Impact of Generator Stroke Length on Energy Production for a Direct Drive Wave Energy Converter

energies

Article Impact of Generator Stroke Length on Energy Production for a Direct Drive Wave Energy Converter

Yue Hong 1,*, Mikael Eriksson 1,2, Cecilia Boström 1 and Rafael Waters 1,2 1 Division for Electricity, Uppsala University, Uppsala 75121, Sweden; [email protected] (M.E.); [email protected] (C.B.); [email protected] (R.W.) 2 Seabased AB, Sylveniusgatan 5 D, Uppsala 75450, Sweden * Correspondence: [email protected]; Tel.: +46-18-471-7285

Academic Editor: Stephen Nash Received: 25 June 2016; Accepted: 31 August 2016; Published: 9 September 2016

Abstract: The Lysekil wave energy converter (WEC), developed by the wave energy research group of Uppsala University, has evolved through a variety of mechanical designs since the ﬁrst prototype was installed in 2006. The hundreds of engineering decisions made throughout the design processes have been based on a combination of theory, know-how from previous experiments, and educated guesses. One key parameter in the design of the WECs linear generator is the stroke length. A long stroke requires a taller WEC with associated economical and mechanical challenges, but a short stroke limits the power production. The 2-m stroke of the current WECs has been an educated guess for the Swedish wave climate, though the consequences of this choice on energy absorption have not been studied. When the WEC technology is considered for international waters, with larger waves and challenges of energy absorption and survivability, the subject of stroke length becomes even more relevant. This paper studies the impact of generator stroke length on energy absorption for three sites off the coasts of Sweden, Chile and Scotland. 2-m, 4-m, and unlimited stroke are considered. Power matrices for the studied WEC prototype are presented for each of the studied stroke lengths. Presented results quantify the losses incurred by a limited stroke. The results indicate that a 2-m stroke length is likely to be a good choice for Sweden, but 4-m is likely to be necessary in more energetic international waters.

Keywords: wave energy converter (WEC); electrical control; damping force; wave energy

1. Introduction Uppsala University, Sweden, has an ongoing wave energy research project that was started in 2002 [1]. The group has a research site at the west coast of Sweden and the ﬁrst wave energy converter (WEC) was installed at the site in 2006. The WEC, categorized as point absorber, consists of a point absorbing buoy ﬂoating on the ocean surface and a directly driven linear generator placed on the seabed. The choice of a directly driven permanent magnet generator was made for the sake of robustness and survivability through the avoidance of moving parts. The small size, relative to many other WECs, was chosen in part for the mild Swedish wave climate, but mainly to facilitate future series production and ease of transportation and deployment at sea. Large-scale parks will be needed to produce relevant energy levels to the grid, yet the many individual WECs create redundancy and allows for repairs and maintenance while maintaining electricity production from the parks. Since the start of the project, twelve different prototypes of WECs, with a variety of mechanical designs and power ratings, have been installed [2]. In addition, relevant control and measurement systems, such as a marine substation [3], have also been developed and tests have been carried out on the WECs’ performances [4]. Collateral research areas include a tidal effect compensator [5], remote operation vehicle (ROV) connections [6], a study of the thermal properties of the power system [7],

Energies 2016, 9, 730; doi:10.3390/en9090730 www.mdpi.com/journal/energies Energies 2016, 9, 730 2 of 11 system [7], and management on the deployment [8]. For a future wave power plant, it will be important to identify its environmental impact. Therefore, environmental studies have been carried out since the start of the project. Studies on biofouling on the buoys and colonization of species on and around the foundations have been performed [9]. Furthermore, research on large‐scale power plants [10] installed in different Energies 2016, 9, 730 2 of 12 park patterns has also been performed. Further details about the progress of the project can be found in [11,12]. Usingand management a direct ondrive the deployment linear generator [8]. For a future to convert wave power the plant, energy it will in be importantthe waves to identify into electricity is used in someits environmentaldifferent wave impact. energy Therefore, projects, environmental see for studies example have beenReferences carried out [13–16]. since the startCurrent of research topics includethe project. how to improve the technology’s energy absorption by optimizing the control and performance ofStudies the WEC. on biofouling Though on the many buoys and options colonization exist of speciesto this on end and aroundthe challenge the foundations is to improve have been performed [9]. Furthermore, research on large-scale power plants [10] installed in different performancepark while patterns not has alsointroducing been performed. technology, Further details which about themakes progress the of thedevices project canmore be found vulnerable or otherwise costlyin [11,12 in]. Usingrelation a direct to drivethe added linear generator benefit. to convert the energy in the waves into electricity is used There arein some several different parameters wave energy on projects, the device see for example that will References bring an [13 –impact16]. Current on researchthe performance topics of the include how to improve the technology’s energy absorption by optimizing the control and performance generator andof the on WEC. the Though power many production. options exist to In this this end the study, challenge the is toimpact improve of performance the stroke while length not will be investigated.introducing The stroke technology, length which is the makes range the that devices the more generator’s vulnerable moving or otherwise part, costly the in translator, relation to can move before beingthe stopped added benefit. by the end stops. In other words, it is the distance between the end stops minus There are several parameters on the device that will bring an impact on the performance of the length of the translator, as shown in Figure 1. The stroke length effects the electrical conversion the generator and on the power production. In this study, the impact of the stroke length will be since it limitsinvestigated. the translator’s The stroke maximum length is the range movable that the distance. generator’s Hence, moving part,it is the important translator, canto moveinvestigate how strongly thebefore energy being absorption stopped by the is endaffected stops. Inby other adjusting words, it the is the stroke distance length, between and the end to determine stops minus the design stroke for differentthe length ofwave the translator, climates. as shown Furthermore, in Figure1. The the stroke manufacturing length effects the cost electrical is an conversion inevitable since factor when it limits the translator’s maximum movable distance. Hence, it is important to investigate how strongly designing athe WEC energy device. absorption The is affected construction by adjusting and the the stroke maintenance length, and to determine at sea are the design basically stroke costly, for a main challenge beingdifferent to wave secure climates. its Furthermore, survivability the manufacturing when exposed cost is an to inevitable the enormous factor when designing wave forces a while remaining WECeconomically device. The constructionsound. To and this the maintenanceend it is atsignificant sea are basically to costly,find aa main compromise challenge being between the to secure its survivability when exposed to the enormous wave forces while remaining economically exploitable sound.wave To energy this end itand is significant the construction to find a compromise cost, and between one the of exploitable the main wave parameters energy and the is the stroke length of theconstruction linear generator. cost, and one of the main parameters is the stroke length of the linear generator.

(a) (b)

Figure 1. IllustrationFigure 1. Illustration of the wave of the wave energy energy converter converter (WEC)(WEC) device device developed developed in Lysekil in Project: Lysekil (a) Project: one (a) one of the WECof prototypes the WEC prototypes L12 was L12 assembled was assembled at at the the harbor; harbor; and and (b) a ( simplifiedb) a simplified mechanical mechanical structure of a structure of direct-drive type WEC device. a direct‐drive type WEC device. 2. Theory 2. Theory The WEC model consists of two parts, a buoy floating on the surface and a linear generator at the seabed. The floating buoy is connected to the generator via a line. Electrical power is converted by the The WEC model consists of two parts, a buoy floating on the surface and a linear generator at relative motion between a fixed stator and a movable translator, as illustrated in Figure1. There are the seabed. The floating buoy is connected to the generator via a line. Electrical power is converted by the relative motion between a fixed stator and a movable translator, as illustrated in Figure 1. There are two end stops installed inside the generator, with the purpose to protect the generator from damage during rough wave conditions. In this study, the floating buoy is restricted to the motion only. The interaction between the waves and the buoy is modeled by the potential theory. The hydrodynamic parameters for the excitation force and the radiation impedance are calculated by the software WAMIT (WAMIT, Inc., Chestnut Hill, MA, USA) [17].

Energies 2016, 9, 730 3 of 12 two end stops installed inside the generator, with the purpose to protect the generator from damage during rough wave conditions. In this study, the ﬂoating buoy is restricted to the motion only. The interaction between the waves and the buoy is modeled by the potential theory. The hydrodynamic parameters for the excitation force and the radiation impedance are calculated by the software WAMIT (WAMIT, Inc., Chestnut Hill, MA, USA) [17]. Equation (1) describes the vertical motion for the buoy x1 and the translator x2 under excitation from the waves. The upper differential equation describes the interaction between the buoy and the waves, where ma is the mass of the buoy, m∞ is the added mass in inﬁnity, fexc is the time dependent excitation force, h (t) is the impulse response function for the radiation impedance, fH is the hydrostatic stiffness and fline is the line force. The lower differential equation describes the motion of the translator driven by the buoy, where mb is the translator mass and fdamp is the generator damping force. The end stops are springs with a high spring constant, as denoted as fupp_es and flow_es respectively in the equation. The line between the buoy and the translator is modelled as stiff spring that becomes active when the translator reaches its end positions. The line force is modeled by Equation (2), where the spring constant is denoted as kline.

( .. . (ma + m∞) x1 = fexc (t) − h (t) x1 (t) − fh − fline (x1, x2) − mag .. . (1) mbx2 = fline (x1, x2) + fdamp x2, x2 − mbg + fupp_es + flow_es

( k (x − x ) if x > x f (x , x ) = line 1 2 1 2 (2) line 1 2 0 else

Equations (3) and (4) describe the upper and lower end stop force. In the equations ks1 and ks2 are the spring constant for the end stops and l1 and l2 are the stroke length to the upper and lower end stop, respectively. ( −ks1 (x2 − l1) if x2 > l1 fupp_es (x ) = (3) 2 0 else ( −k (x − l ) if x < −l f (x ) = s2 2 2 2 2 (4) low_es 2 0 else

The generator damping force is proportional to the translator speed with the damping coefficient γ in Equation (5). . . fdamp x2 = −γx2 (5) In Reference [18], Eriksson proposed a numerical approach for the WEC modeling by using the potential theory and with the generator modeled as a viscous damper. The WEC model was later built up and validated with full-scale experimental test results from the wave power plants installed off the Swedish west coast in the Lysekil project. The validation was published in Reference [19]. Figure2 gives an example of results from the numerical model showing the motion of the WEC buoy and linear generator in response to, in this simplified case, harmonic waves. According to the harmonic waves with known amplitude and energy period, the velocity and the position for both buoy and translator are obtained by solving the set of equations with given parameter settings such as the mass of the translator and buoy, the damping coefficient, buoy draft, etc. In this example case, the natural frequency for the WEC device is 6 Hz. Energies 2016, 9, 730 3 of 11

Equation (1) describes the vertical motion for the buoy and the translator under excitation from the waves. The upper differential equation describes the interaction between the buoy and the waves, where is the mass of the buoy, is the added mass in infinity, is the time dependent excitation force, is the impulse response function for the radiation impedance, is the hydrostatic stiffness and is the line force. The lower differential equation describes the motion of the translator driven by the buoy, where is the translator mass and is the generator damping force. The end stops are springs with a high spring constant, as denoted as _ and _ respectively in the equation. The line between the buoy and the translator is modelled as stiff spring that becomes active when the translator reaches its end positions. The line force is modeled by Equation (2), where the spring constant is denoted as .

, g (1) , , g_ _ if , (2) 0else

Equations (3) and (4) describe the upper and lower end stop force. In the equations and are the spring constant for the end stops and and are the stroke length to the upper and lower end stop, respectively. if (3) _ 0else if (4) _ 0else The generator damping force is proportional to the translator speed with the damping coefficient γ in Equation (5).

γ (5) In Reference [18], Eriksson proposed a numerical approach for the WEC modeling by using the potential theory and with the generator modeled as a viscous damper. The WEC model was later built up and validated with full‐scale experimental test results from the wave power plants installed off the Swedish west coast in the Lysekil project. The validation was published in Reference [19]. Figure 2 gives an example of results from the numerical model showing the motion of the WEC buoy and linear generator in response to, in this simplified case, harmonic waves. According to the harmonic waves with known amplitude and energy period, the velocity and the position for both buoy and translator are obtained by solving the set of equations with given parameter settings such as the mass of the translator and buoy, the damping coefficient, buoy draft, etc. In this example case, the natural frequencyEnergies 2016 ,for9, 730 the WEC device is 6 Hz. 4 of 12

Figure 2. A solutionFigure 2. exampleA solution example from the from numerical the numerical model of differentialof differential Equation Equation (1). In this case, (1). the In this case, the amplitude of the harmonic wave is 1 m and the period is 6 s with a sampling time of 0.1 s. The WEC is amplitude of themodeled harmonic with a translator wave massis 1 ofm 5000 and kg the and aperiod constant is damping 6 s with coefﬁcient a sampling of 60 (kN· s/m).time of 0.1 s. The WEC is modeled with a translator mass of 5000 kg and a constant damping coefficient of 60 (kN∙s/m). 3. Materials and Methods

3.1. The Wave Energy Converter Model The WEC model in this study was built up to simulate one of the prototypes of the Lysekil project [19]. The model consists of two parts—one is the hydrodynamic system and the other is the point absorber system. The hydrodynamic system is utilized to supply the wave energy to the linear generator model. It is possible to model the irregular wave climate at the test sites with information on the energy period and the signiﬁcant wave height. The point absorber system, on the other hand, is the ﬂoating buoy connected to the linear generator. This system is able to model the behavior of the buoy by the irregular wave generated by the hydrodynamic system. The parameters for the WEC are listed in Table1.

Table 1. WEC speciﬁcations.

WEC Specifications Value Unit Vertical stator length 2000 mm Vertical translator length 2000 mm Translator weight 10,000 kg Buoy diameter 4 m Buoy weight 6300 kg Damping coefficient 60 kN·s/m Stroke length 2/4/infinite m

In this paper, the generator’s stroke length is investigated, in order to observe the impact to the power production for the WEC device. The stroke length will be adjusted to 2-m, 4-m, and inﬁnite, respectively. The performance of the WEC is studied with a constant damping coefﬁcient of 60 kN·s/m, which is a compromise between the studied sea states of the three sites and the buoy size. Energies 2016, 9, 730 4 of 11

3. Materials and Methods

3.1. The Wave Energy Converter Model The WEC model in this study was built up to simulate one of the prototypes of the Lysekil project [19]. The model consists of two parts—one is the hydrodynamic system and the other is the point absorber system. The hydrodynamic system is utilized to supply the wave energy to the linear generator model. It is possible to model the irregular wave climate at the test sites with information on the energy period and the significant wave height. The point absorber system, on the other hand, is the floating buoy connected to the linear generator. This system is able to model the behavior of the buoy by the irregular wave generated by the hydrodynamic system. The parameters for the WEC are listed in Table 1.

Table 1. WEC specifications.

WEC Specifications Value Unit Vertical stator length 2000 mm Vertical translator length 2000 mm Translator weight 10,000 kg Buoy diameter 4 m Buoy weight 6300 kg Damping coefficient 60 kN∙s/m Stroke length 2/4/infinite m

In this paper, the generator’s stroke length is investigated, in order to observe the impact to the power production for the WEC device. The stroke length will be adjusted to 2‐m, 4‐m, and infinite, respectively. The performance of the WEC is studied with a constant damping coefficient of 60 kN∙s/m, which is a compromise between the studied sea states of the three sites and the buoy size.

3.2. Irregular Wave Source Energies 2016, 9, 730 5 of 12

3.2.1. Lysekil Test Site 3.2. Irregular Wave Source For the first studies in this paper, the wave data at test Site 6 is provided as the irregular wave 3.2.1. Lysekil Test Site source to the model. Figure 3a displays the location for the test Site 6 (58.38 N, 11.00 E) and the For the ﬁrst studies in this paper, the wave data at test Site 6 is provided as the irregular wave relevant wavesource occurrence to the model. [20] Figure is3 apresented displays the locationin Figure for the 3b. test The Site 6average (58.38 N, 11.00water E) anddepth the relevant is around 80 m at the test sitewave and occurrence it is located [20] is 18 presented km from in Figure coastline.3b. The averageThe wave water data depth for is around test Site 80 m 6 at was the test obtained from Fugro OCEANORsite and it AS is located of Norway 18 km from [21]. coastline. The data The wave available data for spanned test Site 6 was the obtained years from1997 Fugro to 2004. In this OCEANOR AS of Norway [21]. The data available spanned the years 1997 to 2004. In this study, study, this thiswave wave data data will will bebe used used in thein WECthe WEC model tomodel investigate to investigate the impact brought the impact by varied brought stroke by varied stroke length,length, as well as well as as to to constructconstruct power power scatter scatter matrices matrices for the test for site. the test site.

(a) (b)

Figure 3. MapFigure and 3. seaMap states and seaat the states test at Site the test6 studied Site 6 studied by the by Lysekil the Lysekil Project: Project: (a) ( amap) map presenting presenting the location of the studiedthe locationsites. The of the wave studied roses sites. are The waveplaced roses with are placedtheir withcenter their on center the onstudied the studied sites sites and show the and show the distribution in time of the direction on incoming waves; and (b) combined scatter and distributionenergy in time diagrams of the fordirection Site 6. Colors on incoming show annual waves; energy and transport (b) combined per meter of scatter wave front and (kWh/year). energy diagrams for Site 6. ColorsNumbers show annual give average energy occurrence transport in hours per per meter year. of These wave two front ﬁgures (kWh/year). are cited from Numbers a published give average occurrence inresearch hours article per year. [20]. These two figures are cited from a published research article [20].

3.2.2. Other Test Sites In addition to the Lysekil test site, two other test sites in other counties are also studied with the Lysekil WEC model. One site is the west coast of Scotland located at 57◦ N, 9◦ W[22], with data from wave energy Scotland (WES), while the other is located at 21◦300 S, 71◦300 W, off the coast of Chile [23]. In this paper, the wave data for both sites are utilized to predict the power and the energy absorption with the WEC model, and a comparison is made between these three test sites.

4. Results

4.1. Consequences of a Limited Stroke Length A powerful wave climate (Te = 9.5 s, Hs = 6.25 m) was first chosen in order to visualize the impact of a limitation of stroke length on the motion of the translator relative to the sea surface. Although this wave climate is one of the least frequently occurring at test Site 6 near Lysekil on the Swedish west coast [13] it is more common in less sheltered international waters. The translator motion for three different stroke lengths is presented in Figure4 together with the motion of the free water surface for comparison. Figure4a shows a time span of 10 min while Figure4b shows a time span less than 2 min for a more detailed view. The difference between a 2-m, 4-m, or infinite stroke length is clearly observed in the figures. As expected, the motion of the translator Energies 2016, 9, 730 5 of 11

3.2.2. Other Test Sites EnergiesIn 2016 addition, 9, 730 to the Lysekil test site, two other test sites in other counties are also studied with5 of the 11 Lysekil WEC model. One site is the west coast of Scotland located at 57° N, 9° W [22], with data from 3.2.2. Other Test Sites wave energy Scotland (WES), while the other is located at 21°30′ S, 71°30′ W, off the coast of Chile [23]. InIn additionthis paper, to the the Lysekil wave datatest site, for twoboth other sites testare sitesutilized in other to predict counties the are power also studiedand the with energy the Lysekilabsorption WEC with model. the WEC One sitemodel, is the and west a comparison coast of Scotland is made located between at 57° these N, 9°three W [22],test sites.with data from wave energy Scotland (WES), while the other is located at 21°30′ S, 71°30′ W, off the coast of Chile [23].4. Results In this paper, the wave data for both sites are utilized to predict the power and the energy absorption with the WEC model, and a comparison is made between these three test sites. 4.1. Consequences of a Limited Stroke Length 4. Results A powerful wave climate (Te = 9.5 s, Hs = 6.25 m) was first chosen in order to visualize the impact of a limitation of stroke length on the motion of the translator relative to the sea surface. Although 4.1. Consequences of a Limited Stroke Length this wave climate is one of the least frequently occurring at test Site 6 near Lysekil on the Swedish west Acoast powerful [13] it waveis more climate common (Te = in 9.5 less s, Hssheltered = 6.25 m) international was first chosen waters. in order to visualize the impact of a limitationThe translator of stroke motion length for three on the different motion stroke of the lengths translator is presented relative toin theFigure sea 4surface. together Although with the thismotion wave of theclimate free wateris one surface of the forleast comparison. frequently Figure occurring 4a shows at test a Sitetime 6span near of Lysekil 10 min onwhile the FigureSwedish 4b westshows coast a time [13] span it is less more than common 2 min for in a lessmore sheltered detailed internationalview. The difference waters. between a 2‐m, 4‐m, or infinite strokeThe length translator is clearly motion observed for three in the different figures. Asstroke expected, lengths the is motion presented of the in translatorFigure 4 togetherwith a 2‐ mwith stroke the motionis very constrainedof the free water while surface the translator for comparison. with infinite Figure stroke 4a lengthshows isa timefree to span follow of 10 the min wave. while Figure 4b shows a time spanEnergies less2016 ,than9, 730 2 min for a more detailed view. The difference between a 26‐ ofm, 12 4‐m, or infinite stroke length is clearly observed in the figures. As expected, the motion of the translator with a 2‐m stroke is very constrainedwith a while 2-m stroke the is translator very constrained with while infinite the translator stroke with length inﬁnite is strokefree to length follow is free the to follow wave. the wave.

(a) (b)

Figure 4. The translator’s position with three different stroke length settings (2‐m, 4‐m and infinite): (a) with a 10 min time span; and (b) with a 1.5 min time span. The wave climate for (a) and (b) is Hs (a) (b) = 6.25 m, Te = 9.5 s. Figure 4. The translator’sFigure 4. The translator’s position position with withthree three different different stroke stroke length length settings settings (2-m, 4-m and(2‐m, infinite): 4‐m and infinite): Judging from(a )Figure with a 10 4, min it time can span; be and expected (b) with a 1.5that min a time limitation span. The wave in stroke climate for length (a) and ( bwill) is have a negative (a) with a 10 minHs = time 6.25 m, span; Te = 9.5 and s. (b) with a 1.5 min time span. The wave climate for (a) and (b) is Hs impact= 6.25 on m,energy Te = 9.5 absorption. s. This is illustrated in Figure 5, where the power profiles for the three cases are given inJudging relation from to Figure the4 ,significant it can be expected wave that aheight. limitation The in stroke energy length period will have was a negative held at a constant 5.5 s Judgingto clarify from impactthe reasonFigure on energy for4, absorption. it the can different be This expected is illustratedpower that levels. in Figurea limitation 5The, where figure the in power stroke shows profiles length how for the will three 2 ‐havem case a negativestarts to cases are given in relation to the significant wave height. The energy period was held at a constant impactdiverge on when energy the5.5 s tosignificantabsorption. clarify the reason wave This for height theis differentillustrated rises power above in levels. Figure 2.75 The figurem. 5, Thewhere shows 4‐m how the and the power 2-minfinite case profiles starts stroke to for length the threecases casesfollow are the given samediverge inpattern relation when up the to significantto thea wave significant wave height height risesofwave 5.75 above height.m 2.75 when m. TheThe they 4-m energy andalso infinite start period stroke to diverge. lengthwas held cases In atother a constant words, follow the same pattern up to a wave height of 5.75 m when they also start to diverge. In other words, 5.5as expected, s to clarify as asthe long expected, reason as the as longfor translator’s asthe the different translator’s motion motionpower is is not notlevels. hindered The all three figureall three cases shows generate cases how thegenerate same the power. 2 the‐m casesame starts power. to diverge when the significant wave height rises above 2.75 m. The 4‐m and infinite stroke length cases follow the same pattern up to a wave height of 5.75 m when they also start to diverge. In other words, as expected, as long as the translator’s motion is not hindered all three cases generate the same power.

Figure 5. The averageFigure 5. The generated average generated power power for forthree three different different stroke-lengths stroke‐lengths in relation in to relation the signiﬁcant to the significant wave height. The energy period is kept constant at 5.5 s. wave height. The energy period is kept constant at 5.5 s. Figure5 is a simpliﬁed case, since the combinations of wave height and period are more complex Figure 5. Thein reality. average Thus, generated in order to quantifypower thefor impactthree ofdifferent stroke lengths stroke in‐ realisticlengths cases in relation one needs to to the look significant at all natural appearing combinations of wave height and period. With the purpose of studying the wave height.impact The of energy different period stroke lengths is kept at different constant offshore at 5.5 sites s. three power matrices have been generated based on the sea states appearing at Site 6. The results are presented in Figure6. Energies 2016, 9, 730 6 of 11

Figure 5 is a simplified case, since the combinations of wave height and period are more complex in reality. Thus, in order to quantify the impact of stroke lengths in realistic cases one needs to look at all natural appearing combinations of wave height and period. With the purpose of studying the impact of different stroke lengths at different offshore sites three power matrices have been generated Energies 2016, 9, 730 7 of 12 based on the sea states appearing at Site 6. The results are presented in Figure 6.

(a)

(b)

(c)

Figure 6.Figure Power 6. Power matrices matrices for for three three differentdifferent stroke-lengths: stroke‐lengths: (a) 2-m ( strokea) 2‐m length; stroke (b) 4-mlength; stroke (b length;) 4‐m stroke length; andand (c()c) inﬁnite infinite stroke stroke length. length. The power The matrices power arematrices obtained are with obtained a constant with damping a constant coefﬁcient damping coefficientof 60of kN 60· s/mkN∙ ands/m a and translator a translator mass of 10mass tons. of The 10 red tons. line The marks red the line difference marks to the the precedingdifference to the power matrix. preceding power matrix.

The top diagram of Figure6 shows a power matrix resulting from limiting the stroke length to The2-m, top the diagram middle diagramof Figure shows 6 shows the 4-m a case,power and matrix the lower resulting diagram from shows limiting the case where the stroke there is length to 2‐m, theno middle limit to diagram the motion shows of the the translator. 4‐m case, The presentedand the lower values representdiagram the shows average the power case duringwhere there is no limit oneto the hour motion at the corresponding of the translator. sea state. The Some presented common observationsvalues represent can be observed the average in the power during one hourmatrices: at the corresponding (i) the average power sea is state. enhanced Some as thecommon significant observations wave height increases.can be observed This is expected, in the power matrices:and (i) isthe explained average by power the higher is enhanced excitation force as the brought significant by the more wave energetic height waves; increases. (ii) For This identical is expected, significant wave heights the average power generally decreases as the energy period becomes longer. and is explainedThe average by energy the higher absorption excitation is clearly force confined brought by limits by the in stroke more length, energetic as seen waves; in Case (ii) (a) For and identical significantCase wave (b). heights the average power generally decreases as the energy period becomes longer. The averageWhen energy comparing absorption the power is clearly matrices confined of Case (a)by and limits Case in (b), stroke a boundary length, can as be seen observed in Case that (a) and Case (b).relates to the differences in stroke length. The boundary is marked as a red line in Figure6b for the Whenbenefit comparing of the reader. the The power values matrices in the lower of partCase of (a) the and diagram Case (b) (b), matrix a boundary share identical can values be observed as in that Figure6a. However, the values in the upper part are significantly higher compared to the values in relates toFigure the 6differencesa. in stroke length. The boundary is marked as a red line in Figure 6b for the benefit of the reader. The values in the lower part of the diagram (b) matrix share identical values as in Figure 6a. However, the values in the upper part are significantly higher compared to the values in Figure 6a. Similarly, in Figure 6c, a red boundary line is also marked. This line distinguishes the power production in Case (b) from Case (c). Here, it can also be observed that the values in the upper part of the matrix are higher for Case (c) while the values in lower part are the same.

Energies 2016, 9, x FOR PEER 7 of 11

4.2. Other Test Sites The wave climate varies greatly from site to site and Sweden is considered to have a mild climate from an international perspective. In order to study the energy absorption and the effects of limiting the stroke length to 4-m in international waters, two sites were chosen as references—one off the west coast of Scotland, and one off the coast of Chile. The annual sea state occurrence for both sites is displayed in scatter diagrams in Figures 7 and 9, respectively. The values in the scatter diagrams correspond to the average annual occurrence of the sea states in hours. The corresponding power matrices for the two sites are presented in Figures 8 and 10. Multiplying the scatter diagrams with the power matrices and calculating the sum of the resulting values gives the annual energy production, (Table 2). In the table, the calculated energy production is based on a 4-m stroke length for the WEC. The energy conversion presented is from the waves to the power take off (PTO), i.e., the electrical transmission and later losses are not included. Energies 2016, 9, 730 7 of 11

4.2. Other Test Sites The wave climate varies greatly from site to site and Sweden is considered to have a mild climate

from an internationalEnergies 2016, 9, 730perspective. In order to study the energy absorption and the effects8 of 12 of limiting the stroke length to 4‐m in international waters, two sites were chosen as references—one off the west

coast of Scotland,Similarly, and inone Figure off6 c,the a red coast boundary of Chile. line is The also marked. annual This sea line state distinguishes occurrence the power for both sites is displayed inproduction scatter diagrams in Case (b) from in Figures Case (c). Here, 7 and it can 9, respectively. also be observed that the values in the upper part of The valuesthe matrix in the are scatter higher for diagrams Case (c) while correspond the values in to lower the partaverage are the annual same. occurrence of the sea states in hours. The4.2. Othercorresponding Test Sites power matrices for the two sites are presented in Figures 8 and 10. Multiplying theThe scatter wave climate diagrams varies greatlywith the from power site to site matrices and Sweden and is considered calculating to have the a mildsum climate of the resulting values givesfrom the an annual international energy perspective. production, In order (Table to study 2). the In energy the absorptiontable, the and calculated the effects of energy limiting production Figure 7. Scatter diagram of sea states on the west coast of Scotland (centre of area is at 57° N, 9° W). is based on thea 4 stroke‐m stroke length tolength 4-m in for international the WEC. waters, The two energy sites were conversion chosen as references—one presented is off from the west the waves to Numberscoast indicates of Scotland, occurrence and one in off hours the coast per of year. Chile. The annual sea state occurrence for both sites is the power takedisplayed off (PTO), in scatter i.e., diagrams the electrical in Figures7 transmissionand8, respectively. and later losses are not included.

Figure 8. Corresponding energy matrix in kW on the west coast of Scotland (centre of area is at 57° Figure 7. ScatterFigure diagram 7. Scatter diagram of sea of states sea states on onthe the west west coast of of Scotland Scotland (centre (centre of area isof at area 57◦ N, is 9 at◦ W). 57° N, 9° W). N, 9° W). Numbers indicates occurrence in hours per year. Numbers indicates occurrence in hours per year.

◦ 0 ◦ 0 Figure 9. ScatterFigure diagram 8. Scatter diagram of sea of states sea states on on the the west coast coast of Chile of Chile (centre (centre of area is atof 21 area30 S, is 71 at30 21°30W). ′ S, 71°30′ Figure 8. CorrespondingNumbers indicates energy occurrence matrix in hours in per kW year. on the west coast of Scotland (centre of area is at 57° W).N, 9° Numbers W). indicates occurrence in hours per year. The values in the scatter diagrams correspond to the average annual occurrence of the sea states in hours. The corresponding power matrices for the two sites are presented in Figures9 and 10. Multiplying the scatter diagrams with the power matrices and calculating the sum of the resulting values gives the annual energy production, (Table2). In the table, the calculated energy production is based on a 4-m stroke length for the WEC. The energy conversion presented is from the waves to the power take off (PTO), i.e., the electrical transmission and later losses are not included.

Figure 9. Scatter diagram of sea states on the west coast of Chile (centre of area is at 21°30′ S, 71°30′ W). Numbers indicates occurrence in hours per year.

Energies 2016, 9, 730 7 of 11

4.2. Other Test Sites The wave climate varies greatly from site to site and Sweden is considered to have a mild climate from an international perspective. In order to study the energy absorption and the effects of limiting the stroke length to 4‐m in international waters, two sites were chosen as references—one off the west coast of Scotland, and one off the coast of Chile. The annual sea state occurrence for both sites is displayed in scatter diagrams in Figures 7 and 9, respectively. The values in the scatter diagrams correspond to the average annual occurrence of the sea states in hours. The corresponding power matrices for the two sites are presented in Figures 8 and 10. Multiplying the scatter diagrams with the power matrices and calculating the sum of the resulting values gives the annual energy production, (Table 2). In the table, the calculated energy production is based on a 4‐m stroke length for the WEC. The energy conversion presented is from the waves to the power take off (PTO), i.e., the electrical transmission and later losses are not included.

Figure 7. Scatter diagram of sea states on the west coast of Scotland (centre of area is at 57° N, 9° W). Energies 2016 9 Numbers indicates, , 730 occurrence in hours per year. 9 of 12

Figure 8. CorrespondingFigure 9. Corresponding energy energy matrix matrix in in kW kW onon the the west west coast coast of Scotland of Scotland (centre of area(centre is at 57 of◦ N,area is at 57° Energies 2016, 9, x FOR◦ PEER 8 of 11 N, 9° W). 9 W).

◦ 0 Figure 10. CorrespondingFigure 10. Corresponding power power matrix matrix in inkW kW at at the westwest coast coast of Chile of Chile (centre (centre of area is of at 21area30 isS, at 21°30′ S, Figure 9. Scatter71◦300 W).diagram of sea states on the west coast of Chile (centre of area is at 21°30′ S, 71°30′ 71°30′ W). W). Numbers indicates occurrence in hours per year. Table 2. The calculated annual energy production and average climate for three test sites. Table 2. The calculated annual energy production and average climate for three test sites. Scotland Chile Lysekil Annual energy (MWh)Scotland 65.53 36.42 Chile 20.84 Lysekil Annual Energy (MWh)Average climate (kW/m) 65.53 66.60 24.97 36.42 5.00 20.84 Average climate (kW/m) 66.60 24.97 5.00 The wave climate off the west coast of Scotland shows a larger variety of sea states compared with the wave climate at Site 6 off the coast of Lysekil, as shown in Figure7. The signiﬁcant wave The waveheight climate ranges fromoff the 0.25 mwest to 9.25 coast m and of the Scotland energy period shows ranges a larger from 5 svariety to 14 s. As of for sea the states wave compared with the waveclimates climate at the westat Site coast 6 of off Chile, the shown coast in of Figure Lysekil,8, it is milder as shown compared in toFigure the Scottish 7. The site but significant has wave height rangesthe from interesting 0.25 characteristic m to 9.25 ofm being and relatively the energy stable, period i.e., less varyingranges over from time. 5 s to 14 s. As for the wave climates at the5. Discussion west coast of Chile, shown in Figure 9, it is milder compared to the Scottish site but has the interestingThe resultscharacteristic presented inof Figure being4 give relatively a clear picture stable, of the i.e., impact less thatvarying a limitation over of time. the stroke length has on the behavior of the linear generator of the WEC. Case (a) with a 2-m free stroke length is 5. Discussionnaturally most strongly affected. Technically, in the WECs, this limitation is achieved by end stops installed in the top and bottom of the generator enclosure. A large wave will drive the translator into The results presented in Figure 4 give a clear picture of the impact that a limitation of the stroke length has on the behavior of the linear generator of the WEC. Case (a) with a 2-m free stroke length is naturally most strongly affected. Technically, in the WECs, this limitation is achieved by end stops installed in the top and bottom of the generator enclosure. A large wave will drive the translator into the upper end stop where it will remain until the wave subsides after which the translator sinks by its own weight. A close look at the Figure 6 shows that the translator is not totally restricted by the length of 2-m. The reason is that the free stroke length is 2-m and the end stops are large springs allowing for another 0.5 m of movement. For Case (b), 4-m free stroke length, a longer stroke enables the translator to move a longer distance before hitting the end stops. However, during the largest waves this generator will also reach its limits. Case (c) shows how the translator would follow the waves if the generator had an unlimited stroke length. Looking further into the details of Figure 4 one can observe a small phase shift between the wave and the translator, and that even for Case (c) the translator’s range of motion is a little smaller than that of the wave. This is caused by the translator’s mass and the damping force of the generator. The effects of a limited stroke on generated power were then investigated for the three studied cases, as shown in Figure 5. According to the figure the three cases exhibit the same pattern of power production until the wave height reaches approximately 2.7 m when the 2-m stroke length of Case (a) starts to have an effect on the absorption. The next threshold is reached at approximately 6.75 m where the 4-m case start producing significantly less power than Case (c). The purpose of this figure was to investigate, qualitatively, when a generator design of a certain stroke length starts producing less energy. The cost of upgrading to a generator with a longer stroke length should eventually be evaluated against both the decrease in energy absorption with a shorter stroke but also the risks associated with the larger and more frequent end stop forces that will occur. For the Lysekil case, i.e., Site 6 in Reference [19], the most energy relevant significant wave heights are around 2.25 m. Hence in this case, although the difference in energy production between Case (a) and Case (b) is quite large for powerful sea states, it would seem that the search for balance between the WEC cost and power production indicates that a 2-m stroke is sufficient. It is likely that a linear generator for Case (a)

Energies 2016, 9, 730 10 of 12 the upper end stop where it will remain until the wave subsides after which the translator sinks by its own weight. A close look at the Figure6 shows that the translator is not totally restricted by the length of 2-m. The reason is that the free stroke length is 2-m and the end stops are large springs allowing for another 0.5 m of movement. For Case (b), 4-m free stroke length, a longer stroke enables the translator to move a longer distance before hitting the end stops. However, during the largest waves this generator will also reach its limits. Case (c) shows how the translator would follow the waves if the generator had an unlimited stroke length. Looking further into the details of Figure4 one can observe a small phase shift between the wave and the translator, and that even for Case (c) the translator’s range of motion is a little smaller than that of the wave. This is caused by the translator’s mass and the damping force of the generator. The effects of a limited stroke on generated power were then investigated for the three studied cases, as shown in Figure5. According to the figure the three cases exhibit the same pattern of power production until the wave height reaches approximately 2.7 m when the 2-m stroke length of Case (a) starts to have an effect on the absorption. The next threshold is reached at approximately 6.75 m where the 4-m case start producing significantly less power than Case (c). The purpose of this figure was to investigate, qualitatively, when a generator design of a certain stroke length starts producing less energy. The cost of upgrading to a generator with a longer stroke length should eventually be evaluated against both the decrease in energy absorption with a shorter stroke but also the risks associated with the larger and more frequent end stop forces that will occur. For the Lysekil case, i.e., Site 6 in Reference [19], the most energy relevant significant wave heights are around 2.25 m. Hence in this case, although the difference in energy production between Case (a) and Case (b) is quite large for powerful sea states, it would seem that the search for balance between the WEC cost and power production indicates that a 2-m stroke is sufficient. It is likely that a linear generator for Case (a) would be significantly cheaper compared to Case (b). Furthermore, it is meaningful to notice that the power production for Case (b) is not that much different from that of Case (c). This would seem to suggest that even for sites with very powerful wave climates, such as the studied west coast of Scotland, Case (b) might still be the more economic choice compared to, e.g., a generator with a 6-m stroke length. However, since the results in Figure5, due to the fixed energy period of the study, are only qualitative, more comprehensive studies are needed. This motivated the generation of the power matrices of Figures6,9 and 10. In Figure6b, a red boundary line was included to visualize how the power matrix of a 4-m stroke length differs from the 2-m case of Figure6a. The diagrams seem to suggest that Case (b) is much more competitive than the Case (a), due to the large enhancement in power production associated with the longer stroke. However, the most relevant sea states in this case (Lysekil—test Site 6) are below the boundary line. Thus, from the perspective of annual energy production, the area above the boundary line does not seem to contribute to a significant degree. This is quantified in Table3 where the annual energy production for the three cases is presented. An increase of stroke length from Case (a) to Case (b) improves energy production by 7%, and an increase from Case (b) to Case (c) improves it by another 1%. Hence, for the studied WEC and with linear damping one can conclude that a 2-m stroke length is probably the more economic choice for the studied site.

Table 3. The annual energy production at test Site 6 with three different stroke length settings.

2-m 4-m Inﬁnite 19.48 MWh 20.84 MWh 21.10 MWh

For each site where WECs are considered for deployment these types of studies are needed and power matrices such as the ones presented in Figures6,9 and 10 are important tools. The results show that the studied WEC is able to work in an environment with a wide range of sea states. Although the Energies 2016, 9, 730 11 of 12 studied constant linear damping coefficient of 60 kN·s/m was chosen because it is a good compromise for the studies sea states and buoy size, other more advanced methods of control are likely to increase the energy absorption significantly. The presented results will thus provide a reference for future investigations on both the performance of linearly damped WECs in offshore experiments as well as studies on more advanced methods of control. Future research into this field should produce power matrices for more advanced WEC control, e.g., different types of active control [24], for the relevant buoy sizes and geometries, and associated generators.

6. Conclusions The purpose with this paper was to investigate the impact of linear generator stroke length on energy absorption. The study was made by simulating a prototype WEC from the Lysekil project with three different stroke lengths and at three geographical locations with different wave climates. The results indicate that for the studied locations the 2-m stroke length is likely to be sufficient for Sweden, while the economic benefits of a longer stroke length is likely to dominate at the studied locations in Scotland and Chile. Future research should include more advanced control methods of the WECs, as well as in depth cost/benefit economic analyses.

Acknowledgments: The work was supported by SweGRIDS, KIC InnoEnergy-CIPOWER, Vetenskapsrådet, Statkraft AS, Fortum OY, the Swedish Energy Agency, Seabased Industry AB, Chinese Scholarship Council, Draka Cable AB, the Gothenburg Energy Research Foundation, Falkenberg Energy AB, Helukabel, Proenviro, ÅF Group, Vinnova, the Foundation for the Memory of J. Gust, Richert, the Göran Gustavsson Research Foundation, Vargöns Research Foundation, Swedish Research Council Grant No. 621-2009-3417 and the Wallenius Foundation. Author Contributions: Yue Hong was responsible for the modeling results and wrote most of the article. Mikael Eriksson provided the theory for the modeling. Cecilia Boström helped with the correction of parts of the article. Rafael Waters supervised the project and helped with most of the correction. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Leijon, M.; Boström, C.; Danielsson, O.; Gustafsson, S.; Haikonen, K.; Langhamer, O.; Strömstedt, E.; Stålberg, M.; Jan, S.; Svensson, O.; et al. Wave Energy from the North Sea: Experiences from the Lysekil Research Site. Surv. Geophys. 2008, 29, 221–240. 2. Lejerskog, E.; Gravråkmo, H.; Savin, A.; Strömstedt, E. Lysekil research site, Sweden: A status update. In Proceedings of the 9th European Wave and Tidal Energy Conference, Southampton, UK, 5–9 September 2011. 3. Ekström, R.; Kurupath, V.; Svensson, O.; Leijon, M. Measurement system design and implementation for grid-connected marine substation, Renew. Energy 2013, 55, 338–346. 4. Bostrom, C.; Svensson, O.; Rahm, M.; Lejerskog, E.; Savin, A.; Stromstedt, E.; Engstrým, J.; Gravrýkmo, H.; Haikonen, K.; Waters, R.; et al. Design proposal of electrical system for linear generator wave power plants. In Proceedings of the 2009 35th Annual Conference of IEEE Industrial Electronics, Porto, Portugal, 3–5 November 2009; pp. 4393–4398. 5. Castellucci, V.; Waters, R.; Eriksson, M.; Leijon, M. Tidal effect compensation system for point absorbing wave energy converters. Renew. Energy 2013, 51, 247–254. [CrossRef] 6. Remouit, F.; Lopes, M.; Pires, P.; Sebastiao, L. Automation of subsea connections for clusters of wave energy converters. In Proceedings of the 25th International Ocean and Polar Engineering Conference, Kona, HI, USA, 21–26 June 2015. 7. Baudoin, A.; Bostrm, C.; Leijon, M. Thermal Rating of a Submerged Substation for Wave Power. IEEE Trans. Sustain. Energy 2016, 7, 436–445. [CrossRef] 8. Chatzigiannakou, M.A.; Dolguntseva, I.; Ekström, R.; Leijon, M. Offshore Deployment of Marine Substation in the Lysekil Research Site. In Proceedings of the 25th International Offshore and Polar Engineering Conference, Kona, HI, USA, 21–26 June 2015. Energies 2016, 9, 730 12 of 12

9. Langhamer, O.; Wilhelmsson, D. Colonisation of fish and crabs of wave energy foundations and the effects of manufactured holes—A field experiment. Mar. Environ. Res. 2009, 68, 151–157. [CrossRef][PubMed] 10. Rahm, M.; Svensson, O.; Bostrom, C.; Waters, R.; Leijon, M. Experimental results from the operation of aggregated wave energy converters. IET Renew. Power Gener. 2012, 6, 149–160. [CrossRef] 11. Hong, Y.; Hultman, E.; Castellucci, V.; Ekergård, B.; Sjökvist, L.; Elamalayil, S.D.; Krishna, R.; Haikonen, K.; Baudoin, A.; Lindblad, L.; et al. Status update of the wave energy research at Uppsala University. In Proceedings of the 10th European Wave and Tidal Conference, Aalborg, Denmark, 2–5 September 2013. 12. Parwal, A.; Remouit, F.; Hong, Y.; Francisco, F.; Castellucci, V.; Hai, L.; Ulvgård, L.; Li, W.; Lejerskog, E.; Baudoin, A.; et al. Wave energy research at Uppsala University and the Lysekil Research Site, Sweden: A status update. In Proceedings of the 11th European Wave and Tidal Energy Conference (EWTEC), Nantes, France, 6–11 September 2015. 13. Waters, R. Energy from Ocean Waves: Full Scale Experimental Verification of a Wave Energy Converter. Ph.D. Thesis, Uppsala University, Uppsala, Sweden, 2008. 14. De, O.; Falcão, A.F. Wave energy utilization: A review of the technologies. Renew. Sustain. Energy Rev. 2010, 14, 899–918. 15. Gardner, F.E. Learning experience of AWS pilot plant test offshore Portugal. In Proceedings of the 6th European Wave Energy Conference, Glasgow, UK, 29 August–2 September 2005; pp. 149–154. 16. Elwood, D.; Schacher, A.; Rhinefrank, K.; Prudell, J.; Yim, S.; Amon, E.; Brekken, T.; von Jouanne, A. Numerical modelling and ocean testing of a direct-drive wave energy device utilizing a permanent magnet linear generator for power take-off. In Proceedings of the 28th International Conference on Ocean Offshore Arctic Engineering, ASME, Honolulu, HI, USA, 31 May–5 June 2009. 17. Eriksson, M. Modelling and Experimental Verification of Direct Drive Wave Energy Conversion. Ph.D. Thesis, Uppsala University, Uppsala, Sweden, 2007. 18. Eriksson, M.; Isberg, J.; Leijon, M. Hydrodynamic modelling of a direct drive wave energy converter. Int. J. Eng. Sci. 2005, 43, 1377–1387. [CrossRef] 19. Hong, Y.; Eriksson, M.; Castellucci, V.; Boström, C.; Waters, R. Linear generator-based wave energy converter model with experimental verification and three loading strategies. IET Renew. Power Gener. 2016, 10, 349–359. [CrossRef] 20. Waters, R.; Engström, J.; Isberg, J.; Leijon, M. Wave climate off the Swedish west coast, Renew. Energy 2009, 34, 1600–1606. 21. Barstow, S.F.; Mørk, G.; Lønseth, L.; Mathisen, J.P.; Schjølberg, P. The role of satellite wave data in the WORLDWAVES project. In Proceedings of the 5th International Symposium on Ocean Wave Measurement and Analysis, Madrid, Spain, 3–7 July 2005. 22. European Marine Energy Centre. Performance Assessment for Wave Energy Conversion Systems in Open Sea Test Facilities. 2004. Available online: http://www.emec.org.uk (accessed on 5 September 2016). 23. Groenewoud, G.K.P.; de Valk, C.F. Nearshore Waveclimate: Methods and Validation of the Nearshore Branch of waveclimate.com. Available online: http://www.waveclimate.com/ (accessed on 5 September 2016). 24. Hong, Y.; Waters, R.; Boström, C.; Eriksson, M.; Engström, J.; Leijon, M. Review on electrical control strategies for wave energy converting systems. Renew. Sustain. Energy Rev. 2014, 31, 329–342. [CrossRef]

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).