Back Electromotive Force Harmonics Research Articles

Improved Coreless Axial Flux Permanent-Magnet Machine With Nonuniformly Distributed Winding

The windings of coreless axial flux permanent-magnet machine (CAFPM) are exposed to the rotor magnetic field, where each back electromotive force (EMF) harmonic is induced not only by several different spatial field harmonics but also by the winding distribution. In order to reduce the time harmonics of back EMF for CAFPM with non-overlapping winding, one new winding structure with non-uniform distributed coils is proposed in this paper, in which the coils are arranged in a non-uniform way with annular distribution in the stator. Firstly, the relationship between uniform and non-uniform distributed windings is analyzed based on the phasor diagram of each coil EMF, and the analytical expression of back EMF under non-uniform distributed windings is established. Secondly, key performance indexes under different working states, like no-load, are investigated by three dimensional (3-D) finite element analysis (FEA). Finally, comprehensive experiments are carried out to verify related theoretical analysis, which demonstrate that the non-uniform distributed windings can effectively reduce the time harmonics and increase the working efficiency.

Efficiency Improvement of Permanent Magnet BLDC Motors for Electric Vehicles

A permanent magnet Brushless DC (BLDC) motor has been designed with different rotor configurations based on the arrangement of the permanent magnets. Rotor configurations strongly affect the torque and efficiency performance of permanent magnet electric motors. In this paper, different rotor configurations of the permanent magnet BLDC motor with parallel the Halbach array permanent magnet were compared and evaluated. Many applications of electric drives or air-crafts have recently preferred the surface-mounted permanent magnet design due to its ease of construction and maintenance. The finite element technique has been used for the analysis and comparison of different geometry parameters and rotor magnet configurations to improve efficiency and torque performance. A comprehensive design of a three-phase permanent magnet BLDC 35kW motor is presented and simulations were conducted to evaluate its design. The skewing rotor and Halbach magnet array are applied to the permanent surface-mounted magnet on the BLDC motor for eliminating torque ripples. In order to observe the skewing rotor effect, the rotor lamination layers were skewed with different angles and Halbach sinusoidal arrays. The determined skewing angle, the eliminated theoretically cogging torque, and the back electromotive force harmonics were also analyzed.

Back EMF Waveform Comparison and Analysis of Two Kinds of Electrical Machines

In this study, the back electromotive force (EMF) waveforms of a flux switching permanent magnet (FSPM) machine and variable flux memory permanent magnet (VFMPM) machine with same main dimension were researched. Firstly, the simulation result showed that the maximum amplitude of phase back EMF waveform of FSPM machine was 245% larger than that of the VFMPM machine, and this was verified by the experimental result (243%). Secondly, the phase back EMF harmonics of the FSPM machine and VFMPM machine were compared, including the enhance flux condition and weaken flux condition of VFMPM machine. At last, the mutual demagnetization effect, which led to the difference amplitudes of maximum back EMF waveform between FSPM machine and VFMPM machine was analyzed. The comparison and analysis of the back EMF waveform will provide some qualitative advice for the future application research of the FSPM machine and VFMPM machine, such as application selection, optimization control method and so on.

Direct Harmonic Current Control Scheme for Dual Three-Phase PMSM Drive System

The performance of model predictive control mainly depends on the accuracy of model and parameters, such as the back electromotive force (EMF) harmonics in dual three-phase permanent magnet synchronous motors (PMSMs). However, the back EMF harmonics would vary with the operation conditions. Thus, the parameter mismatches in the harmonic subspace would be inevitable. In this article, a direct harmonic current control scheme is proposed to provide further harmonic current suppression under parameter mismatches in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> subspace. First, deadbeat control concept is applied to calculate the reference voltage in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i> subspace. This reference voltage vector is utilized to generate a group of control sets with different voltage vectors in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> subspace. Then, a slide mode control scheme is provided to deal with the inaccurate parameters in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> subspace. The reference voltage vector in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> subspace is obtained with this slide mode control scheme without the remaining inductance parameters. Third, a two-step modulation method and cost function are discussed to further suppress the harmonic currents. The control sets generated by deadbeat control are optimized with the cost function. Moreover, a switching pattern with fixed switching frequency is proposed in this section. Finally, experimental results verify that proposed control scheme could further suppress the harmonic currents.

Compensation of Selective Current Harmonics for Switching-Table-Based Direct Torque Control of Dual Three-Phase PMSM Drives

Current harmonics are ubiquitous in dual three phase (DTP) permanent magnet synchronous machine (PMSM) drives. Due to back electromotive force (EMF) distortion, significant current harmonics are generated in the DTP-PMSM system. The influence of back EMF harmonics is investigated in this paper and a novel switching-table-based direct torque control method to compensate the selected current harmonics caused by the back EMF harmonics is proposed. It shows that by employing different optimal action time durations for voltage vectors in the z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> subspace and setting the synthetic voltage vectors to non-zero, the stator flux harmonics caused by the back EMF harmonics can be selectively compensated, as verified by experiments.

Disturbance Observer Based Predictive Current Control of Six-Phase Permanent Magnet Synchronous Machines for the Mitigation of Steady-State Errors and Current Harmonics

Multiphase machines, associated with state-of-the-art control strategies like finite control set model predictive control (FCS-MPC) are suitable for applications where reliability and disturbance-free operation are key factors. Although FCS-MPC provides good transient performance and straightforward design, the performance of the drive system is affected by model inaccuracies due to parameter mismatch and unmodeled dynamics, such as deadtime effects in the power converters and back-electromotive force harmonics. In this context, this article proposes a novel and robust disturbance observer based predictive current control strategy for six-phase permanent magnet synchronous machine drives that minimizes the steady-state errors due to parameter mismatch errors, while simultaneously reducing the amplitude of the fifth- and seventh-order current harmonics due to unmodeled dynamics, which are non-negligible in six-phase machines. Simulation and experimental results demonstrate the very good performance of the proposed strategy even when considering significant errors in the system parameters and different values of the deadtime in the power converters.

Analytical Method for Calculating the Magnetic Field of Spoke-Type Permanent Magnet Machines Accounting for Eccentric Magnetic Pole

This article proposes an analytical method to calculate the magnetic field, back electromotive force (BEMF), inductance, and torque of spoke-type permanent magnet machine (PMM) accounting for eccentric magnetic pole. The magnetic field in the slotted spoke-type PMM is predicted according to conformal mapping, flux continuity theorem, double reaction theory, superposing principle, and complex relative air-gap permeance. Then, BEMF, inductance, and torque are obtained according to the results of magnetic field. A spoke-type PMM with eccentric magnetic pole is used to verify the analytical model. The harmonics of BEMF and torque ripple of spoke-type PMM with eccentric magnetic pole are very slight. Results of magnetic field, BEMF, inductance, and torque by the analytical model are verified by finite element. The validation to calculate BEMF and electromagnetic torque with analytical model is confirmed by experimental result. The analytical method proposed in this article can be applied to the spoke-type PMM with all kinds of magnetic-pole shape.

Back EMF Harmonic Analysis of Permanent Magnet Magnetic Geared Machine

Permanent magnet magnetic geared machine (PM-MGM) is widely researched as a potential core component of electrical continuously variable transmission system. Due to the dual mechanical port structure, back electromotive force (EMF) characteristics of PM-MGMs are quite different from that of conventional permanent magnet (PM) machines. In this article, back EMF harmonic features of PM-MGMs are thoroughly analyzed. The back EMF harmonic amplitude and order are analytically deduced, it can be found that both of them are variable and related with normalized speed ratio. A simulation/experiment method is proposed to separate and calculate different flux linkage components. A novel distortion factor criterion for PM-MGMs is defined to evaluate the variable back EMF distortion value. Different from existing criteria, the proposed criterion is a function of normalized speed ratio, hence it is more comprehensive for PM-MGM back EMF comparison and machine design. The torque ripple caused by back EMF harmonics is also analyzed. A PM-MGM prototype has been manufactured, and back EMF features as well as validity of the proposed distortion factor are verified by experiment.

Bi‐subspace predictive current control of six‐phase PMSM drives based on virtual vectors with optimal amplitude

Owing to the low equivalent impedance of six-phase machines in the secondary subspace, in which currents do not contribute to torque production, low-order current harmonics with high amplitude are likely to appear in the stator currents, increasing the harmonic distortion and the losses in the machine. In the case of permanent magnet synchronous machines (PMSMs), the main causes of these harmonics are machine asymmetries, non-linearities of the power converters and back-electromotive force harmonics. The existing predictive control strategies based on virtual vectors for six-phase machines only regulate the currents mapped into the fundamental subspace, responsible for flux/torque production and leave the currents mapped into the secondary subspace uncontrolled. This study proposes a novel bi-subspace predictive control strategy for six-phase PMSMs with optimal amplitude virtual vectors, which is able to effectively regulate the currents in both subspaces simultaneously, leading to a significant minimisation of the current harmonic distortion. Moreover, the proposed control strategy also allows operating the six-phase PMSM with a current unbalance between the two sets of windings. Both simulation and experimental results confirm the much better performance of the proposed strategy in comparison with other state-of-the-art predictive control strategies found in the literature.

Influence of Coil Pitch and Stator-Slot/Rotor-Pole Combination on Back EMF Harmonics in Flux-Reversal Permanent Magnet Machines

Harmonics of back electromotive force (back EMF) always have great effects on torque ripples in flux-reversal permanent magnet (FRPM) machines. In this paper, the back EMF in FRPM machines with different magnetization modes and coil pitches is studied. Then, a simple analytical method is developed to judge whether an FRPM machine with an arbitrary slot-pole combination has compensation to eliminate phase back EMF even-order harmonics or not. On this condition, four different types of machines, i.e., FRPM machine with compensation (magnetization mode 1), FRPM machine with compensation (magnetization mode 2), FRPM machine without compensation (magnetization mode 1), and FRPM machine without compensation (magnetization mode 2), are summarized to derive the winding factors when coil pitches varied from 1 to 3. Thus, the influence of the coil pitch on back EMF and its harmonic components as well as their phase angles can be studied by both analytical expression and 2-D finite element analysis. It is found that the optimal magnetization mode and coil pitch can help to increase the winding factor and hence enlarge the fundamental back EMF. Finally, the prototypes are fabricated and the corresponding experiments are conducted to further verify the effectiveness of derived analytical expressions.

Predictive control of permanent magnet synchronous motor with non‐sinusoidal flux distribution for torque ripple minimisation using the recursive least square identification method

To reduce the torque ripple of permanent magnet synchronous motor with non-sinusoidal flux distribution, a new method is presented in this study. This method is based on model predictive control (MPC). MPC is a model-based control and requires an accurate model of the motor. A sliding mode observer, accompanied with a recursive least square estimator, is utilised to determine the magnitudes of the harmonics of the back electromotive force (EMF) waveforms. The appropriate current harmonics, considering the back EMF harmonics, are injected to shape the motor current. The interaction of non-sinusoidal back EMF and the shaped current leads to torque ripple reduction. The experimental results verify the effectiveness of the proposed method.

Analysis of PDT noise originating from driving method of a HDD spindle motor

This paper investigates the prominence discrete tone (PDT) noise originating from the driving method of a hard disk drive (HDD) spindle motor with 12 poles and 9 slots. Torque ripple of a HDD is reconstructed by the multiplication of measured back electromotive force (BEMF) and measured switching current. It shows that the frequency components of PDT noise match with those of torque ripple. It also investigates the frequency change of PDT noise due to two driving methods which have the different switching-off periods to detect the zero-crossing of the BEMF. The BEMF has odd harmonics of the number of pole pair, but the current has even harmonics of the number of pole pair due to the switching-off period as well as those odd harmonics of BEMF. We theoretically derive the torque equation in terms of the frequency components of BEMF and switching current. We also verify that the even harmonics of the driving current due to driving method generate the 54th harmonic of torque ripple, and show that the pure sinusoidal BEMF with the 6th harmonic can decrease the 36th harmonic of torque ripple as well as PDT noise in the HDD spindle systems.