Study of a Wave Energy Converter Connected to a Nonlinear Load

Peer-Reviewed Technical CommunicationStudy of a Wave Energy Converter Connected to a Nonlinear Load Cecilia Boström,Student Member,IEEE,Rafael Waters,Student Member,IEEE,Erik Lejerskog,Olle Svensson, Magnus Stålberg,Student Member,IEEE,Erland Strömstedt,and Mats Leijon,Member,IEEEAbstract—This paper presents experimental results from a wave energy converter(WEC)that is based on a linear generator connected to a rectifier andfilter components.The converter-filter system is installed onshore,while the linear wave generator oper-ates offshore a few kilometers from the Swedish west coast.The power from the generator has been rectified with a diode bridge and thenfiltered using a capacitivefilter.Performance of the whole conversion system was studied using resistive loads con-nected across thefilter.The aim was to investigate the operational characteristics of the generator while supplying a nonlinear load. By changing the value of the resistive component of the load,the speed of the translator can be changed and so also the damping of the generator.The power absorbed by the generator was studied at different sea states as well.The observations presented in this paper could be beneficial for the design of efficient wave energy conversion systems.Index Terms—Electrical system,experimental results,linear generator,power absorption,wave energy.I.I NTRODUCTIONT HE threat of climate change in combination with in-creasing energy demand globally has intensified the research and development in renewable energy systems during the last decades.Many similarities about the importance in finding alternative energy resources exist between the ongoing debate today and the debate that was carried out during the 1970s.At that time,however,the main cause of the debate was a drastic increase in oil price.Ocean wave energy is one of several renewable energy technologies that emerged in Europe during the1970s[1].In spite of this,wave energy technologies are still in a relatively early stage of development,but with the technological developments and the experiences that have been gained over the past40years,the possibility of succeeding isManuscript received October07,2008;accepted February03,2009.First published April07,2009;current version published May13,2009.This work was supported in part by the Swedish Energy Agency,Vattenfall AB, the Gothenburg Energy Research Foundation,Draka Cable AB,the Göran Gustavsson Research Foundation,Statkraft AS,Ångpanneföreningen,Fortum, Vargöns Research Foundation,Falkenberg Energy AB,and the Wallenius Foundation.Associate Editor:H.Maeda.C.Boström,R.Waters,O.Svensson,M.Stålberg,E.Strömstedt,and M. Leijon are with the Swedish Centre for Renewable Electric Energy Conver-sion,Department of Engineering Science,Uppsala University,Uppsala75121, Sweden(e-mail:Cecilia.Bostrom@angstrom.uu.se;Rafael.Waters@angstrom. uu.se;Olle.Svensson@angstrom.uu.se;Magnus.Stalberg@angstrom.uu.se;Er-land.Stromstedt@angstrom.uu.se;Mats.Leijon@angstrom.uu.se).E.Lejerskog is with the Seabased Industry AB,Uppsala75183,Sweden (e-mail:Erik.Lejerskog@).Digital Object Identifier10.1109/JOE.2009.2015021Fig.1.Illustration of the WEC and the electrical system.higher today.The technological development has also madeit easier for researchers to share technical information andresearch results;see,for example,[2].One of the challenges incoming up with a marketable wave energy technology is tofindan efficient and economically viable system that can survivethe harsh climate conditions of the sea.Several strategies toovercome these problems have been attempted and have re-sulted in a number of different wave energy technologies,someof which were presented in[3]–[6].In the latest report from theInternational Energy Agency(IEA),81different wave energyprojects were examined,and out of them,13were estimatedto have reached the stage of having a full-or near-full-scaleprototype at sea[7].The wave energy converter(WEC)presented in this paper isbased on a direct drive linear generator placed at the oceanflooras shown in Fig.1.The translator,which is mounted with per-manent magnets,is connected to a buoy at the ocean surface,andthereby,the motion of the waves is transferred to the generator.The electrical characteristics of the generator have been calcu-lated in afinite element method(FEM)simulation tool.Basedon these results,the generator is designed to produce10kW at atranslator speed of0.7m/s,a line-to-line voltage of200V[rootmean square(RMS)value]when it is connected to a nominalload that is4.The efficiency of the generator in this case is 0364-9059/$25.00©2009IEEEFig.2.Circuit diagram of experimental setup.calculated to be86%.The design was made to match the signif-icant wave height on the Swedish west coast.However,the gen-erator is both electrically and mechanically designed to handle large overloads.More information about the numerical model of the generator can be found in[8].The numerical model is verified with experimental results in[9].A traditional high-speed rotating generator requires several stages between the generator and the source,the waves.This will result in a system with mechanical moving parts such as gear boxes that need maintenance and have a limited lifetime. By using a direct drive generator that is directly coupled to the waves,the needed mechanical parts can be reduced.Having a construction that uses few moving parts can result in a robust generator and this is believed to increase the lifetime and reduce the cost of the WEC[10].A WEC based on this technology was launched outside the Swedish west coast in March2006[11]. Initially,the linear generator was connected to a resistive load and the power absorption of the generator was studied in detail [9],[12],[13].Linear generators,unlike a conventional generator running at constant speed,result in somewhat more complicated energy conversion system.The motion of the translator will vary in speed and direction,and as a result,the voltage and current will have irregular amplitude and a varying frequency,and the output power peaks will reach levels several times higher than the av-erage power production.This results in a generator that has to be overdimensioned in relation to its average power generation in order to handle intermittent overloads.Consequently,compo-nents in the electrical system also need to have a higher power rating compared to the average power.There are various energy conversion schemes for direct drive generators[14]–[17].In our work,the basic strategy is to rectify the voltage from several WECs with a passive diode rectifier and then interconnect them in parallel on a common direct current (dc)bus.Passive diode rectifiers are cheaper and are less com-plex compared to active rectifiers,therefore,we chose to use a diode rectifier in this study.A capacitivefilter is then added. After this step,the dc voltage will be inverted,transformed,and connected to the grid.Several layouts for this are possible de-pending on,e.g.,farm size and distance to shore[18].The in-terconnection of several WECs in parallel on a common dc bus will lead to a possible smoother power output[19].In this study,the same offshore generator is used as in[12], but it is now connected to a nonlinear load resulting from the addition of the rectifier and capacitor.In addition to the infor-mation given on the operation of a single WEC,this study will give a hint on how a farm of WECs will operate when connected to the grid.Simulations and laboratory experiments have been done on this topic before(see,for example,[10]and[19]),but the area lacks offshore experimental results.II.E XPERIMENTThe main object of this paper is to study how the generator works when it is connected to a nonlinear load.These results will be the foundation for the design of a grid connected system containing several WECs.The resistance in the load is varied between four different values.A circuit diagram of the system is shown in Fig.2and a more detailed description of the electrical system used in the experiment is given in[20].The WEC is connected to a diode rectifier and a capacitivefilter with a capacitance of24.3F on both positive and negative dc sides.The capacitance is designed according to the sea state at the site and with help of voltage data from the WEC.This is described in more detail in[20]. During shorter periods of time(approximately10s),due to their large power storage capacity,the ultracapacitors will give a similar effect as if the generator were connected to a dc bus with a constant dc level.Different resistive loads are connected in parallel with the filter.The total resistive values that can be selectedare9.17,13.75,18.34,and27.5.These values were measured before operation with an accuracy of four significant numbers.According to the resistor characteristics,a resistance variationof5%can be assumed.By changing the resistive load,different damping conditions for the whole conversion system are achieved.The three-phasecurrents,,and can be used to calculate the powerlosses in the transmission cable and generatorwindings(1)where is the generator winding resistance0.44,andis the cable resistance0.54.If is added to the power that is measured before therectifier,an approximate value of the total absorbedpower can be obtained.Mechanical and iron losses in the WEC will be neglected in thesecalculations(2)BOSTRÖM et al.:STUDY OF A W A VE ENERGY CONVERTER CONNECTED TO A NONLINEAR LOAD125Fig.3.Data from the generator sampled during30s.(a)and(b)The three phase voltages and three phase currents measured before the diode rectifier.(c)The translator position in the generator.(d)Calculated andfiltered speed of the trans-lator.(e)Generator outputpower.(3)The position of the translator can be calculated from the gen-erator pole configuration and the phase order of the windings.A change in phase order means that the translator has changedits direction.Every period of the voltage represents the fact thatthe translator has moved the length of two pole widths,whichis equivalent to0.1m.Because the time and the position of thetranslator are known,the translator speed can be calculated.Thespeed curve isfiltered to clear out some transients due to noiseand to get a smooth shape.III.R ESULTSV oltage and current data were sampled during three monthsand the results form the study that is presented here.Fig.3shows a typical data for generator operation characteristics fora period of30s.is13.75in the results in Fig.3.Thethree phasevoltages,,and,and three phasecurrents,,and are shown in Fig.3(a)and(b),respectively.Thedc link voltage wasapproximately70V during this period.The corresponding position and speed of the translator can beseen in Fig.3(c)and(d),respectively.Finally,the power pro-duced by the generator(sea cable losses are included)is shownin Fig.3(e).Fig.4.PowerP produced over the loads measured over48h.Fig.5.Average values of absorbed power calculated over30-min periods andplotted against the average energyflux during the same time.The data representsa total of713.5h of measurements.A48-h sequence of thepower is plotted in Fig.4,where was13.75.The power on the dc side has beensmoothened considerably compared to the generator outputpower in Fig.3(e).In Fig.5,the average mean value of the absorbed power by thegenerator is calculated over a30-min period and plotted versusthe mean sea state during the same time.The data represents atotal of713.5h of measurements.The sea state is calculatedusing wave data from a wave measuring buoy located about50m from the generator[21].IV.D ISCUSSIONOne of the most important issues studied in this paper is theeffect of the rectifier andfilter on the power output from theWEC.When the generator was directly connected to resistiveloads as in[12],the extremefluctuations and quality of the pro-duced power made it incompatible for grid connection.The re-sults of Fig.4,however,indicate that long term nearly stablepower output generation is possible.Ideally,the linear generator would produce power all throughthe translator motion with an exception at the turning points.Consider the three phase voltages and three phase currentsplotted in Fig.3(a)and(b)between 4.7and13.5s,16and21.5s,and25and28s,where this is the case.However,duringother time intervals,no power is produced during translatormotion.This is due to the level of the dc bus voltage.A conse-quence of a high dc bus voltage is that the translator must havea high speed to produce energy to the system.The connectionbetween the speed of the translator and the generated power is126IEEE JOURNAL OF OCEANIC ENGINEERING,VOL.34,NO.2,APRIL 2009clearly visible in Fig.3(d)and (e).The control of the dc bus voltage in the electrical system will be a key parameter.Furthermore,with a fixed dc voltage,the three phase currents distribution decides the power production;compare the curves in Fig.3(b)and (e).Thus,by regulating the dc level,the speed of the translator and the generated current can be controlled appro-priately.Due to this effect,it would be desirable to have different dc voltages during different sea states if the power production is to be optimized.This is possible to achieve if,for example,a dc/dc booster or a variable (tap changed)transformer is used together with the inverter.Then,the output voltage can be kept constant despite the variation in dc voltage level.At the upper turning point,the translator is generally motion-less for longer periods of time compared to the lower turningpoints as shown in Fig.3(c)between14and 15.3s and 21.8and 23.8s.This result may indicate a nonoptimized generator operation.The difference in time of standstill can be attributed to ill-dimensioned springs,i.e.,the spring constant is too small and is unable to force the translator to faster downward motion as in the optimal case.Another possible explanation could be that the buoy moves in the surging direction before it starts to descend.The phenomena that can be seen in Fig.3(c),where the translator sometimes loses its speed and stops in its upwardmotion,e.g.,3.8and4.5s and 28.3and 29s,may also be caused by the shape of the wave.Fig.5shows that the highest power absorption is achieved at the lowest load,i.e.,at the highest damping factor.Therefore,finding an optimum load resistance for optimal energy produc-tion is difficult from these results.In two of the four load cases,there are only samples in the region with relatively mild sea states.As a result of this,the shape of the fitted trend lines in Fig.5can be different.If the optimal damping of the gener-ator is to be found,more experiments with lower resistive loads are needed.Fig.5further indicates that the relative power ab-sorption decreases at more powerful sea states.This indicates a power limit due to the WEC design.When the energy flux in the waves increases,in general,the wave period will be larger and the proportion of the absorbed energy by the buoy will de-crease because of its dimensions [1].This is also in agreement with previous studies [9],[12].When studying the amount of absorbed power,it is of interest to compare it to the wave height and wave period.These two parameters will have different im-pacts on the absorbed energy and such a study will give a more detailed picture of the optimal damping at a certain sea state.This study is suggested to be done when the system is upgraded with more loads.The authors also acknowledge that there is always an uncer-tainty in measurements due to the accuracy of measuring instru-ment and data or the accuracy of electrical system devices in the considered range of operation.Those effects are assumed to be small.However,since the measurements were carried out during a longer period,the value of the load resistance could have been changed due to deteriorations caused by the system and deteri-orations caused by the ambient environment.A more accurate result could have been obtained if the value of the load would have been measured continuously during the test period.The speed and position curve was filtered to clear out some noise that occurred in the calculations.Therefore,some points have been smoothened out,and the curve gives a rough value of the speed.V .C ONCLUSIONThis paper has studied the electrical output and motion of a linear generator-based WEC connected to a rectifier and filter in offshore conditions.The most significant finding,in regards to the technology’s viability as a supplier of energy to the elec-tric grid,was that the output power is smoothed to a great ex-tent compared with the fluctuating power of the waves.The power absorption for the studied load cases continued to in-crease with increasing damping of the generator.An optimal level of damping was thus not found and would require more tests at higher levels of damping.An increase in damping,how-ever,will lead to more losses in the system,as a result of higher currents,and is a factor that needs to be taken into account.The overall energy absorption from the waves shows a trend of lev-eling off towards more energetic sea states,a phenomenon that is in agreement with previous studies.In future studies,a system of several generators will be con-sidered.When this is done,the allocation of the generators has to be chosen carefully and the number of generators to be con-nected to each dc bus should be investigated in detail.By con-necting several generators on the dc bus in a suitable way,the needed energy storage will decrease exponentially and the costs of the capacitor will be substantially reduced.Costs and power optimization algorithms are also going to be considered at this stage.A CKNOWLEDGMENTThe authors would like to thank J.Goncalves and K.Yuen for their contribution to the experimental setup.They would also like to thank O.Danielsson for his help with figure layouts and calculation tools and N.Theethayi for the help with the written material.R EFERENCES[1]J.Falnes,“A review of wave-energy extraction,”Mar.Struct.,vol.20,no.4,pp.185–201,2007.[2]C.M.Johnstone,K.Nielsen,T.Lewis,A.Sarmento,and G.Lemonis,“EC FPVI co-ordinated action on energy:A European platform for sharing technical information and research outcomes in wave and tidal energy systems,”Renewable Energy ,vol.31,pp.191–196,2006.[3]A.Muetez and J.G.Vining,“Ocean wave energy conversion—Asurvey,”in Proc.IEEE 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converterproject.Rafael Waters(S’06)received the M.Sc.degree inenergy systems engineering and the Ph.D.degree inengineering physics from Uppsala University,Upp-sala,Sweden,in2005and2008,respectively.He is now working as a Researcher in the waveenergy project discussed in thispaper.Erik Lejerskog received the M.Sc.degree in engi-neering physics from Uppsala University,Uppsala,Sweden,in2007.From2006to2007,he was a Research Engineer atthe Division for Electricity,Uppsala University.Heis now working at Seabased Industry AB,Uppsala,Sweden,where he is developing electrical systemsfor wavepower.Olle Svensson received the University Diplomawith specialization in electrical engineering fromBlekinge Institute of Technology,Karlskrona,Sweden,in1998and the M.Sc.degree in engi-neering physics from Uppsala University,Uppsala,Sweden,in2007,where he is currently workingtowards the Ph.D.degree at the Department ofElectricity.He was a Test Engineer at Ericsson EnergySystems from1988to2003.He joined theDepartment of Electricity,Uppsala University,in2004,as a ResearchEngineer.Magnus Stålberg(S’06)received the M.Sc.degreein energy systems engineering from Uppsala Univer-sity,Uppsala,Sweden,in2005,where he is currentlyworking towards the Ph.D.degree within thefield ofwave power at the Division for Electricity,special-izing in underwater power transmission systems forlinear generator WECarrays.Erland Strömstedt received the B.S.degree inbusiness administration and economics(BBA)fromStockholm University,Stockholm,Sweden,in2003and the M.Sc.degree in materials technology,witha specialization in light weight structures,from theRoyal Institute of Technology,Stockholm,Sweden,in2003.He is currently working towards the Ph.D.degree at the Department of Electricity,UppsalaUniversity,Uppsala,Sweden.He joined the Department of Electricity,UppsalaUniversity,in2005,as a ResearchAssistant.Mats Leijon(M’83)received the Ph.D.degree inelectrical engineering from Chalmers University ofTechnology,Gothenburg,Sweden,in1987.From1993to2000,he was a Head of theDepartment for High V oltage ElectromagneticSystems,ABB Corporate Research,Västerås,Sweden.In2000,he became a Professor of Elec-tricity at Uppsala University,Uppsala,Sweden.Currently,he supervises11Ph.D.students withinwave power and marine current power and he hassupervised ten students to a doctoral degree andtwo students to a licentiate degree.Prof.Leijon received the Chalmers award,John Ericsson Medal,in1984,thePorjus International Hydropower Prize in1998,the Royal University of Tech-nology Grand Prize in1998,the Finnish Academy of Science Walter AlstromPrize in1999,and the2000Chalmers Gustav Dahlen Medal.He also receivedthe Grand Energy Prize in Sweden and the Polhem Prize and the Thureus prize.He is a Member of the Institution of Electrical Engineers(IEE),World EnergyCouncil(WEC),the International Council on Large Electric Systems-Cigre,andthe Swedish Royal Academy of Engineering Science.。