back-EMF Harmonics Research Articles

Open-Circuit Fault-Tolerant Control for Dual Three-Phase PMSM With Minimum Torque Ripple Considering Phase Back EMF Harmonics

This paper proposed an open-circuit fault-tolerant control method for dual three-phase permanent magnet synchronous motor (DTPPMSM), which takes the back electromotive force (back EMF) harmonics into consideration and can achieve the minimum torque ripple. From the perspective of machine ontology and electromagnetic power, this paper analyzed the influence of back EMF harmonics on torque ripple. On this basis, by adjusting the phase of currents, specific order torque ripple components which can offset each other can be generated by the back EMF fundamental wave and harmonics, thus suppressing the specific order torque ripple of the whole motor. Furthermore, not limited to specific order torque ripple, the method can also be used to obtain the minimum overall torque ripple under open-circuit operation. Finite element analysis (FEA) and prototype experiment are employed to verify the proposed method.

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.

Fault-Tolerant Control for Single-Phase Open-Circuit and Short-Circuit Fault in Five-Phase PMSM With Third-Order Harmonic Back EMF Using Coefficients Reconfiguration

Fault-Tolerant Control for Single-Phase Open-Circuit and Short-Circuit Fault in Five-Phase PMSM With Third-Order Harmonic Back EMF Using Coefficients Reconfiguration

Model-Free Predictive Current Control of DTP-PMSM Based on Ultra-Local Model Considering Back EMF Harmonics

Model-Free Predictive Current Control of DTP-PMSM Based on Ultra-Local Model Considering Back EMF Harmonics

A Methodology for Applying Skew in an Automotive Interior Permanent Magnet Rotor for Robust Electromagnetic and Noise, Vibration and Harshness Performance

Interior permanent magnet (IPM) motors in traction applications often employ discrete rotor skewing constructions to reduce torsional excitations and back-EMF harmonics. Although skewing is very effective in reducing cogging torque, the impact on torque ripple is not well understood and can vary significantly over the operating envelope of a motor. Skewing also leads to the creation of a non-zero axial force that may compromise the bearing life if not considered. This paper introduces a holistic methodology for analyzing the effect of skewing, aiming to minimize torsional excitations, axial forces and back-EMF harmonics whilst mitigating the impact on performance and costs. Firstly, analytical models are employed for calculating cogging torque, torque ripple and axial forces. Then, 2D and 3D finite element analysis are used to incorporate the influence of non-linear material behavior. A detailed structural model of the powertrain is employed to calculate the radiated noise and identify key areas allowing a motor designer to reduce noise, vibration and harshness (NVH). A meticulous selection process for the skewing angle, the number of skew stacks and the orientation of skew stacks is developed, giving particular attention to the effect of the selected pattern on NVH in both forward and reverse rotating directions.

Feedback Linearization-Based Direct Torque Control for Asymmetrical Six-Phase PMSM Motor With Back EMF Harmonics Compensation

Feedback Linearization-Based Direct Torque Control for Asymmetrical Six-Phase PMSM Motor With Back EMF Harmonics Compensation

Performance Comparison Between Permanent Magnet Synchronous Motor and Vernier Motor for In-Wheel Direct Drive

Nowadays, in-wheel drive mode is considered as one of the most promising modes for electric vehicles (EVs). The motor type plays a significant role to the vehicle performances. This paper focuses on performance between permanent magnet synchronous motor (PMSM) and vernier motor (PMVM) for in-wheel direct drive. Firstly, the required performances are determined by the vehicle requirements. The prototypes of PMVM and PMSM are manufactured after the comparison. Then, the expressions of air-gap magnetic field harmonic, electromagnetic torque, and power factor are theoretically derived, where the parameter torque ratio is introduced to evaluate the torque ratio between PMVM and PMSM. Based on experiment, the back-EMF harmonics, cogging torque, maximum torque per ampere capability, flux-weakening capability, torque, efficiency, power factor, are compared and analyzed. Subsequently, the discussions are carried out, where the strength and weakness of two-type motors for in-wheel drive are concluded and the future prospects are suggested. Finally, the conclusions of two-type in-wheel motors are then extracted. This paper aims at providing a reference for the exploration of alternating in-wheel motor types, which can promote the development of high-performance in-wheel drive system for EVs.

Sensorless control of PMSM based on third harmonic back EMF and SOGI-FLL

Sensorless control of PMSM based on third harmonic back EMF and SOGI-FLL

Continuous Rotor Position Estimation for Flux Modulated Doubly Salient Reluctance Motor Drives Based on Back EMF Harmonics

DC-biased sinusoidal current excited flux modulated doubly-salient reluctance motor (FMDRM) drives are developed to reduce the torque ripple and vibration of doubly-salient reluctance motors (DRMs). Conventionally, because of the discontinuous quasi-square current excitation, the rotor position of DRMs is estimated by the combination of piecewise estimation of phase angle information for each phase, where the continuous position estimation for the novel FMDRM drives cannot be realized. To solve this issue, this paper proposes a continuous rotor position estimation strategy for FMDRM drives based on back electromotive force (back-EMF) harmonic characteristics. Firstly, the back-EMF harmonics caused by the rotor saliency and their relationship with the rotor position are analyzed in detail. Then, the corresponding harmonic current regulator and quadrature signal generator are investigated to achieve harmonic current suppression and obtain the quadrature harmonic back-EMF components in the rotating reference frame for rotor position estimation simultaneously. Furthermore, a virtual-inductance-based method is developed to calibrate the phase angle offset between the estimated and actual rotor positions. With the proposed scheme, accurate continuous rotor position estimation can be achieved without any additional hardware. Experimental validations are presented on a three-phase 12&#x002F;8 FMDRM prototype to verify the accuracy of the proposed rotor position estimation scheme.

Analysis of Back EMF Harmonics Influenced by Slot–Pole Combinations in Permanent Magnet Vernier In-Wheel Motors

This paper analyzes the back-EMF harmonic characteristics influenced by the slot-pole combinations in permanent magnet vernier motors (PMVM) for in-wheel drive applications. Firstly, the feasible matches between the slot-pole combinations, stator tooth types, as well as winding topologies are given. Secondly, the expressions of fundamental and harmonic back-EMF are then derived, where the equivalent winding factor considering the air-gap permeance harmonics is introduced to evaluate the back-EMF fundamental amplitude. Next, the contribution of each air-gap magnetic field harmonic on the back-EMF harmonic is investigated, which has proven that the air-gap odd-order ineffective magnetic field harmonics are responsible for unexpected back-EMF harmonics. Based on this, the feasible principle of the number of PM poles, armature poles, and flux modulation poles aiming at the low ineffective back-EMF harmonics is established. Finally, extensive finite element analysis (FEA) is conducted, and two prototypes were manufactured and tested, where the experimental results have a good agreement with the FEA and theoretical results.

Arbitrary Current Harmonic Decomposition and Regulation for Permanent Magnet Synchronous Machines

This paper contributes a novel solution for the regulation of arbitrary current harmonics in a permanent magnet synchronous machine (PMSM) system by introducing a virtual three-phase system. The inverter nonlinearity, back-EMF harmonics, and the asymmetry among phases, are considered to derive a comprehensive electrical model of PMSMs. Compared to the conventional harmonic analysis, the derived model indicates that more new current harmonics can exist in the PMSM system. To regulate the current harmonics with arbitrary orders, a virtual three-phase system is established. By properly shifting the spatial and time phase angles between the virtual three-phase system and the original physical three-phase system, the selected current harmonics can be decomposed from the phase current. A simple proportional-integral regulator with adjustable phase compensation angle is designed based on the proposed model to regulate the decomposed current harmonics in the corresponding harmonic synchronous reference frame. The implementation details and experimental results are provided to illustrate the feasibility and correctness of the proposed control strategy.

Hybrid Frame-Based Current Control Scheme for LC-Equipped PMSM With Non-Sinusoidal Back-EMF

Permanent-magnet synchronous machine (PMSM) drive with a sine wave <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> filter has the features of low insulation stress and current harmonics. However, few studies consider the impact of back-electromotive force (EMF) harmonics on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -equipped PMSM drive system. The non-sinusoidal back-EMF can cause current harmonics, meanwhile, it also affects the stability analysis and high-frequency resonance suppression. In order to solve these two problems simultaneously, a hybrid frame-based current control scheme is proposed in this paper. The quantitative effect of back-EMF harmonics on control behaviors is analyzed first. A virtual triple three-phase system with auxiliary currents is developed to decompose the fundamental and harmonic contents, which not only contributes to independent current harmonic regulation in multiple synchronous reference frames, but also simplifies system stability analysis considering non-sinusoidal back-EMF. Then, an active damping method based on stator current feedback is implemented in the stationary frame to suppress the resonance, and no additional passive components or sensors are required. Finally, experimental results are provided to verify the effectiveness and superiority of the proposed method.

Zero-sequence Current Suppressing Strategy for Dual Three-phase Permanent Magnet Synchronous Machines Connected with Single Neutral Point

Dual three-phase permanent-magnet synchronous machines (DTP-PMSM) connected with a single neutral point provide a loop for zero-sequence current (ZSC). This paper proposes a novel space vector pulse width modulation (SVPWM) strategy to suppress the ZSC. Five vectors are selected as basic voltage vectors in one switching period. The fundamental and harmonic planes and the zero-sequence plane are taken into consideration to synthesis the reference voltage vector. To suppress the ZSC, a non-zero zero-sequence voltage (ZSV) is generated to compensate the third harmonic back-EMF. Rather than triangular carrier modulation, the sawtooth carrier modulation strategy is used to generate asymmetric PWM signals. The modulation range is investigated to explore the variation of modulation range caused by considering the zero-sequence plane. With the proposed method, the ZSC can be considerably reduced. The simulated and experimental results are presented to validate the effectiveness of the proposed modulation strategy.

Analysis of power-sizing equations for rotor-permanent-magnet flux-switching machines

In this paper, power-sizing equations of rotor-permanent-magnet flux-switching (RPM-FS) machines are proposed and implemented, where the main decisive factors of the electromagnetic torque, namely electric loading and magnetic loading, are deduced, respectively. Although the topologies of RPM-FS machines are evolved from traditional stator-PM flux-switching machines, there are still seriously flux leakages between poles, and it is hard to derive the peak value of the air-gap flux density directly. Hence, a local simplified magnetic equivalent circuit is utilized to calculate the magnetic loading, which is crucial for the power-sizing equation. The influences of the pole-to-pole flux-leakages and harmonics in back-EMF are considered to improve the calculated accuracy of the power-sizing equation. Consequently, the electromagnetic torque can be predicted with acceptable accuracy. The feasibility of the power-sizing equation is verified by the finite element analysis and experimental results.

An Improved Permanent Magnet Synchronous Motor Rotor Position Observer Design Based on Error Harmonic Elimination

An improved rotor position observer based on sliding mode control was proposed to eliminate estimation error and harmonic ripples for PMSM sensorless control. A multi-proportional resonant filter was designed instead of a low-pass filter to filter out the specific harmonics of back EMF. The improved filter can solve the phase delay problem caused by a low-pass filter, eliminate the rotor angle compensator, simplify the system structure, and effectively suppress the system chattering. Then, a fractional normalized phase-locked loop was adopted to calculate the speed and rotor position, further eliminating the influence of noise. Compared with the traditional sliding mode control and the improved sliding mode control, the improved sliding mode observer can effectively suppress the back EMF chattering and reduce the speed estimation error. The correctness and effectiveness of the proposed improved sliding mode observer were verified through the simulation model and experimental platform of PMSM sensorless control.

Suppression of Major Current Harmonics for Dual Three-Phase PMSMs by Virtual Multi Three-Phase Systems

Dual three-phase (DTP) permanent magnet synchronous machine (PMSM) systems exhibit high current harmonics due to low impedance to voltage disturbance such as inverter voltage errors and back-EMF harmonics. This article proposes a concept of virtual multi three-phase systems to achieve independent regulation of the current harmonics in a DTP PMSM system. The virtual multi three-phase currents are first reconstructed by appropriately shifting the phase of original physical DTP currents, and then decomposed with the help of vector space decomposition techniques. As a result, the fundamental and the major current harmonics, i.e., the 5th, 7th, 11th, and 13th, can be completely separated in several isolated subspaces, where the independent current control loops can be easily designed and implemented. Compared with existing methods, the steady-state and dynamic-state performance of current harmonic regulation are enhanced by the proposed virtual multi three-phase systems and the effectiveness is validated by experimental.

Torque Ripples Reduction and Performance Analysis of Electrically Excited Flux Switching Motor

Torque ripples cause acoustic noise, fluctuation in speed, vibration, and reduce lifetime of the motor. The double salient structure of Flux Switching Motor (FSM) has a high air-gap permeance variation that produces high torque ripples. This paper presents an analytical model to reduce air-gap permeance variation and torque ripples of the proposed octane modular stator 8slots-6poles single-phase Electrically Excited (EE) FSM. Furthermore, the rotor pole shaping technique is used to minimize the air-gap permeance variation and therefore, torque ripples of the proposed design are reduced. The electromagnetic performance of EEFSM is analyzed via the Finite Element Analysis (FEA) method. For the proposed design magnetic flux harmonics are reduced by 71&#x0025; and back-EMF harmonics are suppressed by 48.5&#x0025;. Torque ripples of the proposed EEFSM are reduced by 20&#x0025;, cogging torque is diminished by 42.7&#x0025; and average torque is enhanced by 5.8&#x0025;. Finally, the prototype is fabricated and tested experimentally. Calculated values and experimental results are in good agreement and the difference is 3.5&#x0025;-5&#x0025;.

The Mechanism Analysis on Open-Circuit Back EMF in Fractional-Slot Concentrated Winding Permanent Magnet Machines Using Air-Gap Field Modulation Theory

This article investigates the production mechanism of the open-circuit back-electromotive force (back EMF) in fractional-slot concentrated winding permanent magnet (FSCW-PM) machines based on the air-gap field modulation (AFM) theory. The relationship between spatial PM field harmonics and temporal back EMF harmonics is discovered by using a general model, which is suitable for both stator-PM and rotor-PM machines. The analysis results reveal that the FSCW-PM machines produce their open-circuit back EMF on the basis of AFM, which means that each back EMF harmonic is induced not only by a specific single spatial field harmonic but also by several different spatial field harmonics. Furthermore, a general winding factor calculation formula for FSCW-PM machines is derived together with the general calculation formula of all back EMF harmonics. Finally, the analysis is verified numerically by the finite element method and experimentally.

Torque Ripple Reduction Method in a Multiphase PM Machine for No-Fault and Open-Circuit Fault-Tolerant Conditions

This paper presents a method that has been developed to reduce the torque ripples under healthy and open-circuit fault-tolerant (OCFT) conditions for a multiphase permanent magnet (PM) machine. For smooth torque, both the phase current and the back electromotive force (back-EMF) should be purely sinusoidal. To improve the torque in a multiphase machine, higher-order current harmonics are injected, which are related to the harmonics in the back-EMF. For this reason, generally, multiphase machines are designed with higher-order back-EMF harmonics. However, these harmonics produce ripples in the torque. In light of this, a torque ripple cancellation method has been developed that first determines an additional current component from the harmonic content of the back-EMF and then injects these additional components to cancel the torque ripple. It has been found that this new torque ripple cancellation method works for both faultless and faulty conditions in a five-phase PM machine. The method has been validated using Finite Element Analysis, and the results are presented in this paper.

Sensorless Drive Strategy of Open-End Winding PMSM With Zero-Sequence Current Suppression

The open-end winding permanent magnet synchronous motor (OW-PMSM) with common DC bus configuration provides a path for zero-sequence current (ZSC). Apart from the zero-sequence voltage (ZSV) generated by inverters modulation, ZSC also comes from the third harmonic back-EMF. However, the third harmonic back-EMF contains the position information of the rotor, which can be extracted by an appropriate strategy to achieve position sensorless drive. In order to achieve sensorless drive and ZSC suppression simultaneously, this paper proposes a novel general-integral extended state observer (GI-ESO) based method. The third harmonic back-EMF of the OW-PMSM is estimated and calculated in three-phase stationary coordinate system by GI-ESO. And then, a single-phase phase lock loop observer (SPLL) is exploited to extract the position and speed information of the rotor. Meanwhile, the estimated third harmonic back-EMF is directly fed forward to SPWM as the ZSV reference, then the output voltages of the inverters contains the ZSV that can exactly counteract the third harmonic back-EMF, so as to realize the suppression of ZSC. Compared with the method of combining the fundamental back-EMF detection and proportional resonance (PR) regulator, this method can realize sensorless drive and ZSC suppression at the same time with only one scheme. Benefiting from the use of GI-ESO, the observer bandwidth can be relatively low, which helps suppress noise and extend the speed range of sensorless operation. Moreover, this method has strong robustness against motor parameters. The proposed strategy is validated by experiments.