Research ArticleAnalysis of the Oceanic Wave Dynamics for Generation ofElectrical Energy Using a Linear Generator

Omar Farrok12 Md Rabiul Islam2 and Md Rafiqul Islam Sheikh2

1Department of Electrical and Electronic Engineering Ahsanullah University of Science amp Technology Dhaka 1208 Bangladesh2Department of Electrical and Electronic Engineering Rajshahi University of Engineering amp Technology Rajshahi 6204 Bangladesh

Correspondence should be addressed to Omar Farrok omarruetgmailcom

Received 28 March 2016 Revised 26 May 2016 Accepted 2 June 2016

Academic Editor Yongping Li

Copyright copy 2016 Omar Farrok et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Electricity generation from oceanic wave depends on the wave dynamics and the behavior of the ocean In this paper a permanentmagnet linear generator (PMLG) has been designed and analyzed for oceanic wave energy conversionThe proposed PMLG designis suitable for the point absorber type wave energy device A mathematical model of ocean wave is presented to observe the outputcharacteristics and performance of the PMLG with the variation of ocean waves The generated voltage current power appliedforce magnetic flux linkage and force components of the proposed PMLG have been presented for different sea wave conditionsThe commercially available software package ANSYSANSOFT has been used to simulate the proposed PMLG by the finite elementmethod The magnetic flux lines flux density and field intensity of the proposed PMLG that greatly varies with time are presentedfor transient analysis The simulation result shows the excellent features of the PMLG for constant and variable speeds related towave conditionsThese analyses help to select proper PMLGparameters for better utilization of sea wave tomaximize output power

1 Introduction

At present scientists and engineers are facing twomajor chal-lenges in the world of energy electrical energy productionand environmental issue These problems can be amicablysolved using renewable energy resources (RERs) The vitalfactors which have stimulated the use of RERs are energyindependence financial viability and mainly environmentalprotection [1] The problem of oil crises (1973ndash1983) andenvironmental pollution concerns urged engineers to harvestelectrical energy from the available RERs for example windenergy [2ndash5] solar energy [6ndash9] and hydro power [10] Asthe RER is variable and unpredictable different types of con-verters and controls are associated with the RER-based powerplants that are connected with standalone or grid systems[11 12]The traditional RERs have the problem of uncertaintyof availability and they require a large land area On the otherhand the key advantages of oceanic wave energy (OWE) areas follows (i) it has huge potential compared to the solar andwind energy (ii) it is easy to forecast and (iii) it does not needland area Hence it has been of great interest to the industrial

field particularly in energy generation the use of wave powerhas been more attractive compared to other RERs [13] OWEis a promising environmental pollution-free energy whichwouldmake significant contribution toward saving biochem-ical resources and reducing carbon emissions [14] It isestimated that the total wave energy resource in the opensea around the world is 10 TW (10000GW) a comparableamount of the total power consumption in the world [15]

Different types of oceanic wave energy converters(WECs) have been invented and examined for successfulconversion of wave energy into electrical energy [16ndash19] Thewave energy device may be of a rotational or a translationaltype and each of these devices has different features [20]Thepower takeoff devices play a vital role in converting the irreg-ular wave motion to a regular motion for energy conversionLinear generators (LGs) have directly been implementedto the direct drive wave energy conversion without usingmedium devices which has unique advantages over all otherwave energy devices [21] An LG has twomajor parts namelytranslator and stator The translator mounted to a hollowcylinder is sometimes called a float or floater as shown in

Hindawi Publishing CorporationJournal of EnergyVolume 2016 Article ID 3437027 14 pageshttpdxdoiorg10115520163437027

2 Journal of Energy

Float

Wave peak Wave trough

Connector Direction of oceanicwave propagation

Linear generator

Seabed

Stat

orTr

ansla

tor

Figure 1 Drawing of the LG connected with a float

Figure 1 The stator is mounted to another mechanical bodyin order to make it stationary with respect to the sea wave

The floater tries to float on the surface of the ocean wavewith the translator that moves relative to the stator due towave action The floater utilizes the rise and fall of the seawave at a single point for energy conversion As the translatormoves linearly due to the reciprocating motion of the floaterthe wave energy so extracted is converted into electricalenergy A lot of mathematicians analyzed and proposed dif-ferent mathematical models for understanding the nature ofoceanic wave [22 23]

Different types of permanent magnet linear generators(PMLGs) have been designed and analyzed for improvedperformance The flat and tubular flux switching permanentmagnet linear generators (FSPMLGs) have been proposed[21 24 25] Different analyses have shown that the FSPMLGsmade of PMs and steel cores have suffered from the problemof higher leakage flux leading to the reduction of electricalpower generation Tubular PMLGs have been proposed [1421 26 27] to reduce cogging forces and also increase effi-ciency The maintenance of tubular PMLG is difficult due tothe presence of the coils inside the periphery It is seen in therecent works [28] that the linear switched reluctance gener-ator (LSRG) has been proposed for high power generationExcessive leakage flux and complex control circuit of LSRGsare responsible for the degradation of overall efficiency andreliability

This paper has presented the mathematical model of thewave motion to analyze the behavior of a PMLG that offerslow internal resistance low loading effect and high outputpower It is essential to consider the nature of wave motionfor parameter selection of the PMLG thus maximizing elec-tricity generation A relationship between the oceanic wavemotions with the parameters of PMLG is established Differ-ent significant parameters for example size of PMs polestranslator length and stroke length of the PMLG are foundfrom the relationship and the generated voltage currentpower applied force magnetic flux linkage flux lines flux

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Core

Core

PM

PM

Core

PM

Core

Core

PM

PM

Core

Core

PM

Figure 2 Position of the translator for time 1199051

density and the applied force with force components of theproposed PMLG are shown for different sea wave conditions

2 Design of the PMLG

21 Working Principle The translator moves vertically withthe incident wave therefore the direction may be upwardor downward Considering the translator movement in theupward direction as shown in Figures 2 and 3 for a particulartime interval the stator and translator poles are aligned facingeach otherThe red and green lines are representing the northpole (N) and the south pole (S) of the permanent magnet(PM) respectively S exists in the upper side and N exists inthe lower side of the stator core for a time 119905

1 The position of

the translator varies with time and the direction of magneticflux changesThe translator position changes in Figure 3 fromthe position shown in Figure 2 S now exists in the lower sideand N exists in the upper side of the stator cores for anothertime 119905

2

Journal of Energy 3

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Core

PM

Core

PM

Core

PM

Core

PM

Core

Core

PM

Core

Figure 3 Position of the translator for time 1199052

Hence the direction of magnetic flux according to Fig-ure 2 is opposite for the translator position as in Figure 3within the time interval 119905

2ndash1199051 Therefore the induced voltage

directions across the conductor are opposite to each other anddue to this reason the PMLG generates AC power

22 Vector Diagram and Equivalent Circuit The windingof each phase consists of two coils of opposite phases Theinduced voltages are therefore 180∘ phase shifted to eachotherThe coils of each phase are connected in series in addi-tive polarity to get higher output voltageThe vector diagramsof induced voltages are represented in Figure 4

The equivalent circuit diagram of the proposed PMLGfor a three-phase load is shown in Figure 5 The equivalentseries resistances and inductances of each phase winding coilare considered equal denoted by 119877

119886and 119871

119878 respectivelyThe

winding consists of two series coils therefore the equivalentseries resistance and inductance of each coil are denoted by1198771198862 and 119871

1198782 respectively 119864

119886 119864119887 and 119864

119888are the induced

voltages of phase-A phase-B and phase-C respectively forsimplicity Similarly1198641015840

1198861198641015840119887 and1198641015840

119888are the induced voltages of

phase-A1015840 phase-B1015840 and phase-C1015840 respectivelyThemagneticexcitation is fed from the translatorrsquos PM array as shown inFigure 6 The terminal voltages V

119886 V119887 and V

119888 are measured

across the loadThe induced voltage equation may be represented as

119864119894+ 1198641015840

119894= 119877119894119894119894+ 119871119878

119889119894119894

119889119905+ V119894

= 119870119898cos(120587

120591119911 + 119895

2120587

3) VV (119905)

(1)

where 119894 = A B and C 119895 = 0 1 and minus1 V119894is the terminal

voltage 119894119894is the line current and 119871

119878is synchronous induc-

tance119870119898is the constant representing the machine construc-

tion VV(119905) is the translator vertical velocity or speed 120591 is thepole pitch and 119911 is the vertical displacement The terminalvoltage is

119894= 119894+ 1015840

119894minus 119895119883119878119894minus 119877119894119894 (2)

23 Construction Details The vertical cross section of thePMLG (front side) is shown in Figure 6 The PMLG basicallycontains a translator which is made by some PMs with thesteel coreThe stator contains some copper coils wounded onthe stator cores of steel situated on both sides of the translatorPhase-A phase-B andphase-C are located on the right side ofthe translator Phase-A1015840 phase-B1015840 and phase-C1015840 are locatedon the left side of the translator which are 180∘ phase shiftedfrom phase-A phase-B and phase-C respectively The con-struction supports the translator to move in the verticaldirection with respect to the statorThe orientation of the PMarray should be such that N and S can be formed one afteranother as shown in Figure 6

3 Model of the Oceanic Wave

In most of the cases constant speeds or sinusoidal speedshaving sinusoidal shapes are common approximations forsimulating PMLGs [25ndash27] The typical range of verticalvelocity of wave is 0ndash2ms with a time period from 4 to 6 s[28ndash30] Therefore a free oceanic wave neither forced nordissipated on a flat seabed is presented for analysis of the LGas shown in Figure 7 following the mentioned approxima-tions The amplitude of waveform is 119860 Hence the verticaldistance between the wave crest and the trough is 119867 whichis equal to twice the amplitude 119860 According to the point ofview of oceanographers it is considered as a linear waveThesea surface is lying on 119909119910 plane where 119910 components areconsidered zero as the wave propagates in 119909-direction 120582 iswavelength 119889

119882is water depth of the ocean with respect to 119909119910

plane or water surface seabed is at 119911 = minus119889119882 and the ocean

surface coincides with 119911 = 0

31 GeneralizedWave The general description of almost anytype of oceanic wave may be considered as depending onlyon the interpretation of 120577

120577 = 119860 cos (119896119909 minus 120596119905) (3)

120596 = radic119892119896 tanh (119896119889119882) (4)

Here the number of waves 119896 = 2120587120582 and 120596 is the frequencythat asserts the physics and describes consideration of a waterwave relating frequency and wave number Alternatively itcan be considered as a relation between the phase speed oroceanic wave velocity V and the wavelength Consideringgravitational acceleration 119892 = 98ms2 the phase speedwhich is a single basic wave that moves along the 119909-directioncan be expressed as

V = radic119892120582

2120587tanh(2120587

120582119889119882) (5)

According to (3) and (5) the wave velocity is along 119909-direction only although it has the velocity along 119911-directionSo the velocity of oceanic wave is a vector that depends on119909 119910 and 119911 and time 119905 To obtain a complete description of

4 Journal of Energy

Vphase-A

Vphase-B

Vphase-C

120∘

minus120∘ 120∘

minus120∘

Vphase-A998400

Vphase-B998400

Vphase-C998400

Figure 4 Vector diagram

++

+

Phase-A

Phase-B

Phase-C

Ea

Eb

Ec

LS2 LS2

LS2

LS2

LS2

LS2

Ra2 Ra2

Ra2

Ra2

Ra2

Ra2

E998400a

E998400b

E998400c

+

+

+

Load

va

vb

vc

Figure 5 Equivalent circuit diagram of the PMLG

oceanic wave the components along 119909 119910 and 119911 have to becalculated The motion can be expressed as

119881 (119909 119910 119911 119905)

= (119883 (119909 119910 119911 119905) 119884 (119909 119910 119911 119905) 119885 (119909 119910 119911 119905))

(6)

where119881(119909 119910 119911 119905) represents the velocity of oceanic wave and119883(119909 119910 119911 119905)119884(119909 119910 119911 119905) and119885(119909 119910 119911 119905) are the componentsalong 119909 119910 and 119911 The 119910 components may be considered aszero for the oceanic wave and the 119909 and 119911 components can beexpressed as follows

119883 = 119860120596cosh 119896 (119911 + 119889

119882)

sinh (119896119889119882)

cos (119896119909 minus 120596119905) (7)

119885 = 119860120596sinh 119896 (119911 + 119889

119882)

sinh (119896119889119882)

sin (119896119909 minus 120596119905) (8)

The119909 and 119911 components from (7) and (8) can be simplified forindividual consideration of shallow water wave intermediatedepth wave and deep sea wave

32 Shallow Water Wave In shallow water water depth ismuch lower than the wavelength 120582 that is 119889

119882≪ 120582 or

119896119889119882≪ 1 Another property of shallow water wave is that

the amplitude of wave is much smaller than wavelength so119860 ≪ 120582 or 119860119896 ≪ 1 So (7) and (8) may be written as

119883119878= 119860120596

119890119896(119911+119889119882) + 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cos (119896119909 minus 120596119905) (9)

119885119878= 119860120596

119890119896(119911+119889119882) minus 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

sin (119896119909 minus 120596119905) (10)

Now (9) and (10) may be reduced as

119883119878cong119860120596

119896119889119882

cos (119896119909 minus 120596119905) (11)

119885119878cong 119860120596(1 +

119911

119889119882

) sin (119896119909 minus 120596119905) (12)

Again if 119896119889119882≪ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = 119896radic119892119889119882because

tanh (119896119889119882) =

119890119896119889119882 minus 119890

minus119896119889119882

119890119896119889119882 + 119890

minus119896119889119882

=2119896119889119882

2= 119896119889119882 (13)

As V = 120596119896 phase speed can be expressed as V = radic119892119889119882

Journal of Energy 5

Phas

e-A

Phas

e-B

Phas

e-C

Phas

e-A998400

Phas

e-B998400

Phas

e-C998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

CoilCoil

CoilCoil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

Core

PM

Translator core

Permanent magnet

Copperwindings

Statorcore

North pole

South pole

Tran

slato

r

Figure 6 Construction of the PMLG

33 Deep Water Wave In deep water water depth is muchhigher than wavelength that is 119889

119882≫ 120582 or 119896119889

119882≫ 1 So

119890119896(119911+119889119882) + 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

119890119896(119911+119889119882) minus 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

tanh (119896119889119882) =

119890119896119889119882 minus 119890

minus119896119889119882

119890119896119889119882 + 119890

minus119896119889119882

cong119890119896119889119882

119890119896119889119882

= 1

(14)

Therefore (7) and (8) can be expressed as follows

119883119863cong 119860120596119890

119896119889119882 cos (119896119909 minus 120596119905) (15)

119885119863cong 119860120596119890

119896119889119882 sin (119896119909 minus 120596119905) (16)

6 Journal of Energy

Table 1 Comparison of the oceanic wave parameters

Wave type Shallow water Intermediate depth wave Deep water

Relative depth119889119882

120582lt 005 005 lt

119889119882

120582lt 05

119889119882

120582gt 05

Wave speed radic119892119889119882

radic119892120582

2120587tanh(2120587

119889119882

120582) radic

119892120582

2120587

Wave length radic119892119889119882119879

1198921198792

2120587tanh(2120587

119889119882

120582)

1198921198792

2120587

z

x

y

A

0

120582

120582

Wave trough

H

Wave crest

Seabed

dW

2120582

Figure 7 Waveform of a free oceanic wave

Again if 119896119889119882≫ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = radic119892119896 Phase speed V can be expressed as V = radic119892119896The119909and 119911 components both for shallow and for deep water from(6)ndash(12) (15) and (16) are explained in [31] Comparisons ofrelative depth wave speed and wavelength of shallow waterwave intermediate depth wave and deep sea wave are shownin Table 1

4 The PMLG and Wave Model

41 Selection of Translator Length The translator lengthsmaybe shorter equal or longer compared to the stator The com-mon lengths of the stator and the translator affect the powerrating of the PMLGThe power rating increases with increasein the common length Longer translator has been chosento obtain the same common length as shown in Figure 8for different translator positions The vertical displacementof translator with the incident sea wave is known as strokelength 119871 st There is a relationship between the wave ampli-tude119860

119908 and 119871 st during the energy conversion as 119871 st = 2119860119908

119860119908is smaller than the amplitude of free oceanic wave as in

(7)ndash(12) (15) and (16) because of power dissipation

42 Determination of Frequency The translator pole pitchis the summation of the PM thickness and translator polethickness of the PMLG as shown in Figure 9 The stator polepitch and translator pole pitch may be the same or differentdepending on the design strategy In the proposed design thestator pole pitch is the same as the translator pole pitch andthe stator pole width is the same as the translator pole widthThe pitch and pole width have a vital effect on the generated

voltage shape power frequency and forces The frequency119891 of the PMLG is determined by

119891 =VV (119905)2120591

(17)

43 Direction of Forces The simulation setup of the PMLGdesign is represented using a 3DCartesian coordinate systemThe applied force is working along 119911-axis as shown bybidirectional arrow in Figure 10 The width and thickness ofthis design are along 119910-axis and 119909-axis respectively Coggingforces between stator and translator core act along 119910-axisOther force components except for applied force and coggingforces work along 119909-axis The PMLG converts mechanicalenergy to electrical energy due to the force along 119911-axis andthe forces along 119909-axis and 119910-axis are generated which is thecause of mechanical power loss In the oceanic wave modelthe direction of wave elevation is also along 119911-axis accordingto (8) (10) (12) and (16)

44 Generated Voltage with Waves According to Faradayrsquoslaw of electromagnetic induction the induced voltage isfound as

119864119894(119905) = minus119873

119889Φ

119889119905 (18)

In the wave model the wave elevation is described withrespect to 119909-axis that represents the direction of wave prop-agation The induced voltage and related parameters of thePMLG are related to time The vertical wave displacementis assumed to be sinusoidal and the translator connected tobuoy tries to follow the wave elevation therefore the verticaldisplacement 119889tr and velocity 119904tr of the translator can beexpressed as given in (19) and (20) respectively [14] Hence

119889tr (119905) = 119860119908 sin(2120587

119879119905 plusmn 120579119894) (19)

119904tr (119905) = 1198601199082120587

119879cos(2120587

119879119905 plusmn 120579119894) (20)

Here 119860119908 120579119894 and 119879 represent wave amplitude initial

phase angle and period of oceanic wave respectively Thetranslator and buoy move with the wave elevation thereforethe flux variation with respect to time can be expressed as

Φ (119905) = Φ2120587

120582119889tr (119905) (21)

Journal of Energy 7

Strokelength

Com

mon

leng

th

Com

mon

leng

th

Com

mon

leng

th

Tran

slato

r

Strokelength

(a) (b) (c)

Figure 8 Translator position at different time

If 119881119898

is the peak voltage combining (18) and (21) thegenerated EMF per phase and 119881

119898of the PMLG Vlg are

obtained as [32]

Vlg (119905) = 119898 cos(2120587

119879119905) cos

2120587119860119908

120582sin(2120587

119879119905)

119881119898= 119873Φ

2120587

120582

2120587

119879119860119908

(22)

5 Simulation Results

Two types of speed settings have been used in this simu-lation one is consideration of constant translator speed forobservation of the performance of the PMLG and the otheris translator motion changed with the incident sea wave Thedefault air gap length is 2mm load is 4Ω and the translatorspeed is 1ms for the PMLG unless otherwise specified Theinput of the PMLG is mechanical thrust 119865 in newton Frommechanical power 119875

119898= 119865 times 119904tr and electrical power 119875

119890

efficiency 120578 is calculated by 120578 = 119875119890119875119898

51 Constant Translator Speed The terminal voltage and loadcurrent for default condition are shown in Figure 11

The load voltage and current are in the same phases dueto the resistive load The applied force 119865

119911 cogging force

119865119910 and force component along 119909-axis 119865

119909 are shown in

Figure 12 The induced voltage current and magnetic flux

Translator pole pitch

Thickness of the PM

Coil

CoilCoil

Coil

Stator pole pitch

Stator pole thickness

Translator pole thickness

Figure 9 Stator and translator pole pitch

linkage are shown in Figure 13The generated power is shownin Figure 14

52 Voltage Regulation The terminal voltage depends on theload for a specific PMLG as in (2) which is shown in Figure 15to observe the terminal characteristics

8 Journal of Energy

Table 2 Numerical values for legend of Figure 16

Legend name Load (Ω) RMS current (A) DC offset (A) Period (ms)1198681

4 86656 00377 7993551198682

5 71327 00269 8177821198683

8 46401 00151 8128971198684

10 37586 00118 8114311198685

15 25455 00077 80851198686

20 19233 00057 807523

z-axis

y-axis

x-axis

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Figure 10 Direction of different forces

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

0 50 100 150 200

Time (ms)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 11 Load voltage and current waveforms

Different loads ranging from 2Ω up to 1MΩ are shownon a semilog graph Load voltages measured from any oneof the three phases are similar and remain almost unchangedfrom 25Ω to 1MΩ The RMS values of currents and power ofphase-A for different load conditions are shown in Figures 16and 17 respectively The numerical values of the current andpower graphs used in the legend are tabulated in Tables 2 and3 respectively

53 Variable Translator Speed According to the oceanicwavemodel the vertical position of the wave is sinusoidal so the

3

2

1

0

minus1minus2minus3

Forc

e (kN

)

0 25 50 75 100 125 150 175 200

Time (ms)

Fx (kN)Fy (kN)Fz (kN)

Figure 12 Different forces of the PMLG

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)

Current (A)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

Figure 13 Induced voltage current and flux linkage

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

Voltage (V)

Power (W)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

800

600

400

200

0

Pow

er (W

)

Figure 14 Generated power with voltage and flux

Journal of Energy 9

Table 3 Numerical values for legend of Figure 17

Legend name Load (Ω) RMS power (W) Period (ms) Maximum power (W)1198751

4 2420785 400733 69198961198752

5 2043384 400488 58696831198753

8 1379347 400488 39820451198754

10 1130125 400366 32880751198755

15 77636 400366 22837361198756

20 590638 400244 1749611

25

30

35

40

Volta

ge (V

)

10 100 1000 10000 100000 10000001

R (ohm)

Figure 15 Terminal voltage for different loads

Time (ms)

I1 (A)I2 (A)I3 (A)

I4 (A)I5 (A)I6 (A)

806040200

minus15

minus10

minus5

0

5

10

15

Curr

ent (

A)

Figure 16 Load currents for different loads

700

600

500

400

300

200

100

0

Pow

er (W

)

Time (ms)

P1 (W)P2 (W)P3 (W)

P4 (W)P5 (W)P6 (W)

806040200

Figure 17 Generated power for different loads

Time (s)

Position (m)Velocity (ms)

1086420

minus15

minus10

minus05

00

05

10

15

Vert

ical

pos

ition

(m)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

Figure 18 Position and velocity of the translator

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

2 4 6 80 10

Time (s)

Figure 19 Generated voltage

1 2 3 40

Time (s)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

Velocity (ms)Voltage (V)

Figure 20 Relation between induced voltage and speed

vertical velocity of the wave elevation is a cosine functionThe vertical position and velocity of the translator are shownin Figure 18 The time period 119879 = 4 s and 119871

119878= 16m which

means119860119908= 08mThemagnitude of the generated voltage of

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

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International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

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Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

2 Journal of Energy

Float

Wave peak Wave trough

Connector Direction of oceanicwave propagation

Linear generator

Seabed

Stat

orTr

ansla

tor

Figure 1 Drawing of the LG connected with a float

Figure 1 The stator is mounted to another mechanical bodyin order to make it stationary with respect to the sea wave

The floater tries to float on the surface of the ocean wavewith the translator that moves relative to the stator due towave action The floater utilizes the rise and fall of the seawave at a single point for energy conversion As the translatormoves linearly due to the reciprocating motion of the floaterthe wave energy so extracted is converted into electricalenergy A lot of mathematicians analyzed and proposed dif-ferent mathematical models for understanding the nature ofoceanic wave [22 23]

Different types of permanent magnet linear generators(PMLGs) have been designed and analyzed for improvedperformance The flat and tubular flux switching permanentmagnet linear generators (FSPMLGs) have been proposed[21 24 25] Different analyses have shown that the FSPMLGsmade of PMs and steel cores have suffered from the problemof higher leakage flux leading to the reduction of electricalpower generation Tubular PMLGs have been proposed [1421 26 27] to reduce cogging forces and also increase effi-ciency The maintenance of tubular PMLG is difficult due tothe presence of the coils inside the periphery It is seen in therecent works [28] that the linear switched reluctance gener-ator (LSRG) has been proposed for high power generationExcessive leakage flux and complex control circuit of LSRGsare responsible for the degradation of overall efficiency andreliability

This paper has presented the mathematical model of thewave motion to analyze the behavior of a PMLG that offerslow internal resistance low loading effect and high outputpower It is essential to consider the nature of wave motionfor parameter selection of the PMLG thus maximizing elec-tricity generation A relationship between the oceanic wavemotions with the parameters of PMLG is established Differ-ent significant parameters for example size of PMs polestranslator length and stroke length of the PMLG are foundfrom the relationship and the generated voltage currentpower applied force magnetic flux linkage flux lines flux

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Core

Core

PM

PM

Core

PM

Core

Core

PM

PM

Core

Core

PM

Figure 2 Position of the translator for time 1199051

density and the applied force with force components of theproposed PMLG are shown for different sea wave conditions

2 Design of the PMLG

21 Working Principle The translator moves vertically withthe incident wave therefore the direction may be upwardor downward Considering the translator movement in theupward direction as shown in Figures 2 and 3 for a particulartime interval the stator and translator poles are aligned facingeach otherThe red and green lines are representing the northpole (N) and the south pole (S) of the permanent magnet(PM) respectively S exists in the upper side and N exists inthe lower side of the stator core for a time 119905

1 The position of

the translator varies with time and the direction of magneticflux changesThe translator position changes in Figure 3 fromthe position shown in Figure 2 S now exists in the lower sideand N exists in the upper side of the stator cores for anothertime 119905

2

Journal of Energy 3

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Core

PM

Core

PM

Core

PM

Core

PM

Core

Core

PM

Core

Figure 3 Position of the translator for time 1199052

Hence the direction of magnetic flux according to Fig-ure 2 is opposite for the translator position as in Figure 3within the time interval 119905

2ndash1199051 Therefore the induced voltage

directions across the conductor are opposite to each other anddue to this reason the PMLG generates AC power

22 Vector Diagram and Equivalent Circuit The windingof each phase consists of two coils of opposite phases Theinduced voltages are therefore 180∘ phase shifted to eachotherThe coils of each phase are connected in series in addi-tive polarity to get higher output voltageThe vector diagramsof induced voltages are represented in Figure 4

The equivalent circuit diagram of the proposed PMLGfor a three-phase load is shown in Figure 5 The equivalentseries resistances and inductances of each phase winding coilare considered equal denoted by 119877

119886and 119871

119878 respectivelyThe

winding consists of two series coils therefore the equivalentseries resistance and inductance of each coil are denoted by1198771198862 and 119871

1198782 respectively 119864

119886 119864119887 and 119864

119888are the induced

voltages of phase-A phase-B and phase-C respectively forsimplicity Similarly1198641015840

1198861198641015840119887 and1198641015840

119888are the induced voltages of

phase-A1015840 phase-B1015840 and phase-C1015840 respectivelyThemagneticexcitation is fed from the translatorrsquos PM array as shown inFigure 6 The terminal voltages V

119886 V119887 and V

119888 are measured

across the loadThe induced voltage equation may be represented as

119864119894+ 1198641015840

119894= 119877119894119894119894+ 119871119878

119889119894119894

119889119905+ V119894

= 119870119898cos(120587

120591119911 + 119895

2120587

3) VV (119905)

(1)

where 119894 = A B and C 119895 = 0 1 and minus1 V119894is the terminal

voltage 119894119894is the line current and 119871

119878is synchronous induc-

tance119870119898is the constant representing the machine construc-

tion VV(119905) is the translator vertical velocity or speed 120591 is thepole pitch and 119911 is the vertical displacement The terminalvoltage is

119894= 119894+ 1015840

119894minus 119895119883119878119894minus 119877119894119894 (2)

23 Construction Details The vertical cross section of thePMLG (front side) is shown in Figure 6 The PMLG basicallycontains a translator which is made by some PMs with thesteel coreThe stator contains some copper coils wounded onthe stator cores of steel situated on both sides of the translatorPhase-A phase-B andphase-C are located on the right side ofthe translator Phase-A1015840 phase-B1015840 and phase-C1015840 are locatedon the left side of the translator which are 180∘ phase shiftedfrom phase-A phase-B and phase-C respectively The con-struction supports the translator to move in the verticaldirection with respect to the statorThe orientation of the PMarray should be such that N and S can be formed one afteranother as shown in Figure 6

3 Model of the Oceanic Wave

In most of the cases constant speeds or sinusoidal speedshaving sinusoidal shapes are common approximations forsimulating PMLGs [25ndash27] The typical range of verticalvelocity of wave is 0ndash2ms with a time period from 4 to 6 s[28ndash30] Therefore a free oceanic wave neither forced nordissipated on a flat seabed is presented for analysis of the LGas shown in Figure 7 following the mentioned approxima-tions The amplitude of waveform is 119860 Hence the verticaldistance between the wave crest and the trough is 119867 whichis equal to twice the amplitude 119860 According to the point ofview of oceanographers it is considered as a linear waveThesea surface is lying on 119909119910 plane where 119910 components areconsidered zero as the wave propagates in 119909-direction 120582 iswavelength 119889

119882is water depth of the ocean with respect to 119909119910

plane or water surface seabed is at 119911 = minus119889119882 and the ocean

surface coincides with 119911 = 0

31 GeneralizedWave The general description of almost anytype of oceanic wave may be considered as depending onlyon the interpretation of 120577

120577 = 119860 cos (119896119909 minus 120596119905) (3)

120596 = radic119892119896 tanh (119896119889119882) (4)

Here the number of waves 119896 = 2120587120582 and 120596 is the frequencythat asserts the physics and describes consideration of a waterwave relating frequency and wave number Alternatively itcan be considered as a relation between the phase speed oroceanic wave velocity V and the wavelength Consideringgravitational acceleration 119892 = 98ms2 the phase speedwhich is a single basic wave that moves along the 119909-directioncan be expressed as

V = radic119892120582

2120587tanh(2120587

120582119889119882) (5)

According to (3) and (5) the wave velocity is along 119909-direction only although it has the velocity along 119911-directionSo the velocity of oceanic wave is a vector that depends on119909 119910 and 119911 and time 119905 To obtain a complete description of

4 Journal of Energy

Vphase-A

Vphase-B

Vphase-C

120∘

minus120∘ 120∘

minus120∘

Vphase-A998400

Vphase-B998400

Vphase-C998400

Figure 4 Vector diagram

++

+

Phase-A

Phase-B

Phase-C

Ea

Eb

Ec

LS2 LS2

LS2

LS2

LS2

LS2

Ra2 Ra2

Ra2

Ra2

Ra2

Ra2

E998400a

E998400b

E998400c

+

+

+

Load

va

vb

vc

Figure 5 Equivalent circuit diagram of the PMLG

oceanic wave the components along 119909 119910 and 119911 have to becalculated The motion can be expressed as

119881 (119909 119910 119911 119905)

= (119883 (119909 119910 119911 119905) 119884 (119909 119910 119911 119905) 119885 (119909 119910 119911 119905))

(6)

where119881(119909 119910 119911 119905) represents the velocity of oceanic wave and119883(119909 119910 119911 119905)119884(119909 119910 119911 119905) and119885(119909 119910 119911 119905) are the componentsalong 119909 119910 and 119911 The 119910 components may be considered aszero for the oceanic wave and the 119909 and 119911 components can beexpressed as follows

119883 = 119860120596cosh 119896 (119911 + 119889

119882)

sinh (119896119889119882)

cos (119896119909 minus 120596119905) (7)

119885 = 119860120596sinh 119896 (119911 + 119889

119882)

sinh (119896119889119882)

sin (119896119909 minus 120596119905) (8)

The119909 and 119911 components from (7) and (8) can be simplified forindividual consideration of shallow water wave intermediatedepth wave and deep sea wave

32 Shallow Water Wave In shallow water water depth ismuch lower than the wavelength 120582 that is 119889

119882≪ 120582 or

119896119889119882≪ 1 Another property of shallow water wave is that

the amplitude of wave is much smaller than wavelength so119860 ≪ 120582 or 119860119896 ≪ 1 So (7) and (8) may be written as

119883119878= 119860120596

119890119896(119911+119889119882) + 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cos (119896119909 minus 120596119905) (9)

119885119878= 119860120596

119890119896(119911+119889119882) minus 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

sin (119896119909 minus 120596119905) (10)

Now (9) and (10) may be reduced as

119883119878cong119860120596

119896119889119882

cos (119896119909 minus 120596119905) (11)

119885119878cong 119860120596(1 +

119911

119889119882

) sin (119896119909 minus 120596119905) (12)

Again if 119896119889119882≪ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = 119896radic119892119889119882because

tanh (119896119889119882) =

119890119896119889119882 minus 119890

minus119896119889119882

119890119896119889119882 + 119890

minus119896119889119882

=2119896119889119882

2= 119896119889119882 (13)

As V = 120596119896 phase speed can be expressed as V = radic119892119889119882

Journal of Energy 5

Phas

e-A

Phas

e-B

Phas

e-C

Phas

e-A998400

Phas

e-B998400

Phas

e-C998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

CoilCoil

CoilCoil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

Core

PM

Translator core

Permanent magnet

Copperwindings

Statorcore

North pole

South pole

Tran

slato

r

Figure 6 Construction of the PMLG

33 Deep Water Wave In deep water water depth is muchhigher than wavelength that is 119889

119882≫ 120582 or 119896119889

119882≫ 1 So

119890119896(119911+119889119882) + 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

119890119896(119911+119889119882) minus 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

tanh (119896119889119882) =

119890119896119889119882 minus 119890

minus119896119889119882

119890119896119889119882 + 119890

minus119896119889119882

cong119890119896119889119882

119890119896119889119882

= 1

(14)

Therefore (7) and (8) can be expressed as follows

119883119863cong 119860120596119890

119896119889119882 cos (119896119909 minus 120596119905) (15)

119885119863cong 119860120596119890

119896119889119882 sin (119896119909 minus 120596119905) (16)

6 Journal of Energy

Table 1 Comparison of the oceanic wave parameters

Wave type Shallow water Intermediate depth wave Deep water

Relative depth119889119882

120582lt 005 005 lt

119889119882

120582lt 05

119889119882

120582gt 05

Wave speed radic119892119889119882

radic119892120582

2120587tanh(2120587

119889119882

120582) radic

119892120582

2120587

Wave length radic119892119889119882119879

1198921198792

2120587tanh(2120587

119889119882

120582)

1198921198792

2120587

z

x

y

A

0

120582

120582

Wave trough

H

Wave crest

Seabed

dW

2120582

Figure 7 Waveform of a free oceanic wave

Again if 119896119889119882≫ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = radic119892119896 Phase speed V can be expressed as V = radic119892119896The119909and 119911 components both for shallow and for deep water from(6)ndash(12) (15) and (16) are explained in [31] Comparisons ofrelative depth wave speed and wavelength of shallow waterwave intermediate depth wave and deep sea wave are shownin Table 1

4 The PMLG and Wave Model

41 Selection of Translator Length The translator lengthsmaybe shorter equal or longer compared to the stator The com-mon lengths of the stator and the translator affect the powerrating of the PMLGThe power rating increases with increasein the common length Longer translator has been chosento obtain the same common length as shown in Figure 8for different translator positions The vertical displacementof translator with the incident sea wave is known as strokelength 119871 st There is a relationship between the wave ampli-tude119860

119908 and 119871 st during the energy conversion as 119871 st = 2119860119908

119860119908is smaller than the amplitude of free oceanic wave as in

(7)ndash(12) (15) and (16) because of power dissipation

42 Determination of Frequency The translator pole pitchis the summation of the PM thickness and translator polethickness of the PMLG as shown in Figure 9 The stator polepitch and translator pole pitch may be the same or differentdepending on the design strategy In the proposed design thestator pole pitch is the same as the translator pole pitch andthe stator pole width is the same as the translator pole widthThe pitch and pole width have a vital effect on the generated

voltage shape power frequency and forces The frequency119891 of the PMLG is determined by

119891 =VV (119905)2120591

(17)

43 Direction of Forces The simulation setup of the PMLGdesign is represented using a 3DCartesian coordinate systemThe applied force is working along 119911-axis as shown bybidirectional arrow in Figure 10 The width and thickness ofthis design are along 119910-axis and 119909-axis respectively Coggingforces between stator and translator core act along 119910-axisOther force components except for applied force and coggingforces work along 119909-axis The PMLG converts mechanicalenergy to electrical energy due to the force along 119911-axis andthe forces along 119909-axis and 119910-axis are generated which is thecause of mechanical power loss In the oceanic wave modelthe direction of wave elevation is also along 119911-axis accordingto (8) (10) (12) and (16)

44 Generated Voltage with Waves According to Faradayrsquoslaw of electromagnetic induction the induced voltage isfound as

119864119894(119905) = minus119873

119889Φ

119889119905 (18)

In the wave model the wave elevation is described withrespect to 119909-axis that represents the direction of wave prop-agation The induced voltage and related parameters of thePMLG are related to time The vertical wave displacementis assumed to be sinusoidal and the translator connected tobuoy tries to follow the wave elevation therefore the verticaldisplacement 119889tr and velocity 119904tr of the translator can beexpressed as given in (19) and (20) respectively [14] Hence

119889tr (119905) = 119860119908 sin(2120587

119879119905 plusmn 120579119894) (19)

119904tr (119905) = 1198601199082120587

119879cos(2120587

119879119905 plusmn 120579119894) (20)

Here 119860119908 120579119894 and 119879 represent wave amplitude initial

phase angle and period of oceanic wave respectively Thetranslator and buoy move with the wave elevation thereforethe flux variation with respect to time can be expressed as

Φ (119905) = Φ2120587

120582119889tr (119905) (21)

Journal of Energy 7

Strokelength

Com

mon

leng

th

Com

mon

leng

th

Com

mon

leng

th

Tran

slato

r

Strokelength

(a) (b) (c)

Figure 8 Translator position at different time

If 119881119898

is the peak voltage combining (18) and (21) thegenerated EMF per phase and 119881

119898of the PMLG Vlg are

obtained as [32]

Vlg (119905) = 119898 cos(2120587

119879119905) cos

2120587119860119908

120582sin(2120587

119879119905)

119881119898= 119873Φ

2120587

120582

2120587

119879119860119908

(22)

5 Simulation Results

Two types of speed settings have been used in this simu-lation one is consideration of constant translator speed forobservation of the performance of the PMLG and the otheris translator motion changed with the incident sea wave Thedefault air gap length is 2mm load is 4Ω and the translatorspeed is 1ms for the PMLG unless otherwise specified Theinput of the PMLG is mechanical thrust 119865 in newton Frommechanical power 119875

119898= 119865 times 119904tr and electrical power 119875

119890

efficiency 120578 is calculated by 120578 = 119875119890119875119898

51 Constant Translator Speed The terminal voltage and loadcurrent for default condition are shown in Figure 11

The load voltage and current are in the same phases dueto the resistive load The applied force 119865

119911 cogging force

119865119910 and force component along 119909-axis 119865

119909 are shown in

Figure 12 The induced voltage current and magnetic flux

Translator pole pitch

Thickness of the PM

Coil

CoilCoil

Coil

Stator pole pitch

Stator pole thickness

Translator pole thickness

Figure 9 Stator and translator pole pitch

linkage are shown in Figure 13The generated power is shownin Figure 14

52 Voltage Regulation The terminal voltage depends on theload for a specific PMLG as in (2) which is shown in Figure 15to observe the terminal characteristics

8 Journal of Energy

Table 2 Numerical values for legend of Figure 16

Legend name Load (Ω) RMS current (A) DC offset (A) Period (ms)1198681

4 86656 00377 7993551198682

5 71327 00269 8177821198683

8 46401 00151 8128971198684

10 37586 00118 8114311198685

15 25455 00077 80851198686

20 19233 00057 807523

z-axis

y-axis

x-axis

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Figure 10 Direction of different forces

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

0 50 100 150 200

Time (ms)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 11 Load voltage and current waveforms

Different loads ranging from 2Ω up to 1MΩ are shownon a semilog graph Load voltages measured from any oneof the three phases are similar and remain almost unchangedfrom 25Ω to 1MΩ The RMS values of currents and power ofphase-A for different load conditions are shown in Figures 16and 17 respectively The numerical values of the current andpower graphs used in the legend are tabulated in Tables 2 and3 respectively

53 Variable Translator Speed According to the oceanicwavemodel the vertical position of the wave is sinusoidal so the

3

2

1

0

minus1minus2minus3

Forc

e (kN

)

0 25 50 75 100 125 150 175 200

Time (ms)

Fx (kN)Fy (kN)Fz (kN)

Figure 12 Different forces of the PMLG

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)

Current (A)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

Figure 13 Induced voltage current and flux linkage

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

Voltage (V)

Power (W)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

800

600

400

200

0

Pow

er (W

)

Figure 14 Generated power with voltage and flux

Journal of Energy 9

Table 3 Numerical values for legend of Figure 17

Legend name Load (Ω) RMS power (W) Period (ms) Maximum power (W)1198751

4 2420785 400733 69198961198752

5 2043384 400488 58696831198753

8 1379347 400488 39820451198754

10 1130125 400366 32880751198755

15 77636 400366 22837361198756

20 590638 400244 1749611

25

30

35

40

Volta

ge (V

)

10 100 1000 10000 100000 10000001

R (ohm)

Figure 15 Terminal voltage for different loads

Time (ms)

I1 (A)I2 (A)I3 (A)

I4 (A)I5 (A)I6 (A)

806040200

minus15

minus10

minus5

0

5

10

15

Curr

ent (

A)

Figure 16 Load currents for different loads

700

600

500

400

300

200

100

0

Pow

er (W

)

Time (ms)

P1 (W)P2 (W)P3 (W)

P4 (W)P5 (W)P6 (W)

806040200

Figure 17 Generated power for different loads

Time (s)

Position (m)Velocity (ms)

1086420

minus15

minus10

minus05

00

05

10

15

Vert

ical

pos

ition

(m)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

Figure 18 Position and velocity of the translator

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

2 4 6 80 10

Time (s)

Figure 19 Generated voltage

1 2 3 40

Time (s)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

Velocity (ms)Voltage (V)

Figure 20 Relation between induced voltage and speed

vertical velocity of the wave elevation is a cosine functionThe vertical position and velocity of the translator are shownin Figure 18 The time period 119879 = 4 s and 119871

119878= 16m which

means119860119908= 08mThemagnitude of the generated voltage of

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Energy 3

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Core

PM

Core

PM

Core

PM

Core

PM

Core

Core

PM

Core

Figure 3 Position of the translator for time 1199052

Hence the direction of magnetic flux according to Fig-ure 2 is opposite for the translator position as in Figure 3within the time interval 119905

2ndash1199051 Therefore the induced voltage

directions across the conductor are opposite to each other anddue to this reason the PMLG generates AC power

22 Vector Diagram and Equivalent Circuit The windingof each phase consists of two coils of opposite phases Theinduced voltages are therefore 180∘ phase shifted to eachotherThe coils of each phase are connected in series in addi-tive polarity to get higher output voltageThe vector diagramsof induced voltages are represented in Figure 4

The equivalent circuit diagram of the proposed PMLGfor a three-phase load is shown in Figure 5 The equivalentseries resistances and inductances of each phase winding coilare considered equal denoted by 119877

119886and 119871

119878 respectivelyThe

winding consists of two series coils therefore the equivalentseries resistance and inductance of each coil are denoted by1198771198862 and 119871

1198782 respectively 119864

119886 119864119887 and 119864

119888are the induced

voltages of phase-A phase-B and phase-C respectively forsimplicity Similarly1198641015840

1198861198641015840119887 and1198641015840

119888are the induced voltages of

phase-A1015840 phase-B1015840 and phase-C1015840 respectivelyThemagneticexcitation is fed from the translatorrsquos PM array as shown inFigure 6 The terminal voltages V

119886 V119887 and V

119888 are measured

across the loadThe induced voltage equation may be represented as

119864119894+ 1198641015840

119894= 119877119894119894119894+ 119871119878

119889119894119894

119889119905+ V119894

= 119870119898cos(120587

120591119911 + 119895

2120587

3) VV (119905)

(1)

where 119894 = A B and C 119895 = 0 1 and minus1 V119894is the terminal

voltage 119894119894is the line current and 119871

119878is synchronous induc-

tance119870119898is the constant representing the machine construc-

tion VV(119905) is the translator vertical velocity or speed 120591 is thepole pitch and 119911 is the vertical displacement The terminalvoltage is

119894= 119894+ 1015840

119894minus 119895119883119878119894minus 119877119894119894 (2)

23 Construction Details The vertical cross section of thePMLG (front side) is shown in Figure 6 The PMLG basicallycontains a translator which is made by some PMs with thesteel coreThe stator contains some copper coils wounded onthe stator cores of steel situated on both sides of the translatorPhase-A phase-B andphase-C are located on the right side ofthe translator Phase-A1015840 phase-B1015840 and phase-C1015840 are locatedon the left side of the translator which are 180∘ phase shiftedfrom phase-A phase-B and phase-C respectively The con-struction supports the translator to move in the verticaldirection with respect to the statorThe orientation of the PMarray should be such that N and S can be formed one afteranother as shown in Figure 6

3 Model of the Oceanic Wave

In most of the cases constant speeds or sinusoidal speedshaving sinusoidal shapes are common approximations forsimulating PMLGs [25ndash27] The typical range of verticalvelocity of wave is 0ndash2ms with a time period from 4 to 6 s[28ndash30] Therefore a free oceanic wave neither forced nordissipated on a flat seabed is presented for analysis of the LGas shown in Figure 7 following the mentioned approxima-tions The amplitude of waveform is 119860 Hence the verticaldistance between the wave crest and the trough is 119867 whichis equal to twice the amplitude 119860 According to the point ofview of oceanographers it is considered as a linear waveThesea surface is lying on 119909119910 plane where 119910 components areconsidered zero as the wave propagates in 119909-direction 120582 iswavelength 119889

119882is water depth of the ocean with respect to 119909119910

plane or water surface seabed is at 119911 = minus119889119882 and the ocean

surface coincides with 119911 = 0

31 GeneralizedWave The general description of almost anytype of oceanic wave may be considered as depending onlyon the interpretation of 120577

120577 = 119860 cos (119896119909 minus 120596119905) (3)

120596 = radic119892119896 tanh (119896119889119882) (4)

Here the number of waves 119896 = 2120587120582 and 120596 is the frequencythat asserts the physics and describes consideration of a waterwave relating frequency and wave number Alternatively itcan be considered as a relation between the phase speed oroceanic wave velocity V and the wavelength Consideringgravitational acceleration 119892 = 98ms2 the phase speedwhich is a single basic wave that moves along the 119909-directioncan be expressed as

V = radic119892120582

2120587tanh(2120587

120582119889119882) (5)

According to (3) and (5) the wave velocity is along 119909-direction only although it has the velocity along 119911-directionSo the velocity of oceanic wave is a vector that depends on119909 119910 and 119911 and time 119905 To obtain a complete description of

4 Journal of Energy

Vphase-A

Vphase-B

Vphase-C

120∘

minus120∘ 120∘

minus120∘

Vphase-A998400

Vphase-B998400

Vphase-C998400

Figure 4 Vector diagram

++

+

Phase-A

Phase-B

Phase-C

Ea

Eb

Ec

LS2 LS2

LS2

LS2

LS2

LS2

Ra2 Ra2

Ra2

Ra2

Ra2

Ra2

E998400a

E998400b

E998400c

+

+

+

Load

va

vb

vc

Figure 5 Equivalent circuit diagram of the PMLG

oceanic wave the components along 119909 119910 and 119911 have to becalculated The motion can be expressed as

119881 (119909 119910 119911 119905)

= (119883 (119909 119910 119911 119905) 119884 (119909 119910 119911 119905) 119885 (119909 119910 119911 119905))

(6)

where119881(119909 119910 119911 119905) represents the velocity of oceanic wave and119883(119909 119910 119911 119905)119884(119909 119910 119911 119905) and119885(119909 119910 119911 119905) are the componentsalong 119909 119910 and 119911 The 119910 components may be considered aszero for the oceanic wave and the 119909 and 119911 components can beexpressed as follows

119883 = 119860120596cosh 119896 (119911 + 119889

119882)

sinh (119896119889119882)

cos (119896119909 minus 120596119905) (7)

119885 = 119860120596sinh 119896 (119911 + 119889

119882)

sinh (119896119889119882)

sin (119896119909 minus 120596119905) (8)

The119909 and 119911 components from (7) and (8) can be simplified forindividual consideration of shallow water wave intermediatedepth wave and deep sea wave

32 Shallow Water Wave In shallow water water depth ismuch lower than the wavelength 120582 that is 119889

119882≪ 120582 or

119896119889119882≪ 1 Another property of shallow water wave is that

the amplitude of wave is much smaller than wavelength so119860 ≪ 120582 or 119860119896 ≪ 1 So (7) and (8) may be written as

119883119878= 119860120596

119890119896(119911+119889119882) + 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cos (119896119909 minus 120596119905) (9)

119885119878= 119860120596

119890119896(119911+119889119882) minus 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

sin (119896119909 minus 120596119905) (10)

Now (9) and (10) may be reduced as

119883119878cong119860120596

119896119889119882

cos (119896119909 minus 120596119905) (11)

119885119878cong 119860120596(1 +

119911

119889119882

) sin (119896119909 minus 120596119905) (12)

Again if 119896119889119882≪ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = 119896radic119892119889119882because

tanh (119896119889119882) =

119890119896119889119882 minus 119890

minus119896119889119882

119890119896119889119882 + 119890

minus119896119889119882

=2119896119889119882

2= 119896119889119882 (13)

As V = 120596119896 phase speed can be expressed as V = radic119892119889119882

Journal of Energy 5

Phas

e-A

Phas

e-B

Phas

e-C

Phas

e-A998400

Phas

e-B998400

Phas

e-C998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

CoilCoil

CoilCoil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

Core

PM

Translator core

Permanent magnet

Copperwindings

Statorcore

North pole

South pole

Tran

slato

r

Figure 6 Construction of the PMLG

33 Deep Water Wave In deep water water depth is muchhigher than wavelength that is 119889

119882≫ 120582 or 119896119889

119882≫ 1 So

119890119896(119911+119889119882) + 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

119890119896(119911+119889119882) minus 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

tanh (119896119889119882) =

119890119896119889119882 minus 119890

minus119896119889119882

119890119896119889119882 + 119890

minus119896119889119882

cong119890119896119889119882

119890119896119889119882

= 1

(14)

Therefore (7) and (8) can be expressed as follows

119883119863cong 119860120596119890

119896119889119882 cos (119896119909 minus 120596119905) (15)

119885119863cong 119860120596119890

119896119889119882 sin (119896119909 minus 120596119905) (16)

6 Journal of Energy

Table 1 Comparison of the oceanic wave parameters

Wave type Shallow water Intermediate depth wave Deep water

Relative depth119889119882

120582lt 005 005 lt

119889119882

120582lt 05

119889119882

120582gt 05

Wave speed radic119892119889119882

radic119892120582

2120587tanh(2120587

119889119882

120582) radic

119892120582

2120587

Wave length radic119892119889119882119879

1198921198792

2120587tanh(2120587

119889119882

120582)

1198921198792

2120587

z

x

y

A

0

120582

120582

Wave trough

H

Wave crest

Seabed

dW

2120582

Figure 7 Waveform of a free oceanic wave

Again if 119896119889119882≫ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = radic119892119896 Phase speed V can be expressed as V = radic119892119896The119909and 119911 components both for shallow and for deep water from(6)ndash(12) (15) and (16) are explained in [31] Comparisons ofrelative depth wave speed and wavelength of shallow waterwave intermediate depth wave and deep sea wave are shownin Table 1

4 The PMLG and Wave Model

41 Selection of Translator Length The translator lengthsmaybe shorter equal or longer compared to the stator The com-mon lengths of the stator and the translator affect the powerrating of the PMLGThe power rating increases with increasein the common length Longer translator has been chosento obtain the same common length as shown in Figure 8for different translator positions The vertical displacementof translator with the incident sea wave is known as strokelength 119871 st There is a relationship between the wave ampli-tude119860

119908 and 119871 st during the energy conversion as 119871 st = 2119860119908

119860119908is smaller than the amplitude of free oceanic wave as in

(7)ndash(12) (15) and (16) because of power dissipation

42 Determination of Frequency The translator pole pitchis the summation of the PM thickness and translator polethickness of the PMLG as shown in Figure 9 The stator polepitch and translator pole pitch may be the same or differentdepending on the design strategy In the proposed design thestator pole pitch is the same as the translator pole pitch andthe stator pole width is the same as the translator pole widthThe pitch and pole width have a vital effect on the generated

voltage shape power frequency and forces The frequency119891 of the PMLG is determined by

119891 =VV (119905)2120591

(17)

43 Direction of Forces The simulation setup of the PMLGdesign is represented using a 3DCartesian coordinate systemThe applied force is working along 119911-axis as shown bybidirectional arrow in Figure 10 The width and thickness ofthis design are along 119910-axis and 119909-axis respectively Coggingforces between stator and translator core act along 119910-axisOther force components except for applied force and coggingforces work along 119909-axis The PMLG converts mechanicalenergy to electrical energy due to the force along 119911-axis andthe forces along 119909-axis and 119910-axis are generated which is thecause of mechanical power loss In the oceanic wave modelthe direction of wave elevation is also along 119911-axis accordingto (8) (10) (12) and (16)

44 Generated Voltage with Waves According to Faradayrsquoslaw of electromagnetic induction the induced voltage isfound as

119864119894(119905) = minus119873

119889Φ

119889119905 (18)

In the wave model the wave elevation is described withrespect to 119909-axis that represents the direction of wave prop-agation The induced voltage and related parameters of thePMLG are related to time The vertical wave displacementis assumed to be sinusoidal and the translator connected tobuoy tries to follow the wave elevation therefore the verticaldisplacement 119889tr and velocity 119904tr of the translator can beexpressed as given in (19) and (20) respectively [14] Hence

119889tr (119905) = 119860119908 sin(2120587

119879119905 plusmn 120579119894) (19)

119904tr (119905) = 1198601199082120587

119879cos(2120587

119879119905 plusmn 120579119894) (20)

Here 119860119908 120579119894 and 119879 represent wave amplitude initial

phase angle and period of oceanic wave respectively Thetranslator and buoy move with the wave elevation thereforethe flux variation with respect to time can be expressed as

Φ (119905) = Φ2120587

120582119889tr (119905) (21)

Journal of Energy 7

Strokelength

Com

mon

leng

th

Com

mon

leng

th

Com

mon

leng

th

Tran

slato

r

Strokelength

(a) (b) (c)

Figure 8 Translator position at different time

If 119881119898

is the peak voltage combining (18) and (21) thegenerated EMF per phase and 119881

119898of the PMLG Vlg are

obtained as [32]

Vlg (119905) = 119898 cos(2120587

119879119905) cos

2120587119860119908

120582sin(2120587

119879119905)

119881119898= 119873Φ

2120587

120582

2120587

119879119860119908

(22)

5 Simulation Results

Two types of speed settings have been used in this simu-lation one is consideration of constant translator speed forobservation of the performance of the PMLG and the otheris translator motion changed with the incident sea wave Thedefault air gap length is 2mm load is 4Ω and the translatorspeed is 1ms for the PMLG unless otherwise specified Theinput of the PMLG is mechanical thrust 119865 in newton Frommechanical power 119875

119898= 119865 times 119904tr and electrical power 119875

119890

efficiency 120578 is calculated by 120578 = 119875119890119875119898

51 Constant Translator Speed The terminal voltage and loadcurrent for default condition are shown in Figure 11

The load voltage and current are in the same phases dueto the resistive load The applied force 119865

119911 cogging force

119865119910 and force component along 119909-axis 119865

119909 are shown in

Figure 12 The induced voltage current and magnetic flux

Translator pole pitch

Thickness of the PM

Coil

CoilCoil

Coil

Stator pole pitch

Stator pole thickness

Translator pole thickness

Figure 9 Stator and translator pole pitch

linkage are shown in Figure 13The generated power is shownin Figure 14

52 Voltage Regulation The terminal voltage depends on theload for a specific PMLG as in (2) which is shown in Figure 15to observe the terminal characteristics

8 Journal of Energy

Table 2 Numerical values for legend of Figure 16

Legend name Load (Ω) RMS current (A) DC offset (A) Period (ms)1198681

4 86656 00377 7993551198682

5 71327 00269 8177821198683

8 46401 00151 8128971198684

10 37586 00118 8114311198685

15 25455 00077 80851198686

20 19233 00057 807523

z-axis

y-axis

x-axis

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Figure 10 Direction of different forces

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

0 50 100 150 200

Time (ms)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 11 Load voltage and current waveforms

Different loads ranging from 2Ω up to 1MΩ are shownon a semilog graph Load voltages measured from any oneof the three phases are similar and remain almost unchangedfrom 25Ω to 1MΩ The RMS values of currents and power ofphase-A for different load conditions are shown in Figures 16and 17 respectively The numerical values of the current andpower graphs used in the legend are tabulated in Tables 2 and3 respectively

53 Variable Translator Speed According to the oceanicwavemodel the vertical position of the wave is sinusoidal so the

3

2

1

0

minus1minus2minus3

Forc

e (kN

)

0 25 50 75 100 125 150 175 200

Time (ms)

Fx (kN)Fy (kN)Fz (kN)

Figure 12 Different forces of the PMLG

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)

Current (A)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

Figure 13 Induced voltage current and flux linkage

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

Voltage (V)

Power (W)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

800

600

400

200

0

Pow

er (W

)

Figure 14 Generated power with voltage and flux

Journal of Energy 9

Table 3 Numerical values for legend of Figure 17

Legend name Load (Ω) RMS power (W) Period (ms) Maximum power (W)1198751

4 2420785 400733 69198961198752

5 2043384 400488 58696831198753

8 1379347 400488 39820451198754

10 1130125 400366 32880751198755

15 77636 400366 22837361198756

20 590638 400244 1749611

25

30

35

40

Volta

ge (V

)

10 100 1000 10000 100000 10000001

R (ohm)

Figure 15 Terminal voltage for different loads

Time (ms)

I1 (A)I2 (A)I3 (A)

I4 (A)I5 (A)I6 (A)

806040200

minus15

minus10

minus5

0

5

10

15

Curr

ent (

A)

Figure 16 Load currents for different loads

700

600

500

400

300

200

100

0

Pow

er (W

)

Time (ms)

P1 (W)P2 (W)P3 (W)

P4 (W)P5 (W)P6 (W)

806040200

Figure 17 Generated power for different loads

Time (s)

Position (m)Velocity (ms)

1086420

minus15

minus10

minus05

00

05

10

15

Vert

ical

pos

ition

(m)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

Figure 18 Position and velocity of the translator

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

2 4 6 80 10

Time (s)

Figure 19 Generated voltage

1 2 3 40

Time (s)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

Velocity (ms)Voltage (V)

Figure 20 Relation between induced voltage and speed

vertical velocity of the wave elevation is a cosine functionThe vertical position and velocity of the translator are shownin Figure 18 The time period 119879 = 4 s and 119871

119878= 16m which

means119860119908= 08mThemagnitude of the generated voltage of

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

4 Journal of Energy

Vphase-A

Vphase-B

Vphase-C

120∘

minus120∘ 120∘

minus120∘

Vphase-A998400

Vphase-B998400

Vphase-C998400

Figure 4 Vector diagram

++

+

Phase-A

Phase-B

Phase-C

Ea

Eb

Ec

LS2 LS2

LS2

LS2

LS2

LS2

Ra2 Ra2

Ra2

Ra2

Ra2

Ra2

E998400a

E998400b

E998400c

+

+

+

Load

va

vb

vc

Figure 5 Equivalent circuit diagram of the PMLG

oceanic wave the components along 119909 119910 and 119911 have to becalculated The motion can be expressed as

119881 (119909 119910 119911 119905)

= (119883 (119909 119910 119911 119905) 119884 (119909 119910 119911 119905) 119885 (119909 119910 119911 119905))

(6)

where119881(119909 119910 119911 119905) represents the velocity of oceanic wave and119883(119909 119910 119911 119905)119884(119909 119910 119911 119905) and119885(119909 119910 119911 119905) are the componentsalong 119909 119910 and 119911 The 119910 components may be considered aszero for the oceanic wave and the 119909 and 119911 components can beexpressed as follows

119883 = 119860120596cosh 119896 (119911 + 119889

119882)

sinh (119896119889119882)

cos (119896119909 minus 120596119905) (7)

119885 = 119860120596sinh 119896 (119911 + 119889

119882)

sinh (119896119889119882)

sin (119896119909 minus 120596119905) (8)

The119909 and 119911 components from (7) and (8) can be simplified forindividual consideration of shallow water wave intermediatedepth wave and deep sea wave

32 Shallow Water Wave In shallow water water depth ismuch lower than the wavelength 120582 that is 119889

119882≪ 120582 or

119896119889119882≪ 1 Another property of shallow water wave is that

the amplitude of wave is much smaller than wavelength so119860 ≪ 120582 or 119860119896 ≪ 1 So (7) and (8) may be written as

119883119878= 119860120596

119890119896(119911+119889119882) + 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cos (119896119909 minus 120596119905) (9)

119885119878= 119860120596

119890119896(119911+119889119882) minus 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

sin (119896119909 minus 120596119905) (10)

Now (9) and (10) may be reduced as

119883119878cong119860120596

119896119889119882

cos (119896119909 minus 120596119905) (11)

119885119878cong 119860120596(1 +

119911

119889119882

) sin (119896119909 minus 120596119905) (12)

Again if 119896119889119882≪ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = 119896radic119892119889119882because

tanh (119896119889119882) =

119890119896119889119882 minus 119890

minus119896119889119882

119890119896119889119882 + 119890

minus119896119889119882

=2119896119889119882

2= 119896119889119882 (13)

As V = 120596119896 phase speed can be expressed as V = radic119892119889119882

Journal of Energy 5

Phas

e-A

Phas

e-B

Phas

e-C

Phas

e-A998400

Phas

e-B998400

Phas

e-C998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

CoilCoil

CoilCoil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

Core

PM

Translator core

Permanent magnet

Copperwindings

Statorcore

North pole

South pole

Tran

slato

r

Figure 6 Construction of the PMLG

33 Deep Water Wave In deep water water depth is muchhigher than wavelength that is 119889

119882≫ 120582 or 119896119889

119882≫ 1 So

119890119896(119911+119889119882) + 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

119890119896(119911+119889119882) minus 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

tanh (119896119889119882) =

119890119896119889119882 minus 119890

minus119896119889119882

119890119896119889119882 + 119890

minus119896119889119882

cong119890119896119889119882

119890119896119889119882

= 1

(14)

Therefore (7) and (8) can be expressed as follows

119883119863cong 119860120596119890

119896119889119882 cos (119896119909 minus 120596119905) (15)

119885119863cong 119860120596119890

119896119889119882 sin (119896119909 minus 120596119905) (16)

6 Journal of Energy

Table 1 Comparison of the oceanic wave parameters

Wave type Shallow water Intermediate depth wave Deep water

Relative depth119889119882

120582lt 005 005 lt

119889119882

120582lt 05

119889119882

120582gt 05

Wave speed radic119892119889119882

radic119892120582

2120587tanh(2120587

119889119882

120582) radic

119892120582

2120587

Wave length radic119892119889119882119879

1198921198792

2120587tanh(2120587

119889119882

120582)

1198921198792

2120587

z

x

y

A

0

120582

120582

Wave trough

H

Wave crest

Seabed

dW

2120582

Figure 7 Waveform of a free oceanic wave

Again if 119896119889119882≫ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = radic119892119896 Phase speed V can be expressed as V = radic119892119896The119909and 119911 components both for shallow and for deep water from(6)ndash(12) (15) and (16) are explained in [31] Comparisons ofrelative depth wave speed and wavelength of shallow waterwave intermediate depth wave and deep sea wave are shownin Table 1

4 The PMLG and Wave Model

41 Selection of Translator Length The translator lengthsmaybe shorter equal or longer compared to the stator The com-mon lengths of the stator and the translator affect the powerrating of the PMLGThe power rating increases with increasein the common length Longer translator has been chosento obtain the same common length as shown in Figure 8for different translator positions The vertical displacementof translator with the incident sea wave is known as strokelength 119871 st There is a relationship between the wave ampli-tude119860

119908 and 119871 st during the energy conversion as 119871 st = 2119860119908

119860119908is smaller than the amplitude of free oceanic wave as in

(7)ndash(12) (15) and (16) because of power dissipation

42 Determination of Frequency The translator pole pitchis the summation of the PM thickness and translator polethickness of the PMLG as shown in Figure 9 The stator polepitch and translator pole pitch may be the same or differentdepending on the design strategy In the proposed design thestator pole pitch is the same as the translator pole pitch andthe stator pole width is the same as the translator pole widthThe pitch and pole width have a vital effect on the generated

voltage shape power frequency and forces The frequency119891 of the PMLG is determined by

119891 =VV (119905)2120591

(17)

43 Direction of Forces The simulation setup of the PMLGdesign is represented using a 3DCartesian coordinate systemThe applied force is working along 119911-axis as shown bybidirectional arrow in Figure 10 The width and thickness ofthis design are along 119910-axis and 119909-axis respectively Coggingforces between stator and translator core act along 119910-axisOther force components except for applied force and coggingforces work along 119909-axis The PMLG converts mechanicalenergy to electrical energy due to the force along 119911-axis andthe forces along 119909-axis and 119910-axis are generated which is thecause of mechanical power loss In the oceanic wave modelthe direction of wave elevation is also along 119911-axis accordingto (8) (10) (12) and (16)

44 Generated Voltage with Waves According to Faradayrsquoslaw of electromagnetic induction the induced voltage isfound as

119864119894(119905) = minus119873

119889Φ

119889119905 (18)

In the wave model the wave elevation is described withrespect to 119909-axis that represents the direction of wave prop-agation The induced voltage and related parameters of thePMLG are related to time The vertical wave displacementis assumed to be sinusoidal and the translator connected tobuoy tries to follow the wave elevation therefore the verticaldisplacement 119889tr and velocity 119904tr of the translator can beexpressed as given in (19) and (20) respectively [14] Hence

119889tr (119905) = 119860119908 sin(2120587

119879119905 plusmn 120579119894) (19)

119904tr (119905) = 1198601199082120587

119879cos(2120587

119879119905 plusmn 120579119894) (20)

Here 119860119908 120579119894 and 119879 represent wave amplitude initial

phase angle and period of oceanic wave respectively Thetranslator and buoy move with the wave elevation thereforethe flux variation with respect to time can be expressed as

Φ (119905) = Φ2120587

120582119889tr (119905) (21)

Journal of Energy 7

Strokelength

Com

mon

leng

th

Com

mon

leng

th

Com

mon

leng

th

Tran

slato

r

Strokelength

(a) (b) (c)

Figure 8 Translator position at different time

If 119881119898

is the peak voltage combining (18) and (21) thegenerated EMF per phase and 119881

119898of the PMLG Vlg are

obtained as [32]

Vlg (119905) = 119898 cos(2120587

119879119905) cos

2120587119860119908

120582sin(2120587

119879119905)

119881119898= 119873Φ

2120587

120582

2120587

119879119860119908

(22)

5 Simulation Results

Two types of speed settings have been used in this simu-lation one is consideration of constant translator speed forobservation of the performance of the PMLG and the otheris translator motion changed with the incident sea wave Thedefault air gap length is 2mm load is 4Ω and the translatorspeed is 1ms for the PMLG unless otherwise specified Theinput of the PMLG is mechanical thrust 119865 in newton Frommechanical power 119875

119898= 119865 times 119904tr and electrical power 119875

119890

efficiency 120578 is calculated by 120578 = 119875119890119875119898

51 Constant Translator Speed The terminal voltage and loadcurrent for default condition are shown in Figure 11

The load voltage and current are in the same phases dueto the resistive load The applied force 119865

119911 cogging force

119865119910 and force component along 119909-axis 119865

119909 are shown in

Figure 12 The induced voltage current and magnetic flux

Translator pole pitch

Thickness of the PM

Coil

CoilCoil

Coil

Stator pole pitch

Stator pole thickness

Translator pole thickness

Figure 9 Stator and translator pole pitch

linkage are shown in Figure 13The generated power is shownin Figure 14

52 Voltage Regulation The terminal voltage depends on theload for a specific PMLG as in (2) which is shown in Figure 15to observe the terminal characteristics

8 Journal of Energy

Table 2 Numerical values for legend of Figure 16

Legend name Load (Ω) RMS current (A) DC offset (A) Period (ms)1198681

4 86656 00377 7993551198682

5 71327 00269 8177821198683

8 46401 00151 8128971198684

10 37586 00118 8114311198685

15 25455 00077 80851198686

20 19233 00057 807523

z-axis

y-axis

x-axis

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Figure 10 Direction of different forces

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

0 50 100 150 200

Time (ms)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 11 Load voltage and current waveforms

Different loads ranging from 2Ω up to 1MΩ are shownon a semilog graph Load voltages measured from any oneof the three phases are similar and remain almost unchangedfrom 25Ω to 1MΩ The RMS values of currents and power ofphase-A for different load conditions are shown in Figures 16and 17 respectively The numerical values of the current andpower graphs used in the legend are tabulated in Tables 2 and3 respectively

53 Variable Translator Speed According to the oceanicwavemodel the vertical position of the wave is sinusoidal so the

3

2

1

0

minus1minus2minus3

Forc

e (kN

)

0 25 50 75 100 125 150 175 200

Time (ms)

Fx (kN)Fy (kN)Fz (kN)

Figure 12 Different forces of the PMLG

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)

Current (A)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

Figure 13 Induced voltage current and flux linkage

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

Voltage (V)

Power (W)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

800

600

400

200

0

Pow

er (W

)

Figure 14 Generated power with voltage and flux

Journal of Energy 9

Table 3 Numerical values for legend of Figure 17

Legend name Load (Ω) RMS power (W) Period (ms) Maximum power (W)1198751

4 2420785 400733 69198961198752

5 2043384 400488 58696831198753

8 1379347 400488 39820451198754

10 1130125 400366 32880751198755

15 77636 400366 22837361198756

20 590638 400244 1749611

25

30

35

40

Volta

ge (V

)

10 100 1000 10000 100000 10000001

R (ohm)

Figure 15 Terminal voltage for different loads

Time (ms)

I1 (A)I2 (A)I3 (A)

I4 (A)I5 (A)I6 (A)

806040200

minus15

minus10

minus5

0

5

10

15

Curr

ent (

A)

Figure 16 Load currents for different loads

700

600

500

400

300

200

100

0

Pow

er (W

)

Time (ms)

P1 (W)P2 (W)P3 (W)

P4 (W)P5 (W)P6 (W)

806040200

Figure 17 Generated power for different loads

Time (s)

Position (m)Velocity (ms)

1086420

minus15

minus10

minus05

00

05

10

15

Vert

ical

pos

ition

(m)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

Figure 18 Position and velocity of the translator

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

2 4 6 80 10

Time (s)

Figure 19 Generated voltage

1 2 3 40

Time (s)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

Velocity (ms)Voltage (V)

Figure 20 Relation between induced voltage and speed

vertical velocity of the wave elevation is a cosine functionThe vertical position and velocity of the translator are shownin Figure 18 The time period 119879 = 4 s and 119871

119878= 16m which

means119860119908= 08mThemagnitude of the generated voltage of

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Energy 5

Phas

e-A

Phas

e-B

Phas

e-C

Phas

e-A998400

Phas

e-B998400

Phas

e-C998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

CoilCoil

CoilCoil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Coil

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

PM

Core

Core

PM

Translator core

Permanent magnet

Copperwindings

Statorcore

North pole

South pole

Tran

slato

r

Figure 6 Construction of the PMLG

33 Deep Water Wave In deep water water depth is muchhigher than wavelength that is 119889

119882≫ 120582 or 119896119889

119882≫ 1 So

119890119896(119911+119889119882) + 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

119890119896(119911+119889119882) minus 119890

minus119896(119911+119889119882)

119890119896119889119882 minus 119890

minus119896119889119882

cong119890119896(119911+119889119882)

119890119896119889119882

= 119890119896119889119882

tanh (119896119889119882) =

119890119896119889119882 minus 119890

minus119896119889119882

119890119896119889119882 + 119890

minus119896119889119882

cong119890119896119889119882

119890119896119889119882

= 1

(14)

Therefore (7) and (8) can be expressed as follows

119883119863cong 119860120596119890

119896119889119882 cos (119896119909 minus 120596119905) (15)

119885119863cong 119860120596119890

119896119889119882 sin (119896119909 minus 120596119905) (16)

6 Journal of Energy

Table 1 Comparison of the oceanic wave parameters

Wave type Shallow water Intermediate depth wave Deep water

Relative depth119889119882

120582lt 005 005 lt

119889119882

120582lt 05

119889119882

120582gt 05

Wave speed radic119892119889119882

radic119892120582

2120587tanh(2120587

119889119882

120582) radic

119892120582

2120587

Wave length radic119892119889119882119879

1198921198792

2120587tanh(2120587

119889119882

120582)

1198921198792

2120587

z

x

y

A

0

120582

120582

Wave trough

H

Wave crest

Seabed

dW

2120582

Figure 7 Waveform of a free oceanic wave

Again if 119896119889119882≫ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = radic119892119896 Phase speed V can be expressed as V = radic119892119896The119909and 119911 components both for shallow and for deep water from(6)ndash(12) (15) and (16) are explained in [31] Comparisons ofrelative depth wave speed and wavelength of shallow waterwave intermediate depth wave and deep sea wave are shownin Table 1

4 The PMLG and Wave Model

41 Selection of Translator Length The translator lengthsmaybe shorter equal or longer compared to the stator The com-mon lengths of the stator and the translator affect the powerrating of the PMLGThe power rating increases with increasein the common length Longer translator has been chosento obtain the same common length as shown in Figure 8for different translator positions The vertical displacementof translator with the incident sea wave is known as strokelength 119871 st There is a relationship between the wave ampli-tude119860

119908 and 119871 st during the energy conversion as 119871 st = 2119860119908

119860119908is smaller than the amplitude of free oceanic wave as in

(7)ndash(12) (15) and (16) because of power dissipation

42 Determination of Frequency The translator pole pitchis the summation of the PM thickness and translator polethickness of the PMLG as shown in Figure 9 The stator polepitch and translator pole pitch may be the same or differentdepending on the design strategy In the proposed design thestator pole pitch is the same as the translator pole pitch andthe stator pole width is the same as the translator pole widthThe pitch and pole width have a vital effect on the generated

voltage shape power frequency and forces The frequency119891 of the PMLG is determined by

119891 =VV (119905)2120591

(17)

43 Direction of Forces The simulation setup of the PMLGdesign is represented using a 3DCartesian coordinate systemThe applied force is working along 119911-axis as shown bybidirectional arrow in Figure 10 The width and thickness ofthis design are along 119910-axis and 119909-axis respectively Coggingforces between stator and translator core act along 119910-axisOther force components except for applied force and coggingforces work along 119909-axis The PMLG converts mechanicalenergy to electrical energy due to the force along 119911-axis andthe forces along 119909-axis and 119910-axis are generated which is thecause of mechanical power loss In the oceanic wave modelthe direction of wave elevation is also along 119911-axis accordingto (8) (10) (12) and (16)

44 Generated Voltage with Waves According to Faradayrsquoslaw of electromagnetic induction the induced voltage isfound as

119864119894(119905) = minus119873

119889Φ

119889119905 (18)

In the wave model the wave elevation is described withrespect to 119909-axis that represents the direction of wave prop-agation The induced voltage and related parameters of thePMLG are related to time The vertical wave displacementis assumed to be sinusoidal and the translator connected tobuoy tries to follow the wave elevation therefore the verticaldisplacement 119889tr and velocity 119904tr of the translator can beexpressed as given in (19) and (20) respectively [14] Hence

119889tr (119905) = 119860119908 sin(2120587

119879119905 plusmn 120579119894) (19)

119904tr (119905) = 1198601199082120587

119879cos(2120587

119879119905 plusmn 120579119894) (20)

Here 119860119908 120579119894 and 119879 represent wave amplitude initial

phase angle and period of oceanic wave respectively Thetranslator and buoy move with the wave elevation thereforethe flux variation with respect to time can be expressed as

Φ (119905) = Φ2120587

120582119889tr (119905) (21)

Journal of Energy 7

Strokelength

Com

mon

leng

th

Com

mon

leng

th

Com

mon

leng

th

Tran

slato

r

Strokelength

(a) (b) (c)

Figure 8 Translator position at different time

If 119881119898

is the peak voltage combining (18) and (21) thegenerated EMF per phase and 119881

119898of the PMLG Vlg are

obtained as [32]

Vlg (119905) = 119898 cos(2120587

119879119905) cos

2120587119860119908

120582sin(2120587

119879119905)

119881119898= 119873Φ

2120587

120582

2120587

119879119860119908

(22)

5 Simulation Results

Two types of speed settings have been used in this simu-lation one is consideration of constant translator speed forobservation of the performance of the PMLG and the otheris translator motion changed with the incident sea wave Thedefault air gap length is 2mm load is 4Ω and the translatorspeed is 1ms for the PMLG unless otherwise specified Theinput of the PMLG is mechanical thrust 119865 in newton Frommechanical power 119875

119898= 119865 times 119904tr and electrical power 119875

119890

efficiency 120578 is calculated by 120578 = 119875119890119875119898

51 Constant Translator Speed The terminal voltage and loadcurrent for default condition are shown in Figure 11

The load voltage and current are in the same phases dueto the resistive load The applied force 119865

119911 cogging force

119865119910 and force component along 119909-axis 119865

119909 are shown in

Figure 12 The induced voltage current and magnetic flux

Translator pole pitch

Thickness of the PM

Coil

CoilCoil

Coil

Stator pole pitch

Stator pole thickness

Translator pole thickness

Figure 9 Stator and translator pole pitch

linkage are shown in Figure 13The generated power is shownin Figure 14

52 Voltage Regulation The terminal voltage depends on theload for a specific PMLG as in (2) which is shown in Figure 15to observe the terminal characteristics

8 Journal of Energy

Table 2 Numerical values for legend of Figure 16

Legend name Load (Ω) RMS current (A) DC offset (A) Period (ms)1198681

4 86656 00377 7993551198682

5 71327 00269 8177821198683

8 46401 00151 8128971198684

10 37586 00118 8114311198685

15 25455 00077 80851198686

20 19233 00057 807523

z-axis

y-axis

x-axis

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Figure 10 Direction of different forces

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

0 50 100 150 200

Time (ms)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 11 Load voltage and current waveforms

Different loads ranging from 2Ω up to 1MΩ are shownon a semilog graph Load voltages measured from any oneof the three phases are similar and remain almost unchangedfrom 25Ω to 1MΩ The RMS values of currents and power ofphase-A for different load conditions are shown in Figures 16and 17 respectively The numerical values of the current andpower graphs used in the legend are tabulated in Tables 2 and3 respectively

53 Variable Translator Speed According to the oceanicwavemodel the vertical position of the wave is sinusoidal so the

3

2

1

0

minus1minus2minus3

Forc

e (kN

)

0 25 50 75 100 125 150 175 200

Time (ms)

Fx (kN)Fy (kN)Fz (kN)

Figure 12 Different forces of the PMLG

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)

Current (A)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

Figure 13 Induced voltage current and flux linkage

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

Voltage (V)

Power (W)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

800

600

400

200

0

Pow

er (W

)

Figure 14 Generated power with voltage and flux

Journal of Energy 9

Table 3 Numerical values for legend of Figure 17

Legend name Load (Ω) RMS power (W) Period (ms) Maximum power (W)1198751

4 2420785 400733 69198961198752

5 2043384 400488 58696831198753

8 1379347 400488 39820451198754

10 1130125 400366 32880751198755

15 77636 400366 22837361198756

20 590638 400244 1749611

25

30

35

40

Volta

ge (V

)

10 100 1000 10000 100000 10000001

R (ohm)

Figure 15 Terminal voltage for different loads

Time (ms)

I1 (A)I2 (A)I3 (A)

I4 (A)I5 (A)I6 (A)

806040200

minus15

minus10

minus5

0

5

10

15

Curr

ent (

A)

Figure 16 Load currents for different loads

700

600

500

400

300

200

100

0

Pow

er (W

)

Time (ms)

P1 (W)P2 (W)P3 (W)

P4 (W)P5 (W)P6 (W)

806040200

Figure 17 Generated power for different loads

Time (s)

Position (m)Velocity (ms)

1086420

minus15

minus10

minus05

00

05

10

15

Vert

ical

pos

ition

(m)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

Figure 18 Position and velocity of the translator

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

2 4 6 80 10

Time (s)

Figure 19 Generated voltage

1 2 3 40

Time (s)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

Velocity (ms)Voltage (V)

Figure 20 Relation between induced voltage and speed

vertical velocity of the wave elevation is a cosine functionThe vertical position and velocity of the translator are shownin Figure 18 The time period 119879 = 4 s and 119871

119878= 16m which

means119860119908= 08mThemagnitude of the generated voltage of

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

6 Journal of Energy

Table 1 Comparison of the oceanic wave parameters

Wave type Shallow water Intermediate depth wave Deep water

Relative depth119889119882

120582lt 005 005 lt

119889119882

120582lt 05

119889119882

120582gt 05

Wave speed radic119892119889119882

radic119892120582

2120587tanh(2120587

119889119882

120582) radic

119892120582

2120587

Wave length radic119892119889119882119879

1198921198792

2120587tanh(2120587

119889119882

120582)

1198921198792

2120587

z

x

y

A

0

120582

120582

Wave trough

H

Wave crest

Seabed

dW

2120582

Figure 7 Waveform of a free oceanic wave

Again if 119896119889119882≫ 1 120596 = radic119892119896 tanh(119896119889

119882) can be simplified as

120596 = radic119892119896 Phase speed V can be expressed as V = radic119892119896The119909and 119911 components both for shallow and for deep water from(6)ndash(12) (15) and (16) are explained in [31] Comparisons ofrelative depth wave speed and wavelength of shallow waterwave intermediate depth wave and deep sea wave are shownin Table 1

4 The PMLG and Wave Model

41 Selection of Translator Length The translator lengthsmaybe shorter equal or longer compared to the stator The com-mon lengths of the stator and the translator affect the powerrating of the PMLGThe power rating increases with increasein the common length Longer translator has been chosento obtain the same common length as shown in Figure 8for different translator positions The vertical displacementof translator with the incident sea wave is known as strokelength 119871 st There is a relationship between the wave ampli-tude119860

119908 and 119871 st during the energy conversion as 119871 st = 2119860119908

119860119908is smaller than the amplitude of free oceanic wave as in

(7)ndash(12) (15) and (16) because of power dissipation

42 Determination of Frequency The translator pole pitchis the summation of the PM thickness and translator polethickness of the PMLG as shown in Figure 9 The stator polepitch and translator pole pitch may be the same or differentdepending on the design strategy In the proposed design thestator pole pitch is the same as the translator pole pitch andthe stator pole width is the same as the translator pole widthThe pitch and pole width have a vital effect on the generated

voltage shape power frequency and forces The frequency119891 of the PMLG is determined by

119891 =VV (119905)2120591

(17)

43 Direction of Forces The simulation setup of the PMLGdesign is represented using a 3DCartesian coordinate systemThe applied force is working along 119911-axis as shown bybidirectional arrow in Figure 10 The width and thickness ofthis design are along 119910-axis and 119909-axis respectively Coggingforces between stator and translator core act along 119910-axisOther force components except for applied force and coggingforces work along 119909-axis The PMLG converts mechanicalenergy to electrical energy due to the force along 119911-axis andthe forces along 119909-axis and 119910-axis are generated which is thecause of mechanical power loss In the oceanic wave modelthe direction of wave elevation is also along 119911-axis accordingto (8) (10) (12) and (16)

44 Generated Voltage with Waves According to Faradayrsquoslaw of electromagnetic induction the induced voltage isfound as

119864119894(119905) = minus119873

119889Φ

119889119905 (18)

In the wave model the wave elevation is described withrespect to 119909-axis that represents the direction of wave prop-agation The induced voltage and related parameters of thePMLG are related to time The vertical wave displacementis assumed to be sinusoidal and the translator connected tobuoy tries to follow the wave elevation therefore the verticaldisplacement 119889tr and velocity 119904tr of the translator can beexpressed as given in (19) and (20) respectively [14] Hence

119889tr (119905) = 119860119908 sin(2120587

119879119905 plusmn 120579119894) (19)

119904tr (119905) = 1198601199082120587

119879cos(2120587

119879119905 plusmn 120579119894) (20)

Here 119860119908 120579119894 and 119879 represent wave amplitude initial

phase angle and period of oceanic wave respectively Thetranslator and buoy move with the wave elevation thereforethe flux variation with respect to time can be expressed as

Φ (119905) = Φ2120587

120582119889tr (119905) (21)

Journal of Energy 7

Strokelength

Com

mon

leng

th

Com

mon

leng

th

Com

mon

leng

th

Tran

slato

r

Strokelength

(a) (b) (c)

Figure 8 Translator position at different time

If 119881119898

is the peak voltage combining (18) and (21) thegenerated EMF per phase and 119881

119898of the PMLG Vlg are

obtained as [32]

Vlg (119905) = 119898 cos(2120587

119879119905) cos

2120587119860119908

120582sin(2120587

119879119905)

119881119898= 119873Φ

2120587

120582

2120587

119879119860119908

(22)

5 Simulation Results

Two types of speed settings have been used in this simu-lation one is consideration of constant translator speed forobservation of the performance of the PMLG and the otheris translator motion changed with the incident sea wave Thedefault air gap length is 2mm load is 4Ω and the translatorspeed is 1ms for the PMLG unless otherwise specified Theinput of the PMLG is mechanical thrust 119865 in newton Frommechanical power 119875

119898= 119865 times 119904tr and electrical power 119875

119890

efficiency 120578 is calculated by 120578 = 119875119890119875119898

51 Constant Translator Speed The terminal voltage and loadcurrent for default condition are shown in Figure 11

The load voltage and current are in the same phases dueto the resistive load The applied force 119865

119911 cogging force

119865119910 and force component along 119909-axis 119865

119909 are shown in

Figure 12 The induced voltage current and magnetic flux

Translator pole pitch

Thickness of the PM

Coil

CoilCoil

Coil

Stator pole pitch

Stator pole thickness

Translator pole thickness

Figure 9 Stator and translator pole pitch

linkage are shown in Figure 13The generated power is shownin Figure 14

52 Voltage Regulation The terminal voltage depends on theload for a specific PMLG as in (2) which is shown in Figure 15to observe the terminal characteristics

8 Journal of Energy

Table 2 Numerical values for legend of Figure 16

Legend name Load (Ω) RMS current (A) DC offset (A) Period (ms)1198681

4 86656 00377 7993551198682

5 71327 00269 8177821198683

8 46401 00151 8128971198684

10 37586 00118 8114311198685

15 25455 00077 80851198686

20 19233 00057 807523

z-axis

y-axis

x-axis

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Figure 10 Direction of different forces

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

0 50 100 150 200

Time (ms)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 11 Load voltage and current waveforms

Different loads ranging from 2Ω up to 1MΩ are shownon a semilog graph Load voltages measured from any oneof the three phases are similar and remain almost unchangedfrom 25Ω to 1MΩ The RMS values of currents and power ofphase-A for different load conditions are shown in Figures 16and 17 respectively The numerical values of the current andpower graphs used in the legend are tabulated in Tables 2 and3 respectively

53 Variable Translator Speed According to the oceanicwavemodel the vertical position of the wave is sinusoidal so the

3

2

1

0

minus1minus2minus3

Forc

e (kN

)

0 25 50 75 100 125 150 175 200

Time (ms)

Fx (kN)Fy (kN)Fz (kN)

Figure 12 Different forces of the PMLG

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)

Current (A)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

Figure 13 Induced voltage current and flux linkage

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

Voltage (V)

Power (W)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

800

600

400

200

0

Pow

er (W

)

Figure 14 Generated power with voltage and flux

Journal of Energy 9

Table 3 Numerical values for legend of Figure 17

Legend name Load (Ω) RMS power (W) Period (ms) Maximum power (W)1198751

4 2420785 400733 69198961198752

5 2043384 400488 58696831198753

8 1379347 400488 39820451198754

10 1130125 400366 32880751198755

15 77636 400366 22837361198756

20 590638 400244 1749611

25

30

35

40

Volta

ge (V

)

10 100 1000 10000 100000 10000001

R (ohm)

Figure 15 Terminal voltage for different loads

Time (ms)

I1 (A)I2 (A)I3 (A)

I4 (A)I5 (A)I6 (A)

806040200

minus15

minus10

minus5

0

5

10

15

Curr

ent (

A)

Figure 16 Load currents for different loads

700

600

500

400

300

200

100

0

Pow

er (W

)

Time (ms)

P1 (W)P2 (W)P3 (W)

P4 (W)P5 (W)P6 (W)

806040200

Figure 17 Generated power for different loads

Time (s)

Position (m)Velocity (ms)

1086420

minus15

minus10

minus05

00

05

10

15

Vert

ical

pos

ition

(m)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

Figure 18 Position and velocity of the translator

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

2 4 6 80 10

Time (s)

Figure 19 Generated voltage

1 2 3 40

Time (s)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

Velocity (ms)Voltage (V)

Figure 20 Relation between induced voltage and speed

vertical velocity of the wave elevation is a cosine functionThe vertical position and velocity of the translator are shownin Figure 18 The time period 119879 = 4 s and 119871

119878= 16m which

means119860119908= 08mThemagnitude of the generated voltage of

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Energy 7

Strokelength

Com

mon

leng

th

Com

mon

leng

th

Com

mon

leng

th

Tran

slato

r

Strokelength

(a) (b) (c)

Figure 8 Translator position at different time

If 119881119898

is the peak voltage combining (18) and (21) thegenerated EMF per phase and 119881

119898of the PMLG Vlg are

obtained as [32]

Vlg (119905) = 119898 cos(2120587

119879119905) cos

2120587119860119908

120582sin(2120587

119879119905)

119881119898= 119873Φ

2120587

120582

2120587

119879119860119908

(22)

5 Simulation Results

Two types of speed settings have been used in this simu-lation one is consideration of constant translator speed forobservation of the performance of the PMLG and the otheris translator motion changed with the incident sea wave Thedefault air gap length is 2mm load is 4Ω and the translatorspeed is 1ms for the PMLG unless otherwise specified Theinput of the PMLG is mechanical thrust 119865 in newton Frommechanical power 119875

119898= 119865 times 119904tr and electrical power 119875

119890

efficiency 120578 is calculated by 120578 = 119875119890119875119898

51 Constant Translator Speed The terminal voltage and loadcurrent for default condition are shown in Figure 11

The load voltage and current are in the same phases dueto the resistive load The applied force 119865

119911 cogging force

119865119910 and force component along 119909-axis 119865

119909 are shown in

Figure 12 The induced voltage current and magnetic flux

Translator pole pitch

Thickness of the PM

Coil

CoilCoil

Coil

Stator pole pitch

Stator pole thickness

Translator pole thickness

Figure 9 Stator and translator pole pitch

linkage are shown in Figure 13The generated power is shownin Figure 14

52 Voltage Regulation The terminal voltage depends on theload for a specific PMLG as in (2) which is shown in Figure 15to observe the terminal characteristics

8 Journal of Energy

Table 2 Numerical values for legend of Figure 16

Legend name Load (Ω) RMS current (A) DC offset (A) Period (ms)1198681

4 86656 00377 7993551198682

5 71327 00269 8177821198683

8 46401 00151 8128971198684

10 37586 00118 8114311198685

15 25455 00077 80851198686

20 19233 00057 807523

z-axis

y-axis

x-axis

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Figure 10 Direction of different forces

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

0 50 100 150 200

Time (ms)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 11 Load voltage and current waveforms

Different loads ranging from 2Ω up to 1MΩ are shownon a semilog graph Load voltages measured from any oneof the three phases are similar and remain almost unchangedfrom 25Ω to 1MΩ The RMS values of currents and power ofphase-A for different load conditions are shown in Figures 16and 17 respectively The numerical values of the current andpower graphs used in the legend are tabulated in Tables 2 and3 respectively

53 Variable Translator Speed According to the oceanicwavemodel the vertical position of the wave is sinusoidal so the

3

2

1

0

minus1minus2minus3

Forc

e (kN

)

0 25 50 75 100 125 150 175 200

Time (ms)

Fx (kN)Fy (kN)Fz (kN)

Figure 12 Different forces of the PMLG

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)

Current (A)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

Figure 13 Induced voltage current and flux linkage

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

Voltage (V)

Power (W)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

800

600

400

200

0

Pow

er (W

)

Figure 14 Generated power with voltage and flux

Journal of Energy 9

Table 3 Numerical values for legend of Figure 17

Legend name Load (Ω) RMS power (W) Period (ms) Maximum power (W)1198751

4 2420785 400733 69198961198752

5 2043384 400488 58696831198753

8 1379347 400488 39820451198754

10 1130125 400366 32880751198755

15 77636 400366 22837361198756

20 590638 400244 1749611

25

30

35

40

Volta

ge (V

)

10 100 1000 10000 100000 10000001

R (ohm)

Figure 15 Terminal voltage for different loads

Time (ms)

I1 (A)I2 (A)I3 (A)

I4 (A)I5 (A)I6 (A)

806040200

minus15

minus10

minus5

0

5

10

15

Curr

ent (

A)

Figure 16 Load currents for different loads

700

600

500

400

300

200

100

0

Pow

er (W

)

Time (ms)

P1 (W)P2 (W)P3 (W)

P4 (W)P5 (W)P6 (W)

806040200

Figure 17 Generated power for different loads

Time (s)

Position (m)Velocity (ms)

1086420

minus15

minus10

minus05

00

05

10

15

Vert

ical

pos

ition

(m)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

Figure 18 Position and velocity of the translator

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

2 4 6 80 10

Time (s)

Figure 19 Generated voltage

1 2 3 40

Time (s)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

Velocity (ms)Voltage (V)

Figure 20 Relation between induced voltage and speed

vertical velocity of the wave elevation is a cosine functionThe vertical position and velocity of the translator are shownin Figure 18 The time period 119879 = 4 s and 119871

119878= 16m which

means119860119908= 08mThemagnitude of the generated voltage of

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

8 Journal of Energy

Table 2 Numerical values for legend of Figure 16

Legend name Load (Ω) RMS current (A) DC offset (A) Period (ms)1198681

4 86656 00377 7993551198682

5 71327 00269 8177821198683

8 46401 00151 8128971198684

10 37586 00118 8114311198685

15 25455 00077 80851198686

20 19233 00057 807523

z-axis

y-axis

x-axis

Phas

e-A

Phas

e-A998400

Coil

CoilCoil

Coil

Coil

CoilCoil

Coil

Figure 10 Direction of different forces

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

0 50 100 150 200

Time (ms)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 11 Load voltage and current waveforms

Different loads ranging from 2Ω up to 1MΩ are shownon a semilog graph Load voltages measured from any oneof the three phases are similar and remain almost unchangedfrom 25Ω to 1MΩ The RMS values of currents and power ofphase-A for different load conditions are shown in Figures 16and 17 respectively The numerical values of the current andpower graphs used in the legend are tabulated in Tables 2 and3 respectively

53 Variable Translator Speed According to the oceanicwavemodel the vertical position of the wave is sinusoidal so the

3

2

1

0

minus1minus2minus3

Forc

e (kN

)

0 25 50 75 100 125 150 175 200

Time (ms)

Fx (kN)Fy (kN)Fz (kN)

Figure 12 Different forces of the PMLG

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

30

20

10

0

minus10

minus20

minus30

Curr

ent (

A)

Voltage (V)

Current (A)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

Figure 13 Induced voltage current and flux linkage

0 50 100 150 200

Time (ms)

75

50

25

0

minus25

minus50

minus75

Volta

ge (V

)

Voltage (V)

Power (W)

10

05

00

minus05

minus10

Flux

link

age (

Wb)

Flux (Wb)

800

600

400

200

0

Pow

er (W

)

Figure 14 Generated power with voltage and flux

Journal of Energy 9

Table 3 Numerical values for legend of Figure 17

Legend name Load (Ω) RMS power (W) Period (ms) Maximum power (W)1198751

4 2420785 400733 69198961198752

5 2043384 400488 58696831198753

8 1379347 400488 39820451198754

10 1130125 400366 32880751198755

15 77636 400366 22837361198756

20 590638 400244 1749611

25

30

35

40

Volta

ge (V

)

10 100 1000 10000 100000 10000001

R (ohm)

Figure 15 Terminal voltage for different loads

Time (ms)

I1 (A)I2 (A)I3 (A)

I4 (A)I5 (A)I6 (A)

806040200

minus15

minus10

minus5

0

5

10

15

Curr

ent (

A)

Figure 16 Load currents for different loads

700

600

500

400

300

200

100

0

Pow

er (W

)

Time (ms)

P1 (W)P2 (W)P3 (W)

P4 (W)P5 (W)P6 (W)

806040200

Figure 17 Generated power for different loads

Time (s)

Position (m)Velocity (ms)

1086420

minus15

minus10

minus05

00

05

10

15

Vert

ical

pos

ition

(m)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

Figure 18 Position and velocity of the translator

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

2 4 6 80 10

Time (s)

Figure 19 Generated voltage

1 2 3 40

Time (s)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

Velocity (ms)Voltage (V)

Figure 20 Relation between induced voltage and speed

vertical velocity of the wave elevation is a cosine functionThe vertical position and velocity of the translator are shownin Figure 18 The time period 119879 = 4 s and 119871

119878= 16m which

means119860119908= 08mThemagnitude of the generated voltage of

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Energy 9

Table 3 Numerical values for legend of Figure 17

Legend name Load (Ω) RMS power (W) Period (ms) Maximum power (W)1198751

4 2420785 400733 69198961198752

5 2043384 400488 58696831198753

8 1379347 400488 39820451198754

10 1130125 400366 32880751198755

15 77636 400366 22837361198756

20 590638 400244 1749611

25

30

35

40

Volta

ge (V

)

10 100 1000 10000 100000 10000001

R (ohm)

Figure 15 Terminal voltage for different loads

Time (ms)

I1 (A)I2 (A)I3 (A)

I4 (A)I5 (A)I6 (A)

806040200

minus15

minus10

minus5

0

5

10

15

Curr

ent (

A)

Figure 16 Load currents for different loads

700

600

500

400

300

200

100

0

Pow

er (W

)

Time (ms)

P1 (W)P2 (W)P3 (W)

P4 (W)P5 (W)P6 (W)

806040200

Figure 17 Generated power for different loads

Time (s)

Position (m)Velocity (ms)

1086420

minus15

minus10

minus05

00

05

10

15

Vert

ical

pos

ition

(m)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

Figure 18 Position and velocity of the translator

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

2 4 6 80 10

Time (s)

Figure 19 Generated voltage

1 2 3 40

Time (s)

minus15

minus10

minus05

00

05

10

15

Velo

city

(ms

)

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

Velocity (ms)Voltage (V)

Figure 20 Relation between induced voltage and speed

vertical velocity of the wave elevation is a cosine functionThe vertical position and velocity of the translator are shownin Figure 18 The time period 119879 = 4 s and 119871

119878= 16m which

means119860119908= 08mThemagnitude of the generated voltage of

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

10 Journal of Energy

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 21 The induced voltage and current

Voltage (V)Flux (Wb)

minus100

minus50

0

50

100

Volta

ge (V

)

minus10

minus05

00

05

10

Flux

link

age (

Wb)

05 10 1500 20

Time (s)

Figure 22 Magnetic flux linkage and terminal voltage

minus75

minus50

minus25

0

25

50

75

Volta

ge (V

)

00 10 1505 20

Time (s)

minus30

minus20

minus10

0

10

20

30

Curr

ent (

A)

Voltage (V)Current (A)

Figure 23 Terminal voltage and current

the PMLG depends on velocity according to (20) and isshown in Figure 19

As 119879 = 4 s the voltage waveform is repeated in each halfcycle or 1198792 = 2 s as shown in Figure 19 The voltage wave-form due to the translator velocity for the time period of onecycle is shown in Figure 20 The induced voltage and currentfor a half-cycle time interval are shown in Figure 21 Theterminal voltage lags by 90∘ from themagnetic flux linkage asshown in Figure 22

The voltage magnitude is directly proportional to thetranslator velocity According to (17) and (20) the frequencyof voltage increases with the increase in velocityThe terminalvoltage and current in a winding are shown in Figure 23 Thecogging force is the reason of force ripples and is liable for

Fy (kN)Fz (kN)

minus4

minus2

0

2

4

6

Forc

e (kN

)

05 10 15 2000

Time (s)

Figure 24 Different forces of the PMLG

05 10 15 2000

Time (s)

minus10

minus5

0

5

10

Forc

e (kN

)

Fz (kN)Power (W)

0

500

1000

1500

Pow

er (W

)

Figure 25 Applied force and power

Figure 26 Magnetic flux density at 119905 = 20ms

abnormal operation of the PMLG so it is maintained at alower value as shown in Figure 24 with the applied force Themagnitude of power is related to the frequency The powergeneration due to the applied force is shown in Figure 25

Different dimensions of the PMLG active materials of thestator and translator as shown in Figure 6 are given in Table 4The significant parameters that mainly affect the PMLGperformance are given in Table 5

54 Selection of the PM Size According to Figure 18 thevertical displacement of the translator is 16m owing to theminimum and maximum vertical displacement of minus08mand 08m respectively On the other hand the translator

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Energy 11

Figure 27 Magnetic flux density at 119905 = 30ms

Figure 28 Magnetic flux density at 119905 = 40ms

B(te

sla)

000013027040053067080093107120133147160173187200

(a)

B(te

sla)

0

H (kAm)10080604020

00

05

10

15

20

25

(b)

Figure 29 (a) Scale of 119861 and (b) magnetizing curve

Table 4 Dimensions of the PMLG

Name of the item Value UnitWidth of the translator 8 cmWidth of the stator 56 cmWidth of the PMLG 196 cmThickness of pole shoe 16 cmDepth of the PMLG 10 cmThickness of PM 24 cmCross section of the conductor 25 mm2

Stroke length 16 m

length is the summation of stator length and stroke lengthCombining the stroke length of 16m and the stator length

of 14m the translator length becomes 3m From Table 5the translator and stator pole pitch is 4 cm which is the sum-mation of the PM and the pole thickness Therefore 75 PMsand poles are required to make 3m length of translator Thedimension of the translator PMs is selected as 8 times 10 times 24 cm

6 Analysis of Magnetic Flux

The magnetic flux density 119861 flux lines and magnetic fieldintensity of the PMLG are analyzed to observe 119861 in the differ-ent portions The value of 119861 for different time 119905 is shown inFigures 26ndash28119861 varies for different positions of the translatorwhich can be realized from the scale given in Figure 29(a)The magnetizing curve of the steel used in the stator andtranslator core is shown in Figure 29(b)

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

12 Journal of Energy

Figure 30 Magnetic flux at 119905 = 20ms

Figure 31 Magnetic flux at 119905 = 30ms

The translator position varies with time and the flux linestravel through the low reluctance path The magnetic fluxlines for different times are shown in Figures 30ndash32

There is a relation between magnetic flux lines and 119861Figures 33(a)ndash33(c) represent the scale of flux lines for 119905 =20ms 30ms and 40ms respectively The magnetic proper-ties inside the PMLG are needed for analyses proper designand performance check

The values for the magnetic field intensity at differenttimes are shown in Figures 34ndash36 and the scale is shown inFigure 37 The magnetomotive force mainly exists in the airgapWhen the stator and translator cores come close togetherthe magnetomotive force reaches a high value Neodymiumiron boron (NdFeB) permanent magnets have been used formagnetic excitation

7 Conclusions

The simulation results with synchronized translator verticalvelocity with wave velocity reflect the model presented inthis paper Different voltages currents power and magnetic

Table 5 The parameters of the PMLG

Name of the item Value UnitPole pitch of translator and stator 4 cmPitch factor of pole shoe 04Turn number of copper coil 70 TurnsNumber of coils in a winding 2Winding factor 06Velocityspeed of the translator 0ndash15 msAir gap length 2 mmInternal resistance of windings 03 Ω

Load resistance 2ndash25 Ω

Maximum power (depends on some factors) 175ndash692 W

Figure 32 Magnetic flux at 119905 = 40ms

A(W

bm

)

minus00209

minus00187

minus00165

minus00143

minus00121

minus00099

minus00077

minus00055

minus00033

minus00011

00011

00033

00055

00077

00099

00122

00144

(a)

A(W

bm

)

minus00239

minus00213

minus00187

minus00161

minus00135

minus00109

minus00083

minus00058

minus00032

minus00006

00020

00046

00072

00098

00123

00149

00175

(b)

A(W

bm

)

minus00270

minus00238

minus00205

minus00172

minus00140

minus00107

minus00075

minus00042

minus00010

00023

00055

00088

00121

00153

00186

00218

00251

(c)

Figure 33 Scale of magnetic flux

flux linkages of phase-A are shown for the three-phase PMLGbecause the other two phases are just 120∘ phase shifted fromeach other and are not necessary to explain the dynamics ofenergy conversion fromwave energy to electrical energyThecogging force and force ripples are low compared to appliedforce that helps to prevent mechanical vibration and also

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of Energy 13

Figure 34 Magnetic field intensity at 119905 = 20ms

Figure 35 Magnetic field intensity at 119905 = 30ms

Figure 36 Magnetic field intensity at 119905 = 40ms

H (kAm)21500

20000

18500

17000

17000

15500

14000

12500

11000

11000

9500

8000

6500

5000

5000

3500

2000

500

minus1000

Figure 37 Scale of119867

minimize mechanical power loss Low core loss is achieved(127) which would produce less heat to prevent overheat-ing of the PMLG and increase service life The maximumefficiency is calculated as 83 for full-load condition Theloading effect is low and voltage regulation of the PMLG is1393measured from terminal characteristicsThick copper

conductor with smaller turn number is used in the coil tominimize internal resistance

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] H Polinder M E C Damen and F Gardner ldquoLinear PMgenerator system for wave energy conversion in the AWSrdquo IEEETransactions on Energy Conversion vol 19 no 3 pp 583ndash5892004

[2] P Tokat T Thiringer and P Chen ldquoDevelopment of ananalytically described pitch regulator for a wind turbine to beused for grid disturbance studiesrdquo Journal of Energy vol 2013Article ID 203174 9 pages 2013

[3] KMohammadi AMostafaeipour YDinpashoh andN PouyaldquoElectricity generation and energy cost estimation of large-scalewind turbines in Jarandagh Iranrdquo Journal of Energy vol 2014Article ID 613681 8 pages 2014

[4] M R Islam Y Guo J G Zhu H Y Lu and J X Jin ldquoHigh-frequency magnetic-link medium-voltage converter for super-conducting generator-based high-power density wind genera-tion systemsrdquo IEEE Transactions on Applied Superconductivityvol 24 no 5 Article ID 5202605 2014

[5] B Jain S Singh S Jain and R K Nema ldquoFlexible modecontrol of grid connected wind energy conversion system usingwaveletrdquo Journal of Energy vol 2015 Article ID 152898 12 pages2015

[6] A O Adelaja and B I Babatope ldquoAnalysis and testing of anatural convection solar dryer for the tropicsrdquo Journal of Energyvol 2013 Article ID 479894 8 pages 2013

[7] M R Islam Y G Guo and J G Zhu ldquoA multilevel medium-voltage inverter for step-up-transformer-less grid connection ofphotovoltaic power plantsrdquo IEEE Journal of Photovoltaics vol 4no 3 pp 881ndash889 2014

[8] J Basheer Sheeba and A Krishnan Rohini ldquoStructural andthermal analysis of asphalt solar collector using finite elementmethodrdquo Journal of Energy vol 2014 Article ID 602087 9 pages2014

[9] O SOmogoye A BOgundare and IOAkanji ldquoDevelopmentof a cost-effective solardiesel independent power plant for aremote stationrdquo Journal of Energy vol 2015 Article ID 82874510 pages 2015

[10] D Borkowski and T Wegiel ldquoSmall hydropower plant withintegrated turbine-generators working at variable speedrdquo IEEETransactions on Energy Conversion vol 28 no 2 pp 452ndash4592013

[11] M Sarvi I Soltani N NamazyPour and N Rabbani ldquoA newsliding mode controller for DCDC converters in photovoltaicsystemsrdquo Journal of Energy vol 2013 Article ID 871025 7 pages2013

[12] M R Islam Y G Guo and J G Zhu ldquoA high-frequency linkmultilevel cascaded medium-voltage converter for direct gridintegration of renewable energy systemsrdquo IEEE Transactions onPower Electronics vol 29 no 8 pp 4167ndash4182 2014

[13] R Watanabe J-S Shin T Koseki and H-J Kim ldquoOptimaldesign for high output power of transverse-flux-type cylindricallinear synchronous generatorrdquo IEEE Transactions onMagneticsvol 50 no 11 Article ID 8202704 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

14 Journal of Energy

[14] C Liu H Yu M Hu Q Liu S Zhou and L Huang ldquoResearchon a permanentmagnet tubular linear generator for direct drivewave energy conversionrdquo IET Renewable Power Generation vol8 no 3 pp 281ndash288 2014

[15] F Wu X-P Zhang P Ju and M J H Sterling ldquoModelingand control of AWS-based wave energy conversion system inte-grated into power gridrdquo IEEE Transactions on Power Systemsvol 23 no 3 pp 1196ndash1204 2008

[16] T Setoguchi S Raghunathan M Takao and K Kaneko ldquoAir-turbine with self-pitch-controlled blades for wave energy con-version (estimation of performances in periodically oscillatingflow)rdquo International Journal of Rotating Machinery vol 3 no 4pp 233ndash238 1997

[17] M Takao Y Kinoue T Setoguchi T Obayashi and K KanekoldquoImpulse turbine with self-pitch-controlled guide vanes forwave power conversion (effect of guide vane geometry on theperformance)rdquo International Journal of RotatingMachinery vol6 no 5 pp 355ndash362 2000

[18] M Takao and T Setoguchi ldquoAir turbines for wave energyconversionrdquo International Journal of Rotating Machinery vol2012 Article ID 717398 10 pages 2012

[19] A Thakker J Jarvis and A Sahed ldquoQuasi-steady analyticalmodel benchmark of an impulse turbine for wave energyextractionrdquo International Journal of Rotating Machinery vol2008 Article ID 536079 12 pages 2008

[20] BDrewA R Plummer andMN Sahinkaya ldquoA reviewofwaveenergy converter technologyrdquo Proceedings of the Institution ofMechanical Engineers Part A Journal of Power and Energy vol223 no 8 pp 887ndash902 2009

[21] L Huang J Liu H Yu R Qu H Chen and H Fang ldquoWindingconfiguration and performance investigations of a tubularsuperconducting flux-switching linear generatorrdquo IEEE Trans-actions on Applied Superconductivity vol 25 no 3 2015

[22] A J Garrido E Otaola I Garrido et al ldquoMathematical mod-eling of oscillating water columns wave-structure interactionin ocean energy plantsrdquoMathematical Problems in Engineeringvol 2015 Article ID 727982 11 pages 2015

[23] Z Liu Y Cui H ZhaoH Shi and B-SHyun ldquoEffects of damp-ing plate and taut line system onmooring stability of small waveenergy converterrdquo Mathematical Problems in Engineering vol2015 Article ID 814095 10 pages 2015

[24] M-J Jin C-F Wang J-X Shen and B Xia ldquoA modularpermanent-magnet flux-switching linear machine with fault-tolerant capabilityrdquo IEEE Transactions onMagnetics vol 45 no8 pp 3179ndash3186 2009

[25] L Huang H Yu M Hu J Zhao and Z Cheng ldquoA novel flux-switching permanent-magnet linear generator for wave energyextraction applicationrdquo IEEE Transactions onMagnetics vol 47no 5 pp 1034ndash1037 2011

[26] L Huang H Yu M Hu C Liu and B Yuan ldquoResearch on atubular primary permanent-magnet linear generator for waveenergy conversionsrdquo IEEE Transactions on Magnetics vol 49no 5 pp 1917ndash1920 2013

[27] V D Colli P Cancelliere F Marignetti R Di Stefano and MScarano ldquoA tubular-generator drive for wave energy conver-sionrdquo IEEE Transactions on Industrial Electronics vol 53 no 4pp 1152ndash1159 2006

[28] J F Pan Y Zou N Cheung and G-Z Cao ldquoOn the voltageripple reduction control of the linear switched reluctancegenerator for wave energy utilizationrdquo IEEE Transactions onPower Electronics vol 29 no 10 pp 5298ndash5307 2014

[29] E S Vidal R H Hansen and M Kramer ldquoEarly performanceassessment of the electrical output of avestarrsquos prototyperdquo inProceedings of the 4th International Conference on Ocean Energy(ICOE rsquo12) Dublin Ireland October 2012

[30] K Lu and W Wu ldquoElectromagnetic lead screw for potentialwave energy applicationrdquo IEEE Transactions on Magnetics vol50 no 11 Article ID 8205004 2014

[31] R Salmon Introduction to Ocean Waves Scripps Institution ofOceanography University of California San Diego Calif USA2008

[32] P R M Brooking and M A Mueller ldquoPower conditioningof the output from a linear vernier hybrid permanent magnetgenerator for use in direct drive wave energy convertersrdquo IEEProceedingsmdashGeneration Transmission and Distribution vol152 no 5 pp 673ndash681 2005

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014