Tubular Permanent Magnet Linear Synchronous Generator forWave-power Generation

Behrooz Rezaeealam, Assistant Professor

Lorestan University, Khorramabad, IRANrezaeealam@gmail.com

Abstract:In this paper tubular type slotless Permanent Magnet Linear Synchronous Generator (PMLSG), which produces neitherthe detent force nor normal force is proposed for wave power generator. The characteristics of the stator configurationare estimated using the Finite Element (FE) analysis and the relation between the output and loss characteristics withpole pitch is examined. Moreover, the operating performance of the generator is analyzed under the no-load and loadswith variable resistance. In the generator performance with variable resistance load, while the load increases, thecharacteristics of the induced voltage and load current are investigated and the efficiency is also defined from thecomparison between electrical output (induced voltage and load current) and mechanical input (external force) in eachload.

Keywords: PMLSG, Wave power, Finite element method

١. IntroductionRecently, the environmental problems such as globalwarming caused by excessive use of fossil fuels havebeen produced over the world. In order to overcomethis problem, renewable energy has received spotlightand the wave power, especially, has infinitude ofpotentiality. According to one research, ٢TW ofenergy, equivalent of twice the world’s electricityproduction, could be harvested from the world’s oceans[١]-[٣].However, the conventional method of the wave powergeneration using air turbine has many disadvantagessuch as its huge size, high cost and low efficiency. Thewave power generation using a linear generator hasreceived attention and has begun to be researched.The linear generator has an advantage which canconvert the reciprocating motion of a wave directly intoelectrical energy without any intermediate mechanism.As such, linear generator system is expected to bemade smaller and to have high efficiency [١]-[٣].Meanwhile, a linear generator is structurally equal to alinear motor but there are some points to be consideredas generator. First of all, despite the small wave power,an obstacle to motion such as the detent force andnormal force should be minimized in order to obtaineasy reciprocating motion of the mover. When a lineargenerator is applied to the general application system,the aspect of structural stability should be consideredfor the useful wave power generation [١]-[٣].In this paper, hence, the tubular type slotless PermanentMagnet Linear Synchronous Generator (PMLSG),which produces neither the detent force nor normal

force, is designed to overcome the these problems. Firstof all, the characteristics of the stator configuration areestimated using the Finite Element (FE) analysis andthe relation between the output and loss characteristicswith pole pitch is examined. Moreover, the operatingperformance of the generator is analyzed under the no-load and loads with variable resistance. In the generatorperformance with variable resistance load, while theload increases, the characteristics of the inducedvoltage and load current are investigated and theefficiency is also defined from the comparison betweenelectrical output (induced voltage and load current) andmechanical input (external force) in each load.

٢. Structural Property of LinearGenerator٢.١. Flat type PMLSGThe flat type PMLSG has been used in a wide range ofgeneral application system. However, there are somedisadvantages in the structural aspect. The attractiveforce that makes bad influence to the bearings must beexisted between the stator and the mover. In case of thedouble side type, both sides have a balanced attractiveforce and it does not have the normal force. But it ishard to keep the ideal air-gap caused by the bearingloads [١].Furthermore, the normal force is also produced largelyand acts as a friction force between the linear guide andmover. A general the friction force curve is shown inFigure ١. Fs signifies the static fiction force and Fslidingrefers the sliding friction force.The stopped mover must have a larger force than themaximum value of static friction in order to start

moving. The maximum value of static friction force isdescribed as below:

NF s max (١)

where, Fmax is the maximum value of static frictionforce, s is the coefficient of static friction force andN is the normal force. The equation above shows thatthe Fmax is proportional to N. This means that themaximum value of the static friction force is increasedbased on certain increasing amounts of normal force.The efficiency of the machine should decrease due tothe increasing mechanical input, if the normal force islarger. Therefore, it is necessary for the normal force tobe reduced in order to the high efficiency and desiredinduced voltage.

Fig. ١: Friction force change curve

Fig. ٢: Cross section of flat type PMLSG

Figure ٢ shows the configuration of the flat typePMLSG with the Halbach magnet array. Thispermanent magnet array makes bigger flux than othersin air-gap. In this model, the normal force is ٢۶٨۵.٠۴N;it could be large enough to cause a mechanicalproblem. In this paper, the tubular type lineargenerator, which structurally does not cause normalforce, is proposed.

٢.٢. Tubular type PMLSGFigure ٣ indicates the cross section of the typicaltubular type PMLSG. The tubular type PMLSG hashigher efficiency than the flat type linear generator,

because it does not have the end-turn of windings,which is not related to the effective magnetic flux.In case of the cylindrical structure, the normal force isnot produced, from the balanced attractive force andthe friction loss can be reduced because the mechanicaldevice such as a linear guide is not required.In this paper, the three-phase concentrated windings arewound on the stator and the permanent magnet of themover is magnetized in direction of the z-axis.Moreover, the Halbach array is applied for theconcentration of magnetic flux and the high averageflux density in air-gap.The length of core, which located between permanentmagnet, and thickness of back-iron are calculated byFE analysis for unsaturated core.

Fig. ٣: Cross section of tubular type PMLSG

a) Compare configuration of statorThere are two stators: the slotted-type stator, and theslotless-type stator in terms of stator structure. In thecase of the slotted-type, the maximum value of fluxdensity and the availability of the permanent magnetare higher than slotless-type, but the large detent forceand vibration of the apparatus are generated by theharmonic component, which is generated from relationof teeth and the permanent magnet. On the other hand,in the case of the slotless-type, the maximum value offlux density and the availability of the permanentmagnet are lower, but the detent force is not producedand the induced voltage waveform is sinusoidal inshape because the harmonic component caused by theslotted structure does not exist.The induced voltage is analyzed by the two-dimensionFE analysis using cylindrical coordinates under theassumption of the mover velocity of ١m/s.The induced voltage of slot and slotless-type areillustrates based on configuration of the stator. TheRMS value of the fundamental harmonic component ofthe induced voltage was calculated. Compared to twovalues between the slotted and slotless-type, theinduced voltage of slotted-type is approximately ١٠ Vgreater than that of slotless-type. The higher fluxdensity is produced by teeth.By the way, the induced voltage waveform is distortedby the harmonic components and magnetic saturationin teeth.The frequency analysis of two induced voltagewaveforms is shown in Figure ۵. In the case of theslotted-type, the undesired effects of ٣rd, ۵th and ٧th

harmonic components are remarkably presented on theinduced voltage waveform.