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This paper proposes some effective approaches to address the inherent issues of consequent-pole (CP) permanent magnet (PM) machines, such as saturation of the salient rotor core and unipolar PM leakage flux of the end region caused by asymmetric field. The effect of CP Halbach PM array with different magnetization direction and parameters that affect the saturation have been investigated for the CP PM machine with short pole pitch. By employing the CP Halbach array, the saturation issue can be solved and superior performance can be obtained without reducing the PM pole arc. In addition, unequal and multistep staggered rotors with magnetic barriers have been proposed to reduce the unipolar leakage flux in the end region. Compared with regular staggered rotors, not only better electromagnetic performance can be achieved, but also the end unipolar leakage flux can be reduced. Finally, a prototype is manufactured and the predictions have been validated by measurements.

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.

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 ) 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.

This paper investigates the effect of airgap length on the electromagnetic performance of direct-drive surface mounted permanent magnet Vernier (SPM-V) machines with different power ratings. Using 3kW machine as an example, its performance is comprehensively compared with a conventional surface mounted permanent magnet (SPM) machine with the same airgap lengths using 2D Finite Element Analysis (FEA). For each airgap length, the slot/pole number combination for the SPM-V machine is investigated to achieve the optimal performance compared to the conventional SPM machine. In order to make the study more generic, the slot/pole number and the airgap length variations are expressed as normalized pole pitch, i.e. () (ratio of rotor pole pitch to electromagnetic airgap length). The results show that for 3kW machines, ()>2.2 is a good design criterion for the SPM-V machines to achieve higher average torque and efficiency than the conventional SPM machines. In addition, a reasonably good power factor (>0.9 in this case) can be achieved. Although the power factor of SPM-V machines drops significantly at multi-MW power level, i.e. 3MW and 10MW, the criterion ()>2.2 still results in achieving a performance closest to their optimal capability. However, when ()>2.2, special consideration should be paid to avoid potential irreversible magnet demagnetization at multi-MW power levels.

An equivalent magnetic circuit (EMC) analytical method for a 3-phase doubly salient permanent magnet (DSPM) machine with Π-shaped stator iron core segments (Π-core DSPM machine) is presented in this paper. This method is based on the airgap field modulation theory. First, the airgap permeance of the doubly salient machine is calculated, based on which the influence of slotting on modulation effect is analyzed. Then, an EMC model of this machine is established according to its main magnetic field distribution. Considering the slotting effect on the average airgap flux density, Carter's coefficient is used to calculate the equivalent airgap length and the airgap magnetomotive force (MMF). Subsequently, the flux density is calculated, which allows the calculation of no-load electromotive force (EMF) and also on-load torque. In addition, the relationship between machine performances and key dimensions can be obtained by analytical expressions without complicated finite element analysis (FEA). Analytical results are validated by both the 2-dimension FEA and experimental results.

This article investigates the impact of scaling on the electromagnetic performance of surface-mounted permanent-magnet Vernier (SPM-V) machines with a main focus on open-circuit induced Electro Motive Force (EMF). Three different power ratings, i.e., 3 kW, 500 kW, and 3 MW, have been chosen for this article. For each power rating, the SPM-V machines are analyzed for different slot/pole number combinations to compare their optimal performance with a conventional SPM machine. Step-by-step development of an analytical equation is presented for the prediction of induced EMF taking into account the interpole leakage of rotor permanent-magnets. 2-D finite-element analysis (FEA) has been used to validate the analytical equation across different power ratings. The analytical equation is thereafter utilized to study the influence of different geometric parameters on the performance of the SPM-V machines. It reveals that the back EMF and torque of SPM-V machines, for a given normalized pole pitch (rotor pole pitch to magnetic airgap length), are unaffected by the increase in airgap length due to scaling. However, the power factor of SPM-V, unlike the conventional SPM, reduces significantly with the increase in electrical loading due to the scaling effect. The analytical model for induced EMF and the 2-D FEA predicted results are validated by experiments using conventional SPM and SPM-V machine prototypes.

Surface mounted permanent magnet Vernier (SPM-V) machines are known for their high torque density but relatively poor power factor compared to conventional SPM machines. The high torque density feature of the SPM-V machines is desirable for direct-drive offshore wind power applications as it leads to reduced generator size, mass and cost. However, their poor power factor can negatively affect the converter cost and efficiency. This paper compares the system-level performance, including generator active and structural components and converter, between the SPM-V and the conventional SPM generator systems. Four different power ratings, i.e. 0.5MW, 3MW, 5MW and 10MW, have been considered to study the trend of system-level performance with increasing power rating. The study shows that the SPM-V generators can be lighter and cheaper than their conventional SPM counterparts. However, after the consideration of converter cost and efficiency, the conventional SPM generator exhibited slightly better overall performance. Nonetheless, with the development of novel Vernier topologies and reduction in converter costs in the future due to emerging technologies, the Vernier generators can still be competitive for direct-drive offshore wind power applications.

In this paper, the transient thermal response of a conventional double-layer switched-flux permanent-magnet machine is studied for both healthy and fault conditions such as inter-turn short-circuit. A highly optimized and accurate cosimulation model for different operating conditions is developed requiring low computation and time resources. The electromechanical models for both healthy and faulty operation are implemented in MATLAB/Simulink while the thermal model is implemented using three-dimensional (3-D) finite-element model (FEM) software. Both models are dynamically coupled to enable the influence of temperature rise on the electromagnetic performance and vice versa to be predicted. Operation under various conditions are investigated, and it is found that the temperature rise under fault conditions and high speed can lead to irreversible demagnetization of the permanent magnets. The superposition principle is used to accurately estimate the impact of short-circuit currents on the temperature rise. A series of dynamic tests are carried out to validate the transient thermal response prediction when operating during both the healthy and fault conditions.

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.

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.

In recent years, permanent magnet vernier (PMV) machines have been attracting more and more attention due to the inherently exhibited advantages such as high torque density and simple mechanical structure. In this paper, a consequent pole (CP) PMV machine with single-layer concentrated winding is proposed. The novelty is that the asymmetric air-gap field distribution is introduced to improve its working harmonics and to reduce the PM consumption. By employing a CP structure, the flux density amplitude can be enhanced. Moreover, due to uneven distribution of modulator poles on the armature teeth and fault tolerant teeth, the number of periods of modulator poles is only half of that of the stator teeth. Then, significant improvement in flux density working harmonics can be achieved. Furthermore, the superior electromagnetic decoupling capability can be achieved by introducing the fault-tolerant teeth. The relevant electromagnetic performance such as flux density, back electromotive forces, cogging torque and on-load torque have been calculated by using finite-element analyses, which have also been validated by experiments.

In this paper, a forced oil cooling scheme is proposed for a novel modular consequent-pole permanent magnet machine (CPM) with E-core stator. In this modular machine, flux gaps (FGs) that are normally used for improving electromagnetic performance and simplifying the winding process, can also be utilized as cooling channels for the oil to pass through, leading to significantly improved machine internal cooling. Computational fluid dynamics (CFD) analyses have been carried out and the results indicate that circa 15°C reduction in the peak temperature can be achieved based on the initial design. Moreover, the influences of several other critical parameters such as inlet position and geometry have been investigated, and optimal inlet configurations have been identified to realize the temperature uniformity. Some useful design guidelines for thermal management in the modular CPMs have also been provided in this paper.

This paper proposes a general analytical model of surface-mounted permanent magnet (SPM) machines with series-connected coils under inter-turn short circuit (ITSC) fault. One prominent feature of this model is that the air-gap and slot-leakage components of inductances under fault are calculated separately, which consider the influences of pole number and spatial distribution of coils. In the model, winding function approach (WFA) is used to calculate the air-gap inductance components by considering all space harmonics whilst slot-leakage inductance components are obtained by using slot permeance method. The proposed faulty machine model built in Matlab/Simulink is validated by time stepping FE simulations for a 3kW 96-slot 32-pole SPM machine. The model is suitable for the fast evaluation of fault performance of SPM machines and the development of faulty model considering core saturation if necessary. Other power ratings (0.5MW and 3MW) have also been investigated to study scaling effect on machine fault-tolerant capability.

In this paper, a novel cooling method utilizing the flux gaps (FGs) as cooling channels in modular consequent pole PM machines has been proposed. With numerical calculations such as computational fluid dynamics (CFD) analyses, it is proven that the proposed forced air cooling method with inlets and outlets on the end-caps can take advantage of the FGs and a remarkable reduction of temperature rise can be achieved in modular machines. The optimal FG width for better cooling effect has been identified. Moreover, several design parameters of the inlets such as inlet position, inlet dimension have been investigated. Some design guidelines of such modular machines considering particularly the thermal performance are given at the end of this paper.

This paper investigates the vibrations and acoustic noise behavior of some equal tooth width, unequal tooth width and modular surface mounted permanent magnet machines. The investigations are based on finite element analysis (ANSYS) and the performances such as radial force (and airgap magnetic pressure), vibration modes (shapes and resonant frequencies), radial displacement and acceleration of the stator, and sound pressure level have been calculated and compared amongst different machines. It has been found that due to the existence of flux gaps in stator alternate teeth, at the same operating condition (phase current and rotor speed), the modular machines can reduce the sound pressure level by up to 15dB compared to the equal tooth width permanent magnet machines. A similar reduction in sound pressure level can be achieved by adopting the unequal tooth width permanent magnet machine.

This paper investigates the effect of airgap length on the electromagnetic performance of 3kW surface mounted permanent magnet Vernier (SPM-V) machine. The performance is compared with a conventional surface mounted permanent magnet (SPM) machine with same airgap length using 2D Finite Element Analysis (2D FEA). For each airgap length, the slot/pole number combination for the SPM-V machine is investigated to achieve the optimal performance compared to the conventional SPM machine. The results show that the SPMV machine can achieve much higher torque capability than the conventional SPM machine at smaller airgap length. However, there is an optimal airgap length beyond which the torque performance of SPM-V machines drops below the conventional SPM counterparts. Moreover, unlike the conventional SPM machines, the power factor of SPM-V machines drops significantly with increase in airgap length.

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.

Compared to nonmodular machines, modular topologies become increasingly attractive due to their simplified manufacture process, better fault-tolerant capability, and potentially reduced material consumption. In order to maintain or even enhance the machine performance while achieving high fault-tolerant capability, novel modular, single-layer winding switched reluctance machines (SRMs) with different pole numbers are proposed, which are supplied by rectangular wave current with different conduction angles. The influences of the pole number and flux gap width between E-core segmented stators on the electromagnetic performance have been investigated in terms of self- and mutual inductances, electromagnetic torque, copper loss, iron loss, and radial force. It has been found that the modular structures with higher rotor pole numbers than stator slot numbers (12-slot/14-pole and 12-slot/16-pole SRMs) can maintain and even improve the average torque due to the nature of self and mutual inductances. In addition, the torque ripples for modular machines are significantly reduced (below 50%), so do the iron loss and radial force, leading to higher efficiency albeit with potentially lower vibration and acoustic noise. Two prototypes with 12-slot/8-pole and 12-slot/14-pole combinations have been built with both nonmodular and modular structures to validate the predictions in terms of inductances and static torques.

This paper investigates the influence of concentrated winding configurations and stator core structures on torque performance of fractional-slot surface-mounted permanent magnet (SPM) machines. From analyzing the separated torque components of prototype SPM machines with 12-slot/10-pole (12S/10P) combination by frozen permeability (FP) method, it can be found that the torque ripple is closely related with local saturation in fully closed slot (FCS) machines. Besides, the heavier local saturation will also jeopardize the merit of using alternate teeth wound windings, such as obtaining higher average torque than electrical machines with all teeth wound windings. The further analysis of stator tooth relative permeability variation over one electrical period demonstrates that the major reason for torque ripple difference among these electrical machines with different stator topologies is the asymmetric saturation between the adjacent teeth. Both the subharmonic due to armature reaction (determined by winding connection and current value) and the asymmetry of stator core structure contribute to such asymmetric saturation. In order to more clearly verify this, the complementary slot/pole number combination (12S/14P) is also analyzed. The conclusion is effective for electrical machines with other slot/pole number combinations as well. Experiments have been carried out to validate the predictions.

This paper reviews the performances of some newly developed reluctance machines with different winding configurations, excitation methods, stator and rotor structures, and slot/pole number combinations. Both the double layer conventional (DLC-), double layer mutually-coupled (DLMC), single layer conventional (SLC-), and single layer mutuallycoupled (SLMC-), as well as fully-pitched (FP) winding configurations have been considered for both rectangular wave and sinewave excitations. Different conduction angles such as unipolar120o elec., unipolar/bipolar 180 oelec., bipolar 240 o elec. and bipolar 360oelec. have been adopted and the most appropriate conduction angles have been obtained for the SRMs with different winding configurations. In addition, with appropriate conduction angles, the 12-slot/14-pole SRMs with modular stator structure is found to produce similar average torque, but lower torque ripple and iron loss when compared to non-modular 12-slot/8-pole SRMs. With sinewave excitation, the doubly salient synchronous reluctance machines with the DLMC winding can produce the highest average torque at high currents and achieve the highest peak efficiency as well. In order to compare with the conventional synchronous reluctance machines (SynRMs) having flux barriers inside the rotor, the appropriate rotor topologies to obtain the maximum average torque have been investigated for different winding configurations and slot/pole number combinations. Furthermore, some prototypes have been built with different winding configurations, stator structures, and slot/pole combinations to validate the predictions.

This paper compares the electromagnetic\ud performance of 10MW superconducting (SC) generators with\ud three different topologies, i.e., iron-cored stator and rotor\ud (ISIRT), iron-cored stator and air-cored rotor (ISART), and\ud air-cored stator and rotor (ASART). The objective is to provide a\ud powerful insight into the advantages and disadvantages of the\ud different topologies, and to establish some design guidelines for\ud selecting an appropriate direct drive SC generator for offshore\ud wind turbine applications. Firstly, the structures of the three SC\ud generator topologies are introduced. Then, the influence of the SC\ud coil cross sectional area on torque capability is compared. After\ud that, three SC generators with different topologies are optimized\ud respectively for further comparison, including the active material\ud cost, weight, harmonics in the electromotive force (EMF), torque\ud ripple, field harmonics in the SC coil, and forces on the rotor and\ud stator components, etc. It is found that, with the same SC\ud quantity, the torque capability of the iron-cored stator and rotor\ud topology is much better than that of the other two topologies.\ud However, the advantage becomes less significant when a larger\ud area of the SC coil is employed. The air gap flux density waveform\ud of the ASART is much smoother than those of the ISIRT and\ud ISART. The torque ripples of the ISIRT and the ISART are much\ud higher than that of the ASART. The field harmonics (both\ud amplitude and frequency) in the SC coil of the ASART are the\ud lowest. For the ISIRT, most of the force on the rotor is acting on\ud the rotor iron, and thus, the SC coil is more likely to be safe from a\ud mechanical performance point of view and the design of the\ud corresponding supporting structure is simple. However, for the\ud air-cored rotor topologies, nearly all the force is acting on the SC\ud coil. For the air-cored stator, the force mainly acts on the\ud armature winding, while for the iron-cored stator, it is mainly on\ud the stator teeth. Due to the excellent mechanical performance of\ud iron, the iron-cored stator is therefore more robust.\ud

The design of power electronic converters for the integration of wind generated power into the grid is more and more important due to a new class of superconducting generators (SG) with power ratings of up to 20 MW. High efficiency of power converters for high-power applications is mandatory in order to reduce the overall cost of the system. This study proposes a design method to minimise the cost of the system by finding the optimal number of power devices and capacitors for different high-power converter topologies. The investigation focuses on determining the optimal number of voltage levels for a back-to-back (BTB) neutral point clamped (NPC) converter. The design method is demonstrated by estimating the cost of different BTB NPC power converter topologies for the integration of a 10 MW SG to the grid.

This paper investigates the influence of rotor topologies and winding configurations on the electromagnetic performance of 3-phase synchronous reluctance machines with different slot/pole number combinations, e.g. 12-slot/4-pole and 12-slot/8-pole. Transversally laminated synchronous reluctance rotors with both round flux barrier and angled flux barrier have been considered, as well as the doubly-salient rotor as that used in switched reluctance machines. Both concentrated and distributed winding configurations are accounted for, i.e., single layer and double layer conventional and mutually coupled windings, as well as fully-pitched winding. The machine performance in terms of d- and q-axis inductances, on-load torque, copper loss, and iron loss have been investigated using 2-D finite-element analysis. With appropriate rotor topology, 12-slot/4-pole and 12-slot/8-pole machines with fully-pitched and double layer mutually coupled windings can achieve similar torque capacity, which are higher than the machines with other winding configurations. In addition, the synchronous reluctance machine with round flux barrier can have lower iron loss than doubly salient reluctance machine under different working conditions. The prototypes of 12-slot/8-pole single layer and double layer, doubly salient synchronous reluctance machines have been built to validate the predictions in terms of inductances and torques.

This paper investigates the influence of pole number and stator outer diameter on the performance of superconducting (SC) generators. The SC generator has an iron-cored rotor topology. Firstly, the generator structure is introduced and the optimization procedure is described. Then the influence of design parameters on performance, in terms of generator volume, weight, SC wire utilization, and active material cost, etc., is presented. Some relationships for the optimal combinations for different performance attributes are established. In addition, the influence of SC material price on the determination of optimal stator outer diameter and pole number is discussed. Finally, the influence of SC coil area per pole on performance is also investigated.

This study presents the design considerations for a fractional slot multi-phase modular permanent magnet (PM) machine with single-layer concentrated windings. The winding factors for various slot/pole number combinations are calculated to identify the optimal slot/pole number combinations for different phase numbers. In addition, the electromagnetic performance influenced by flux gaps (FGs), such as air-gap magneto-motive force, back-electro-motive force, cogging torque, on-load torque and torque ripple etc. are comprehensively investigated by using the two-dimensional finite element (FE) method. Several general rules with respect to the influence of FGs on multi-phase modular PM machines performance are established. The prototypes of modular PM machines are built and the FE results are validated with experiments.

The irreversible magnet demagnetization phenomena are investigated in this paper\ud ,\ud under \ud both \ud healthy and short -\ud circuit conditions for a switched flux permanent magnet (SFPM) machine. The \ud temperature effects on permanent magnet material are taken into account and the influence of short\ud -\ud circuit \ud current over demagnetization is evaluated. In order to \ud calculate the short\ud -\ud circuit current (mainly inter\ud -\ud turn \ud short\ud -\ud circuit), the MATLAB/Simulink model has been employed. The aforementioned short\ud -\ud circuit current \ud is then fed to the finite element model, so the demagnetization analysis can be carried out. \ud Variou\ud s fault \ud scenarios are investigated, including high speeds and high fault severity. \ud It is found that the short\ud -\ud circuit \ud current has li\ud mited\ud effect on the magnet demagnetization due to particular features of the SFPM machines. \ud The mechanism of demagnetization\ud has been revealed and found out to be mainly due to temperature rise \ud and poor PM materials\ud utilization\ud . Experiments have been carried out to validate \ud the \ud MATLAB/Simulink \ud model for short\ud -\ud circuit current predictions.

The fault-tolerant capabilities are compared in this paper for the conventional double-layer switched-flux permanent-magnet machine and its single-layer counterparts, i.e., C-core, E-core, and modular. The comparison includes the interturn short-circuit and irreversible demagnetization faults. A combination of Simulink and finite element models is used in the study. Based on the predictions, it is found that the modular topology produces the lowest short-circuit current and also has the best demagnetization withstand capability while the conventional one produces the highest short-circuit current and has the worst demagnetization withstand capability. The frozen permeability method is employed to separate the flux produced by armature current and magnets, and the results showed that, besides the influence of short-circuit current, the available magnet volume and magnetic circuit configuration play an important role in the demagnetization process. It is also found that removing half of the magnets, such as using C-core, E-core, and modular topologies, generally improves the demagnetization withstand capability and also increases the torque per magnet volume. Measured results are also presented to validate the short-circuit current predictions and magnet demagnetization.

This paper investigates the influence of conduction angles on the performances of two 3-phase 12-slot/8-pole short-pitched switched reluctance machines (SRMs): single-layer SRM with conventional winding (SL-CSRM) and single-layer SRM with mutually coupled winding (SL-MCSRM). Both unipolar and bipolar excitations are employed for the SRMs with different conduction angles such as unipolar 120° elec., unipolar 180° elec., bipolar 180° elec., bipolar 240° elec., and bipolar 360° elec. Their flux distributions, self- and mutual-flux linkages, and inductances are analyzed, and followed by a performance comparison in terms of on-load torque, average torque, torque ripple, using 2-D finite-element method. Copper loss, iron loss, and machine efficiency have also been investigated with different phase currents and rotor speeds. The predicted results show that the conduction angle of unipolar 120° elec. is the best excitation approach for the SL-CSRM at low current and also modest speed, as its double-layer (DL) counterpart. However, at high current, the higher average torque is achieved by a conduction angle of unipolar 180° elec. For the SL-MCSRM, bipolar 180° elec. conduction is the most appropriate excitation method to generate a higher average torque but lower torque ripple than others. The lower iron loss is achieved by unipolar excitation, and the SL-CSRM with unipolar 120° elec. conduction produces the highest efficiency than others at 10 $\text{A}_{\mathrm{ rms}}$ . In addition, the performances of single-layer machines have been compared with those of the established DL-SRMs with conventional and mutually coupled windings. The prototype SRMs for both SL-CSRM and SL-MCSRM have been built and tested to validate the predictions.

A current harmonic injection method is adopted to improve the average torque and to reduce the torque ripple of a doubly salient synchronous reluctance machine. However, the interaction between the inductance harmonics and the injected current harmonics will lead to non-negligible distortion in the voltage, which will influence machine’s dynamic performance in the flux-weakening region. In order to predict such influence, the analytical torque model in dq-axis has been proposed in this paper to investigate the dynamic performance such as torque speed curve and efficiency map with current harmonic injection. It has been found that, for the same phase root-mean-square current, although the 5th and 7th order current harmonics can reduce the torque ripple, they also cause significant voltage distortion and lead to deteriorated dynamic performance.