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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 963093, 11 pages

http://dx.doi.org/10.1155/2013/963093

## Design and Analysis of a Linear Hybrid Excitation Flux-Switching Generator for Direct Drive Wave Energy Converters

^{1}Engineering Research Center for Motion Control of MOE, School of Electrical Engineering, Southeast University, Nanjing 210096, China^{2}College of Mechanical and Electronic Engineering, China University of Petroleum (Huadong), Qingdao 266580, China

Received 28 June 2013; Revised 31 August 2013; Accepted 31 August 2013

Academic Editor: Fabrizio Marignetti

Copyright © 2013 Lei Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Linear generators have the advantage of a simple structure of the secondary, which is suitable for the application of wave energy conversion. Based on the vernier hybrid machines (VHMs), widely used for direct drive wave energy converters, this paper proposes a novel hybrid excitation flux-switching generator (LHEFSG), which can effectively improve the performance of this kind of generators. DC hybrid excitation windings and multitooth structure were used in the proposed generator to increase the magnetic energy and overcome the disadvantages of easily irreversible demagnetization of VHMs. Firstly, the operation principle and structure of the proposed generator are introduced. Secondly, by using the finite element method, the no-load performance of the proposed generator is analyzed and composed with ones of conventional VHM. In addition, the on-load performance of the proposed generator is obtained by finite element analysis (FEA). A dislocation of pole alignments method is implemented to reduce the cogging force. Lastly, a prototype of the linear flux-switching generator is used to verify the correctness of FEA results. All the results validate that the proposed generator has better performance than its counterparts.

#### 1. Introduction

Sea wave energy, originating from sun, is huge, clean, and renewable [1]. Wave energy is a widely distributed, highest-grade energy density, most easily directly used, clean, and renewable ocean energy [2]. Wave energy generation system, using electrical machines to convert energy from wave motion to electricity, is the main form of the development and utilization of wave energy. Since 1970s, there have been many different wave energy generation systems to be proposed. Direct drive power take-off systems have been proposed and widely concerned. Linear generators have directly been implemented to the drive of wave motion without using medium devices, such as air turbines, so that the generation system is simplified. A typical direct drive power take-off system is shown in Figure 1.

This system consists of two buoys, inner and outer buoys, a damper plate, and a linear generator. Because of the special design of inner buoy and damper plate, the inner buoy is not up and down with the wave undulating. Therefore, the stator (primary) of linear generator is seen as static suspended in water. The mover (secondary) of the generator is connected with the outer buoy and moved with the motion of a sea wave.

The linear generators are the core of direct drive wave power systems. The performances of linear generators directly determine the performances of the systems, such as the efficiency, power density, and quality of electric energy. At present, the major linear generators used for direct drive wave energy extraction are linear synchronous permanent magnet motor, which have permanent magnets (PMs) on the mover (secondary) [2–5]. This kind of linear permanent magnet machines has disadvantages of complex structure of the secondary, which might cause unexpected temperature rise and higher costs. In addition, these generators, evolved from conventional rotating generator, cannot obtain a high power density at a low speed motion environment. This is not suitable for direct drive wave energy converters. In order to obtain a high rate of change of energy in the air gap and a higher power density, based on the rotating stator-permanent magnet machines [6–8], some researches were focused on the primary permanent magnet linear generator, whose permanent magnets are assembled in the primary, such as vernier hybrid machine (VHM) [9–11] and switched reluctance generator [12, 13]. Compared with the primary permanent magnet linear generators, secondary permanent magnet linear generators cannot be designed as small pole pitch, because of the limitation of the machining dimension [14]. For VHMs and switched reluctance generators, by using the secondary slotted surface, the reluctance variation produces a rapid flux changing, resulting in shear stresses orders of magnitude increased. However, in order to increase the rate of flux changing, the size of permanent magnet of the VHMs must be designed very small. It suffers from the disadvantages of easily irreversible demagnetization. Therefore, to overcome shortcomings of the VHMs and increase the controllability of air gap flux, a novel linear hybrid excitation flux-switching generator is proposed for wave energy extraction in this paper.

Firstly, the operation principle and structure of the proposed generator were introduced. Secondly, by using the finite element method, the power density, cogging force, efficiency of energy transfer, and output voltage regulation of the proposed generator were optimized and analyzed. Lastly, a prototype of linear permanent magnet flux-switching machine was used to verify the correctness of the finite element analysis results.

#### 2. The Structure and Operation Principle of the Proposed Generator

Based on the magnetic gear effect, the pole pitch of VHM is smaller than conventional PM machine. Thus, these modulate the magnetic field produced by PMs to the high-speed traveling magnetic field. Therefore, the VHM has advantages of high shear stresses, high rate of change of flux. These make it attractive in cases where a conventional machine would be very large and heavy in low speed environment, such as direct drive wave energy converters. Figure 2 shows the typical topology of VHM.

However, because of smaller pole pitch of PMs, the VHMs inevitably suffer from easily irreversible demagnetization and severe flux leakage.

In order to obtain maximizing power extraction, the force generated by the directly coupled linear generator should be controlled. The electrical analogue of the direct drive power take-off system is shown in Figure 3 [6].

As shown in Figure 3, the EMF source represents the wave excitations force, the inductance represents the mass of the device, and the resistance and the capacitance represent the mechanical damping and the spring stiffness force, respectively. The generator is represented by the load and . When the sum of the imaginary components of the total impedance adds up to zero, maximum power will be obtained. Consider

Therefore,

According to the principle of PM machine, the reaction force of the linear generator can be expressed as [15] where, is the equivalent current of the magnetics in the primary. Therefore, to obtain the maximum power, the current of the generator should be controlled according to (4) and (5). Consider

From (4), it can be seen, with the changing of the frequency , that the RMS phase current should have a large scope of working. However, the current of the linear generator is limited by the rated current value of armature and cannot increase unrestrictedly. Therefore, the working range during maximum energy output is very small and limited.

For the shortcomings of VHMs, such as easily irreversible demagnetization, severe flux leakage, and small working range, a novel linear hybrid excitation flux-switching generator (LHEFSG), shown in Figure 4, is proposed in this paper.

By using hybrid excitation, the can be controlled to change with the , and the RMS phase current is optimized. The multitooth structure which is used to increase the rate of change of magnetic flux will not change the pole pitch of PMs.

As shown in Figure 5, when the translator moves, the fundamental of PM flux linkage in one-phase coil changes with magnetic reluctance at different positions and induces electromotive force (EMF).

#### 3. Performance Analysis

To investigate the characteristics of the proposed generator, a typical VHM, used for wave energy conversion, is employed to compare with the proposed generator. The 2-D FEM combined with an equivalent circuit is employed to analyze electromagnetic characteristics of the two generators.

The basic parameters and materials of the respective member of the TPPMLG and the TSPMLG are listed in Tables 1 and 2, respectively.

##### 3.1. The No-Load Performance

Firstly, the no-load performances of the two generators are analyzed. The voltage of one phase can be expressed as where and are flux linkage due to DC exciting winding and PM excitation, respectively.

When the speed of mover is 0.5 m/s, the flux linkage and the no-load voltage are obtained by FEA and shown in Figure 6.

As can be seen, compared with the VHM, the proposed generator has advantages of higher voltage and magnetic energy density. The harmonic component of the proposed is smaller. In addition, output voltage has a greater range of adjustment.

The field distribution of two generators obtained by FEM is shown in Figure 7.

It can be seen that the flux leakage of the VHM is more severe than the one of the proposed generators.

The cogging force, which is produced by slot effect and end effect and may cause the mechanical vibration, is unexpected. The cogging forces of two generators are obtained by static finite element analysis and shown in Figure 8.

Obviously, because there is no PM at the end sides of primary and secondary, the major component of cogging force of the proposed generator is caused by slot effect and is far less than the one of VHM, even with the maximum excitation current 15 A.

In addition, the inductance performance is studied. By moving the mover, when the coil phase coincides with the axis of , the coil phase is effectively axis coil ; thus,

When the coil phase coincides with the axis of , the coil is equivalent to axis coil ; thus,

The -axis inductance and -axis inductance are obtained and shown in Figure 9.

The inductance performance of the proposed generator is similar to the one of the permanent magnet synchronous machines.

##### 3.2. The Load Performance

Considering copper loss and core loss, the output power and the efficiency are calculated by the next equations: where is the core loss, is the output power, is the total input power, is the load resistance per phase, and are the frequency and the peak value of magnetic flux density, respectively, and , , , and are the loss coefficients of steel sheet provided by the supplier.

The performances of output power, output voltage, and efficiency of the proposed generator with different resistance are shown in Figure 8.

From Figure 10, it can be seen that the proposed generator has acceptable voltage regulation and high energy conversion efficiency.

Under the DC excitation, the DC filed loss can be calculated by

Therefore, under 15 A excitation, the performances of output power and efficiency of the proposed generator, considering the exciting loss, are shown in Figure 11.

The flux density distribution of the proposed generator, under the maximizing power output, is shown in Figure 12.

Because of the use of hybrid excitation, the output power, obtained by FEA, can reach to 720 W. It is far greater than the output power of the typical VHM. At this moment, the phase current is 4.23 A and the current density is 4.3 A/mm^{2}. These are reasonable values. As we can see, under the maximizing power output condition, local magnetic saturation is appearance. The saturation level is still within the acceptable range. However, because of the excitation loss, the output efficiency is slightly lower than the ones of the VHM.

#### 4. The Optimization of Cogging Force

The cogging force, which may cause the mechanical vibration, is unexpected and unavoidable for linear generator. Therefore, minimized cogging force is the goal of PM generator design. To further reduce the cogging force, a dislocation of pole alignments method is implemented to suppress the fluctuations caused by cogging force. Figure 13 shows the structure dislocation of stator and pole alignments.

According to the cogging force shown in Figure 7, the major harmonic component of the cogging force is six-order harmonics. Therefore, the distance of dislocation is . The optimal cogging force is obtained and shown in Figure 14.

It can be seen that the cogging force is reduced significantly, by using the method of dislocation of pole alignments. The electromagnetic force under the same load, with the dislocation of pole alignment and not, is obtained and shown in Figure 15.

The thrust ripple is reduced significantly, by using the method of dislocation of pole alignments. Because the output voltage is reduced at the same speed, the output power has a slight decrease.

#### 5. Experimental Results

To investigate the performance of this kind of generator, a linear permanent magnet flux-switching machine, shown in Figure 16, is studied. The electromagnetic parameters of the machine are listed in Table 3.

To verify proposed methods using dislocation of stator and pole alignments, the double sides secondaries were staggered 1.2 mm (about ) distance. The cogging force and voltage are measured and shown in Figures 17 and 18.

As shown in Figure 18, the results of FEA, by using dislocation of stator and pole alignments, the cogging force and the harmonic component of voltage are both reduced effectively. The output voltage under different speed obtained and load resistance by FEA and the experiment were shown in Figure 19.

The results of FEA value agree with the experimental ones. As shown in the experiment results, the proposed generator has advantages of higher frequency, higher power density, and minor cogging force.

#### 6. Conclusions

In this paper, a novel linear hybrid excitation flux-switching generator is proposed for direct drive wave energy converters. The operation principle has been analyzed. The proposed generator is compared with the typical VHM. The no-load and on-load performances are obtained and analyzed by using FEM. In addition, a dislocation of pole alignments method is implemented to suppress the cogging force. Lastly, a prototype of linear permanent magnet flux-switching machine has been employed to validate the results of FEA. All the results indicate that the proposed linear generator, with simple structure, minor cogging force, higher power density, higher output frequency, and larger range of output power, is suitable for the application of wave energy conversion.

#### Acknowledgments

This work was supported by the Special Foundation for State Oceanic Administration of China (GHME2011GD02) and by the National Natural Science Foundation of China under Grant no. 41076054.

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