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In this article, a new dual-permanent magnet spoke-type flux-reversal machine (dual-PM SFRM) for direct-drive applications is proposed. Tangentially magnetized permanent magnets (PMs) sandwiched with iron poles are set in stator slots. To increase the torque density within the geometric restrictions, PMs are introduced in the rotor as well and magnetized radially to form a consequent-pole rotor. Global optimizations are conducted and comparisons are made on torque, torque ripple, and torque/PM volume with the existing single-PM SFRM. It is found that the proposed dual-PM SFRM can produce 22.6% larger torque with an optimal PM volume and a 17.5% larger torque with the same PM volume compared with the single-PM counterpart. Moreover, major magnetic field space harmonics are derived analytically and verified by finite-element analysis (FEA) and the torque components produced by the working harmonics are calculated and compared in terms of different stator/rotor pole number combinations. Comparisons are made on back electromotive force, cogging torque, torque performance, and efficiency between dual-PM SFRM and conventional flux-reversal machine. The influence of different stator configurations, i.e., the slot opening, the iron bridge, and the unequal tooth, on torque performance in the proposed dual-PM SFRM has been studied and highlighted. A prototype has been built and tested to validate the FEA calculations. [ABSTRACT FROM AUTHOR]

Consequent-pole (CP) permanent magnet (PM) configuration suffers asymmetric electromagnetic characteristics although it saves PM usage. The CP-based stator-PM synchronous machines are investigated in this paper, with particular reference to symmetrical issues. The electromagnetic performances of the CP-based stator-PM synchronous machines are firstly evaluated. Afterwards, the rule of even order harmonics cancellation is presented for different slot/pole number combinations and winding layouts, based on which symmetrical phase flux-linkages can be obtained although the unbalanced magnetic flux naturally occurs. Moreover, based on the three-dimensional finite element analysis, the unipolar end leakage-flux caused by the asymmetric magnetic field is identified, and the risk of the shaft magnetization is revealed. Finally, a pair of prototype machines are fabricated and measured to validate the analyses. [ABSTRACT FROM AUTHOR]

Voltage induced in the dc winding by the armature field in wound field switched flux (WFSF) machines will induce voltage perturbation in the voltage supply and cause dc winding current ripple and field excitation fluctuation. This will challenge the dc voltage controller and deteriorate the control performance, especially when the load and/or the rotor speed are high. In this article, the dual three-phase armature winding design with a phase-shift of 30 electrical degrees is employed in the partitioned stator WFSF machines to reduce the on-load dc winding-induced voltage. Analytical deductions and finite element (FE) results demonstrate that the dominant sixth-order-induced voltage harmonic can be suppressed to zero. Hence, the peak-to-peak induced voltage in the 12/11- and 12/13-pole partitioned stator WFSF machines can be reduced by 83.35% and 82.53%, respectively. Due to the improvement of winding factors, the torque densities are 4.85% and 5.60% higher, respectively. Prototypes are built and tested to verify the analytical and FE results. [ABSTRACT FROM AUTHOR]

Consequent-pole (CP) permanent magnet (PM) machines have attracted considerable interest as a means of reducing machine cost through a marked reduction in the volume of PM required to meet a particular torque specification. However, the presence of a large torque ripple that can result from the CPPM structure can hinder their adoption in some applications, especially for the dominant third-order torque ripple. Although several design-specific modifications have been proposed to ameliorate torque ripple, the generalized principles underpinning this behavior have not been fully established. In this article, it will be illustrated that an aggregation of the fluctuations in inductance, back electromotive force, and cogging torque contributes to increased torque ripple. Meanwhile, an asymmetric pole shaping method is proposed to reduce the torque ripple, taking the dominant third-order torque ripple as an example. Both simulated and experimental results of the 12-slot/8-pole prototypes show that compared to the symmetrical pole shaping model and the plain pole model, the proposed asymmetric shaping method is effective in reducing torque ripple. [ABSTRACT FROM AUTHOR]

Consequent pole (CP) permanent magnet (PM) machines offer scope for reducing the quantity of PM material and hence cost compared to more conventional PM machine topologies of the same rating. In this type of machine, the rotor pole arc is usually optimized to realize the largest output torque with pole shaping methods used to reduce torque ripple. However, such approaches tend to be limited by constraints imposed on the pole shapes. It is a common practice to adopt similar PM and iron pole shapes, an approach that does not fully account for the different characteristics of PM and iron poles in CPPM machines, often leading to large even order harmonics in the airgap flux density. This article proposes a shaping method with a variable rotor profile and pole arc span being established by means of optimization by Genetic Algorithm. It is demonstrated that for a fixed quantity of PM material, different PM and iron pole shapes in combination with optimal PM and iron pole arc spans are essential for ensuring both maximum output torque and lower torque ripple when the due account is taken of flux leakage. It also demonstrates that since the flux density in the region under a PM pole is governed by the magnetic potential produced by magnets while it is governed by magnetic reluctance under iron pole, different PM pole and iron pole shapes are necessary to reduce the even-order harmonics in a CPPM machine and consequently to reduce torque ripple. The performances of optimized and more conventional CP machines are compared by finite-element method on 12-slot/8-pole prototype motors. [ABSTRACT FROM AUTHOR]

In this article, two novel sinusoidal pulsewidth modulation (SPWM) strategies with simple implementation are proposed for an open-winding machine fed by isolated dc-bus dual two-level three-phase inverters to reduce switching frequency and current harmonics. The proposed strategies utilize zero sequence voltage injection and unbalanced reference voltage distribution to generate discontinuous PWM with low current harmonics and less switching action. Two different zero sequence voltages are introduced in this article corresponding to two proposed PWM strategies with different switching actions in a PWM cycle. The novelty of this article is low current harmonics and less switching actions in a PWM cycle compared with the conventional SPWM strategy. Moreover, compared with the subhexagonal center PWM strategy, the proposed SPWM strategies have advantages of easy implementation and half switching commutations with the same current harmonic characteristics. The superiority of the proposed SPWM strategies is validated by simulation and experiment results. [ABSTRACT FROM AUTHOR]

This article develops a new closed-form analytical solution to the harmonic spectrum of the full-bridge (FB) modular multilevel converter (MMC) with phase shifted carrier pulse width modulation. It considers FB-MMC operation in boost mode where the negative-voltage states of the FB submodules (SMs) are utilized to extend the ac operating voltage range and/or reduce the dc link voltage which is known to reduce the energy storage requirement. The solution is based on double Fourier series expansion in two variables. The harmonic distribution of the output voltage is analyzed and the effects of the modulation index and the number of SMs on the output voltage harmonics are revealed. The influence of the upper/lower arm carrier phase shift angle is also investigated. Using the analysis, selection of the number of SMs, the modulation index and the upper/lower arm carrier phase shift angle are specified for output voltage harmonic minimization. The findings are verified by simulation and experimental results. [ABSTRACT FROM AUTHOR]

For dual three-phase machines, vector space decomposition allows the control of fundamental and main harmonic components in αβ and xy subspaces, respectively. However, the modulation of voltage references in the two subspaces using the space vector pulsewidth modulation (SVPWM) is not independent but coupled. In that, voltage references of two subspaces cannot be modulated simultaneously beyond the modulation restraints, thereby distorting the voltage regulation and causing harmonics or even system misbehavior. Meanwhile, the fundamental voltage in αβ subspace responsible for electromagnetic torque generation should be prioritized and secured. Thus, this article proposes a systematic analysis of modulation restraints of three representative SVPWM techniques, i.e., the linear modulation range of xy subspace under an assured modulation index of the fundamental voltage. Voltage references of xy subspace within this range can be modulated successfully without affecting the assured modulation index and the margin left for harmonic control in xy subspace is then acknowledged. This can be used to limit the output of current controllers not to exceed the voltage modulation restraint, thereby avoiding the modulation failure. Finally, the experimental results validate the linear modulation range and demonstrate the modulation behaviors within and out of the linear modulation range. [ABSTRACT FROM AUTHOR]

This article develops a new closed-loop analytical steady-state model of low-capacitance half-bridge Modular Multilevel Converters (MMCs) operated with the average arm energy control and submodule capacitor voltage (SMCV) ripple above the conventional value of 10%. In this control approach, the level of average SMCVs is regulated directly. As has been already shown in the literature, if the average SMCVs are not controlled, the circular interactions of the inherent low-frequency SMCV ripple and the modulation signal which affect the dc arm voltages will also lead to the variations in the average SMCVs. In order to compensate for these variations, a dc component has to be introduced in the modulation signal (in addition to the second harmonic which suppresses the second-order circulating currents). This is included in the proposed analytical modeling where the three key nonlinear equations are established and solved iteratively using Newton Raphson's method to calculate the steady-state modulation signal parameters. The effects of the introduced dc component in the modulation signal on the MMC electrical quantities are demonstrated and analyzed. The developed model is also compared with the existing analytical steady-state MMC models in the literature. It is further employed to optimize the parameters of the grid-connected MMC. The optimization is based on the improved utilization of the available modulation signal window and is performed with the aim to minimize the voltage stresses on the power devices. The analysis is supported by simulation and experimental results. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel switching-table-based direct torque control (ST-DTC) method to eliminate the current harmonics in dual-three-phase permanent-magnet synchronous machines due to the back electromotive force (back EMF) harmonics and voltage vector selection. By employing a novel space voltage vector selection strategy and the optimal action time for different groups of vectors, a novel ST-DTC method is developed. Furthermore, in order to implement standard pulsewidth modulation (PWM) switching sequence, a centralization PWM method for 36 voltage vectors is introduced. The proposed method can effectively reduce the phase current harmonics caused by both back EMF distortion and voltage vector selection, and still reserve the advantages of the conventional ST-DTC, such as fast torque response and simple structure. Its effectiveness is verified by simulations and experiments. [ABSTRACT FROM AUTHOR]

High-speed brushless dc (BLDC) drives usually operate with low carrier–fundamental frequency ratio, which causes abundant sideband harmonic current components. Some sideband harmonics will be induced in low-frequency range, leading to low-frequency current oscillations and low-frequency torque ripples. To minimize these undesired sideband harmonics, a novel pulsewidth modulation commutation pattern, i.e., carrier-synchronized commutation (CSC), is proposed in this article. For comparison, two conventional commutation patterns, including regular-sampled commutation (RSC), and natural-sampled commutation (NSC), are analyzed. To reveal the characteristics of sideband harmonics caused by RSC and NSC patterns, an extended geometric wall model is introduced, which can be used for the Fourier decomposition of complex vectors. Theoretical, simulation, and experimental results demonstrate the conventional RSC and NSC patterns will produce additional sideband harmonic currents and torque ripples, while the proposed CSC pattern can considerably suppress these adverse influences and meanwhile presents high performance and robustness. [ABSTRACT FROM AUTHOR]

This paper combines the use of multi-phase configurations and current harmonic injection methods to achieve significantly improved performance for doubly salient synchronous reluctance machines (DS-SRMs). In order to understand the torque production mechanism of multi-phase DS-SRMs with current harmonic injection, some general analytical torque models have been developed. The models are based on Fourier Series analysis of self- and mutual-inductances. It has been established that with current harmonic injection, the torque ripple of both 5-phase and 6-phase DS-SRMs can be significantly reduced and the average torque can be enhanced. It contrast, harmonic injection always has a detrimental impact on 4-phase machines. The investigations of losses and dynamic performance with current harmonic injection for multi-phase machine have also been carried out and demonstrated that the proposed method can improve the efficiency in constant torque region and maintain comparable performance to fundamental current supply in the flux weakening region. Experimental validation based on single layer, 6-phase, DS-SRM has been performed. [ABSTRACT FROM AUTHOR]

This article first proposes a generalized decomposition model for dual three-phase (3-ph) permanent magnet synchronous machines (PMSMs) with 0°, 30°, and 60° angle displacements between two sets of windings, allowing machines controlled in two-dimensional orthogonal αβ and xy subspaces. This model can decouple mutual inductances coupling phases from two sets, respectively. However, there often exist asymmetric impedances, due to inherent asymmetric machine parameters, cables with unequal lengths, manufacture tolerances, etc., in dual 3-ph PMSMs inevitably causing unbalanced phase currents and deteriorating the decoupling performance of the generalized machine model. Therefore, the generalized decomposition model incorporating asymmetric impedances is further developed, in which additional terms incurred by asymmetric impedances lead to the cross-coupling of αβ subspace and xy subspace. Through this model, the compensation capability of asymmetries is derived at a given dc link voltage. Then, a compensation strategy is illustrated to suppress unbalanced phase currents together with current harmonics caused by nonlinearities. Finally, experimental results testify the current balancing performance and simulation results further validate the machine model and the compensation capability. [ABSTRACT FROM AUTHOR]

This article investigates some novel modular consequent pole PM machines (CPMs) with E-core and C-core stators. Different slot-pole number combinations including 12-slot/10-pole (Ns>2p) and 12-slot/14-pole (Ns<2p) have been investigated. Their static and dynamic electromagnetic performances have been investigated, e.g. the phase back-EMF, on-load torque, torque-speed curves, power factor-speed curves and also efficiency maps are compared. It is found that the existence of flux gaps (FGs) can improve the average torque of the 12-slot/14-pole E-core modular CPMs while the C-core structure can be a better candidate where relatively low torque ripple is desirable. Moreover, by selecting proper FG width, the 12-slot/14-pole E-core modular CPMs can achieve better flux-weakening capability and higher efficiency while the 12-slot/10-pole C-core modular CPMs can have higher power factors over the whole speed range. The finite element simulation results have been validated by a series of experiments using 12-slot/14-pole modular CPMs with both C-core and E-core stators. [ABSTRACT FROM AUTHOR]

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 z1z2 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. [ABSTRACT FROM AUTHOR]

The commutation errors undermine the control performance of a brushless direct current (BLdc) drive especially at high-speed operation. In this article, a novel commutation error compensation strategy for BLdc drive that eliminates the phase deviation between the current and the back electromotive force is proposed. The d-axis current is introduced and used as the criterion to determine the commutation errors. Since the phase currents of BLdc drive contain large amounts of harmonics, which makes the d-axis current hard to detect, a least-mean-square-algorithm-based adaptive linear neuron filter is proposed. The optimal phase advance angle is adaptively generated by reducing the filtered d-axis current to zero. The proposed method does not need the motor parameter information or additional hardware, and can be implemented in general inverter controllers. The effectiveness of the proposed strategy is verified by both simulation and experimental results. [ABSTRACT FROM AUTHOR]

This article investigates novel fractional slot nonoverlapping winding hybrid excited (HE) machines with consequent-pole permanent magnet (PM) rotors. The proposed machines accommodate the rotor PM and stator field winding separately, which has solved the spatial confliction of double excitations. Different consequent-pole interior PM rotor configurations are extended to retain the PMs and utilize the flux-concentrating effect. Then, the relationship of field and armature current ratio with the PM and wound field fluxes is identified theoretically, which provides design and optimization guidelines for the HE machines. Furthermore, the HE machines are optimized and compared with conventional PM machines. It is revealed that the HE machines exhibit enhanced torque density with flux-enhancing field excitation, and extended operation range with flux-weakening field excitation. Besides, the HE machine utilizing flux-concentrating effect exhibits the highest PM torque but sacrificed flux regulation capability due to magnetic saturation. Finally, the HE prototypes with different rotor configurations are fabricated and tested to validate the analyses. [ABSTRACT FROM AUTHOR]

In this article, a new type of consequent pole flux reversal permanent magnet (CFRPM) machine, which features more iron poles than PM poles under one stator tooth, is proposed to improve the torque density. The proposed CFRPM machine with 6 slots and 16 poles (6S16P) is compared with a 12S16P FRPM machine and its consequent pole type, as well as a conventional 6S4P surface-mounted PM (SPM) machine. The proposed 6S16P CFRPM shows the highest torque among the four machines, together with the highest torque per PM volume. For a fair comparison with the 12S16P FRPM machine and its consequent pole type, the torque ripple of the proposed 6S16P CFRPM is suppressed by using two-step skewed rotor. After employing 4° two-step skewed rotor, while exhibits comparable torque ripple, the proposed 6S16P CFRPM still has 43% and 22% higher torque compared with the 12S16P FRPM machine and its consequent pole type. [ABSTRACT FROM AUTHOR]

This article investigates the virtual third harmonic back electromotive force (EMF)-based sensorless drive method for high-speed brushless dc (BLDC) motors. Conventional zero-crossing point (ZCP) detection methods of virtual third harmonic back EMF require hardware low-pass filters and voltage comparators, causing serious phase lag. To avoid the undesired phase lag of hardware, the proposed method employs algorithmic oversampling technique to reconstruct the envelope of virtual third harmonic back EMF. Besides, the number of sampling points is dynamically adjusted according to the pulsewidth modulation duty ratio to guarantee the accuracy of ZCP detection. In addition, the influence of asymmetric motor parameters, i.e., phase resistance and inductance, on sensorless commutation is analyzed in depth. With asymmetric impedances, ZCPs of virtual third harmonic will deviate from their ideal positions. Consequently, the commutation events, which are searched based on ZCPs, will also be triggered at inaccurate positions and then the control performance will be deteriorated. In order to suppress the negative influence, a novel phase compensation method is proposed. All the theoretical analyses are validated by experiments at a 60 000 r/min BLDC drive platform. [ABSTRACT FROM AUTHOR]

In this article, an adaptive linear neuron based current harmonics suppression method for permanent magnet synchronous motors with nonsinusoidal back electromotive force (EMF) is presented, with due account for dead-time effect. The current harmonics can be well-suppressed by feedforwarding a self-tuning compensation voltage. The proposed method does not rely on the knowledge of back-EMF harmonic components and dead-time effect. Moreover, the proposed method is easy to implement, since it does not need the process to extract the current harmonics. The effectiveness of the proposed method is verified by both simulation and experimental results without requiring additional hardware. [ABSTRACT FROM AUTHOR]

In this article, a current profiling technique is proposed for the torque density enhancement in switched reluctance machines (SRMs). The novel current profile is initially developed from the harmonic current injection method and is then modified into a unipolar waveform to allow the application of an asymmetric bridge inverter. It is found that, neglecting the magnetic saturation, the optimal current profile for the maximum torque per ampere operation in an SRM is close to a pulse with high-order harmonics. However, an optimized current with relatively low-order harmonics can provide better performance in the practical situation. Based on the analytical and the finite element results, the proposed method is proved to be able to enhance the torque density by 20% at the light load condition and by 15% at the rated condition compared with the conventional SRM excitation. Also, the large torque ripple and core loss in SRMs are suppressed and the efficiency is improved. More importantly, unlike many other current profiling techniques, the proposed current profile has fixed parameters and is easily adaptable to different machine specifications. The effectiveness of the proposed method is verified by both the finite-element analyses and the experiments. [ABSTRACT FROM AUTHOR]

The second harmonic current injection method is recently developed to enhance the torque density of variable flux reluctance machines (VFRMs). This article investigates the feasibility and effectiveness of the second harmonic current injection method in VFRMs with different stator/rotor pole combinations. By using magnetic gearing effect, it is found that the second harmonic injection method can only be applied to the 6j/(6i ± 2)j (i, j = 0, 1, 2…) stator/rotor pole VFRMs for the torque density enhancement. For the other stator/rotor pole combinations, the second harmonic current has no contribution in average torque production but only leads to excessive torque ripple. Further, by using global optimization method and finite element analysis, 6/8 stator/rotor pole combination is proved to be the optimal stator/rotor pole combination for 6-stator-slots VFRMs with the second harmonic current injection method, being able to exceed the maximal torque density of conventional VFRMs by 12% at a fixed copper loss. [ABSTRACT FROM AUTHOR]

In the past, various fundamental model based sensorless control methods have been proposed. However, most of them are developed under a healthy condition. Hence, in this article, fundamental model based sensorless control of permanent magnet synchronous machines (PMSM) under rotor eccentricity (RE) is investigated which is a common issue in many drive systems. It is known that under RE, three-phase back-EMFs, flux-linkages, inductances, and torque will be influenced. Mathematical derivation reveals that these effects will cause undesired harmonics in the position estimation. Since the frequencies of these low-order harmonics are much smaller than the bandwidth of position observer such as phase-locked loop, it is difficult to effectively eliminate them. Hence, the conventional back-EMF method is modified by adding an adaptive notch filter to suppress these undesired harmonics. Furthermore, the RE effects on PMSM characteristics are examined by measurements. The modified position estimator is implemented on a dSPACE platform and is verified by experiment results. [ABSTRACT FROM AUTHOR]

In this article, spoke array permanent magnet (PM) flux reversal machines (SAPM FRM), which feature spoke array PMs distributed along the stator inner surface, are proposed to improve the torque density. Compared with the conventional surface mounted PM flux reversal machine (SPM FRM), the proposed SAPM FRM can produce about 100% larger torque with negligible torque ripple, as well as higher efficiency and higher power factor. Two prototypes have been built and tested to validate the theoretical analyses. [ABSTRACT FROM AUTHOR]

A new analytical torque model based on dq0-axis frame has been developed for 3-phase, 12-slot/8-pole single layer doubly salient synchronous reluctance machines. This newly developed torque model, compared to the one often based on abc-axis frame, is necessary to simplify the investigation of dynamic performance such as torque–speed curve and efficiency maps. It has been found that the third-order current harmonic injection not only improves the torque performance (increased average torque and reduced torque ripple) in constant torque region but also maintains a similar torque level as the fundamental current supply in the flux weakening region. Moreover, although the fifth- and seventh-order current harmonic injection can reduce the torque ripple of machine, their dynamic performances are compromised due to low average torque and significant voltage distortion. Finite element simulations and dynamic tests have been carried out to prove the accuracy of the developed torque model and also the efficiency of the proposed current harmonic injection method. [ABSTRACT FROM AUTHOR]

This article investigates the duty-ratio-based direct torque control strategies for dual three-phase permanent magnet synchronous machine (PMSM) drives. The classical switching-table-based direct torque control (ST-DTC) for the dual three-phase drives usually suffers from significant harmonic currents and a large torque ripple. To reduce the harmonic currents, 12 combined voltage vectors are generated and employed as active vectors. Then, the duty-ratio-based ST-DTC is introduced to reduce the torque ripple. Considering that the typical duty-ratio-based ST-DTC exhibits the drawbacks of machine parameter dependent and a certain degree of failure rate in the duty ratio regulation, a simple and effective method taking into account the effect of the machine speed is employed to obtain the duty ratio. Afterward, to prevent the issue of the inverter thermal imbalance caused by using only one type of zero vectors, two types of zero vectors are employed in the switching sequences. With the proposed method, not only the harmonic currents have been suppressed, but also the torque ripple can be considerably reduced, while the merits of the classical ST-DTC such as simple structure and excellent dynamic performance are preserved. The experimental results validate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper aims to identify the optimal number of flux modulation pole (FMP) in Vernier permanent magnet synchronous machines (VPMSMs) with concentrated tooth-coil windings. First, the influence of number of FMP on machine performance is revealed based on the unified permanent magnet magnetomotive force permeance analytical model. It is found that for a fixed stator slot number, there always exists an optimal number of FMP to maximize the torque, thanks to the enhanced contribution by the fundamental permeance harmonic. Then, the influence of critical dimensional parameters, including the machine diameter, the permanent magnet thickness, and the width of FMP, on the electromagnetic performance of VPMSMs with different numbers of FMP are parametrically analyzed by both analytical and finite element analyses. Results show that the VPMSMs with the optimal number of FMP always have advantages of a higher torque density together with a reduced PM volume, particularly for those with a relatively large diameter. Finally, two VPMSM prototypes with different numbers of FMP are manufactured and tested to validate the analyses. [ABSTRACT FROM AUTHOR]

Fractional slot concentrated winding (FSCW) permanent magnet synchronous machines (PMSMs) have been a research hotspot over the past few decades. Recently, the magnetic gearing effect in FSCW PMSMs is revealed along with its gear ratio, which is a function of slot/pole number combination. At the design stage of FSCW PMSMs, one of the key issues is the selection of the slot/pole number combination. This paper shows that the gear ratio can contribute to a proper slot/pole number selection in any multiphase FSCW PMSMs by acting as a unified index for a quick overall performance comparison. In this paper, first, the magnetic gearing effect in FSCW PMSMs is explained and the gear ratio is further discussed. The advantages of adopting gear ratio as the overall performance index over other indices are revealed. The influence of the gear ratio on the winding factor, torque output, cogging torque, inductance, and rotor losses of three- and six-phase FSCW PMSMs is analyzed and validated by experiments, thus proving the analyses. [ABSTRACT FROM AUTHOR]

This paper proposes a coordinated control strategy for the rotor-side converter (RSC) and the grid-side converter (GSC) of an LC-filtered doubly fed induction generator (DFIG) under distorted grid voltage condition, to eliminate the distortion of the total output current (including the stator current, the GSC current, and the filter capacitor current). For an LC-filtered DFIG connected to a distorted grid, the low-order current harmonics can freely flow into the filter capacitor thereby polluting the total output current, even when the stator current and the GSC current are both controlled as sinusoidal. Although this problem can be addressed by measuring the output current or the capacitor current, the extra current sensors are undesired in industrial applications. In this paper, a novel hybrid virtual impedance method is implemented in both the RSC and the GSC, to reshape the parallel impedance of the stator, the GSC and the filter capacitor to nearly infinite for low-order harmonics, thus, the freely flowing output current harmonics can be mitigated. Meanwhile, the low-order current harmonics required by the output current compensation can be flexibly distributed between the stator and the GSC according to their operating conditions, to disperse the side-effects on the drive train and the GSC, thereby better protecting the whole system. The effectiveness of the proposed strategy is theoretically analyzed and verified with both simulation and experiment. [ABSTRACT FROM AUTHOR]

This paper aims to comprehensively analyze the influence of number of permanent magnet (PM) pieces on electromagnetic performance of flux reversal permanent magnet (FRPM) machines. First, the unified analytical model of FRPM machines having different numbers of PM pieces is established, from which the optimal number of PM pieces and the corresponding rotor pole number can be identified. It shows that by employing the optimal number of PM pieces instead of the conventional two on each stator tooth, additional back-EMF component can be generated which is beneficial to boost the machine performance. Then, the influence of critical design parameters including stator slot opening ratio, split ratio, and stator slot number is investigated, providing a guidance to the design of FRPM machines aiming at maximum output torque. In addition, both finite element analyses and experimental tests are conducted to verify the analytical analyses. For 6-slot-stator FRPM machines, experimental results show that more than 40% higher output torque can be achieved in the machine with optimal number of PM pieces when compared to the conventional one. [ABSTRACT FROM AUTHOR]

Variable flux reluctance machines (VFRMs) are developed as magnetless electrical machines. To extend the application of VFRMs, the enhancement of torque density is a key during machine design. In this paper, a novel second-harmonic current injection method is developed for torque density enhancement for 6-stator-slot/4-rotor-tooth (6/4) VFRM. By using the analytical method, the optimal current profile with injected second-harmonic current is obtained. The average torque of 6/4 VFRM is improved by 20% with the proposed method under all load conditions. Moreover, the proposed current profile has fixed harmonic proportions and is easily applicable to machines with different specifications. All the conclusions are confirmed by both finite-element analyses and experimental results. [ABSTRACT FROM AUTHOR]

A total of three types of doubly salient synchronous reluctance machines have been comparatively studied to improve the torque performance using current harmonic injection methods. These machines are derived from the switched reluctance machines (SRMs) with different winding configurations, such as the double/single-layer mutually coupled SRMs (MCSRMs) and fully pitched SRMs (FPSRMs), by supplying them with sinewave current. Such current supply mode can lead to higher torque/power density and lower vibrations and acoustic noise compared with the conventional rectangular current supply. The proposed torque analytical model can predict the instantaneous torque of the doubly salient SRMs with sinewave current excitation and the current harmonics also can be selected in order to reduce the torque ripple and/or increase the average torque. It has been found that the third current harmonic injection shows the best performance for single-layer MCSRMs and FPSRMs because it improves the average torque and reduces the torque ripple at the same time. However, it has little influence on doubly-layer MCSRMs. To improve the torque performance of such machines, other harmonic currents, e.g., fifth and seventh, need to be used. Both static and dynamic tests have been carried out to validate the predictions. [ABSTRACT FROM AUTHOR]

This paper investigates the torque production and the torque ripple reduction of a six-stator/seven-rotor-pole (6/7) variable flux reluctance machine (VFRM). As a main advantage, the 6/7 VFRM produces higher torque density, but less torque ripple compared with the 6/4 VFRM. The instantaneous torque equation of the 6/7 VFRM is derived by considering the spectra of the winding inductance and current. Based on the derived equation, the average torque is found to be mainly produced by the mutual inductance between the field and armature windings. The even-order harmonics of self-inductance and odd-order harmonics in mutual inductance between the field and armature windings are eliminated due to the opposite polarity connection of the armature coils in each phase. This results in the elimination of the third harmonic torque ripple, while a multiple of the sixth harmonic torque ripple exists. In order to mitigate the sixth harmonic torque ripple, the harmonic current injection method is implemented into the field winding. The field harmonic current is calculated from the analytical torque ripple equation. The performance of the proposed methods is verified by both finite element analysis (FEA) and experiment. [ABSTRACT FROM AUTHOR]

This paper investigates the contribution of each order inductance harmonic to the torque (both average torque and torque ripple) of multiphase doubly salient synchronous reluctance machines (DS-SRMs). Such machines are similar to switched reluctance machines but supplied with sine wave currents. The investigations in this paper are as follows. First, a general analytical torque model based on Fourier series analysis of inductances has been built for machines with different phase numbers, slot/pole number combinations, and also winding configurations. The instantaneous torque for DS-SRMs with any given phase number can then be accurately predicted. Using such model, contribution of each order inductance harmonic to torque can be investigated separately. It is found that the torque ripple frequency of the DS-SRM only depends on phase number. For example, for an m-phase machine, there will be m $\times $ kth-order torque ripple if mod(mk, 2) = 0, where m is the phase number and k is a natural number. This paper also explains why certain phase numbers inherently produce lower torque ripple than others. The findings in this paper provide a future direction for potential torque ripple reduction methods either from machine design or advanced control. The simulations have been validated by experiments using a six-phase DS-SRMs. [ABSTRACT FROM AUTHOR]

This paper provides a comprehensive analysis of performance difference among various kinds of flux reversal permanent magnet (FRPM) machines having different permanent magnet (PM) arrangements. Four PM arrangement types are, first, identified by the number and relative polarities of PMs on the stator teeth, and their influence on the equivalent pole-pair number of the armature winding and working harmonics of the air-gap field is revealed. Then, the torque variation against the rotor pole number of each PM arrangement is analyzed. The electromagnetic performance of four PM arrangements with a 14-pole rotor is compared in detail. It shows that the FRPM machine, in which four PM pieces are mounted on each stator tooth and two adjacent magnets on different stator teeth are of opposite polarities, offers the highest torque density and the highest efficiency, which make it promising in low-speed high-torque applications. In addition, four prototype machines are manufactured and tested to validate the findings. [ABSTRACT FROM AUTHOR]

This paper comprehensively studies the electromagnetic performance of flux-reversal permanent-magnet (FRPM) machines with different consequent-pole PM (CPM) topologies. Four CPM topologies are first introduced and classified by different numbers of PM pieces and PM locations on stator teeth. Then, the distribution and working harmonics of air-gap flux density of each CPM topology are analyzed and compared, from which the CPM topology with the highest torque density is identified. The influence of critical design parameters on machine performance is also parametrically investigated. By comparing the torque performance of CPM topologies with their surface-mounted PM counterparts, the advantages of CPM topologies, i.e., torque improvement and magnet volume reduction, are clearly revealed. Four FRPM prototypes are manufactured and tested to verify the analyses. [ABSTRACT FROM AUTHOR]

This paper proposes a novel dual-sided permanent magnet memory machine (DSPM-MM) by combing the distinct advantages of “high torque density” of conventional rotor-PM machine and “convenient online PM flux control” of stator-PM MM. In the proposed design, the consequent-pole NdFeB PMs are placed in the rotor, whereas the low coercive force (LCF) PMs are mounted between the adjacent stator teeth to enable flexible air-gap flux adjustment. Meanwhile, since the LCF PMs can be either remagnetized or demagnetized bidirectionally by a current pulse, the associated flux-weakening copper loss is eliminated, and hence, the proposed DSPM-MM can maintain high efficiency operation over a wide operating range. The machine topology and operating principle are introduced and addressed from the perspective of the nonlinear hysteresis behavior of LCF PMs as well as dual flux modulation effect, respectively. Then, the electromagnetic characteristics of the proposed machines having various available rotor poles are investigated and compared. The feasibility of the proposed design is validated by both finite element and experimental results. [ABSTRACT FROM AUTHOR]

In this paper, an 18-slot/26-pole vernier permanent magnet synchronous machine (VPMSM) with coil pitch of two slot pitches is proposed based on a nine-slot/18-flux-modulation-pole/26-pole VPMSM with concentrated tooth-coil windings. Compared with the original VPMSM, the number of slots is doubled and the phase winding connection is adjusted to reduce the space harmonic content, the phase inductance, and hence, improve the power factor. This paper shows that the proposed VPMSM increases power factor from 0.73 to 0.95 with better torque and flux-weakening capability. Moreover, a series of VPMSMs with high-power factor is proposed from the same design principle and given design guidelines. [ABSTRACT FROM AUTHOR]

In this paper, the torque production mechanisms of flux-reversal permanent magnet (FRPM) machine and Vernier permanent magnet (PM) machine are analyzed and compared based on air-gap field modulation. Working harmonics of PM magnetomotive force (MMF) and air-gap permeance in two machines are analytically identified and compared, indicating that the fundamental PM MMF together with all permeance harmonics contribute to the torque production of Vernier machine whereas all PM MMF harmonics but only fundamental permeance in FRPM machine produces the torque. Thanks to the utilized large dc component of air-gap permeance, the torque density of Vernier machine is revealed to be better. Influence of critical parameters on machine performance, such as PM thickness and slot width ratio of the modulation pole, is also investigated. It shows that FRPM machine is more sensitive to the design parameters. Both finite-element analysis and experimental validation are conducted to verify the conclusion. [ABSTRACT FROM AUTHOR]

In this paper, four rotor shaping methods, i.e., eccentric circular, inverse cosine, inverse cosine with third harmonic, and multi-step shaping methods, are developed and compared for torque ripple mitigation in variable flux reluctance machines (VFRMs). By using a 6-stator-pole/7-rotor-pole (6/7) VFRM as an example, the design criterions and capabilities of these four methods are illustrated. It is found that all the rotor shaping methods are capable of torque ripple mitigation and applicable to all the VFRMs except those with 6k/(6i ± 2) k (k, i = 1, 2, 3…) stator/rotor pole combinations. Moreover, the inverse cosine with third harmonic and multi-step shaping methods are found to have the best performance. They are able to reduce the torque ripple by 90% at a cost of only 3% torque density reduction. A 6/7 VFRM with both conventional and shaped rotors is prototyped and tested for verification. [ABSTRACT FROM AUTHOR]

This paper analytically derives the optimal third harmonic current to improve the output torque in five-phase surface-mounted permanent magnet (SPM) machines under the constraints of the same peak/rms value. The relationship between the output torque and the third harmonic current is established and its optimal value for maximizing the output torque is derived. It is found that the optimal third harmonic current is dependent on the ratio of the third harmonic back electromotive force (EMF) to the fundamental one but it is not 1/6 of the fundamental one as pulse width modulation in an inverter. In order to improve the output torque by increasing the fundamental and third harmonic winding factors and the third harmonic airgap flux density, the unequal width tooth and permanent magnet (PM) segmentation are employed in the 10-slot/8-pole five-phase SPM machine. The optimal unequal tooth dimensions and the number of PM segmentations are analyzed for maximizing the output torque. The airgap flux density, back EMF, cogging torque, and output torque of the machine with equal/unequal tooth width and unsegmented/segmented PM are compared. Finally, the experiments on the prototype 10-slot/8-pole PM machine with unequal tooth width and segmented rotor are given to verify the analytical and finite element analyses. [ABSTRACT FROM AUTHOR]

This paper adopts simple analytical modeling to investigate the contribution of air-gap field harmonics to the torque production in some three-phase, 12-slot/8-pole doubly salient synchronous reluctance machines (DSRMs) with both conventional and mutually coupled winding configurations. The air-gap flux density has been calculated based on the analytically obtained magnetomotive force and doubly salient air-gap permeance for both the double-layer and single-layer DSRMs with different winding configurations. Then, the contribution of different air-gap field harmonics to average torque and torque ripple can be investigated and validated by direct finite-element analyses. It has been found that in the DSRMs, the 10th-order harmonic in the double-layer conventional winding (DLC), the 4th-order harmonic in the double-layer mutually coupled winding (DLMC), the 7th-order harmonic in the single-layer conventional winding (SLC), and the 10th-order harmonic in the single-layer mutually coupled winding (SLMC) have the highest contribution to positive average torque and with positive influence on torque ripple reduction. However, the 2nd-order harmonic in the DLC, the 8th-order harmonic in the DLMC, the 5th-order harmonic in the SLC, and the 2nd-order harmonic in the SLMC machines mainly reduce the average torque. [ABSTRACT FROM AUTHOR]

This paper presents a flexible compensation strategy for voltage source converter (VSC) connected to an unbalanced and harmonic distorted grid, which can achieve flexible tradeoff between the two common control targets, i.e., compensating the voltage at the point of common coupling (PCC), and compensating the output current of the VSC. To achieve the control target, a hybrid virtual impedance method is proposed, which uses both the feedforward of the PCC voltage and the feedback of the output current to develop the harmonic (including the negative sequence) voltage references. Compared with the conventional virtual impedance methods using only feedforward or only feedback, the proposed hybrid method can control the harmonic output impedance of the VSC in a wider range, without the potential overmodulation or instability problems caused by the conventional methods when the desired virtual impedance varies in a wide range. The effectiveness and superiority of the proposed strategy is theoretically analyzed and experimentally verified. [ABSTRACT FROM AUTHOR]

In this paper, the torque production of fractional-slot concentrated-winding (FSCW) permanent-magnet synchronous machines (PMSMs) is analyzed from the perspective of the air-gap field harmonics modulation accounting for slotting effect. It is found that the average torque of FSCW PMSM is produced by both the principle of conventional PMSM and the magnetic gearing effect. A finite-element analysis (FEA) based equivalent current sheet model and harmonic restoration method is first used in FSCW PM machines with different slot–pole number combinations to quantify the respective contribution of the conventional PMSM and the magnetic gearing effect to the average torque. The influence of slot opening on the magnetic gearing effect, cogging torque, and torque ripple is analyzed. The results show that the magnetic gearing effect makes a nonignorable contribution to the average torque when a large slot opening stator is used. The expression of the gear ratio in FSCW PMSMs is derived. The influence of gear ratio on the contribution of the magnetic gearing effect to the total torque is investigated by FEA. The FEA-predicted torques are validated by experiments on the prototypes. [ABSTRACT FROM PUBLISHER]

In order to increase the torque density of the five-phase machines, the third harmonic is commonly employed. In this paper, the optimal and critical ratios for the third harmonic current injection are analytically derived and validated by finite element (FE) analyses. It is found that the optimal and critical injection ratios along with the torque improvement are dependent on the ratio of the third harmonic back electromotive force to the fundamental one. In order to improve the electromagnetic torque contributed by the third harmonic component, this paper employs unequal tooth to increase both the fundamental and third harmonic winding factors. Meanwhile, the optimal unequal tooth width combination is deduced and demonstrated by the FE method. When the third harmonic current is injected under the same amplitude constraint, the output torque can be improved. When the third harmonic current is injected under the same RMS value constraint, for the ten-slot/eight-pole equal tooth machine, the output torque can barely be increased, whilst for the unequal tooth machine, the output torque can be increased by 2.1%. Finally, the ten-slot/eight-pole machine with unequal teeth is prototyped and tested to prove the analyses. [ABSTRACT FROM PUBLISHER]

In this paper, the torque production mechanism of variable flux reluctance machines (VFRMs) is investigated. Initially, based on an analytical instantaneous torque model developed from the Lorentz force law and airgap field harmonic analysis, the magnetic gearing effect is revealed in the torque production of VFRMs. Then, by using a 6-stator-pole/4-rotor pole (6s/4r) VFRM as an example, all its torque components, including synchronous torque, reluctance torque, and cogging torque, are analyzed separately under linear condition. Their average torque and torque ripple characteristics are comprehensively illustrated. Finally, the influence of saturation effect is also accounted for with the help of finite element and frozen permeability methods. The analysis results are verified experimentally. [ABSTRACT FROM AUTHOR]

This paper investigates the interaction of the zero sequence component into both permanent magnet (PM) shape and phase current to improve the output torque in dual three-phase surface-mounted PM (SPM) machines. The optimal zero sequence components are analytically derived and validated by finite element (FE) analyses. It is found that the optimal zero sequence components into both PM shape and current waveform are dependent on the fundamental and zero sequence harmonic winding factors. For the dual three-phase SPM machines having rotors without shaping, Sine shape, Sine shape with the zero sequence components, the electromagnetic performances including the back electromotive force (EMF) waveform, cogging torque, average torque, and torque ripple are compared. It is demonstrated that the average torque with the optimal zero sequence component in PM shaping and current waveform can be improved by >30% while the torque ripple remains similar to that of the one with Sine shaping. Finally, the experiments are given to verify both the analytical and FE analysis. [ABSTRACT FROM AUTHOR]

A method for enhancing torque capability of a dual three-phase permanent magnet synchronous machine (PMSM) based on conventional dual three-phase drive system by injecting the fifth and seventh current harmonics without any hardware re-configuration is proposed in this paper. Compared with the third current harmonic injection, which is commonly used to enhance the torque capability of dual three-phase machine, the two isolated neutral points of each set of single three-phase windings do not need to be reconnected to the middle point of dc-link capacitors or an additional power switching bridge to provide flowing path for zero-sequence current. Further, no additional current sensors are required to obtain the feedback of zero-sequence current to regulate it effectively. For a prototype dual three-phase PMSM, the average torque increases approximately by 9% at the cost of 0.56% increase in the 12th harmonic torque ripple. The effectiveness of the torque capability enhancement is confirmed by experiments. [ABSTRACT FROM AUTHOR]

The relationship between the two-individual current control and the vector space decomposition (VSD) control for a dual three-phase permanent magnet synchronous machine (PMSM) is investigated in this paper. It is found that the VSD control is more flexible in controlling the fundamental current in \alpha \beta subplane and the fifth, seventh current harmonics in z_{1}z_{2} subplane with different proportional and integral (PI) gains, while the two-individual current control is comparable with the VSD control in having the same PI gains in the \alpha \beta $ and z_{1}z_{2} subplanes. It is also found that the two-individual current control may have potential instability issues due to the mutual coupling between the two sets of three-phase windings. If the mutual coupling between the two sets is weak to some extent, then the two-individual current control could have the same dynamic performance as the VSD control without the stability issues. Experiments are conducted on a prototype dual three-phase PMSM to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper proposes a flexible compensation strategy for parallel-connected doubly fed induction generators (DFIGs) when connected to an unbalanced weak grid. The proposed strategy has two main advantages, the voltage unbalance factor at the point of common coupling (PCC) can be continuously controlled, thus, the flexible tradeoff between the balanced DFIG output current and the balanced PCC voltage can be achieved, and the negative sequence current required by the compensation can be properly shared among the parallel DFIGs and their grid side converters according to their respective operation conditions without the need of real-time communication. The operation performance and stability of the proposed strategy are analyzed. Simulation and experimental results are carried out to verify the proposed compensation strategy. [ABSTRACT FROM AUTHOR]