I.Introduction Direct drive wave energy conversion (DD-WEC) is a typical low-speed long-stroke application, harvesting wave energy presents enormous challenges, because wave energy naturally exists in the form of extremely low speed, high force, or torque motion [1]. In DD-WEC, linear generators with multi-pole design all suffer from drawbacks such as low power density [2]. However, the frequency of flux linkage in field-modulated machine can be increased by the magnetic gear effect, and the output voltage and power density can also be effectively enhanced. Therefore, field-modulated machines have attracted more attentions in DD-WEC. A magnetic field-modulated linear permanent magnet (PM) generator for DD-WEC is proposed. The generator with a high power density converts wave energy effectively and enhances power density in DD-WEC [2]. A mover separated linear magnetic-field modulated motor for long stroke applications is proposed, the motor exhibits high thrust force by effectively employing the magnetic-field modulation effect [3]. A large-scale inner stator radial flux magnetically geared generator for wave energy conversion is proposed, the magnetic gear will not be damaged when exposed to overload torques [1]. Most recent work on field-modulated machines in DD-WEC focuses on the radial flux and axial flux machine, there is few literature about field-modulated transverse flux machine. In this paper, based on the field modulated principle, a field-modulated hybrid excitation transverse flux linear generator (FM-HE-TFLG) is proposed. Different combinations of PM pole pair, armature winding pole pair and translator pole pair are selected and their performances are compared and analyzed. II.Machine Configuration and Operation Principle Fig.1 In the proposed structure, as shown in Fig. 1, the armature winding is placed in outer stator slots. Excitation methods include electric excitation and PM excitation. Direct current (DC) field winding and PM are both located in inner stator. The translator consists of spiral silicon steel sheets and nonmagnetic sheets. In the proposed FM-HE-TFLG, armature winding pole pair paw, translator pole number Nt, and PM pole pair match pPM: Nt,=pPM+paw (1) The relationship between the translator position in electric and mechanical degrees is as follows: θe=Ntθm (2) where θe and θm are translator positions in electric and mechanical degrees respectively. III.Results Fig.2 The 18/12/17 topology has higher electric frequency, and the amplitude of flux linkage is lower than 12/12/11 counterpart. As the armature current increases, the saturation of 12/12/11 topology is earlier than that of 18/12/17, so the structure with higher modulation ratio is more suitable for high current applications. IV.Conclusion The simulation results support several interesting conclusions. As the modulation ratio increases, the electric frequency is enhanced. The structure with higher modulation ratio is more suitable for high current applications. The proposed 18/12/17 FM-HE-TFLG is a good candidate for DD-WEC.

**References:**

[1] M. Johnson, M. C. Gardner, H. A. Toliyat, S. Englebretson, W. Ouyang and C. Tschida, "Design, Construction, and Analysis of a Large-Scale Inner Stator Radial Flux Magnetically Geared Generator for Wave Energy Conversion," in IEEE Transactions on Industry Applications, vol. 54, no. 4, pp. 3305-3314, July-Aug. 2018. [2] N. Feng, H. Yu, M. Zhao, P. Zhang and D. Hou, "Magnetic field-modulated linear permanent-magnet generator for direct-drive wave energy conversion," in IET Electric Power Applications, vol. 14, no. 5, pp. 742-750, 5 2020. [3] W. Zhao, S. Wang, J. Ji, L. Xu and Z. Ling, "A New Mover Separated Linear Magnetic-Field Modulated Motor for Long Stroke Applications," in IEEE Transactions on Magnetics, vol. 53, no. 11, pp. 1-5, Nov. 2017, Art no. 4002205.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/18a90a429fe6f3e23b7a5005670edb71.jpg)
Fig.1 Sectional view and trimetric view of FM-HE-TFLG

![](https://assets.underline.io/uploads/markdown_image/1/image/b646b6fc5585d660f766fd9417590852.jpg)
Fig. 2. Waveforms of flux linkage and back EMF in 12/12/11 and 18/12/17 FM-HE-TFLG

 Analysis of Magnetic Gearing Effect in Field-modulated Hybrid Excitation Transverse Flux Linear Generator for Direct Drive Wave Energy Conversion

Magnetic lead screw (MLS) is a new type of linear actuator with high force density. Its output force depends not only on the arrangement of the permanent magnet (PM), but also on the materials used for the PMs, and the different materials of the PM directly affect the cost of the MLS. Therefore, based on this, a proposed MLS is given based on the combination of PM structure and magnetization direction and the combination of different PM materials. Compared with the traditional structures, it can not only improve the output force of the MLS, but also reduce the cost of the MLS. The results show that the size of air gap, the size of PM and the proportion of different materials combinations have great influence on the performance and cost of MLS. Finally, the performance of the proposed structure is compared with the traditional structures. The results show that the output force is increased by 21.5% and the cost is reduced by 21.4% under the same volume of MLS and PM. Index Terms — MLS, PM structure, magnetization direction, output force, cost. I.Introduction In recent years, as a new type of high force density linear actuator, magnetic lead screw (MLS) has been widely used in many fields, ranging from CNC machine tools, wave power generation to artificial heart [1-3]. MLS is similar to mechanical lead screw, which can convert linear motion into rotary motion, and vice versa. Compared with mechanical lead screw, MLS has the characteristics of inherent overload, minimum friction and low maintenance [4]. But for the existing applications and MLS structure, in addition to its output force is still low, there is also a problem of high cost caused by the use of high-performance PM materials in order to improve the output force of the MLS. Based on the above problems, a proposed MLS is given based on the combination of PM structure and magnetization direction and the combination of different PM materials, which improves the output force and decreases its cost. Detailed proposed structure introduction and operation principle are introduced in the second part. In the third part, the influence of the main parameters on the output force and cost is designed and optimized, and finally the size parameters of the structure are given. Finally, the performance of the proposed model is simulated and compared with the traditional structures to verify the superiority and economy of the proposed model. II.Structure and Operation Principle Compared with the traditional MLS structures, the proposed structure is shown in Fig. 1. The blue block and red block are radially magnetized PMs, in which the blue block is rectangular shape and the red block is salient pole shape, and both are made of NdFeB material. Green and yellow block are axially magnetized PMs with rectangular shape, and are made of other materials. Compared with the traditional halbach magnetizing array, this structure has higher output force and lower cost, and the structure is not difficult to process. The detailed operation principle of MLS is introduced in this paper. Fig.1. The proposed model. III.Design and Optimization The main design point of MLS is how to design the 3D structure of PM. There are three kinds of processing and installation structures, which are cylindrical, spiral and discrete surface mounted. In this part, the three structures will be compared in detail and the advantages and disadvantages of the description, and finally choose the appropriate shape for processing. After the structure is determined, the structure of the PM is optimized, mainly discussing the influence of the size of the air gap and PM on the output force and its cost of the MLS. In addition, the combination of different materials also has a great impact on the performance and cost of MLS, such as NdFeB, Ferrite, SmCo and Alnico. Finally, the best set of structural parameters of the MLS is obtained through the optimization, and the specific description is shown in the full text. IV.Results and Conclusion After design, optimization and analysis, the output force of the proposed model is shown in Fig. 2. It can be seen that the output force has increased by 21.5%. Moreover, after calculation, the cost of the proposed MLS is reduced by 21.4%, and the weight of the proposed MLS is also reduced by 8.6% due to the use of the combined materials of NdFeB and Ferrite, in which the proportion of NdFeB is 75.9% and Ferrite is 24.1%. In particular, limited by the number of words and pictures, we choose the traditional MLS for comparison, in which the PMs are rectangular and are made of NdFeB material. Fig.2. Performance comparison of the proposed model.

**References:**

[1] R. K. Holm, N. I. Berg, M. Walkusch, P. O. Rasmussen and R. H. Hansen, "Design of a Magnetic Lead Screw for Wave Energy Conversion," in IEEE Transactions on Industry Applications, vol. 49, no. 6, pp. 2699-2708, Nov.-Dec. 2013. [2] N. I. Berg, R. K. Holm and P. O. Rasmussen, "Theoretical and Experimental Loss and Efficiency Studies of a Magnetic Lead Screw," in IEEE Transactions on Industry Applications, vol. 51, no. 2, pp. 1438-1445, March-April 2015. [3] J. Ji, Z. Ling, J. Wang, W. Zhao, G. Liu and T. Zeng, "Design and Analysis of a Halbach Magnetized Magnetic Screw for Artificial Heart," in IEEE Transactions on Magnetics, vol. 51, no. 11, pp. 1-4, Nov. 2015, Art no. 8108604. [4] Z. Ling, J. Ji, J. Wang and W. Zhao, "Design Optimization and Test of a Radially Magnetized Magnetic Screw with Discretized PMs," in IEEE Transactions on Industrial Electronics, vol. 65, no. 9, pp. 7536-7547, Sept. 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/813f2c217de6006d1e11f97bf88afb43.jpg)
The proposed model

![](https://assets.underline.io/uploads/markdown_image/1/image/dffae9c2b87389d02da5ebb1d06a6e7e.jpg)
Performance comparison of the proposed model

 Optimization Design of Performance and its Cost of a Novel Magnetic Lead Screw by Combination of Different Permanent Magnet Materials

I. Introduction Direct drive wave energy conversion (DDWEC) device using permanent magnet linear generator (PMLG) eliminates the inefficient transmission device and achieves simpler mechanical structure. However, due to the direct connection between buoy and translator, the low-speed linear reciprocating wave motion will be directly transmitted to the translator. So PMLG needs to adopt a low-speed design [1]. It is necessary to increase the number of pole pairs of the generator or use power electronic devices to increase the output voltage and power density. But this will increase the loss and reduce the efficiency of the whole system. The linear-rotating axial flux permanent magnet generator (AFPMG) is proposed to improve the output voltage and power density of the DDWEC. By employing the magnet screw (MS) and AFPMG, it combines the merits of MS and AFPMG and realizes the soft connection between the buoy and generator rotor. The nut and screw of MS are directly connected to the buoy and generator rotor, respectively. When approximately 0.5m/s reciprocating wave motion comes, the movement can be accelerated by MS and magnetic field modulation and finally the speed of the rotor will reach 1200 rpm/min, which can improve the output voltage and power density consequently. While this structure brings advantages, at the same time, due to the use of a large number of rare-earth PMs, it will increase power generation costs and reduce practical competitiveness. Therefore, a hybrid excitation axial flux permanent magnet generator (HE-AFPMG) is proposed to reduce the amount of PMs and become a candidate for DDWEC. Not only that, because the wave conditions (typically 3-20s) are constantly changing, the corresponding wave excitation forces of the same buoy vary widely. By using hybrid excitation, the excitation current can easily adjusted to regulate the magnetic field of the air gap [2], which make generator suitable for different working conditions in wave energy conversion. II. Machine Configuration and Operation Principle In the proposed topology, as shown in Fig. 1, the armature winding and field winding are placed in upper stator and lower stator of AFPMG, respectively. PMs are placed at the slots of the upper stator and work as parallel excitation source. There is no risk of irreversible demagnetization in PMs with this configuration, meanwhile, it can reduce flux linkage and back electromotive force (EMF) harmonics. The operation principle of AFPMG based on modulation effect is similar to a magnetic gear and a magnetically geared machine when the rotor is consists of modulation teeth. The magnetic field will be accelerated due to the magnetic gear effect, when the excitation magnetic field passes through the air gap and modulation teeth. Eventually, potentials are induced in the armature windings. The number of pole pairs and speed of armature magnetic field are expressed as follow: paw = | pfw ± pmt | Ωaw = ( pfwΩfw ± pmtΩmt ) / ( pfw ± pmt ) where paw, Ωaw, pfw, Ωfw are the number of pole pairs and rotational speed of magnetic field in armature winding and field winding, respectively. pmt and Ωmt are the number and rotational speed of modulation teeth, respectively. In proposed AFPMG, the upper stator pole number Nus = 12, hence the number of pole pairs of magnetic field in armature winding paw = 2 or paw = 1 when the number of modulation teeth satisfies pmt = Nus ±2 or pmt = Nus ±1. Fig.1 III. Results Fig.2 The output power versus excitation current in proposed HE-AFPMG with armature winding having different load current is shown in Fig.2. IV. Conclusion The application of hybrid excitation in AFPMG used in DDWEC can eliminate risk of irreversible demagnetization in PMs and reduce flux linkage and back electromotive force harmonics. Meanwhile, it can adjust the air gap magnetic field to suit different sea conditions.

**References:**

[1] W. Li, K. T. Chau and J. Z. Jiang, "Application of Linear Magnetic Gears for Pseudo-Direct-Drive Oceanic Wave Energy Harvesting," in IEEE Transactions on Magnetics, vol. 47, no. 10, pp. 2624-2627, Oct. 2011. [2] C. Ye, Y. Du, J. Yang, X. Liang, F. Xiong and W. Xu, "Research of an Axial Flux Stator Partition Hybrid Excitation Brushless Synchronous Generator," in IEEE Transactions on Magnetics, vol. 54, no. 11, pp. 1-4, Nov. 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/951d474bb6205f855448b547badaaa7c.jpg)
Fig. 1

![](https://assets.underline.io/uploads/markdown_image/1/image/53fb22268e717a1e38e511372a0a531b.jpg)
Fig. 2

 A Hybrid Excitation Axial Flux Permanent Magnet Generator for Direct Drive Wave Energy Conversion

I.Introduction Direct drive wave energy conversion (DDWEC) has attracted wide attention [1]. Various ways have been employed to further reduce the cost of wave energy conversion and promote the commercialization process, including the application of permanent magnets (PMs). PM generator has better electromagnetic performance for its high energy density [2,3]. The configuration of DDWEC proposed in this paper is combining the axial flux generator (AFG) and magnetic lead screw (MLS). However, the extensive use of PM will increase the manufacturing cost. For reducing the PM cost in DDWEC, a modified consequent-pole PM AFG (CPM-AFG) is proposed in this paper. By changing one side of PMs into iron-cores, which is called iron-pole, the volume of PM can be reduced. II.Generator Topology The whole configuration of the DDWEC system is that AFG located inside of the MLS is connected softly to the buoy when the screw and nut of MLS is connected directly to the buoy and rotor, respectively, as is shown in Fig. 1. Through MLS, the linear reciprocating motion of the wave can be transformed into the rotational motion of nut. When the buoy moves up and down, the rotor composed of modulation teeth in AFG rotate to generate energy. The rotor's angular velocity can be expressed as: ω=Gv=πv/τ where G is defined as gear ratio of MLS, v is screw's linear velocity and τ is the pole width of MLS. Similar to magnetic gear, the pole pairs of armature windings paw, the pole pairs of PM pPM and the iron pieces of rotor Ni should satisfy: Ni= paw + pPM Fig. 1 III.Results The simulation result shown in Fig. 2 indicates that although the volume of PM in the CPM-AFG is reduced by half, the flux linkage and torque are not reduced to half compared with the conventional surface-mounted PM axial flux generator (SPM-AFG). The amplitudes of SPM-AFG and CPM-AFG are 0.14Wb and 0.11Wb, respectively. The average electromagnetic torques of them are 23.2 Nm and 19.1 Nm, respectively. Fig. 2 IV.Conclusion Simulation results shown that the proposed CPM-AFG is suitable for DDWEC which can reduce the consumption of PM, reduce the cost of manufacture and improves the utilization ratio of PM.

![](https://assets.underline.io/uploads/markdown_image/1/image/a5eebdd0cf9d759514ecdbe29a474d50.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/23cca77093f4d4271bf6d7183a5badbc.jpg)

Axial Flux Generator with Consequent-Pole PM Stator for Direct Drive Wave Energy Conversion

I.Introduction Recently, a variety of wave energy converters have been proposed with increasing concerns on low carbon electricity, of which direct drive wave energy converter (DD-WEC) requires fewer moving parts since the translator of the generator is coupled with the wave energy converter directly [1]. Permanent magnet linear generator (PMLG) is widely used for DD-WEC and permanent magnet transverse flux linear machine is a member of the variable reluctance PM linear machines family which are known to achieve high thrust density. So permanent magnet transverse flux linear generator (PMTFLG) is a good candidate in DD-WEC which is a typical low-speed high thrust application. Also, the air-gap flux can be adjusted by variable reluctance to extend the working range. Hence, in order to balance between extending the working range and achieving high thrust, more research should be done on PM positioning, number and shape of PMs and magnet material [2]. In this paper, a field-modulated transverse flux linear generator is proposed. By adjusting the machine topology and PM position, the generator can operate in a wide working range without sacrificing too much thrust density. II.Machine Topology and Operation Principle As shown in Fig. 1, the generator consists of outer stator, inner stator and moving translator. Some PMs and direct current field coils are placed in the inner stator, while the armature coils are placed in the outer stator slot and some PMs are inserted between the adjacent outer stator shoes. The moving part of the generator is translator and the moving direction is along z-axis. Silicon steel sheets and nonmagnetic sheets are arranged in the moving translator. The PMs which are inserted between the adjacent outer stator shoes can reduce the harmonics of back electromotive force (EMF). Fig. 1 III.Results Fig. 2 IV.conclusion Simulation results show that the air-gap flux can be adjusted by variable reluctance to extend the working range. The generator can operate in a wide working range without sacrificing too much thrust density.

![](https://assets.underline.io/uploads/markdown_image/1/image/93a8770a3fe2c80a6e7b3bdd2fa7f88e.jpg)

Fig. 1. Configuration of the proposed PMTFLG.

![](https://assets.underline.io/uploads/markdown_image/1/image/25ba2b9a683651ea55dcea34b5f1d0ec.jpg)

Fig. 2. Thrust of variable reluctance and variable reluctance and PM.

Analysis of a Variable Reluctance Field-modulated Transverse Flux Linear Generator

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Analysis of Magnetic Gearing Effect in Field-modulated Hybrid Excitation Transverse Flux Linear Generator for Direct Drive Wave Energy Conversion

Optimization Design of Performance and its Cost of a Novel Magnetic Lead Screw by Combination of Different Permanent Magnet Materials

A Hybrid Excitation Axial Flux Permanent Magnet Generator for Direct Drive Wave Energy Conversion

Axial Flux Generator with Consequent-Pole PM Stator for Direct Drive Wave Energy Conversion

Analysis of a Variable Reluctance Field-modulated Transverse Flux Linear Generator

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