one.

Extraction of Rotor Eddy-Current Harmonic Losses in High-Speed Solid-Rotor Induction Machines by an Improved Virtual Permanent Magnet Harmonic Machine Model

High-speed induction machines equipped with a solid steel rotor are capable of achieving a high-rotating speed than other types of machines, because of their simpler and more robust rotor structure. At the same time, however, the eddy-current losses in the solid rotor may be critical, because of the high conductivity of the rotor material, which makes it easy for axial eddy currents to travel in the solid rotor. To efficiently mitigate the rotor eddy-current losses, it is important to accurately determine the rotor eddy-current losses induced by a particular harmonic in advance. In this paper, an improved virtual permanent magnet harmonic machine (VPMHM) model equipped with a sinusoidally magnetized virtual magnet based on the finite element method (FEM) is proposed for determination of the rotor eddy-current harmonic losses. The 2-D fast Fourier transform was used to accurately analyze the time-spatial air-gap flux density harmonics. The VPMHM model was enhanced to ensure that it was able to exactly produce the required flux density harmonics in the air gap. Two algorithms for the improved VPMHM models with different hybrid excitations were proposed to determine the harmonic losses together with the other important harmonic behavior. The model was further investigated to separate the electromagnetic transients from different harmonics. Finally, the simulation time for the harmonic losses required by the enhanced VPMHM model was significantly reduced by separating the harmonic transients. All the results and conclusions presented in this paper are based on the FEM analysis.

Modeling and Mitigation of Rotor Eddy-Current Losses in High-Speed Solid-Rotor Induction Machines by a Virtual Permanent Magnet Harmonic Machine

Being much more rugged than a rotor made of traditional steel sheets, a solid rotor is frequently used in high-power high-speed induction machines (IMs). Furthermore, by a solid-rotor machine, a higher rotating speed can be achieved. However, the solid rotor also has certain disadvantages, the relatively high solid-rotor eddy-current losses being the most serious one. Basically, solid-rotor eddy-current losses are mainly induced by time–spatial air-gap flux density high-order harmonics. The suppression of the high-order harmonics is the key means to mitigate the rotor eddy-current losses. In this paper, a novel computational model is proposed for evaluating the rotor harmonic eddy-current losses of a 2 MW, 12 000 r/min IM. The model was built on a special machine referred to as a virtual permanent magnet harmonic machine (VPMHM). The model was constructed by applying the finite-element method (FEM), and it is based on the time–spatial harmonics produced by a rotating magnet with sinusoidal magnetization. The VPMHM model links the air-gap flux density harmonics directly to the specific rotor eddy-current losses. Furthermore, according to the proposed model, three options, namely, the use of air-gap permeance modifying notches on the stator teeth, semimagnetic wedges, and their combination, were investigated in detail for mitigating the rotor eddy-current losses in the motor nominal operating point. The results and conclusions in this paper are based on the FEM analysis.