back-EMF Harmonics Research Articles

Multistage Predictive Current Control Based on Virtual Vectors for the Reduction of Current Harmonics in Six-Phase PMSMs

The most recent finite control set model predictive control (FCS-MPC) strategies for six-phase electric drives avoid the excitation of the secondary subspace by using virtual vectors to minimize the current ripple. However, these strategies can only control the fundamental current components, which adjust the machine flux and torque and leave the secondary current components unregulated, which should be zero during regular operation in order to reduce the losses in the machine. Due to this limitation and also due to the low impedance of the secondary subspace in machines with distributed windings, the stator currents might contain non-negligible low-frequency harmonics caused by small asymmetries in the machine, non-linear dynamics of the semiconductors in the power converters and back-EMF harmonics. This article proposes a novel multistage predictive current control strategy based on virtual vectors (MVV-PCC) for six-phase drives based on permanent magnet synchronous machines (PMSMs), which contains a fundamental and a secondary control stages that are responsible for tracking the reference currents in both subspaces separately. The obtained experimental results validate the effectiveness of the proposed strategy in the minimization of the current harmonics and the reduction of the torque ripple for different operating conditions of the six-phase drive.

Recent Challenges and Advances in the Sensorless Commutation of Brushless DC Motors

Background: Brushless DC motors are highly efficient motors due to their high torque to weight ratio, compact design, high speed operating capability and higher power density. Conventional Hall sensor based rotor position sensing is affected by the heating, vibration, interference and noise. Objective: The innovative, cost-effective and easily implementable sensorless techniques are essential in order to achieve high efficiency, reduced current and reduced torque pulsations. Furthermore, a delay free, high load fast startup is also an important issue. Methods: In this paper, an extensive review of various techniques based on the detection of freewheeling diode current, phase back EMF zero crossing point detection, back EMF integration method and third harmonic back EMF was done. The effect of various PWM strategies on back EMF detection were studied. Later on, the sensorless schemes based on flux linkage estimation and flux linkage increment were introduced. The load torque observers, unknown input observers, sliding mode observers, L∞ − induced observers, H∞ − deconvolution filter for back EMF estimation were also reviewed. As the brushless DC motors have no back EMF at starting and for back EMF based commutation, minimum speed is required for sufficient back EMF. Therefore various strategies of an open and close-loop reduced current startup have been studied to achieve effective commutation without reverse torque. Initial Position Detection (IPD) schemes, which are mostly based on saliency and current response to inductance variation, are effective where reverse torque is strictly prohibited. A detailed review of these Initial Position Detection techniques (IPD) has also been presented. Results: The detailed mathematical and graphical analysis has been presented here in order to understand the working of the state-of-the-art sensorless techniques. Conclusion: The back EMF detection using direct and indirect methods of terminal voltage filtering has the problem of delay and attenuation. PWM noise, freewheeling diode spikes and disturbance in detected back EMFs are also major drawbacks. The problems such as, parameter detuning, underestimation and overestimation, offset problem, system noise and observer gain variation, etc. limit the applicability of observer based technique. Therefore, a more robust and precise position estimation scheme is essential.

Open-Circuit Fault-Tolerant Control of Multi-Phase PM Machines by Compensating the d-q Axes Currents

This paper presents a novel method to control sinusoidal distributed winding or sinusoidal back electromotive force (back-EMF) multi-phase permanent magnet (PM) machines under open-circuit fault conditions. In this study, five different fault conditions are considered: single-phase, adjacent double-phase, non-adjacent double-phase, adjacent three-phase, and non-adjacent three-phase open circuit conditions. New current sets for the remaining healthy phase under open-circuit fault conditions are obtained by compensating the direct-quadrature (d-q) axes currents. For this purpose, an iterative method has been used to get the new set of currents. D-q axes currents, due to faulty phase/phases, are shared to the healthy phases to obtain the same d-q axes currents as in the healthy condition. Therefore, the same torque is produced as in the healthy condition. The developed method is simulated in MATLAB/Simulink by using a d-q modelled sinusoidal back-EMF five-phase machine. A vector control block diagram has been designed to run the machine under healthy and faulty conditions. The machine model has been run successfully under fault tolerant conditions. Additionally, a finite element analysis (FEA) has been undertaken to simulate the five-phase PM model machine by using MagNet software. Open-circuit fault-tolerant control currents are fed into the coils of the machine model. Satisfactory torque results have been obtained. Because the model five-phase PM machine includes higher order back-EMF harmonics, especially the third harmonic, torque has ripple due to interaction between the fault-tolerant control currents and the higher order back-EMF harmonics.

A Design Technique for Shaping of Back-EMF Using Heuristic Optimization and Winding Factors in Brushless AC and DC Machines

One of the requirements for the electric machine designer is to provide an optimal back-EMF waveform in a high-performance application such as electric vehicles (EV) or hybrid EVs (HEV) systems. This paper presents a design technique for the shaping of back-EMF waveforms in brushless permanent magnet (PM) AC and DC machines. At first, back-EMF waveforms are calculated by an analytical model based on the subdomain field model and the complex permeance function. The finite element and experimental results are used for the verification of the analytical model. Secondarily, the heuristic optimization algorithm is applied to the analytical model in order to search for optimal solutions where the objective function is composed of harmonics in target back-EMF. As a result, the optimal back-EMF waveform can be traced by matching the odd harmonics of the design candidate with those of the target waveform. Also, a detailed investigation of the winding factor is carried out to provide the key design techniques regarding the shape of back-EMF.

Back-EMF Analysis of a Variable Flux Machine for Different Magnetization States

This article presents the effect of different magnetization pulse widths and methods on the back electromotive force (EMF), no-load losses, and minimum inverter rating at different operating conditions of a variable flux permanent magnet synchronous machine (VF-PMSM/VFM). Precise information of the back-EMF helps to estimate the cogging torque and torque ripple. An accurate determination of the core loss leads to a better efficiency estimation and machine design. An experimentally determined minimum inverter rating reduces the cost of the motor drive system. An adaptive nonlinear filter is used to estimate the VFM back-EMF during the motoring mode. The VFM is often demagnetized and remagnetized by injecting a current pulse to achieve the high-speed and high-torque requirements. The sudden injection of a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -axis current pulse will change the magnet flux linkage and back-EMF harmonics. In this article, harmonics present in the machine back-EMF due to different magnetization and demagnetization current pulse widths and magnetization methods are analyzed. Besides, the quality of the back-EMF for different speeds and machine no-load losses are presented for different magnetization levels. The minimum inverter current rating is determined for magnetizing current and magnetizing current at full load considering the minimum pulse amplitude and width to magnetize the VF-PMSM.

Optimized Current Waveform for Torque Ripple Mitigation and MTPA Operation of PMSM with Back EMF Harmonics based on Genetic Algorithm and Artificial Neural Network

Interior permanent magnet synchronous motors (IPMSMs) with nonsinusoidal flux develop undesirable torque ripple under conventional control strategies, leading to vibration and increase of mechanical stress. To overcome this problem, active torque ripple compensation based on harmonic stator current injection is widely investigated in the literature. However, the combination of the torque ripple minimization strategy with the maximum torque per Ampère (MTPA) operation is a challenge to the field. In this paper, a control strategy based on genetic algorithm (GA) and artificial neural network (ANN) is proposed to achieve low torque ripple with MTPA operation of a three-phase IPMSM with significant magnitude of zero sequence back-electromotive force (back-EMF) component. Investigations have found that the consideration of back-EMF zero sequence in torque prodution can increase the torque per Ampère ratio. Further, the results shows that the proposed strategy effectively reduces the torque ripple in real time operation, including steady state and transient torque performances.

Consequent Pole Permanent Magnet Machine With Modular Stator

Owing to a group of permanent magnets (PMs) with the same magnetization direction are replaced by salient iron core, the consequent-pole (CP) PM machines generally suffer from asymmetry flux density. This will leads to the even-order back-EMF harmonics, which have negative influence on the electromagnetic performance. It is widely known that the even-order back-EMF harmonics cannot be eliminated for the machines with odd back-EMF phasor belongs to one phase in one machine periodicity, i.e., ${\boldsymbol{N}_0}$ is odd ( ${\boldsymbol{N}_0} = {\boldsymbol{N}_{\boldsymbol S}}/\boldsymbol{mt}$ , where ${\boldsymbol{N}_{\boldsymbol S}}$ is the number of slot for one machine, t is the unit sub-machine periodicity, m is the number of phase). Hence, this paper proposes a general modularization method solving this problem. The elimination principle of even-order back-EMF harmonics in the modular stator (MS) is explained by the star of slots. Further, the MS with auxiliary winding (AW) and auxiliary teeth (AT) are proposed to improve the electromagnetic performance of the MS CP (MSCP) PM machine. Then, the electromagnetic characteristics, including open circuit field distribution and back-EMFs, torque characteristics, unbalanced magnetic force (UMF), loss distribution characteristics as well as efficiency contours are comprehensively compared. Finally, the MSCP PM machine with auxiliary winding (MSCP-AW) is fabricated and tested to verify the theoretical analysis as well as the finite element (FE) results.

Harmonic Torque Suppression Methods for Single-Phase Open-Circuit Fault-Tolerant Operation of PMSM Considering Third Harmonic BEMF

This article proposes a novel type of the 2nd and 4th harmonic torque suppression methods during conventional single-phase open-circuit fault-tolerant operation when considering the 3rd harmonic back-EMF of permanent magnet synchronous motor (PMSM). These suppression methods are based on injecting the 3rd harmonic currents into the two remaining healthy phases, which produces harmonic torque of opposite phase to cancel the original one. The suppression can have three different constraints: maintaining the average torque, eliminating the 2nd harmonic torque, and eliminating the 4th harmonic torque. They cannot be achieved simultaneously. Combining any two of them leads to a particular injection method. Three particular methods are developed and their performance are investigated by theoretical analysis and compared against the conventional one. The proposed fault tolerant control strategies are applicable to various fault-tolerant inverter topologies by using these novel phase current references, whereas the current tracking algorithms could be different. To ease validation, a four-leg inverter topology is selected to implement such injection methods to a three-phase star-connected 10-pole/9-slot PMSM. The experiments validate that tracking the proposed current references can effectively suppress the harmonic torque, which confirms the theoretical analysis.

Sensorless current model control for permanent magnet synchronous motor based on IPID with two‐dimensional cloud model online optimisation

In this study, a sensorless current model control algorithm for permanent magnet synchronous motor (PMSM) is investigated based on intelligent proportion integration differentiation (IPID) with two-dimensional cloud model online optimisation. To obtain a relatively accurate rotor position and speed estimation, in virtual γ-δ rotating coordinate system, estimation of the position and speed is performed using a current error between an actual current and the model current obtained from a current model of the motor. Simultaneously, a type of IPID with parameter dynamic real-time self-tuning function is designed to adjust the speed and current loop in the current model control. By introducing the chaos particle swarm optimisation (CPSO) algorithm to optimise the control parameters offline, the entire control system is in the optimised state, then the two-dimensional cloud model online adjustment module is used to perform real-time tuning. The experimental results show that the new control algorithm proposed can accurately estimate the real-time rotor position and speed, which effectively avoids the influence of back EMF harmonics, and it has the robustness to motor internal parameter perturbation and external load disturbance.

Cancelation of Torque Ripples in PMSM via a Novel Minimal Parameter Harmonic Flux Estimator

This paper presents a novel approach for treating the harmonic torque in permanent magnet motors at selected harmonic orders. The method is based on the online estimation of the motor harmonic flux. For this purpose, a novel minimal parameter harmonic flux estimator (MPHFE) is developed. The MPHFE is formulated such that the inductance, resistance, and stator current and its derivative are not necessary for the estimation of the harmonic flux. This was achieved by forcing the harmonic current to zero through the combined action of a field-oriented controller (FOC) and a feedforward controller. Subsequently, the harmonic flux can be obtained directly from the estimated harmonic back EMF without the involvement of other motor parameters. Finally, the estimated flux is used in conjunction with a comprehensive model of the motor harmonic torque to determine the stator current compensation for eliminating the torque harmonic. Experimental results presented from a permanent magnet motor confirm the theoretical claims in this paper as well as demonstrate the effectiveness of the proposed method to reduce the magnitude of the harmonic torque significantly.

Operation Principle and Torque Component Quantification of Short-Pitched Flux-Bidirectional-Modulation Machine

This paper analyzes the operation principle of a short-pitched flux-bidirectional-modulation machine, with especial efforts in terms of its torque component quantification and back EMF harmonics reduction. With the bidirectional-flux-modulation effect, increased equivalent permeance of the air gap is constructed to enhance the machine torque production. Meanwhile, with the shorted-pitched distributed winding design, the electrical gear ratio of machine is increased to realize boosted torque production, and a variety of back-EMF harmonics are eliminated, thus the torque ripple is reduced. In this paper, the machine operation principle is analyzed based on a simple magnetomotive force-permeance analytical model. The torque components and back EMF harmonics are deduced by winding factor analysis. It is revealed that in the proposed machine, the excitation fields with pole pairs of 2, 22 and 46 have generated the effective back-EMF and constant torque and their contribution percentages are 77%, 20% and 3% respectively. Rotor-PM and stator-PM contribute 59% and 41% of the torque respectively. With the 5/6 short-pitch design, the $3^{\mathrm {rd}}$ , $5^{\mathrm {th}}$ and $7^{\mathrm {th}}$ back-EMF harmonics are reduced by 55%, 88% and 88% respectively and the THD of back-EMF is reduced 56.8%. A prototype is fabricated and tested for experimental verification.

Influence of Various Magnetic Pole on Electromagnetic Performance of Consequent-Pole Permanent Magnet Machine

Permanent magnet (PM) machine with consequent pole (CP) rotor can improve the PM utilization ratio. However, one group PMs with the same polarity is replaced by iron core which deteriorating the electromagnetic performance of the machine, including even-order back-EMF harmonics, torque ripple, as well as unipolar leakage flux. Therefore, CP PM machine with various magnetic pole, i.e., equal pole-arc magnetic pole (EMP) and asymmetric magnetic pole (AMP) structure is proposed, with smaller torque ripple can be achieved, without deteriorating the torque ability compared with the conventional CP PM machine. Further, the influence of various CP PM magnetic pole on the end leakage flux is analyzed by three-dimensional (3-D) finite element (FE), which includes leakage flux distributions as well as magnetization of shaft. The electromagnetic characteristics of the machine with EMP and AMP rotor are compared with traditional surface-mounted and CP PM machines by FE analysis. It is demonstrated that EMP and AMP rotor structure can reduce even-order harmonics, torque ripple and end leakage flux for the machines. Finally, one prototype with CP AMP rotor is tested to confirm the theoretical and FE analysis, which includes suppression effect of even back-EMF harmonics, torque characteristics as well as leakage flux at the end shaft.

Loss model based efficiency optimized control of brushless DC motor drive

Energy efficiency improvement of electrical motor drives has recently become a very interesting subject. Several methods have been proposed in the literature to improve the efficiency of permanent magnet synchronous machine (PMSM) with sinusoidal back-EMF. These methods are not precise and appropriate for brushless DC machine (BLDCM) with trapezoidal back-EMF. As a unique solution, this work introduces a flux controlled based loss minimization algorithm suitable for BLDCM that considers iron loss as well as influence of back-EMF harmonics; consequently promotes efficiency of machine. In this regard, the loss model of PMSM is extended based on multiple reference frame analysis to include back-EMF harmonics of BLDCM. As an advantage, proposed modified loss model does not require any additional data about the dimensions of machine that makes it suitable for industrial motor drive applications. The Proposed loss model is validated through experimental tests in different operating conditions. Afterward, by applying direct torque and indirect flux control of BLDCM as the control technique, d-axis current in the rotor reference frame is controlled to reduce the air gap flux and consequently iron loss of the machine. Finally, a procedure is presented to determine the optimum d-axis current which maximizes the efficiency. Effectiveness of proposed control system is evaluated using simulation results in MATLAB/Simulink and experimental results on a practical prototype. It is indicated that depending on the operating conditions, about 2% to 11% of efficiency improvement would be achieved in the proposed method.

Rotor position estimation scheme with harmonic ripple attenuation for sensorless controlled permanent magnet synchronous motors

To achieve high-performance sensorless control of permanent magnet motors with non-sinusoidal back electromotive force (EMF), an improved sliding mode observer (SMO) adopting synchronous rotating low-pass filter (SRLPF) is proposed. The SRLPF is utilised to reduce the back-EMF harmonics and extract the fundamental component. Different from the traditional rotor position observer, the proposed observer can calculate the rotor position with the back-EMF fundamental component. Owing to the decrease in the influence of non-sinusoidal back-EMF, the estimated rotor position harmonic ripple error can be greatly reduced. Then, the high estimated accuracy and excellent sensorless control performance can be obtained. In addition, the proposed strategy is easy for implementation. With the comparison between the traditional SMO and the proposed observer, the experiments of the system steady-state error, the speed tracking performance, and the disturbance rejection ability in the speed range from 60 r/min to the rated speed 750 r/min are presented. The validity of the proposed method is conformed.

Design of Doubly Complementary Stator-PM Machine With High Magnet Utilization Factor for Low-Cost Applications

Aiming to improve permanent magnet (PM) utilization factor, suppress cogging torque, and reduce back-EMF harmonics in stator-PM machines, a new type of stator-PM doubly complementary machines (DCMs) are proposed in this paper. These machines employ two complementarities in the structure, as one exists in double rotors and the other exists in the units belonging to same phases. The first complementary characteristic supplies a consecutive switching path for PM exciting flux, so that shorted or open magnetic path could be avoided to reduce cogging torque and improve PM utilization. The second one is designed to reduce back electromotive force (EMF) harmonics and improve the torque density. The topology, operation principle, characteristics, and design methodology for DCMs are presented. Simulation and experiments are conducted for a 12/11(stator teeth/rotor teeth) DCM to evaluate its performance and verify this design methodology. It is revealed that this machine could obtain good sinusoidal back-EMF waveform, small torque ripple, and high PM utilization factor due to the doubly complementary characteristic.

High-Precision Sensorless Drive for High-Speed BLDC Motors Based on the Virtual Third Harmonic Back-EMF

In order to improve the performance of the high-speed brushless direct current motor drives, a novel high-precision sensorless drive has been developed. It is well known that the inevitable voltage pulses, which are generated during the commutation periods, will impact the rotor position detecting accuracy, and further impact the performance of the overall sensorless drive, especially in the higher speed range or under the heavier load conditions. For this reason, the active compensation method based on the virtual third harmonic back electromotive force incorporating the SFF-SOGI-PLL (synchronic-frequency filter incorporating the second-order generalized integrator based phase-locked loop) is proposed to precise detect the commutation points for sensorless drive. An experimental driveline system used for testing the electrical performance of the developed magnetically suspended motor is built. The mathematical analysis and the comparable experimental results have been shown to validate the effectiveness of the proposed sensorless drive algorithm.

Comparisons of Rare-Earth and Rare-Earth-Free External Rotor Permanent Magnet Assisted Synchronous Reluctance Motors

This paper presents the comparisons of five-phase external rotor permanent magnet assisted synchronous reluctance motors (PMa-SynRMs) with neodymium (Nd) and ferrite (Fe) based PMs. Five-phase PMa-SynRMs, in general, have been proposed as an alternative to conventional three-phase motors utilized in automobile applications. However, with increased attention towards higher torque density and lower torque pulsations in electric motor designs, five-phase external rotor PMa-SynRMs can be highly attractive. In addition to increased fault tolerance and reliability of five-phase PMa-SynRMs, an adaptation of external rotor design can significantly increase the average torque developed with reduced torque pulsations and back-electromotive force (EMF) harmonics. However, with the design complexity involved in such high performance five-phase PMa-SynRM designs, the shape of flux barrier and choice of PMs have been one of the main challenges. In this study, novel five-phase external rotor PMa-SynRM designs with optimal flux barrier number and shape with Nd and Fe PMs are presented. Finite element simulations are conducted on the 2-D designs to compare their performance characteristics such as torque developed, torque pulsations, structural stability, thermal heat flow, demagnetization effects, and back-EMF harmonics. Optimal 3.8 kW Nd-based and 3.7 kW Fe-based five-phase external rotor PMa-SynRM designs are fabricated, and experimental tests are conducted on the prototypes to compare the results with a benchmark internal rotor PMa-SynRM.

Comparison of the Characteristics of Cost-Oriented Designed High-Speed Low-Power Interior PMSM

In this paper, the characteristics of interior permanent magnet synchronous machine (IPMSM) with concentrated windings are evaluated for three different rotor geometries. The reference machine is a fractional horsepower IPMSM with single-layer magnets (1-layered IPMSM). The maximum output power of the machine is 820 W. Based on the electrical properties and machine cost of the reference machine, IPMSM with two different rotor geometries are designed. The first one is an IPMSM with v-shaped magnets and the second one is an IPMSM with double-layer magnets topology (2-layered IPMSM). The machines are compared in two operating points: one in the base speed area and one in the field weakening range. The focus of the machine comparison is the parasitic effects due to the nonsinusoidal rotor field, e.g., back-EMF harmonics, torque harmonics, radial force densities, and iron losses.

A Novel Flux-Switching Permanent Magnet Machine With Overlapping Windings

In this paper, in order to enlarge its torque density, an overlapping winding (OW) is applied to the 24/16-stator/rotor-pole flux-switching permanent magnet (FSPM) machine. By adopting an OW-configuration with full-pitch coils, the pitch factor and coil-flux cross-sectional area in the 24/16-pole FSPM machine with nonoverlapping winding (NOW) can be doubled. Thus, the fundamental open-circuit phase flux-linkage and back-EMF can be effectively enhanced by 115.28%, making it comparable to the conventional 12/10-pole NOW-FSPM machine. Therefore, by injecting the same current density, the proposed OW-FSPM machine can produce 65.2% higher torque density than its NOW counterpart, and 17.6% higher torque density than the conventional 12/10-pole NOW machine despite 21.5% lower ampere turns due to a smaller slot area. However, the proposed machine suffers from high torque ripple due to high cogging torque and back-EMF harmonics. Torque ripple reduction by harmonics current injection and rotor skewing in the proposed machine are investigated. Results show that both methods can effectively reduce the torque ripple in the proposed 24/16-pole NOW-FSPM machine, albeit with the level of torque density being compromised. Experiments are performed in order to validate the analysis.

Rotor position estimation for single- and dual-three-phase permanent magnet synchronous machines based on third harmonic back-EMF under imbalanced situation

In this paper, an improved rotor position estimation strategy based on third harmonic back-EMF for single- and dual-three-phase permanent magnet synchronous machines (PMSMs) under imbalanced situation is proposed. Due to the imbalanced machine impedance, back-EMF or sensing resistor network, the measured triplen harmonic back-EMF will contain certain fundamental component distortion which may severely deteriorate the performance of rotor position estimation. With the aid of the fundamental component compensator, this distortion can be significantly compensated, and the rotor position estimation error can be minimized considerably. The proposed strategy has been implemented on a dSPACE platform with a prototype of dual-three-phase PMSM with serious imbalanced parameters, and operate at single- and dual-three-phase conditions. The experimental results prove that the proposed strategy can significantly improve the steady-state and dynamic performance of rotor position estimation under imbalanced situation.