Experimental Testing and Model Validation for Ocean Wave Energy Harvesting Buoys

Transcription

1 Expermental Tetng and Model Valdaton for Ocean Wave Energy Harvetng Buoy Dougla A. Gemme 1, Steven P. Baten 1, Raymond B. Sepe, Jr. 1, John Montgomery 2, Stephan T. Grll 2, Annette Grll 2 1 Electro Standard Laboratore 36 Wetern Indutral Drve Cranton, RI 02921, USA 2 Unverty of Rhode Iland Department of Ocean Engneerng arraganett, RI 02882, USA Abtract Methodology and reult are preented for numercal mulaton and feld experment ung pont aborpton ocean wave energy harvetng buoy ytem, ung the heave moton of the buoy to produce ueful electrcal power. Two approache, a drect-drve ytem and a reonantdrve ytem are analyzed. Thee ytem are not degned for large cale grd power applcaton, but rather for relatvely low-power ocean enor and communcaton applcaton, wth power requrement n the 1-10 W range. The feld experment provded ueful data for model verfcaton and valdaton purpoe. Reult howed that RMS value for armature dplacement and armature velocty and mean harveted electrcal power were generally wthn 10% between model mulaton and expermental data. Index Term energy converon, wave energy harvetng, lnear generator, ocean energy, heavng buoy I. OMECLATURE A rgd-drve-ytem an energy harvetng ytem whch force the lnear generator armature to perfectly track (or mrror) the ocean wave urface elevaton wthout amplfcaton or attenuaton of ampltude. A drect-drve-ytem an energy harvetng ytem whch attempt to force the lnear generator armature to track (or mrror) the ocean wave urface elevaton, but unable to do o perfectly, reultng n attenuaton of the ampltude. A reonant-drve-ytem an energy harvetng ytem whch allow the lnear generator armature and/or the buoy to reonate wth, and amplfy, the ocean wave urface elevaton. II. ITRODUCTIO Ocean wave energy harvetng ytem, degned for enor buoy, convert wave moton nto electrcty, to allow operaton under all weather condton, whle enablng enhanced functonalty, hgher performance and contnuou operaton. Such ytem generate and accumulate energy that can be ued to ndefntely power remote buoy, equpped wth enor array, a well a electronc for proceng and communcaton. Thee power ource can be ntegrated wth buoy ytem to mnmze the ze of battere, or elmnate the need for battere f upercapactor are ued. Recently, a gnfcant amount of work ha been performed on the degn, numercal modelng and feld tetng of buoy ytem to be ued a pont aborber to harvet energy from ocean wave [1-5]. A majorty of thee wave energy converter (WEC) target large amount of power for grd applcaton. Th paper, however, wll focu on relatvely low-power, dtrbuted, pont aborpton WEC' and an extenon of prelmnary degn and numercal modelng work on drect-drve and reonant-drve ytem amed at harvetng power n the 1-10 W range n mall ea tate for enor and communcaton applcaton [6]. An mportant contrbuton of th work wa the development of accurate wave-to-wre mulaton model that enable optmzaton of the varou energy harvetng ytem, whle ncludng mportant ub-ytem nteracton. The theoretcal ytem equaton are tructured a a nonlnear tate-pace model wth a fnte number of tate, whch lend telf to effcent numercal technque, and well uted to mulaton ung the well-etablhed Smulnk tool, whch allow relable and fat mplementaton of coupled and complcated nonlnear tate-pace ytem equaton. Laboratory and feld tetng of 1:10 and 1:4 cale model prototype of the two ytem have been performed wth reaonable reult [7]. The followng ecton wll provde an overvew of the two type of ytem developed, the numercal model developed to mulate thee ytem and reult from feld experment of the ytem a well a attempt to valdate the model wth the expermental reult. III. SYSTEM OVERVIEW Two type of ocean wave energy harvetng ytem have been developed; a drect-drve and a reonant-drve ytem. The drect-drve ytem cont of a lnear electrc generator (LEG), whch mounted vertcally and drectly drven by the wave nduced heave moton of a urface float. It attempt to force the lnear generator armature to move exactly wth the ea urface elevaton, but unlke a rgd-

2 drve ytem, t unable to track the moton perfectly, whch reult n dfference between the buoy repone and the ea urface elevaton. The reonant-drve ytem ue a mlar LEG, although t drven by the moton of an nertal ma and reonant tunng of the ytem, whch hould amplfy the ea urface elevaton. In both ytem, the LEG cont of a permanent magnet lder (armature), whch upended by a prng ytem and allowed to ocllate wthn a two-phae col tator. Electrcty produced by the coupled ocllaton through the wave nduced buoy moton. The challenge n degnng mot ocean energy harvetng ytem tem from the hghly coupled nteracton of the ea tate and the many component/ubytem, whch are all ndvdually dffcult to analyze, even when olated. Fg. 1 provde a block dagram howng the nteracton. The randomne and complexty of ocean wave one ue, and a ueful ytem hould operate over a wde range of condton. Whle tool ext to decrbe ocean wave under lnearzed theory, and tandard em-emprcal wave energy pectra are avalable a model, there large couplng between the hydrodynamc and the buoy ytem, nce gnfcant energy ether extracted, dpated or radated by the buoy ytem. There are tandard method and model olvng wave-buoy nteracton (ncludng ncdent, dffracted and radated feld) when aumng mall dplacement and no vcou dpaton. The latter, whch are mportant for mall ytem, ntroduce moton dependent nonlnear effect. Further, the LEG mechancally nteract wth the buoy, and the force reultng trong nce t drectly related to energy generaton. Alo, the predcton of electrcal performance of the LEG, whch nteract wth the mechancal dynamc of the LEG armature, requre electromagnetc calculaton, and the LEG drve an energycapturng load, whch a controlled chargng ytem n whch the optmum parameter for the control algorthm depend on the ea-tate. In order to deal wth th complexty, t neceary to analyze the concept of a rgddrve ytem, whch dffcult to acheve n practce. However, the performance reult of the rgd-drve ytem prove ueful n th dcuon to provde of benchmark to determne the utablty of any real-world drect-drve or reonant-drve degn. The analy of thee ytem, ncludng relevant equaton, wll be dcued n the followng ecton on the numercal model whch wa developed for th work. Random Ocean Wave Buoy Mechancal Sytem ocean tate etmated va tattc of armature moton Central Proceng Unt for Chargng Control and Sytem Montorng Voltage to Sytem Swtchng Regulator Lnear Generator Mechancal Lnear Generator Electrcal Chargng Controller Energy Storage Fgure 1. Block dagram of ytem nteracton Fgure 2. DC2 wave energy buoy; conceptual drawng (left) and 1:4 cale prototype (rght) The drect-drve ytem that wa developed referred to a the DC2 (Fg. 2). It cont of a phercal float whch rgdly attached to a watertght cylndrcal canter, nde whch the LEG rgdly mounted. The permanent magnet armature of the LEG then connected to a rod that ext through the bottom of the canter and attached to a large retance plate through a unveral jont. The moton of the armature contraned by a retorng prng attached at the top of the canter and by a bottom force produced from the retance plate. Electrcty produced through the ocllatng moton of the armature, wth nuodaldtrbuted magnetc feld, through a poly-phae col tator. The connecton between the armature and the retance plate mple the ue of a low-frcton eal, whch allow the rgd connectng rod to move freely through the bottom of the canter wthout water leak. The DC3 (Fg. 3) the reonant-drve ytem and a multple-par buoy (or tarpar). The LEG houed n the permanently ealed central par, whch urrounded by four atellte par located at equal dtance from the central par every 90. The atellte par provde tablty agant roll a well a reducton of overall draft of the buoy. The magnetc armature attached to an nertal ma upended by a ytem of prng, whch ha a natural reonant perod defned by the prng contant of the ytem. In addton, the buoy ha t own natural reonant perod baed on t croectonal area and draft. The coupled reonance of the entre ytem hould be tuned to the expected ea-tate peak pectral perod to obtan the optmum heave moton of the buoy and therefore, maxmze armature moton. A major beneft to th ytem that there are no external movng part or eal that could potentally leak, however, th beng a reonant baed ytem mple a narrow band repone whch decreae performance when the ea-tate peak pectral perod not matched to that of the ytem. Th

3 requre that the ytem tuned to match the peak pectral perod that wll be een mot often at a pecfc deployment te. Th could be overcome to ome degree through the ue of actve tunng of the ytem, through varou electrcal or mechancal control, but not part of the cope of th work. Fgure 3. DC3 wave energy buoy; conceptual drawng (left) and 1:4 cale prototype (rght) IV. UMERICAL MODEL Reference [6] provde a full ummary of model development and prelmnary dry tetng of the LEG for ntal model valdaton, of whch the man pont wll be repreented here. In order to ether mulate or expermentally meaure the expected performance of a LEG rgdly drven by the ocean wave urface elevaton, a realtc model of the ocean wave and ther knematc frt etablhed wth the ue of tandard lnear wave theory wth harmonc uperpoton [5]. Equaton (1) decrbe the ocean urface elevaton η at the ytem locaton a the um of w nuodal wave component, each wth ampltude A, crcular frequency ω, phae ψ and wavenumber k. Each wavenumber atfe the well-known lnear dperon relaton gven n (2), where h the ocean depth and g the local gravtatonal acceleraton. ote, that w = 50 aumed n the followng. = w ( t) A co( k y ω t ψ ) η (1) = 1 ( k h) 2 ω = g k tanh (2) For th work, the nuodal component ampltude are provded by a modfed JOSWAP pectrum for developng ea. The JOSWAP pectral hape a two parameter model n whch both A and T p are pecfed, and thee parameter are not completely arbtrary, nce they mut take on value that are content wth a realtc wnd peed. Equaton (3) how the relaton for wnd peed n the cae of JOSWAP pectra. Undertandng of thee relaton clearly mportant for ocean energy harvetng ytem degn, nce the value of the ea-tate parameter A and T p are not arbtrary n the ocean envronment. u 10 = ( 53 A ) T 7 p 4 (3) For a rgd-drve ytem, tandard lnear wave theory and the ue of the modfed JOSWAP pectra allow for greatly mplfed modelng and tetng of the LEG performance, nce the armature moton movng n concert wth the urface elevaton. Th leave the electrcal performance a the more crtcal apect for modelng rgdly drven ytem. Electromagnetc feld analy provde a et of equaton that capture the mportant voltage and current repone of the LEG output. The model a drect phycal model (.e. not an equvalent crcut model) wth no equvalent parameter and no requrement for fnte element analy. Eentally, very accurate predcton are obtaned for known geometrcal, phycal and materal properte of the devce. The only free parameter n the LEG model a peed dependent power effcency curve related to heatng lo, whch expermentally calbrated. The effcency ha expermentally been found to be hgh for LEG, n th applcaton, due to the low armature peed aocated wth the drect drvng by ocean wave. Ignorng copper loe, whch can be ealy handled n the model, other loe whch affect the LEG effcency (e.g. hytere, eddy current, etc) generally are no more than 10%. Hence, a key fndng n th work that LEG analy mplfed for the low power and the low peed range content wth th applcaton. The electrcal/mechancal nteracton of the LEG, wth the external drvng force from wave acton, are clearly mportant to determne output power generaton. Fve LEG force are condered: gravty, drve force, electromagnetc thrut, armature frcton and prng force. Th lead to addtonal tate equaton that are combned wth the wave equaton, buoy hydrodynamc equaton and load model equaton to form a complete ytem of equaton. The LEG ytem create two addtonal mechancal nonlnear tate pace equaton. Thu, two more tate and tate equaton are created and thee are documented n the lterature [5], [9], [10]. Electrcal equaton are alo neceary, but do not necearly requre addtonal tate varable n th formalm nce generator nductance uually neglgble wth low peed. The LEG model conder a cylndrcal armature, much longer than the tator, made from permanent magnet. The magnet are fxed at equal pacng to generate an approxmate nuodal dtrbuton, n the longtudnal z- drecton, for the radal component of magnetc flux denty B r. The radal component of magnetc flux denty B r approxmated by a truncated Fourer ere expanon wth b term a hown n (4). Here, C pp the number of magnet par per unt length and the ere coeffcent b k are dependent on radal dtance. The reference frame move wth the armature, at velocty υ a relatve to the tator, n the longtudnal z-drecton.

4 B = B ( C z) r( z) bk 2π ( 2 k 1) k = 1 co (4) The hort length tator ha col that cover an nteger number of magnet par c. The effectve average dameter of the col D col. The number of col turn for each lot, on a partcular phae col, ndcated a mn wth n=1 or 2 for each of the 2 phae and m beng a lot ndex. The longtudnal coordnate z m, for each lot n the movng reference frame, gven by (5), where x a the armature dplacement and z an arbtrary dplacement offet that allow ntal potonng of the tator at any pont along the length of the armature. z m ( t) = z x ( t) a pp pp m 1 (5) 4 C The longtudnal force F z from both phae and all lot gven by (6), where the 2 phae current n, for n=1, 2 are orthogonal to the radal magnetc flux denty B r. Ung the perodcty and ymmetry allow mplfcaton to the formula, a hown. z 2 2 ( t) = 2 π Dcol c Br ( z = zm( t) ) mn n( t) F (7) n= 1 m= 1 Gven that the preent applcaton brute-force power harneng by converon to DC through a rectfer, the harmonc dtorton of the generated AC output waveform le mportant and there eem lttle beneft to have perfect nuodal dtrbuton of the permanent magnet feld or for the col wndng denty. A a reult, the LEG degn and the analy can be mplfed by ung the mot bac col wndng method, whch to et =1, 11 = 22 and 12 = 21 =0. Even th mple arrangement can generate a reaonable approxmate nuodal dtrbuton wth only one gnfcant upper harmonc (.e. b =2). It become neceary to calculate the effectve magnetc feld een by a col wound n a relatvely wde lot; hence, many detal are left out here. Snce the applcaton of Faraday law non-trval n th geometry, determnaton of voltage handled by conderng power conervaton, and equatng mechancal power to electrcal power and conderng an equvalent peed dependent effcency curve, whch determned expermentally. Th work nce effcency very hgh (>90%) wth the LEG degn and low peed, preently. The electrcal model mut be completed by pecfyng the load crcut condton. For tet purpoe t ometme ueful to ue mple retve loadng whch traghtforward to model. However, for practcal mplementaton, a more ophtcated rectfyng crcut ued. A DC/DC converter ung an emulated retance allow the power to be tored on battere or uper-capactor for ue by on-board enor or communcaton module. The crcut equaton for the load crcut are traghtforward to mplement, and are ncluded n the model. Fg. 4 how a mplfed chematc for the equvalent generator and load crcut. The generator hown a an equvalent two phae ource wth phae retance R and phae nductance L. The load part of the crcut accurate a a model, and hown a a full-wave two-phae brdge confguraton wth an emulated load retance, R emul. va ( t ) t vb ( ) Lnear Generator Ra Rb La a( t ) b ( t ) Generator Termnal Lb Ra << ωg Rb << ωg Rectfer Retve Load Emulator Fgure 4. Equvalent crcut of generator and load Remul(t) vgen( t ) Smulaton of practcal drectly drven and reonantly drven ytem requre conderable extenon to the model dcued above n order to properly model. Frt, the buoy are not perfectly wave complant and have ther own repone that mut be accurately calculated. In the cae of the drect-drve ytem, the retance plate not an unmovable object and alo ha t own repone that mut be quantfed. In general, a mplfed model wth added ma and dpaton, but gnorng vortex heddng ued. Conderable effort ha been made to accurately calculate the repone of the buoy. The tartng pont the uual equaton of moton ncludng all force (prng force, generator force, hydrodynamc force, frcton force, radaton force, etc), and buoy added ma. Thee force equaton are etablhed and dcued throughout the lterature [6] and only the hydrodynamc force F 3 wll be dcued here. A nonlnear correcton made for the buoy added ma, at nfnte frequency, whch aumed to be equal to one half of the ntantaneou value of dplaced water ma, wth the um of the ndvdual par added mae beng ued for the reonant drve ytem. For hydrodynamc force F 3, the well-known WAMIT program ued to calculate the frequency dependent modulu r 3 and phae φ 3 of exctaton force for the buoy under conderaton. Thee parameter are typcally ued n a force formula, vald n the lnear regme, and both modulu and phae depend on wave frequency, a well a on buoy hape, ze and draft. The lnear hydrodynamc force equaton modfed wth nonlnear correcton that account for large heave dplacement, nce buoy dameter comparable to the nteretng range of wave ampltude n practcal cae. The man purpoe of the nonlnear correcton to hydrodynamc force and added-ma are to prevent the mulaton from dplayng unrealtc behavor when occaonal large heave excuron happen. Mot of the tme the buoy moton n the lnear excuron range, but wth random wave, there are perodc large devaton whch are then quckly damped. Equaton (7) how the formula for F 3 for the drect-drve ytem, where ρ water n( t )

5 denty, x b buoy heave dplacement and D b buoy dameter. Lkewe, Equaton (8) how the formula for F 3 for the reonant-drve ytem, where A the ampltude of the th wave component, D j and d j are the j th par dameter and draft, repectvely. xb F3 ρ g 2 = 1 b 3 t 3 D b = 1 F w ( t) = ρ g A 3 = 1 j= 0 2 w (7) ( 1 k x ) A r ( ω ) co( ω φ ( ω ) ψ ) 3 ˆ coh D rˆ ω j 3 co t ω ω φ 3 ψ D D coh j j V. PROTOTYPE TESTIG ( ) (8) k ( h dj) ( k ( h 10) ) Full cale buoy degn baed on a targeted ea tate of the 20 year average for Rhode Iland helf water; wth gnfcant wave heght H = 1.2 m and peak pectral perod T p = 4.5. Pror to contructon and tetng of full cale prototype, t neceary to perform mall cale tetng n both laboratory ettng and at-ea. Laboratory tetng of 1:10 cale mn-prototype of each ytem wa frt performed and decrbed n [7]. The reult of thee tet, whch compared favorably wth numercal mulaton, provded confdence n the degn and allowed for 1:4 cale prototype to be bult and teted. The followng ecton provde bref decrpton of the 1:4 cale prototype and feld experment n arraganett Bay [8]. The expermental data wa then compared to model mulaton reult for the purpoe of model verfcaton and valdaton. The model matche all buoy and generator parameter ued n the feld experment and ue the JOSWAP pectrum determned from a waverder buoy a nput to create a tme ere of ea urface elevaton to repreent the wave forcng een durng the feld tet. A. Drect-Drve Buoy (DC2) Ung Froude calng, the 1:4 cale buoy degned for a ea tate of H = 0.3 m and T p = The 1:4 cale DC2 cont of a 0.92 m dameter phercal float, rgdly attached to a 0.15 m dameter cylndrcal canter whch houe the LEG. The retance plate ha a dameter of 1.02 m a ma of kg. The total buoy ma kg to et the draft of the buoy uch that the float half ubmerged. In t tatc ret poton, the buoy ha a length of jut over 3.5 m and the armature ha a maxmum dplacement of ±0.21 m. Two feld tet of the DC2 are decrbed n [8]; the frt n December 2011 and the econd n May A decrbed earler, the LEG cont of a two-phae tator wth a ere of lot flled wth copper wndng through whch a permanent magnet lder (armature) pae. The phae retance of the tator ued n the December tet wa R = 1.6 Ω. For the May tet, the LEG wa upgraded wth addtonal wndng. The phae retance of the tator for the May tet wa R = 4.8 Ω. The buoy equpped wth a 3- ax accelerometer and gyrocope for meaurng and recordng buoy moton a well a two Hall Effect enor for meaurng the poton of the permanent magnet armature relatve to the buoy canter. The wave condton for the December tet were meaured ung a waverder buoy degned and contructed by the Department of Ocean Engneerng at URI. The waverder ue a 3-ax accelerometer and gyrocope to record acceleraton and rate of rotaton of the buoy. The meaured buoy acceleraton and angular velocte are converted to true acceleraton relatve to a non-rotatng frame of reference and corrected for effect of buoy rotaton. The heave acceleraton calculated by projectng meaured acceleraton to true vertcal. A lnear tranfer functon then appled to the buoy acceleraton pectrum to determne the wave pectrum. A JOSWAP wave pectrum ft to the meaured wave pectrum to provde the charactertc ea tate parameter. Th proce decrbed n detal by [8]. The wave condton for the perod of uable data durng the December tet were equvalent to a JOSWAP pectrum wth H = 0.63 m, T p = 3.33 and peak enhancement factor γ = 2. The meaured wave pectrum and JOSWAP pectrum are for th tet hown n Fg. 5. Thee condton are gnfcantly larger than the degn condton of H = 0.3 m and T p = Durng the tet, the LEG wa loaded wth a varable retve load, whch repreented by an equvalent (emulated) retance R emul = Ω. Armature dplacement ranged between m and 0.20 m wth armature velocty between -0.5 m/ and 0.9 m/. The RMS armature dplacement (z a ), armature velocty (z ȧ ) and harveted electrcal power (P) are gven n Table I along wth the reult from numercal model mulaton for the December tet. Fgure 5. Wave pectrum meaured ung waverder (blue) and bet-ft JOSWAP pectrum (green) For the May tet a commercally avalable waverder manufactured by Datawell BV of the etherland wa utlzed to meaure the wave condton. The Datawell waverder rated for wave pectral perod between 1-30 wth an accuracy wthn 0.5% of meaured value [11]. Approxmately 15 mnute of data from the tet, where the wave condton were cloet to the degn wave condton, wa analyzed. The wave condton were equvalent to a JOSWAP pectrum wth H = 0.29 m and T p = 2.5 and γ = 2.3. The LEG wa loaded wth a fxed retance R L = 10 Ω on each phae. Fg. 6 how the armature dplacement durng the May tet a well a the mulated armature dplacement. The RMS armature dplacement (z a ), armature velocty (z ȧ ) and harveted electrcal power (P) are

6 gven n Table I along wth the reult from numercal model mulaton for the May tet. Fgure 6. Armature dplacement durng May 2012 DC2 feld tet (top) and model mulaton reult (bottom) The model mulaton and expermental data appear to match very well for both the December and May feld tet of the DC2. Whle RMS armature dplacement lghtly greater for the mulaton, the RMS velocty and mean harveted electrcal power for the mulaton and experment are wthn 10%. The feld tet of the DC3 wa performed n June 2012, and a wa the cae wth the May 2012 feld tet of the DC2, the Datawell waverder wa ued to meaure wave condton durng the tet. Approxmately 25 mnute of data wa collected and analyzed for the DC3 tet, wth wave condton durng the tet beng equvalent to a JOSWAP pectrum wth H = 0.31 m, T p = 2.52 and γ = 6. Throughout the tet, the LEG wa loaded wth an average emulated retance R emul = 8 Ω. The buoy heave acceleraton, armature dplacement (z a ), armature velocty (z ȧ ) and harveted electrcal power (P) are hown n Fg. 7 through 10 along wth the reult from numercal model mulaton for the DC3 feld tet. RMS armature dplacement and velocty, a well a mean power are hown n Table I. The RMS buoy heave acceleraton wa 1.38 m/ 2 for the June tet, compared wth 1.44 m/ 2. ote the drft n armature poton for the expermental reult n Fg. 8, whch mot lkely due to low data decmaton. It can be een that the armature wa ung t full troke range of ±0.32 m. otce that the plot generally agree n magntude, however do not lne up exactly, whch due to ung a manufactured tme ere from a JOSWAP pectrum ntead of a tme ere wth an exact replcaton of the ea urface durng the tet, whch not avalable. TABLE I. COMPARISO OF EXPERIMETAL AD MODEL RESULTS Tet Date (Sytem) Dec. 11 (DC2) May 12 (DC2) June 12 (DC3) Table column ubhead Data z a RMS z ȧ RMS P mean Experment 0.07 m 0.21 m/ 0.42 W Model 0.08 m 0.19 m/ 0.40 W Experment 0.04 m 0.12 m/ 1.29 W Model 0.05 m 0.13 m/ 1.38 W Experment 0.14 m 0.40 m/ 0.41 W Model 0.14 m 0.39 m/ 0.44 W B. Reonant Buoy (DC3) Lke the 1:4 cale DC2, the 1:4 cale DC3 buoy wa degned for a ea tate wth H = 0.3 m and T p = The central par, whch houe the LEG, cont of a 0.15 m dameter alumnum tube wth an overall length of 3.5 m, ncludng noe cone. The four atellte par ue the ame 0.15 m dameter tube wth overall length of 1.6 m (ncludng noe cone) and are placed uch that the overall wdth of the buoy 0.97 m. The total ma of the buoy (ncludng armature ma) kg, whch et the draft of the central par and atellte par at 2.3 m and 0.8 m, repectvely. Wth an armature ma of 6.8 kg and armature prng contant of /m, the combned natural perod of the buoy The maxmum armature dplacement for the DC3 wa ±0.32 m. Lke the DC2, the DC3 equpped wth a 3-ax accelerometer and gyrocope for meaurng and recordng buoy moton. The phae retance of the LEG for the June tet wa R = 9.8 Ω and nternal Hall Effect enor meaure poton of the magnetc armature. Fgure 7. Buoy heave acceleraton durng June 2012 DC3 feld tet (top) and model mulaton reult (bottom) Fgure 8. Armature dplacement durng June 2012 DC3 feld tet (top) and model mulaton reult (bottom)

7 acheve thee requrement. In addton, the expermental data were ued for verfcaton and valdaton of the model. The reult of the experment were hown to match well wth thoe from model mulaton, wth RMS armature dplacement, RMS armature velocty and mean harveted electrcal power generally fallng wthn 10% of the meaurement. Th gve confdence n ung model mulaton to optmze the ytem a well a provdng atance n the degn of full cale wave energy harvetng ytem. Fgure 9. Armature velocty durng June 2012 DC3 feld tet (top) and model mulaton reult (bottom) Fgure 10. Intantaneou electrcal power harveted durng June 2012 DC3 feld tet (top) and model mulaton reult (bottom) In the tme nce the June 2012 feld tet, the LEG for the DC3 ha been replaced wth a new generator more lke the type ued n the DC2. The new LEG tator ha more wndng and cover more magnet par of the lder than the prevou DC2 LEG. The phae retance of the new generator ha ncreaed to R = 12.7 Ω. In addton, the armature ma ha been ncreaed to provde more drvng force though the tator to counteract the ncreae electromagnetc thrut and frcton from the larger generator. ew prng wth the proper prng contant to obtan the correct degn frequency were ntalled a well. A feld tet wth the modfed DC3 ha not yet been performed, but wll take place wthn the econd half of Prelmnary modelng ha hown that harveted electrcal power antcpated to be n the range of 5-10 W. VI. COCLUSIO Th paper preented a revew of a wave-to-wre numercal model developed to analyze drect-drve and reonant-drve buoy ytem for ocean wave energy harvetng. Feld tetng wa completed wth 1:4 cale prototype ytem n arraganett Bay and howed reult that are n lne wth expected performance. The applcaton of nteret have power requrement n the 1-10 W range. Wth generator mprovement and calng taken nto conderaton, th work ha demontrated the ablty to REFERECES [1] K. Rhnefrank, E. B. Agamloh, A. von Jouanne, A. K. Wallace, J. Prudell, K. Kmble, J. All, E. Schmdt, P. Chan, B. Sweeny and A. Schacher, "ovel ocean energy permanent magnet lnear generator buoy," Renewable Energy, vol. 31, no. 9, pp , [2] D. Elwood, S. C. Ym, J. Prudell, C. Stllnger, A. von Jouanne, T. Brekken, A. Brown, R. Paach, Degn, contructon, and Ocean tetng of a taut-moored dual-body wave energy converter wth a lnear generator power take-off, Renewable Energy, vol. 35, no. 2, pp , [3] D. Elwood, A. Schacher, K. Rhnefrank, J. Prudell, S. Ym, E. Amon, T. Brekken, A. von Jouanne, umercal Modelng and Ocean Tetng of a Drect-Drve Wave Energy Devce Utlzng a Permanent Magnet Lnear Generator for Power Take-Off, 28 th Int. Conf. on Ocean, Offhore and Arctc Eng., Honolulu, HI, USA, OMAE2009, vol. 4, pp , [4] M. Stalberg, R. Water, O. Danelon, and M. Lejon, Influence of Generator Dampng on Peak Power and Varance of Power for a Drect Drve Wave Energy Converter, Journal of offhore mechanc and Arctc engneerng, ASME, vol. 130, no. 3, [5] A. R. Grll, J. Merrll, S. T. Grll and M. L. Spauldng, " Expermental and numercal tudy of par buoy-magnet-prng ocllator ued a energy aborber," n Proc. 17 th Intl. Conf. Offhore and Polar Eng, o JSC-569, [6] S. P. Baten, R. B. Sepe, Jr., A. R. Grll, S. T. Grll, and M. L. Spauldng, Ocean Wave Energy Harvetng Buoy for Senor, Proc. IEEE Energy Converon Congre and Expoton, ECCE09, San Joe, CA, USA, pp , [7] S. T. Grll, A. R. Grll, S. P. Baten, R. B. Sepe, Jr., and M. L. Spauldng, Small Buoy for Energy Harvetng: Expermental and umercal Modelng Stude, Proc. 21 t Int. Offhore and Polar Eng. Conf., ISOPE, Mau, HI, USA, pp , [8] J. Montgomery, Expermental and umercal Study of a Wave Energy Harvetng Buoy, MS The, Dept. of Ocean Engneerng, Unverty of Rhode Iland, Kngton, [9] A. Babart, G. Duclo, A. H. Clement and J. C. Glloteaux, Latchng control of a power take-off ocllator carred by a wave actvated body, Proc. 20 th Int. Workhop on Wave & Floatng Bode, pp , [10] A. Babart and A. H. Clement, Optmal latchng control of a wave energy devce n regular and rregular wave, Appl. Ocean Re., [11] Datawell BV, Waverder SG,