Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> This thesis is concerned with the development of linear generators for use as the power take off mechanism in marine renewable energy converters. Delivering significant power at the low velocities demanded by wave and tidal stream energy converters requires a large force, which must be reacted by an electrical machine in a direct drive system. Attention is focused on the development of two novel topology linear permanent magnet machines suitable for use in this application. For each topology, models are presented that are capable of predicting the force characteristics and dynamic generator performance. The models, which are verified experimentally, reveal significant behavioural differences between the two topologies. The designer is thus provided with an interesting choice when considering a direct drive power take off strategy. In short, a variable reluctance machine is shown to develop a high shear force in its airgap, offering the potential of a compact generator, yet its performance is hindered by a poor power factor and the presence of significant airgap closure forces. The second machine, an air cored stator encompassing a permanent magnet translator, is shown to lend itself favourably as a generator, but only at the expense of requiring a large quantity of magnetic material and developing a significantly lower shear stress. Mechanical issues involved in the direct integration of linear electrical machines into the marine environment are examined. Details of two existing marine renewable energy devices are used to hypothesise about the characteristics of realistic sized generators of both the topologies investigated. Direct drive power take off is shown to represent a feasible alternative to the complex systems frequently proposed in these applications. <s> BIB001 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> Variable reluctance permanent magnet machines exhibit shear stresses higher than conventional machine topologies. However, analysis and design of these machine topologies is not straightforward owing to the nature of the flux paths in the machine. In a transverse flux machine flux flows in all three dimensions and the machine structure is non-conventional. The vernier hybrid machine is another member of this family, but the flux paths are restricted to two dimensions, and can therefore be constructed using laminations. Significant leakage flux paths exist in the vernier hybrid machine, which must be modelled accurately during machine design. The use of flux-linkage maps to determine the performance of a linear vernier hybrid machine is described. Experimental results are presented to verify the model. The technique can be applied to any variable reluctance permanent magnet machine topology. <s> BIB002 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> This paper presents a new class of linear permanent magnet (PM) vernier machines which is suitable for low speed and high thrust force applications. The machine is composed of a tubular stator and a tubular translator. The stator consists of an iron core with salient teeth wound with 3-phase armature windings and PMs mounted on the surface of stator teeth. The translator is designed as a simple tubular iron core with salient teeth so that it is very robust to transmit high thrust force. By using the finite element method, the characteristics and performances of the proposed machine are analyzed and verified. <s> BIB003 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> The purpose of this paper is to describe a theory study of the linear stator permanent magnet vernier (LSPMV) machine. The fundamental operating principle, design criteria, characteristics and performances of the machine are discussed in this paper. In order to confirm the advantages, a quantitative comparison between the LSPMV machine and the linear vernier hybrid (LVH) machine is performed under the conditions of the same magnetic loading, electric loading and rated speed by using the finite element method. The results show that the proposed machine has higher power density and lower cogging force than the LVH machine. <s> BIB004 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> This paper presents the comparison of linear primary permanent magnet vernier (LPPMV) machine and linear vernier hybrid (LVH) machine. The LPPMV machine and the LVH machine both operate based on the magnetic gear principle, hence possessing the advantages of low speed and high thrust force density. In addition, both machines employ similar configurations between which the key difference is that a one-piece primary iron core is employed in the LPPMV machine instead of the modular cores in the LVH machine. Using the finite element method (FEM), the characteristics and performances of two machines are analyzed and compared. The results show that the LPPMV machine exhibits higher thrust force and lower cogging force. Finally, the FEM results are validated by experiments based on a prototype of the LPPMV machine. <s> BIB005 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> The linear permanent magnet (PM) vernier machine is very suitable for direct-drive applications. This paper proposes a linear consequent pole stator PM vernier (LCPSPMV) machine, which can offer high thrust force due to the use of magnetic gear effect. The key of the proposed machine is the introduction of consequent pole. Thus the volume of the PM can be reduced, and the initial cost can be reduced consequently. Based on the finite element analysis, the static characteristics of the proposed machine including the PM flux linkage, no-load EMF, detent force and thrust force are accurately analyzed. Compared with the existing linear stator PM vernier (LSPMV) machine, the proposed machine can offer higher no-load EMF, lower detent force and enhanced power density in the conditions of the same rated speed, winding turns, electric loading. Hence, the validity of the proposed machine is verified. <s> BIB006 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> This paper proposes a high force density tubular permanent-magnet (PM) motor, termed as tubular stator-PM venier motor, for artificial hearts. The novelty of the proposed motor is to artfully integrate two different magnetization directions of PMs and ferromagnetic poles together. The proposed motor incorporates the merits of vernier PM motors and stator-PM motors, offering high back electromotive force, improved force density, minimized cogging force, and reduced PM volume. The influence of the magnet pole ratio on the performance is investigated. The proposed motor is designed and compared with an existing vernier PM motor by using the time-stepping finite-element method, verifying the validation and the advantageous performance of the proposed motor. <s> BIB007 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> Vernier permanent-magnet (VPM) machines are well known for high torque density but low power factor. This paper deals with the low power factor of VPM machines. The goal is not obtained by reducing the electrical loading or adjusting current advance angle but by proposing a novel vernier topology, i.e., a dual-stator spoke-array (DSSA) VPM topology. In this paper, the characteristics of the DSSA VPM topology, such as active part, auxiliary mechanical structure, and rotor anisotropy, are analyzed in detail. Performances are evaluated based on finite-element analysis, including power factor, torque density, and cogging torque. The results show that the DSSA VPM topology exhibits high power factor, viz., ~0.9, and significantly high torque capability. The verification of the mechanical structure scheme is also done in this paper. Finally, theoretical analyses are validated by the experimental results by a 44-rotor pole 24-slot DSSA VPM prototype. <s> BIB008 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> Due to high torque at low speed, vernier machines are proposed for many direct-drive applications such as robotic arms, industrial applications and electric vehicles. In this paper, a vernier permanent magnet (PM) machine with 9-48 stator- rotor pole combination is designed for electric vehicle application and compared with the 2010 Toyota Prius IPM machine including the electromagnetic performances, the torque/power speed characteristics, as well as the efficiency map under full load operation. It shows that the vernier PM machine is superior at low speeds in terms of electromagnetic performance and efficiency. However, it has relatively low operating speed range and lower power factor, and therefore is not desirable for automotive application. <s> BIB009 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> In this paper, a new dual stator linear permanent-magnet (PM) vernier (LPMV) machine with toroidal winding is proposed and analyzed. The proposed machine enjoys the advantages of less copper usage and copper loss without sacrificing the thrust force performance. For a fair comparison, the proposed machine is designed with the same geometrical parameters based on the conventional dual stator LPMV machine with concentrated winding. Finally, the electromagnetic performances of the proposed machine and the conventional one are compared and analyzed by using finite element method, verifying that the proposed machine with the low copper loss can obtain high force density. <s> BIB010 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> Wave energy conversion can be simplified by using direct drive linear generators which may improve reliability. Numerous topologies of direct drive linear generators have been proposed in the last few decades such as the linear vernier hybrid permanent magnet (LVHPM) machine. However, the cost of this kind of machine is driven by the quantity of permanent magnet (PM) material. This paper proposes a linear vernier hybrid permanent magnet machine with consequent pole and concentrated windings for wave energy converters, which requires less magnet material for comparable performance. The key of the proposed design is the modular stator where the unbalanced magnetic circuit caused by consequent pole can be eliminated. Based on finite element analyses (FEA) the present machine is capable of higher thrust force, higher back EMF and lower cogging force as well as force ripple compared to that of a baseline LVHPM machine. <s> BIB011 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> Linear flux-switching permanent magnetic (LFSPM) machines are good choices for long stroke applications. These machines deliver high thrust force density in addition to the machine structure where permanent magnetics (PMs) and windings are all on the short mover. For LFSPM machines, their performance is always affected by big thrust force ripple. In this paper, for two C-core LFSPM machines of high thrust force capability, including a 6/13 C-core LFSPM (6/13LFSPM-C) machine and a sandwiched C-core LFSPM (SLFSPM-C) machine, and a thrust force ripple reduction method is proposed. The proposed method is developed by reducing the slot effect component of the cogging force based on staggered stator tooth, and suppressing the thrust force ripple caused by unbalanced three phase back-electromagnetic forces (EMFs) based on two end PMs. Based on finite element analysis (FEA) results, both C-core LFSPM machines can achieve small thrust force ripples as well as high sinusoidal back-EMFs, and at the same time, maintain high thrust force capability with the proposed method. It was also found that, the improved SLFSPM-C machine exhibited the same thrust force capability as the improved 6/13LFSPM-C machine, but with a much smaller thrust force ripple. <s> BIB012 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> A novel interior permanent magnet linear vernier machine (IPM-LVM) is proposed and analyzed in this paper. Compared to the existing surface-mounted permanent magnet linear vernier machine (SPM-LVM) and the SPM-LVM with Halbach arrays, the proposed machine can offer higher flux density in both the air-gap and armature iron core, which lead to a higher back electric motive force (back EMF) and higher thrust density under the same mover volume and heat capacity. Besides, it is proven that the proposed IPM-LVM also has a lower demagnetization risk compared to the SPM-LVM. Furthermore, in order to reduce the thrust ripple of the proposed machine, the three-sectional structure is adopted in this paper, which makes the proposed IPM-LVM exhibit high thrust density and low thrust ripple at the same time. <s> BIB013 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> Linear permanent magnet Vernier machines (LPMVM) have received more and more attention in recent years due to the advantages of high thrust density and low thrust ripple, which are both required in many direct-drive applications. In this paper, a double-sided toroidal-winding LPMVM (DSTWLPMVM) is proposed, and the thrust ripple sources for this type of machine are analyzed. To emphasize the specificity of LPMVM in aspect of thrust ripple optimization, a traditional fractional-slot linear permanent magnet synchronous machine is selected as a reference. Two indexes [amplitude difference (AD) and phase shifting (PS)] are defined to quantify the thrust ripple caused by the AD and the PS among three-phase electromotive force (EMF), respectively. Additionally, detent force is also considered when optimizing the three-phase EMF. Finally, a prototype of DSTWLPMVM is manufactured and tested. The measured EMF is basically symmetrical sinusoidal waveforms and the peak-to-peak value of the detent force is lower than 10 N. <s> BIB014 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> This paper proposes a new flux concentrated version of a consequent pole linear Vernier hybrid permanent magnet machine. The Vernier hybrid machine stator has alternatively magnetised adjacent magnets directly in contact with each other. A salient rotor then switches the direction of flux past the stator coils. Alternate magnets can be removed to make the consequent pole version, where inset rectangular magnets are magnetized in a common direction and separated by soft magnetic poles. In a flux concentrated consequent pole configuration, each magnet pole comprises of two magnets forming a V -shape. This topology hence possesses a combination of consequent poles, flux concentration and flux switching machine topologies. Magnetic flux concentration increases the airgap flux density, which potentially leads to an improvement of the force density and operating power factor. This paper compares the inset and V -shape consequent pole topologies using finite element analysis simulations. Both machines have the same dimensions, magnet volume, rated speed and current density. The simulation results imply that the V-shape machine offers higher electromagnetic performance. To confirm this, two linear prototypes are currently under construction, where the key parts that already produced are presented in this paper. <s> BIB015 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> This paper discusses the development of linear vernier hybrid machines for use in wave energy converters. A number of topology options are explored to reduce magnet usage and improve performance for use as a linear generator. Consequent pole, V-shape, and Halbach arrays are designed for a target 25 kW specification. A discussion of overall cost of energy produced is used to justify using efficiency and power factor to asses fixed magnet mass topology variants. A power factor improvement from 0.38 to 0.72 is presented. Physical integration of the electrical machine into wave energy converters is considered including flooded experimental results of thermal behavior and polymer bearing wear. <s> BIB016 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> In low-speed applications, variable-reluctance permanent magnet machines are often proposed due to their efficient use of magnet material and high torque density. This becomes even more important in large linear applications, where the translator is longer than the stator. Often, however, very low power factors are experienced by this class of machines. This paper proposes a V-shaped flux concentrated version of a consequent pole linear Vernier hybrid permanent magnet machine and compares it to a surface-mounted magnet variant. Using finite-element analysis validated by two laboratory prototypes, it is shown that the flux-concentrated version increases the airgap flux density, which potentially leads to an improvement in the force density and efficiency or can be used to increase the operating power factor. <s> BIB017 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> Permanent magnet vernier machines (PMVMs) gained a lot of interest over the past couple of decades. This is mainly due to their high torque density enabled by the magnetic gearing effect. This study will provide a thorough review of recent advances in PMVMs. This review will cover the principle of operation and nature of magnetic gearing in PMVMs, and a better understanding of novel PMVM topologies using different winding configuration as well as different modulation poles and rotor structures. Detailed discussions on the choice of gear ratio, slot-pole combinations, design optimisation and role of advanced materials in PMVMs will be presented. This will provide an update on the current state-of-the art as well as future areas of research. Furthermore, the power factor issue, fault tolerance as well as cost reduction will be discussed highlighting the gap between the current state-of-the art and what is needed in practical applications. <s> BIB018 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> In some wave energy converters, there is a need for linear electrical machines where all the active parts are mounted on the stator. For this reason the linear Vernier hybrid machine has been investigated. In other research, it is analyzed in 2D and assumed to have a flat cross section. In this paper a cylindrical version of the Vernier hybrid machine is presented and analyzed. A geometrical model is used to investigate potential mass savings of the cylindrical version, and a finite element analysis design study is used to demonstrate a potential improvement in performance. A proof of concept laboratory scale model has been built and tested to validate the predictions. <s> BIB019 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> Cost-effective and high-performance linear motors attract more and more attention for many applications. This paper proposes a novel double-side linear flux-modulation permanent-magnet (DS-LFMPM) motor with low cost, high thrust force density, and high power factor. The novelty of the proposed DS-LFMPM motor is to improve power factor by using double-side topology. Its topology is presented, and its operation principle is investigated. From the harmonic spectrums of the flux density in the air gap before and after the modulation of the mover teeth and the stator teeth, it can be concluded that the proposed motor has good flux-modulation effect. Also, the expression of the orders of the harmonic spectrums is given. The design process of sizes and structure is particularly explained. The electromagnetic performances are predicted by using the finite-element method and the proposed motor is prototyped for verification. The results show that the proposed DS-LFMPM motor can produce high thrust force density and high power factor. <s> BIB020 </s> Linear Machines for Long Stroke Applications—A Review <s> D. VERNIER MACHINES <s> This paper designs a double-side linear vernier permanent-magnet motor, which incorporates the merits of high thrust force capability, high power factor, and high efficiency. Since the parameters of the motor are very sensitive and the high thrust force capability comes along with the high force ripple, a framework of multiobjective optimization is proposed to improve the overall motor performances. The sensitivity analysis is used to select significant variables and the multiobjective differential evolution with ranking-based mutation operator is conducted with the response surface models to generate the Pareto solution set. The electromagnetic performances of the optimal motor are compared with the initial motor by simulating step by step based on finite-element analysis. Finally, a prototype motor is manufactured and the experimental results validate the improved motor performances. <s> BIB021
Linear vernier machines employ the so-called magneticgearing effect to produce high thrust force and to work at low speed BIB005 . LVPMs can be configured with the PMs on either the primary BIB005 , BIB017 or the secondary side BIB013 , BIB014 . For long stroke applications, the cost of the secondary PM LVPM is excessive, so it has been left out of the scope of this review. Generally, LVPMs show excellent shear-stress values and a high thrust density BIB001 - BIB005 . In addition, these machines exhibit high efficiency values even at low speed, thanks to the aforementioned magnetic gear effect BIB009 . Furthermore, very low thrust ripple values can also be achieved with LVPMs BIB009 , BIB010 , BIB014 , BIB018 . Contrary to other machines, LVPMs can achieve low speeds and still maintain a reasonable size and number of primary slots BIB006 , BIB015 , BIB017 , which simplifies its structure. Much like LFRPMs, LVPMs have the PMs mounted on the surface of the primary teeth, but the amount of PMs is larger in order to increase the rate of change of the flux and achieve higher back-EMF values BIB007 . Two main topologies of LVPMs have been found in the literature: Linear Vernier Hybrid Machines (LVHMs) and Linear Primary Permanent Magnet Vernier Machines (LPPMVMs). For the former type, the operating principle is quite similar to that of LFRPMs. The flux is reversed when the secondary poles are displaced from one primary magnet to the adjacent one. The only difference is that there are more poles and magnets in LVHMs. Thus, the relative displacement between the mover and the stator needs to be much lower for the flux to fulfil an entire period, as it can be observed in Fig. 20 . The main difference between LVHMs and LPPMVMs is that the modulation of the airgap flux is done progressively in LPPMVMs. In these machines, the secondary teeth modulate the flux density from the magnets so that the primary core perceives a lower amount of poles, to work at a higher frequency. The modulation effect is displayed in Fig. 21 . The effective pole pair number in the primary p ef , travelling speed of the flux in the primary core v ef and gear-ratio G r of LPPMVMs can be calculated with: where p PM , n t and v m stand for PM pole pair number, number of secondary teeth and mechanical speed. If analysed closely, it can be seen in Fig. 19 that the alignment between the primary magnets and the secondary poles is constant within a primary tooth for LVHMs. In contrast, this alignment is not kept constant in LPPMVMs. This is the main reason why LVHM machines suffer from a higher cogging force BIB003 , BIB005 than LPPMVMs. In fact, the cogging force of LPPMVMs is usually very low BIB004 , BIB003 , BIB005 . Even if their structures are slightly different, both of these machines are usually controlled in the BLAC mode, with the sinusoidal currents injected in phase with the back-EMFs  , BIB017 , BIB019 . LPPMVMs adopt overlapping distributed windings for their primary armature, in order to maximize the gear ratio BIB005 . On the other hand, LVHM machines employ concentrated windings. This results in a thicker yoke and bulky end windings for LPPMVMs, and thus, LVHMs exhibit a higher thrust density BIB005 . In addition, LVHMs adopt a modular structure most of the times BIB001 , BIB002 , BIB005 , BIB011 , so their performance is less affected by the end effect BIB005 . A detailed comparison between these two machines is done in BIB005 . For variable speed drives, it was shown that vernier machines have a very narrow constant thrust speed range BIB009 . The performance at the constant power speed range is not good either for this machines, as the operating efficiency is low when compared to an Interior Permanent Magnet (IPM) machine BIB009 . However, the main drawback for all LVPMs is their low power factor BIB015 - BIB018 . This means that LVPMs require costly inverters that can manage high currents if phase voltage is fixed. That is the reason why power factor improvement has received much attention in the last years. Baker et al. compare different PM configurations for a consequent-pole LVHM in BIB016 . The authors conclude that the most effective topology is the V-shape IPM. With such solution, the power factor is improved from 0.45 to 0.67. The optimal shape of PMs for the same type of machine is discussed in BIB017 . Another consequent pole structure is proposed in BIB006 to reduce the volume of PMs. Not only does the proposed machine reduce 25 % of the PM volume, but also the thrust capability of the consequent pole machine is 34 % higher than the one from the original machine. Thrust capabilities of a conventional LVHM and a consequent-pole LVHM are also compared in BIB011 . In this case, an improvement of 14.3 % is obtained in the thrust density, and the PM volume is 50 % lower. The usage of halbach arrays is proposed in BIB007 for an artificial heart machine, in order to improve the usage of PMs. The proposed configuration can generate higher thrust force and lower detent force than the conventional LVPM. A high power factor LVPM can be designed by combining a double-sided structure and a series magnetic circuit BIB008 , BIB020 , BIB021 (Fig. 22) . The design parameters of the machine in BIB021 are globally optimised for maximising thrust and power factor. The final design achieves a power factor of 0.945, but the experimental measurements of thrust differ from the expected values in up to 17.2 %, and the value of the power factor is not verified with the prototype. Further research must be done in order to validate this solution. Another double-sided LPPMVM with a series magnetic circuit is proposed in  . The power factor is not directly analysed, but the proposed machine exhibits 45 % lower inductance values, so an improvement in the power factor should be expected. Moreover, the presented machine improves the thrust density and shear stress of the previous machine, from 283 kN/m BIB012 