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The mechanism and the influence of the on-load terminal phase voltage distortion by the armature reaction in interior permanent magnet (IPM) machines with fractional-slot concentrated windings (FSCWs) are investigated in this paper, by taking a 12-slot/8-pole machine as an example. The phenomenon is presented first, which shows that the peak voltage will be much higher than the fundamental value, especially under the flux-weakening operation. Then, the mechanism is investigated with the aid of the frozen permeability method. Due to the geometric feature of the FSCW IPM rotor, the armature reaction flux will asymmetrically enhance the local magnetic saturation in the tooth-tips and the rotor lamination region near the rotor ribs, which disrupt the smooth variation of phase flux linkage and lead to a voltage distortion. With the increasing of current advancing angle ( $\beta $ ), this effect will become more obvious and result in the higher distortion level. Furthermore, the influences of voltage distortion on the machine torque performance are investigated, which show that it will only contribute to the torque ripple in the constant torque region, but will largely reduce the flux-weakening operation region compared with the ideal one calculated by the fundamental voltages only. Finally, a prototype is manufactured and tested to validate the analyses. [ABSTRACT FROM AUTHOR]

The on-load voltage distortion in fractional slot surface-mounted permanent magnet machines refers to the phase terminal voltage distorted by armature reaction. With the aid of frozen permeability method, the mechanism of this phenomenon has been investigated based on a 12-slot/8-pole model as an example, showing that the local magnetic saturation in tooth-tips is the main cause, especially when small or closed slot openings are adopted. Then, its impacts on machine performance under vector control have been investigated. If the dc-link voltage is sufficient to satisfy all distorted voltage, i.e., operating in constant torque region, the phenomenon mainly contributes to torque ripple. However, it becomes more problematic in the flux weakening region if the dc-link voltage is limited. Both base-speed and torque-speed curve will significantly differ from the expected results calculated by fundamental voltages. Meanwhile, if the machine operates beyond the base speed, or considering the limited bandwidth in real systems, the phase currents may be distorted, which consequently increase the current harmonics and reduce the average torque. Finally, a prototype machine is manufactured and tested to validate the analyses. [ABSTRACT FROM AUTHOR]

This paper proposes a combined parameter estimation for permanent-magnet synchronous machines (PMSMs), by which the rotor permanent-magnet (PM) flux linkage and mechanical parameters, such as the combined moment of inertia and viscous friction coefficient, are estimated without the aid from nominal machine parameter values. The proposed estimation of rotor PM flux linkage is based on the addition of position offsets and does not need the information of other machine parameters or injection of currents. With the aid from estimated rotor PM flux linkage, the electromagnetic torque can be consequently calculated for the estimation of mechanical parameters at no-load condition, and a two-step method is employed to achieve a higher ratio of signal to noise. This combined parameter estimation is finally validated on a surface-mounted PMSM (SPMSM) and an interior PMSM (IPMSM), respectively. It is found that the estimation error of combined moment of inertia with reference to its nominal value can be less than 10 $\%$ even if it (the combined moment of inertia) is lower than 1\times 10^-3\ \kg\cdot \m^2 , while the estimation error will be further decreased to less than 3 \%$ if it is higher than 7\times 10^-3\ \kg\cdot \m^2. [ABSTRACT FROM PUBLISHER]

Several switched flux permanent magnet (SFPM) machines with mechanically movable flux adjusting technique are proposed, analyzed, and compared for applications which demand high speed and efficiency. By using ferromagnetic pieces-–one per every stator pole or every alternative stator pole, which are named as flux adjusters (FAs) and located on the outside surface of the stator—the airgap flux density can be weakened and therefore the operation speed range and flux weakening capability can be improved. The influence of using all or alternative FAs on the open circuit results, electromagnetic performance, and torque–speed characteristics of the SFPM machine is investigated through three SFPM machines with different stator/rotor pole combinations, i.e., 12/10, 12/13, and 12/14. Moreover, although using FAs in all stator poles can significantly improve the flux weakening capability, alternative FAs can also achieve remarkable improvement although higher torque ripple is observed. Additionally, it has been found that the 12/13 combination is considered to be the most suitable candidate for alternative FAs technique. In addition to 2-D finite-element analysis (FEA) and analytical methods, 3-D FEA results accounting for the end-effect are presented. Furthermore, experiments are performed to validate the results. [ABSTRACT FROM AUTHOR]

A novel variable reluctance (VR) resolver with nonoverlapping tooth–coil windings is proposed in this paper. It significantly simplifies the manufacturing process of multilayer windings in conventional products. Finite element (FE) analysis is used to illustrate the basic operating principle, followed by analytical derivation of main parameters and optimization of major dimensions, including air-gap length and slot opening width. Based on winding distributions and FE results, it is shown that identical stator and winding can be employed for a resolver with three different numbers of rotor poles. Further, other stator slot/rotor pole combinations based on the nonoverlapping tooth–coil windings are generalized. In addition, the influence of eccentricity and end-winding leakage on the proposed topology is investigated. Finally, a prototype is fabricated and tested to verify the analysis, including main parameters and electrical angle error. [ABSTRACT FROM AUTHOR]

In this paper, a double stator (DS) wound field (WF) switched flux (SF) (DS-WFSF) machine is proposed. In the DS-WFSF machine, field and armature windings are separately placed in two different stators. Compared with the conventional WFSF machine with single stator, in which both field and armature windings are located, nonoverlapping concentrated windings and large slot areas can be obtained in the DS-WFSF machine. The proposed DS-WFSF machine exhibits >19% higher torque than the conventional WFSF machine, with both machines having the same space envelope and being globally optimized. The influence of leading design parameters, such as copper loss ratio between the field and armature windings, air-gap diameter, and rotor iron piece thickness and widths, on the average output torque is investigated for the DS-WFSF machines having 12/10, 12/11, 12/13, and 12/14 stator slots/rotor iron pieces. All the analyses are confirmed by both finite element and experimental results. [ABSTRACT FROM AUTHOR]

This paper analyzes the sensorless operation capability of a surface-mounted permanent-magnet (PM) (SPM) machine based on high-frequency (HF) voltage injection techniques. To investigate the machine saliency, the magnetic saturation-induced rotor saliency by PM is experimentally measured and analyzed under various load conditions. Moreover, the influence of cross-saturation and the magnetic polarity identification are also examined. Furthermore, the investigation has considered the resistance-based saliency due to HF eddy-current loss. In order to highlight the effectiveness of the sensorless operation capability, the tests are carried out under different operating conditions. [ABSTRACT FROM AUTHOR]

In this paper, novel partitioned stator doubly salient permanent magnet (PS-DSPM) machines with separated PM excitation and armature windings are proposed. Compared with conventional DSPM machines with single stator in which PMs are inserted in the yoke and windings are arranged on the teeth, the proposed PS-DSPM machine has two stators with PMs and windings located separately. Two sets of PS-DSPM machines, i.e., PS-DSPM-I and PS-DSPM-II machines, are proposed based on the conventional DSPM-I and DSPM-II machines in which the PMs are located on the stator yoke with intervals of every number of phases and every stator pole, respectively. The electromagnetic performance including back electromotive force (EMF) and torque characteristics of the proposed PS-DSPM machines are analyzed and compared with those of the conventional DSPM machines based on the optimal designs for the highest average electromagnetic torque by finite-element (FE) analysis in this paper. FE results show that the proposed PS-DSPM-I and PS-DSPM-II machines exhibit 8.49% and 207% higher torque density than the conventional DSPM-I and DSPM-II machines with same copper loss, respectively. The influence of main design parameters on the average electromagnetic torque in the proposed PS-DSPM machines is investigated, together with the conventional DSPM machines. A prototype machine of PS-DSPM-II is manufactured and tested to verify the FE analysis. [ABSTRACT FROM AUTHOR]

In this paper, switched flux permanent magnet (SFPM) machines are analyzed from the perspective of the air-gap field harmonics. It is found that the modulation of the salient rotor to PM and armature reaction fields in SFPM machines is similar to that of the iron pieces to those fields in the magnetic gear and magnetically geared machine. The magnetic gearing effect is analyzed in SFPM machines with different stator/rotor pole combinations, winding configurations, and stator lamination segment types by a simple magnetomotive force-permeance model, and validated by finite-element (FE) analysis. Different from fractional-slot surface-mounted PM machines in which the working air-gap field harmonic generates >95% of the average electromagnetic torque, >95% of the average electromagnetic torque in SFPM machines having \boldsymbol p\boldsymbol {s} stator pole pairs and nr rotor poles are contributed by several dominating field harmonics, i.e., rotating ones with \vert kn\boldsymbol {r}\,\pm \, (\textbf {2}\boldsymbol {i}-\textbf {1})\boldsymbol {p}\boldsymbol {s}\vert pole pair ( \boldsymbol k=\textbf 1, \boldsymbol i=\textbf 1, 2, 3 ) and static ones with (2\boldsymbol i-\textbf 1)\boldsymbol p\boldsymbol {s} pole pair ( \boldsymbol i=\textbf 1, 2, 3 ). The FE predicted average static torques in SFPM machines are validated by measurements on prototype machines. [ABSTRACT FROM AUTHOR]

In this paper, the relationship between the numbers of stator slots, winding polarities, and rotor poles for variable reluctance resolvers is derived and verified, which makes it possible for the same stator and winding to be shared by the rotors with different poles. Based on the established relationship, a simple factor is introduced to evaluate the level of voltage harmonics as an index for choosing appropriate stator slot and rotor pole combinations. With due account for easy manufacturing, alternate windings are proposed without apparent deterioration in voltage harmonics of a resolver. In particular, alternate windings with nonoverlapping uniform coils are proved to be possible for output windings in some stator slot and rotor pole combinations, which further simplify the manufacture process. Finite element method is adopted to verify the proposed design, together with experiments on the prototypes. [ABSTRACT FROM AUTHOR]

Novel multi-tooth variable flux reluctance machines (VFRMs), which adopt doubly salient stator and rotor structure with nonoverlapping stator ac armature and dc field windings, are investigated in this paper. The rotor pole number can be any integer except the phase number and its multiples. Meanwhile, to obtain symmetrical bipolar phase flux-linkage and back electromotive force waveforms, the ratio of stator pole number to the greatest common divisor of stator- and rotor-pole numbers should be even integers. Furthermore, under the same rated copper loss and stator outer radius as well as 6-pole stator, 4-tooth per stator pole VFRMs in which the stator and rotor pole number determined by Nr= nN s\pm 1 ( n is the number of small teeth per stator pole) exhibit the highest average torque. Moreover, compared with the optimal 6/7 stator/rotor pole single-tooth VFRM, the 6/25 stator/rotor pole 4-tooth VFRM has more sinusoidal and larger back EMF, negligible cogging torque, lower torque ripple, and higher torque capability at relatively low copper loss. Similar to single-tooth VFRMs, 4-tooth VFRMs with Nr= nN s\pm 1 exhibit more sinusoidal back EMF and larger torque than that of VFRMs with Nr= nN s\,\pm \,2 . The analyses are experimentally validated by several prototype machines. [ABSTRACT FROM AUTHOR]

This paper proposes how to use the addition of rotor position offsets as perturbation signals for the parameter estimation of permanent-magnet synchronous machines (PMSMs), which can be used for the condition monitoring of rotor permanent magnet and stator winding. During the proposed estimation, two small position offsets are intentionally added into the drive system, and the resulting voltage variation will be recorded for the estimation of rotor flux linkage. With the aid from estimated rotor flux linkage, the stator winding resistance can be subsequently estimated at steady state. This method is experimentally verified on two prototype PMSMs (150 W and 3 kW, respectively) and shows good performance in monitoring the variation of rotor flux linkage and winding resistance. [ABSTRACT FROM PUBLISHER]

This paper proposes a multiparameter estimation scheme for permanent-magnet (PM) synchronous machines (PMSMs) under variable-speed control, of which the estimation model is full rank and has taken into account the estimation and compensation of voltage-source-inverter nonlinearity. During the proposed estimation, the PMSM will work under variable speed control, and two sets of machine data corresponding to two sets of different rotor speeds will be recorded and used for the calculation of the proposed estimation model. It shows that the proposed estimation model can be solved by using a conventional quantum genetic algorithm and can ensure the identifiability of all needed parameters owing to its inherent full rank feature. The performance test of the proposed estimation is then conducted on an interior PMSM, and it shows that parameters such as rotor PM flux linkage and winding resistance can be accurately estimated without the aid from nominal parameter values of PMSM. Therefore, the proposed method can be used for the condition monitoring of stator winding and rotor PMs. [ABSTRACT FROM PUBLISHER]

This paper systematically presents the development of novel stator electrically field excited synchronous machines having salient pole rotors without any coils or magnets. This kind of new machine does not use slip-rings/brushes required in the conventional rotor wound field machines and combines the synergies of wound field machines, permanent magnet (PM) machines, switched reluctance, and synchronous reluctance machines. This paper describes the machine topologies, winding configurations, electromagnetic performance, and torque/power density, as well as acoustic noise and vibration, together with a comparison with the Toyota Prius interior PM machine in terms of torque/power speed characteristics. [ABSTRACT FROM AUTHOR]

A novel switched flux permanent magnet (PM) machine with a partitioned stator structure is proposed, consisting of a conventional switched flux machine with the PMs removed from the stator teeth and placed on a secondary stator within a salient rotor. This novel machine harnesses two distinct synergies in machine design: magnetically geared and switched flux machines. The machine is optimized and the performance is compared with different numbers of rotor poles and validated by experiment. This machine benefits from reduced copper loss, improved torque density, and torque per magnetic volume, compared with conventional switched flux machines. [ABSTRACT FROM AUTHOR]

In this paper, stator/rotor pole combinations, winding configurations, and electromagnetic performance of novel variable flux reluctance machines (VFRMs), which employ a doubly salient structure similar to switched reluctance machines (SRMs) but with stator-located dc field windings, are investigated. VFRMs with 12 stator poles are taken as examples to illustrate the method for determining the winding connections and winding factors. The back-electromotive force (EMF), self- and mutual inductances, cogging torque, static torque, torque ripple, and unbalanced magnetic force (UMF) are investigated by finite-element analyses. It is found that many stator/rotor pole combinations, i.e., 12/8 (which may be derived from the conventional three-phase SRM), 12/10, 12/11, 12/13, and 12/14, are feasible for the 12-stator-pole VFRMs. Among these pole number combinations, the 10- and 14-rotor-pole VFRMs can eliminate the inherent UMF in 6/5 and 6/7 VFRMs and exhibit more sinusoidal back-EMF waveforms and have higher torque density than an 8-rotor-pole VFRM, whereas the 11- and 13-rotor-pole VFRMs exhibit similar torque density as the 10- and 14-rotor-pole VFRMs, but with negligible cogging torque and torque ripple, albeit with UMF. Five prototype VFRMs with 12 stator poles and different rotor poles have been designed, manufactured, and tested to verify the analyses. [ABSTRACT FROM AUTHOR]

This paper investigates the electromagnetic performance of an 18-slot/10-pole fractional-slot surface-mounted permanent-magnet (SPM) machine and compares its performance with conventional fractional-slot 9-slot/10-pole, 12-slot/10-pole, and integer-slot 30-slot/10-pole SPM machines by 2-D finite-element (FE) analysis (FEA). The winding factors of the 18-slot/10-pole machine are first analyzed, and then its back electromagnetic force, average torque, cogging torque, and torque ripple are investigated. In addition, the influence of stator current excitation on the average torque and torque ripple, the impact of end windings on the average torque, the flux-weakening capability, the fault-tolerant capability, the magnet loss, and the mutual coupling between phases are also studied by 2-D FEA. The results show that the torque ripple can be suppressed in the 18-slot/10-pole SPM machine, whereas the average torque can be improved compared with the 12-slot/10-pole SPM machine. The unbalanced magnetic force in the 9-slot/10-pole SPM machine can be eliminated. Although the flux-weakening and fault-tolerant capabilities are reduced compared with the conventional 9-slot/10-pole and 12-slot/10-pole machine, the mutual coupling between phases can be eliminated. The magnet loss is slightly higher than that of a 30-slot/10-pole machine but significantly lower than those in both 9-slot/10-pole and 12-slot/10-pole machines. Finally, the experimental results are given for validation of theoretical analyses and FE results. [ABSTRACT FROM AUTHOR]

This paper proposes a three-phase wound-field switched-flux (WFSF) machine. It is found that this machine has much higher average torque compared with the conventional 12-slot/8-pole machine with a segmented rotor and 12-slot/5-pole WFSF machine under the constraint of the same copper loss. All of those machines have been optimized to achieve the maximum torque for comparison. The performances of four machines, including back electromotive force, cogging torque, and static torque, are analyzed and compared by 2-D finite-element analysis and validated by experiments on the prototype machines. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of two types of low-cost single-phase wound-field switched-flux machines with dc field and ac armature windings having the same coil-pitch of 2 slot-pitches and having different coil-pitches of 1 and 3 slot-pitches, respectively. Both can share the same stator lamination, but the latter can have shorter end windings and lower iron loss for the 12-slot/6-pole configuration. The performance, including back electromotive force, cogging torque, and static torque, of both machines are analyzed and compared by 2-D finite-element analysis and validated by experiments on the prototype machines. [ABSTRACT FROM AUTHOR]

This paper describes the operation principle and analyzes the electromagnetic performance of synchronous reluctance (SynR) machines having the structure of switched reluctance machines but excited by an ac sinusoidal current with dc bias, i.e., salient-pole SynR with nonoverlapping concentrated windings and a dc bias excitation. Under such excitation, these machines become similar to permanent magnet (PM) counterparts. The dc bias, which is equivalent to the PM excitation, produces back electromotive force (EMF) in the ac coils as well as cogging torque. Thus, injecting the ac coils by sinusoidal currents results in output torque on the machine shaft. The produced back EMF and cogging torque, and torque ripple magnitudes and periods, as well as the optimal ac current angle and the ac/dc current density ratio, strongly depend on the winding connection configuration. The maximum average torque can be achieved when the ac/dc current density ratio is 2 and the symmetrical winding connection, which results in a lower torque ripple, is employed. A prototype machine is built and tested to confirm the analyses and conclusions. [ABSTRACT FROM AUTHOR]

With the aid of finite-element and analytical methods, this paper investigates the influence of static/rotating eccentricities on the cogging torque of permanent-magnet machines having various pole/slot number combinations (2p/Ns), including fractional-slot topologies, such as 2p = Ns\pm 1, 2p = Ns\pm\break 2, and 2p/Ns = 8/12, as well as an integer-slot machine 2p/Ns = 4/12. It is found that the influence of eccentricity reduces significantly with the number of structure cyclic symmetry, which is equal to the greatest common divisor of slot and pole numbers. Hence, the eccentricity shows the largest influence in machines having 2p = Ns\pm 1, small influence in machines having 2p = Ns\pm 2, and the smallest influence in the other machines. The static and rotating eccentricities result in cogging torque components multiples of $(2p)$th and (N_{s})th orders, respectively. Both static and rotating eccentricities produce similar cogging torque magnitude. The experimental results validate the FE and analytical investigation. [ABSTRACT FROM PUBLISHER]

A rotor shaping technique with optimal third harmonic is presented to enhance the average torque of interior permanent-magnet (IPM) machines in this paper. The optimal value of third harmonic injected into the rotor outer surface shape has been derived and further confirmed by both finite-element analyses and experiments. The impact of the optimal third harmonic to the rotor shape on the electromagnetic performance, including harmonics in the back electromotive forces, cogging torque, average torque, and torque ripple, is investigated. It is demonstrated that without any modification of the costly rare earth permanent magnet employed for the inverse-cosine-shaped rotor, the average torque of the machine of an inverse cosine injected with an optimal third-harmonic-shaped rotor can be improved by > 6%. Simultaneously, the torque ripple remains almost unchanged, and the saliency ratio is also improved, further boosting the average torque. Finally, the machines with both conventional and optimal third harmonic rotors are prototyped and tested to validate the analysis. [ABSTRACT FROM PUBLISHER]

This paper presents the simplified analytical optimization and comparison between electrically excited (EE) and permanent-magnet (PM) machines in terms of torque per volume T/V and torque per weight T/G for low-speed applications when their copper loss and overall size are the same. Analytical torque models for both machines are individually developed and optimized to obtain the optimal flux density ratio, split ratio, and maximum torque densities. Furthermore, the variation of optima with the number of poles and machine size is also investigated. The analytical analyses are validated by both finite-element analyses and experiments. It is concluded that torque densities of PM machines can be more than \sqrt2 times higher than those of EE machines. For EE machines, there is an optimal pole number to maximize torque densities, and large volume applications are preferred. In actual applications, EE machines are more likely to compromise the torque density to meet the thermal constraints. It also shows that the optimal T/G designs have significantly higher split ratio and are more cost- and weight-effective than the optimal T/V designs. [ABSTRACT FROM PUBLISHER]

This paper presents optimal third harmonics in both permanent magnet (PM) shaping and current waveform to improve the output torque of five-phase surface-mounted PM (SPM) machines. The optimal value of third harmonic injected into the sinusoidal PM shape and current waveform for maximum torque improvement is analytically derived and validated by both finite element (FE) analyses and experiments. It is found that the optimal third harmonic is 1/6 of the fundamental one for both PM shape and current waveform. For the five-phase SPM machines having rotors without shaping, Sine shaping, or Sine shaping with third harmonic injected, the electromagnetic performance including the back EMF waveform, cogging torque, average torque, torque ripple, copper loss, iron loss, impact on power inverter, and demagnetization withstand capability are compared. It is demonstrated that, although the copper loss and iron loss increase due to additional third harmonic in the winding current and magnet shape, the average torque with optimal third harmonics injected in PM shaping and current waveform can be improved by >30% while the torque ripple and remains similar to that of the one with Sine shaping. In addition, this will reduce the dc bus voltage while maintaining the machine torque density. Furthermore, the machine with Sine and Sine+3rd rotors presents much better demagnetization withstand capability performance than conventional rotor. [ABSTRACT FROM PUBLISHER]

In order to simplify manufacture processes and improve fault-tolerant capabilities, modular electrical machines, especially the ones with segmented stators, are increasingly employed. However, flux gaps between segments are often inevitable. In this paper, to take advantage of these flux gaps to enhance the machine performance, novel modular permanent magnet machines with different slot/pole combinations have been proposed. The influence of these flux gaps on the electromagnetic performance of modular PM machines, such as winding factor, open-circuit air-gap flux densities, back-EMFs, cogging torque, on-load torque, inductances, magnetic saturation and copper losses, are comprehensively investigated and general rules have been established. It is found that for modular machines having slot number higher than pole number, the flux gaps between stator segments degrade the electromagnetic performance due to the lower winding factor and the flux defocusing effect. However, for modular machines having slot number lower than pole number, the electromagnetic performances can be significantly improved using proper flux gap width due to the higher winding factor and the flux focusing effect. The finite element results are validated by experiments using two prototype modular machines. [ABSTRACT FROM PUBLISHER]

In this paper, a novel sensorless control strategy with the injection of a high-frequency pulsating carrier signal into a stationary reference frame is proposed. Differing from the two most commonly used conventional high-frequency carrier signal injection methods, i.e., the injection of a rotating carrier voltage into a stationary reference frame and the injection of a pulsating carrier voltage into an estimated synchronous reference frame, the new proposed strategy injects a pulsating high-frequency carrier voltage into a stationary reference frame, which is as stable as the rotating carrier signal injection method. Then, the rotor position information can be retrieved from the carrier current response that is amplitude-modulated by the machine saliency, which is as simple as the pulsating carrier signal injection method. The signal demodulation process, the compensation of the cross-saturation effect, and magnetic polarity detection are also discussed and analyzed in detail. The experimental results on an interior permanent-magnet synchronous machine demonstrate that the new proposed strategy has a robust magnetic polarity detection and that it can achieve an accurate rotor position estimation with good steady-state performance and dynamic performance. [ABSTRACT FROM AUTHOR]

This paper presents an improved rotor position estimator based on a third-harmonic flux linkage which is the integration of third-harmonic back electromotive force. Different from the conventional rotor position estimation based on zero crossings of a third-harmonic flux linkage, the continuous signal is taken as reference, and the phase difference between the estimated and reference third-harmonic flux linkages is derived and used to compensate the estimation error in the speed calculated from the zero crossings at each sampling instant. Then, the rotor position can be derived from the compensated rotor speed, and the accuracy of rotor position estimation can be significantly improved, particularly under a dynamic condition. Several experiments have been implemented on a dSPACE platform with a laboratory permanent-magnet synchronous machine, and the experimental results validate that the improved rotor position estimator based on the continuous signal of third-harmonic flux linkage can achieve accurate rotor position estimation and outstanding dynamic performance. [ABSTRACT FROM PUBLISHER]

This work presents a permanent magnet (PM) shaping technique with optimal third harmonic to improve the output torque without deteriorating the torque ripple in surface-mounted PM (SPM) machines. The optimal value of third harmonic injected into the sinusoidal PM shape for maximum torque improvement is analytically derived and confirmed by finite-element analysis. Further, the influence of magnet edge thickness on the airgap field distribution is investigated and utilized to compensate the inter-pole flux leakage and curvature effect. It is found that the optimal third harmonic is 1/6 of the fundamental one. For the SPM machines having rotors without shaping, Sine shaping, Sine shaping with third harmonic injected, the electromagnetic performance, including the back-EMF waveforms, cogging torque, average torque, and torque ripple are compared. It is demonstrated that the average torque in the machine of a Sine shaping with an optimal third harmonic injected can be improved by >9\%, while the torque ripple remains similar to that of the one with Sine shaping. Finally, the machines with both conventional (without shaping) and optimal third harmonic PM rotors are prototyped and measured to validate the analyses. [ABSTRACT FROM PUBLISHER]

This paper proposes a method for online estimating the rotor flux linkage and voltage-source inverter (VSI) nonlinearity of permanent magnet synchronous machine (PMSM) drives. Thermocouples are employed for measuring the temperature variation of the stator winding in order to obtain the actual value of stator winding resistance. An Adaline estimator is used for online estimation of distorted voltage Vdead due to VSI nonlinearity. Both are subsequently used for the estimation of the rotor flux linkage. The proposed method is experimentally validated on a PMSM drive system and shows good performance in tracking the variation of the rotor flux linkage and compensating the VSI nonlinearity. [ABSTRACT FROM AUTHOR]

Winding resistance and rotor flux linkage are important to controller design and condition monitoring of a surface-mounted permanent-magnet synchronous machine (PMSM) system. In this paper, an online method for simultaneously estimating the winding resistance and rotor flux linkage of a PMSM is proposed, which is suitable for application under constant load torque. It is based on a proposed full-rank reference/variable model. Under constant load torque, a short pulse of id \neq 0 is transiently injected into the d-axis current, and two sets of machine rotor speeds, currents, and voltages corresponding to id = 0 and id \neq 0 are then measured for estimation. Since the torque is kept almost constant during the transient injection, owing to the moment of system inertia and negligible reluctance torque, the variation of rotor flux linkage due to injected id \neq 0 can be taken into account by using the equation of constant torque without measuring the load torque and is then associated with the two sets of machine equations for simultaneously estimating the winding resistance and rotor flux linkage. Furthermore, the proposed method does not need the values of the dq-axis inductances, while the influence from the nonideal voltage measurement, which will cause an ill-conditioned problem in the estimation, has been taken into account and solved by error analysis. This method is finally verified on two prototype PMSMs and shows good performance. [ABSTRACT FROM PUBLISHER]

In sensorless control of permanent-magnet brushless ac machines, it is necessary to identify the initial rotor position prior to start-up of the machine. Although saliency-tracking-based sensorless techniques are proven to be a good candidate to estimate the initial rotor position in sensorless control, magnetic polarity identification is another important issue. Since the machine saliency undergoes two cycles in a single electrical period, the estimated position information based on machine saliency has an angle ambiguity of \pi. With the aid of magnetic saturation effect, this paper proposes a robust initial rotor position estimation scheme, which utilizes both d- and q-axis carrier currents, instead of only the q-axis carrier current, in conventional pulsating-carrier-signal-injection-based sensorless control algorithm. Integrated with conventional carrier-signal-injection-based sensorless algorithm, the proposed technique could obtain the initial rotor position for both standstill and free-running rotors. Finally, the experimental results confirm the effectiveness and robustness of the proposed method. [ABSTRACT FROM PUBLISHER]

Cogging torque, as one of the main parasitic demerits of permanent magnet brushless machines, is of particular importance and primary concern during the machine design stage in many high-performance applications. Hence, numerous design techniques have been proposed and employed to effectively alleviate the cogging torque in permanent magnet brushless machines. The effects of rotor step skewing techniques including both conventional and herringbone styles on the cogging torque of permanent magnet brushless machine are comprehensively investigated and compared by synthesized 2-D and 3-D finite-element analysis in this paper. The results have revealed that both the conventional and herringbone rotor step skewing techniques can reduce the cogging torque significantly, but the latter is less effective than the former especially with small skewing step numbers. Moreover, the machine with herringbone rotor step skewing technique has rather peculiar and asymmetric cogging torque profiles, while the machine with conventional rotor step skewing technique exhibits normal and symmetric ones. The validity of the obtained results and findings is underpinned by the experiments on the prototype machine. [ABSTRACT FROM AUTHOR]

The paper investigates the influence of slot/pole number combination and winding configuration on the electromagnetic performance, such as flux density, back-EMF and electromagnetic torque, of permanent magnet machines having static or rotating rotor eccentricities. It shows that the eccentricity does not affect the back-EMF and electromagnetic torque of rotational symmetrical machines whose configuration repeats every certain amount of angle. However, it significantly distorts the back-EMF and torque waveforms of rotational asymmetric machines. Further, the static eccentricity does not change the harmonic contents of back-EMF, but results in unbalanced three phase back-EMF. Hence, the temporal order of the main torque ripple due to the static eccentricity is equal to the pole number. On the other hand, the rotating eccentricity results in more back-EMF harmonics of orders equal to the PM magnetisation order plus/minus one. Therefore, the temporal order of the main torque ripple due to the rotating eccentricity is equal to the triplen number closest to the pole number. The prediction is validated by the experiment. [ABSTRACT FROM PUBLISHER]

This paper presents a comparative study between novel variable flux reluctance machines (VFRMs) and doubly-fed doubly salient machines (DFDSMs), having the same stator outer diameter and axial length. For comparison, a 6-pole stator is used in VFRMs and DFDSMs, while a 5-pole rotor is optimized for VFRMs and a 4-pole rotor for DFDSMs. Compared with DFDSMs in which the flux-linkage and back-EMF are asymmetric particularly under heavy magnetic saturation, they become symmetrical and essentially sinusoidal in the VFRMs. Hence, the torque ripple in VFRMs can be significantly reduced. Further, due to the shorter flux path in the VFRMs, their average torque under the same copper loss can also be increased by 20% \sim 30% for the optimally designed VFRMs and DFDSMs within the same space envelop. [ABSTRACT FROM AUTHOR]

Skewing is one of the most widely used methods to reduce the torque ripples. However, it was reported that the on-load torque ripple was not always reduced by the conventional skewing, in which the skewing angle is one period of torque ripple. This paper proposes the way of improving the skewing to reduce the torque ripple when the conventional skewing fails. It is found that by optimizing the skewing angle and current phase advance angle together, the improved skewing is able to meet the stringent torque ripple requirement over the whole load range. [ABSTRACT FROM AUTHOR]

This paper proposes a novel sandwiched switched flux permanent magnet (SSFPM) machine using V-shaped magnets for maximizing output torque and improving magnet usage efficiency. The operation principle of conventional 6/10-stator/rotor-pole SSFPM machine is firstly described. Such SSFPM machine and a novel one with V-shaped magnets are optimized and then compared with the conventional 12/10-stator/rotor-pole SFPM machine by two-dimensional (2-D) finite element analysis (FEA). It is found that the SSFPM machine with V-shaped magnets exhibits higher torque density and higher magnet usage efficiency. In addition, the influence of step-skew angle on the torque ripple suppression is investigated in the SSFPM machine with V-shaped magnets. The FEA predicted back-EMF, cogging torque, torque-current characteristic are validated by experiments on the prototype machines. [ABSTRACT FROM AUTHOR]

In this paper, novel variable flux reluctance machines (VFRMs) with different rotor pole numbers, which employ a doubly salient structure together with field windings identically located in the stator for each phase, are investigated and compared. Different from other doubly salient machines, such as switched reluctance machines (SRM) and doubly fed doubly salient machines (DFDSM), the equation for determining the stator/rotor pole numbers, i.e., Nr=Ns\pm 2k, is no longer limited in VFRMs. More feasible selections of rotor pole numbers can be used if the stator/rotor pole numbers can satisfy Nr\ne kNph. Thus, for a 6-stator pole machine not only the rotor pole number can be selected as even numbers, such as 4- and 8-rotor poles, which are commonly used for SRM and DFDSM, but odd numbers, such as 5- and 7- rotor poles, are also feasible. The benefits of using 5- and 7-rotor poles are the cancellation of even-order harmonics together with the third-order harmonic in the flux-linkage and back-EMF. Hence, more sinusoidal back-EMF can be obtained to produce a lower torque ripple. The cancellation in 5- and 7-rotor pole machines is because the flux generated by field and armature windings can pass through the adjacent stator poles to form a shorter flux path, which can further increase their average torque. To validate the analysis, four prototype machines with different rotor pole numbers are manufactured and tested. [ABSTRACT FROM PUBLISHER]

This paper investigates the influence of skewing on torque ripples, including the electromagnetic (EM) torque ripple, and the cogging torque, in permanent magnet (PM) machines. It is found that the effectiveness of skewing largely depends on the axial variation of a torque ripple phase but less on its magnitude under skewing. It is further found that, in both linear and nonlinear cases, the EM and the on-load torque ripple cannot be fully eliminated by skewing one on-load torque ripple period or any other angles, except 360^\circ electrical, which is impractical. This is due to the fact that the EM torque ripple, especially its phase, of each slice is different due to the axial variation of the equivalent current phase advance angle introduced by skewing. In nonlinear cases, the EM torque ripple variation is further aggravated by the axial variation of magnetic saturation. The EM torque ripple as well as the on-load torque ripple may be even increased by skewing, especially when the cogging torque is low and electric loading is high. [ABSTRACT FROM AUTHOR]

Unbalanced magnetic forces (UMFs) exist in permanent magnet machines with diametrically asymmetric windings, e.g., machines having pole and slot numbers differed by one and two, even when there is no rotor eccentricity. In machines having pole and slot numbers differed by two, the on-load UMF results only when the single-layer winding is employed and the number of coils is odd. This paper investigates the influence of slot and pole number combinations on the UMF by using an analytical method based on the finite-element predicted airgap flux densities. A UMF may be divided into two components due to the radial and circumferential traveling stresses. It is found that they are additive for machines having pole number 2p = 3k - 1, e.g., 8-pole/9-slot and 8-pole/6-slot, but partially canceling for machines having 2p = 3k + 1, e.g., 16-pole/15-slot and 16-pole/18-slot. Furthermore, due to the additive and canceling effects, for the same slot number, the machine having a smaller pole number exhibits a larger UMF when the slot/pole numbers differ by one, whereas the machine having a larger pole number exhibits a larger UMF when the slot/pole numbers differ by two and the slot number is higher than 6. For the same pole number, machines having slot/pole numbers differed by two exhibit a smaller UMF than machines having slot/pole numbers differed by one. It is also found that, if 2p = 3k + 1, the UMF gradually diminishes to 0 with the increase in pole number. On the other hand, when 2p = 3k - 1, it reduces to a certain value with the increase in pole number. The experimental results are provided to verify the analysis. [ABSTRACT FROM AUTHOR]

Switched-flux permanent magnet (PM) (SFPM) machines have attracted considerable interest in recent years, since the flux focusing can be utilized, both armature windings and PM excitation sources are on the stator, while the salient pole rotor is very simple and robust. In SFPM machines, the high variable flux densities throughout the stator core result in iron loss being a significant proportion of the total losses. This paper presents a novel modular-rotor SFPM machine that facilitates a reduction in iron loss for a marginal reduction in output torque. The modular rotor also offers a reduction in rotor mass over the conventional-rotor topology. The electromagnetic performance of both conventional- and modular-rotor SFPM machines is analyzed by 2-D finite element analyses and is verified by measurements on small-scaled prototype SFPM machines. [ABSTRACT FROM AUTHOR]

The torque ripple of a permanent magnet (PM) machine is mainly due to the cogging torque and distortions of the back-emf waveforms, winding inductances and current waveforms. Both the cogging torque and back-emf are normally calculated at open-circuit conditions. However, they are affected by the electric loading and magnetic saturation. This paper investigates the influence of the load conditions on the cogging torque and back-emf waveform by employing a frozen permeability finite element technique. Furthermore, the effectiveness of the rotor skew on the minimization of the cogging torque, thus torque ripple, is also highlighted. It is found that the cogging torque magnitude is significantly increased under load conditions due to more flux leakage through tooth tips. However, the more important issue is that the cogging torque periodicity also changes, thus the rotor skew technique becomes less effective. In addition, the back-emf waveform under load conditions contains more harmonics, which leads to more electromagnetic torque ripple. It is also proven that the cogging torque, back-emf harmonics and consequently the output torque ripple are effectively diminished if the machine is skewed by one actual cogging torque period, i.e., when the electrical loading influence is considered. The analysis results are supported by experimental measurements. [ABSTRACT FROM PUBLISHER]

In order to improve the electromagnetic performance and ease the manufacture process, particularly stator winding, it is often preferable to employ a modular stator, e.g., individual stator tooth/back-iron segments, or separate stator tooth segments and back-iron segments. However, due to manufacture limits, there always exhibit additional air gaps between the stator teeth and back-iron segments. In practice, such gaps are likely to be nonuniform due to manufacture tolerances. This paper investigates the influence of uniform and nonuniform additional gaps on the cogging torque of permanent-magnet machines having either unskewed or step-skewed rotors. It is found that the presence of these gaps increases the cogging torque magnitude due to increased flux leakage through the tooth tips, while the uneven gaps can cause a significant increase in both the peak and periodicity of cogging torque waveform, which causes the skew method ineffective, as confirmed by both finite-element analyses and experiments. [ABSTRACT FROM PUBLISHER]

This paper presents a comparative study of torque–speed characteristics and cogging torque of the fractional-slot interior permanent magnet brushless ac machines having different slot openings, viz. open slot, closed slot, and hybrid slot (sandwiched open and closed slots), and unskewed and step skewed rotors. The influence of such alternate slot openings on the magnetic cross-coupling and cogging torque is particularly emphasized. Furthermore, the repercussion of the manufacturing limitations and tolerances on the cogging torque of machines having these alternate slot openings is also investigated. The magnetic cross-coupling level and the sensitivity of cogging torque to manufacturing limitations and tolerances strongly depend on the slot opening materials. The finite-element analyses are experimentally validated. [ABSTRACT FROM PUBLISHER]

This paper investigates the influence of nonideal voltage measurements on the parameter estimation of permanent-magnet synchronous machines (PMSMs). The influence of nonideal voltage measurements, such as the dc bus voltage drop, zero shift in the amplifier, and voltage source inverter nonlinearities, on the estimation of different machine parameters is investigated by theoretical and experimental analysis. For analysis, a model-reference-adaptive-system-based estimator is first described for the parameter estimation of the q-axis inductance, stator winding resistance, and rotor flux linkage. The estimator is then applied to a prototype surface-mounted PMSM to investigate the influence of nonideal voltage measurement on the estimation of various machine parameter values. It shows that, at low speed, the inverter nonlinearity compensation has significant influence on both the rotor flux linkage and winding resistance estimations while, at high speed, it has significant influence only on the winding resistance estimation and has negligible influence on the rotor flux linkage estimation. In addition, the inverter nonlinearity compensation will not influence the q-axis inductance estimation when it is under id = 0 control. However, the dc bus voltage drop due to the load variation and zero shift in the amplifier will significantly influence the q-axis inductance estimation. [ABSTRACT FROM PUBLISHER]

Based on the subdomain field model accounting for tooth-tips, the eddy current losses in magnets are calculated for surface-mounted permanent magnet machines. The contributions of both self action of each harmonic and mutual interaction between field harmonics of different orders to magnet loss are accounted for in the developed model. It allows for predicting magnet losses due to the open-circuit, armature reaction and load fields. By using the model, the influence of the slots, tooth-tips, tooth body shape, and current angle on the magnet loss is studied and the mutual interaction between field harmonics of different order are analysed. Extensive finite element analysis demonstrates excellent accuracy of the developed analytical model. [ABSTRACT FROM PUBLISHER]

Surface mounted permanent magnet Vernier (SPM-V) machines, because of their high torque density and multi-pole structure, are promising candidates for low-speed direct-drive applications. To achieve high torque density, the SPM-V machines are generally designed with high gear ratios. Therefore, their operating frequencies can be much higher than those of the conventional SPM machines. This potentially increases the alternating current (AC) winding losses, especially those with form-wound coils proposed for high-power applications. This article investigates the AC losses (including skin effect, proximity effect, rotor PM induced, and circulating current losses) in form-wound stator coils of a 3 MW direct-drive SPM-V machine with different slot/pole number combinations. The study reveals that the SPM-V machines have significantly higher AC winding losses than their conventional SPM counterparts for similar operating conditions. To reduce the AC winding losses in SPM-V machines, a novel flux shunt concept is proposed along with other conventional techniques such as increasing the number of turns/coil (with terminal voltage being kept constant) and parallel strands/turn, providing extra clearance at slot opening. With the loss reduction techniques implemented, the SPM-V machines can achieve comparable efficiency but much higher torque density than their conventional counterparts. Moreover, the proposed flux shunt was also found to be very effective in reducing the potential risk of permanent magnet (PM) irreversible demagnetization, a key issue for SPM-V machines at high power ratings. [ABSTRACT FROM AUTHOR]

The split ratio is one of the most important design parameters for permanent-magnet (PM) brushless machines. It has been optimized for maximum torque density with both internal rotor and tubular PM brushless machines in existing papers. This paper proposes an analytical model to determine the optimal split ratio for external rotor PM brushless machine having nonoverlapping winding. The influence of winding factor, tooth tip, and end winding on the split ratio is considered. The theoretical analyses are verified by finite element analysis and validated with experimental measurement. [ABSTRACT FROM AUTHOR]

In this paper, two identical surface-mounted permanent magnet machines are analyzed, with particular reference to rotor eddy current loss, when they are back-to-back connected and used as a motor and a generator, respectively, the motor being driven by pulsewidth modulation (PWM) inverters and the generator being connected to the 3-phase resistance load. Losses in both motor and generator under three different DC supply voltages and PWM duty ratios, including the eddy current losses in sleeves and magnets, and the iron losses, are predicted using finite element analysis. Thermal fields are analyzed using analytical lumped-circuit method based on the obtained losses. Predicted temperature rises of machines are compared with measured results and good agreement is achieved. The analysis reveals that the mmf time harmonics due to nonsinusoidal phase current and PWM carrier harmonics induce significant eddy current losses in magnets and sleeve of the motor, causing very large difference in temperature rises of the motor and generator. It is also found that the difference becomes more significant with the decrease of PWM duty ratio and increased DC supply voltage. [ABSTRACT FROM AUTHOR]