Aalborg Unverstet Predctablty of the Power Output of Three Wave Energy Technologes n the Dansh orth Sea Chozas, Jula Fernandez; Jensen,. E. Helstrup; Sørensen, H. C.; Kofoed, Jens Peter; Kabuth, Alna Krstn Publshed n: 9th ewtec 20 Publcaton date: 20 Document Verson Publsher's PDF, also known as Verson of record Lnk to publcaton from Aalborg Unversty Ctaton for publshed verson (APA): Chozas, J. F., Jensen,. E. H., Sørensen, H. C., Kofoed, J. P., & Kabuth, A. K. (20). Predctablty of the Power Output of Three Wave Energy Technologes n the Dansh orth Sea. In A. S. Bahaj (Ed.), 9th ewtec 20: Proceedngs of the 9th European Wave and Tdal Conference, Southampton, UK, 5th-9th September 20 Unversty of Southampton. General rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts.? Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research.? You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan? You may freely dstrbute the URL dentfyng the publcaton n the publc portal? Take down polcy If you beleve that ths document breaches copyrght please contact us at vbn@aub.aau.dk provdng detals, and we wll remove access to the work mmedately and nvestgate your clam. Downloaded from vbn.aau.dk on: januar 06, 209
Predctablty of the Power Output of Three Wave Energy Technologes n the Dansh orth Sea J. Fernández Chozas,2,.E. Helstrup Jensen 3, H.C. Sørensen, J.P. Kofoed 2 and A. Kabuth 4 Spok ApS Blegdamsvej 4, 2200 Copenhagen (Denmark) jula@spok.dk; consult@spok.dk 2 Aalborg Unversty, Department of Cvl Engneerng Sohngaardholmsvej 57, 9000 Aalborg (Denmark) jfch@cvl.aau.dk; jpk@cvl.aau.dk 3 Energnet.dk Frederca (Denmark) neh@energnet.dk 4 Unversty of Copenhagen, Department of Geography and Geology Copenhagen (Denmark) akk@geo.ku.dk Abstract The paper addresses an mportant challenge ahead the ntegraton of the electrcty generated by wave energy converson technologes nto the electrc grd. Partcularly, t looks nto the role of wave energy wthn the day-ahead electrcty market. For that the predctablty of the theoretcal power outputs of three wave energy technologes n the Dansh orth Sea are examned. The smultaneous and co-located forecast and buoy-measured wave parameters at Hanstholm, Denmark, durng a non-consecutve autumn and wnter 3-month perod form the bass of the nvestgaton. The objectve of the study s to provde an ndcaton on the accuracy of the forecast of ) wave parameters, ) the normalsed theoretcal power productons from each of the selected technologes (Pelams, Wave Dragon and Wavestar), and ) the normalsed theoretcal power producton of a combnaton of the three devces, durng a very energetc tme perod. Results show that for the 2 to 36 hours tme horzon forecast, the accuracy n the predctons (n terms of scatter ndex) of the sgnfcant wave heght, zero crossng perod and wave power are 22%, % and 68%, respectvely; and the accuracy n the predctons of the normalsed theoretcal power outputs of Pelams, Wave Dragon and Wavestar are 44%, 52% and 62%, respectvely. The best compromse between forecast accuracy and mean power producton results when consderng the combned producton of the three devces. Keywords Pelams, Wave Dragon, Wavestar, Denmark, orth Sea, Hanstholm, electrcty market, grd ntegraton, power output, predctablty, wave energy. I. ITRODUCTIO As wave energy technologes approach the commercal stage, t s necessary to nvestgate some of the ssues ahead the ntegraton of wave energy nto the electrc grd. Above all, the paper focuses on the role of wave energy predctablty wthn the current electrcty markets and ther establshed rules []. Transmsson System Operators (TSOs) have a major role n the functonng of electrcty markets. They are the natonal bodes responsble for operatng the grd and assurng the electrcty demand s fulflled. TSOs also publsh the dayahead load forecast and plan grd operaton before real-tme, generally one-day n advance. In the case of Denmark, the day-ahead electrcty market closes at 2 am. Thus, Energnet.dk as the Dansh TSO requres the predcton of the followng 2 to 36 hour electrcty generaton. Electrcty markets were frst desgned to accommodate conventonal power generaton. Besdes hydropower, the contrbuton from renewable energy sources was scarce. owadays, as the percentage of renewable generaton wthn the electrcty mx ncreases [2], the uncertanty on the planned generaton has also rsen. The reason s that some of the most promsng renewable energy sources such as wave power or wnd power are not entrely predctable. Ths partal unpredctablty s causng TSOs, producers and/or electrcty users large expendtures to cope wth the costs of the electrc system balancng mechansms [3]. Consequently, the paper examnes wave energy predctablty. It nvestgates the correlaton of forecast and buoy-measured wave data as well as the correlaton of forecast based and buoy-measured based theoretcal power productons of three wave energy converters (WECs).
The objectve of ths study s to provde some ntal ndcaton on the extent the power productons from WECs can be predcted to be ntegrated nto the day-ahead forecast of the day-ahead market. Moreover, wave energy forecast plays also a major role n the operaton of WECs. It allows estmatng and evaluatng future power producton of a gven WEC, plannng perods of tests and mantenance actvtes, and defnng the storm protecton strategy, f needed. The study s based on avalable smultaneous and colocated forecast and buoy-measured wave data from Hanstholm ste, Denmark, durng a 5-month perod. Also the power matrces of the selected devces form the bass of the study. The WECs chosen are Pelams [4], an offshore floatng heavng and ptchng artculated converter, Wave Dragon [5], an offshore floatng overtoppng technology and Wavestar [6], a near-shore mult-pont absorber. Ths paper presents the frst approach of the Dansh TSO towards the study of predctablty of WECs power output. The noveltes of ths paper are frst, comparng forecast based and buoy-measured based theoretcal power productons; second, consderng the separated as well as the combned power outputs of three dfferent WECs, and thrd, locatng the study n the orth Sea waters, an area wth ncreasng nterest on wave energy [7]. The content of the paper s as follows: ) Methodology of the study; ) Results of the study n terms of forecast accuracy of the wave parameters and of the theoretcal power productons of the devces; ) Dscusson of results and lmtatons of the study; v) Conclusons and further recommended work. The power output of a devce s also nfluenced by some of these envronmental features, the degree of nfluence dependng on the workng prncple. An accurate performance evaluaton requres the ncluson of several parameters although a WEC s also well defned by H m0 and T 02. As a result, ths study s based on records of H m0 and T 02. The maxmum wave heght H max has also been ncluded, snce ts evaluaton can lead to useful results on buoy measurement errors and WECs operaton and survvablty condtons. C. Study Locaton - Hanstholm The selected research ste s Hanstholm, at the west coast of Jutland, Denmark, n the Dansh part of the orth Sea. The mean energy flux s 6 kw/m at water depths of 2 to 30 meters, comng prmarly from western drecton, and the 0 years desgn H s s 6.6 meters [0-]. The wave clmate s characterzed by a wnd sea on top of a non-constant swell arrvng from the northern part of the Atlantc Ocean. The study refers to a pont approx..3 km offshore and at 7 m water depth (coordnates 8.582 E, 57.35 ). Fg. depcts the wave energy condtons at ths ste throughout the study perod, n terms of H m0, T 02 and the contrbuton of each sea state, n percentage, to the mean wave power n the study perod. The scatter dagram s based on buoy-measurements of H m0 and T 02 over 4 months. It shows a domnant wnd sea wth a peak at H m0 = 2.2 m and T 02 = 5.3 s and a secondary swell sea at H m0 = 4 m and T 02 = 6.5 s. II. METHODOLOGY A. Tme perod The analyss embraces three complete and non-consecutve months of wave measurements. The overall perod covers from end of October 200 to mddle of February 20; vald data s from 26/0 to 20//200, from /2/200 to 3/0/20 and from 6/0 to 09/02/20. All tme and dates are expressed n the Coordnated Unversal Tme (UTC) system. Generally at Hanstholm, January s the month wth the most energetc wave clmate, about 6 tmes more n terms of monthly mean wave power than the less energetc months, usually May, June and July [8]. Therefore, the tme perod consdered n ths study represents the most energetc season. B. Wave parameters Dfferent envronmental parameters such as wave heght, wave perod, wave drecton, wnd speed, wnd drecton, water depth or current speed fully characterze the envronmental condtons at a partcular locaton. However, as a frst analyss and at 7 meter water depths at Hanstholm, t s sutable to defne the wave resource by the sgnfcant wave heght H s and the zero crossng perod T z. These parameters can be approxmated by H m0 =4 m 0 and T 02 = (m 0 /m 2 ), respectvely [9]. Fg.. Scatter Dagram of Hanstholm throughout the study perod n terms of H m0, T 02 and contrbuton n percentage of each sea state to the mean wave power n the study perod. The wave condtons of the study perod provde a vald representaton of the long-term wave clmate at Hanstholm. However, the mean wave power n ths perod.e. 7.4 kw/m s hgher than the mean annual wave power.e. 6 kw/m, due to the strong seasonal varablty of the wave condtons at Hanstholm. Table I presents the probablty of occurrence of the dfferent wave parameters H m0, H max, T 02 and wave power P w at Hanstholm n ths perod. P w (power per unt of crest wdth) has been calculated accordng to the wave power densty formula smplfed for rregular waves under the deep water assumpton, whch s true at the selected locaton for the consdered wave perods
and wave lengths [2]. ρ (kg/m 3 ) represents the water densty g (m/s 2 ) the gravty acceleraton and T e the energy perod. Assumng a Person-Moskowtz spectral shape T e s related to T 02 by T e =.2 T 02 [0]. 2 g 2 W P H T () w m0 e 64 m Hanstholm locaton has been selected due to several postve reasons, although t also brngs some lmtatons. On one hand, there are comprehensve data sets of smultaneous and co-located half-hourly forecast and buoymeasured wave data. Moreover, there s an ncreasng nterest on the characterstcs at ths partcular locaton, snce a new wave energy test ste,.e. DanWEC, Dansh Wave Energy Centre [3] s beng developed. A :2 scale model of Wavestar and a :5 scale model of Dexa [4] are currently deployed there. These prototype tests can complement the current study by provdng actual power producton data. On the other hand, the wave energy potental at Hanstholm s lmted compared to other nterestng deployment stes. In addton, the three WECs selected have not been optmzed for the wave clmate of the orth Sea, charactersed by shorter perod waves than the Atlantc Ocean longer perod swells. D. Forecast and Buoy-Measured Data Forecast data has been calculated by the spectral wave module of MIKE 2 from the Dansh Hydraulc Insttute, a model based on the wave acton conservaton equaton. The servce s part of The Water Forecast program [5]. The forecast reaches 5 days nto the future, s calculated every 2 hours and provdes half-hourly records. Envronmental measurements have been provded by a Datawell Waverder buoy from The Dansh Coastal Authorty (.e. Kystdrektoratet). Data conssts of half-hour records of H m0, T 02 and H max. The data sets of forecast H m0 and T 02, and buoy-measured H m0 and T 02 have been used to develop tme seres of forecast P w and buoy-measured P w, respectvely, accordng to Eq.. A varable has been ntroduced nto the study to compare the accuracy of the forecast to the measured data. T-hour represents the forecast hour or the tme horzon, n hours, before real tme. In other words, t s the tme-span, n hours, between the forecast s calculated and the buoy measures the correspondng parameters. E. Statstcal parameters The verfcaton of forecast data aganst buoy-measured data has been evaluated by the statstcal parameters descrbed below, where MOD corresponds to modeled, calculated or forecast data and OBS to observed or buoy-measured data. The Mean value of observatons s defned as: Mean OBS (2) where corresponds to the number of vald observatons. The mean of dfference or Bas represents an error that remans prmarly constant n magntude for all forecasts. It s defned as: Bas ( MOD OBS) (3) The mean of absolute dfference or AME s defned as: AME ( MOD OBS ) The root mean square of dfference or RMSE s calculated assumng a normal dstrbuton and represents the standard devaton of the mean (confdence level of 68.27%). It s defned as: RMSE ( MOD OBS) The unbased scatter ndex or SI unbased s also calculated assumng a normal dstrbuton. It provdes a non-dmensonal measure of the error and s defned as: 2 ( MOD OBS Bas) SI unbased (6) Mean The correlaton coeffcent or CC ndcates the degree to whch the varaton n one parameter s reflected n the varaton of the other parameter. It s a non-dmensonal varable rangng from 0 to, the former ndcatng no correlaton between the two data sets and the latter perfect correlaton. It s defned as: CC ( MOD MOD) 2 2 ( OBS (4) (5) ( MOD MOD)( OBS Mean) (7) Mean) F. WECs Pelams, Wave Dragon and Wavestar To take advantage of the varablty of the wave energy resource along the coasts t s generally expected that several wave converson solutons reman attractve for the market. Moreover, to extend the scope of ths study towards dfferent WECs responses to the wave clmate as well as to consder the dfferences n the operatng condtons among the exstng WECs, three dfferent technologes have been selected for the study. These are: ) Pelams, a floatng heavng and ptchng converter. 2) Wave Dragon, an offshore floatng overtoppng devce. 3) Wavestar, a near-shore mult-pont absorber. Power productons of the three WECs have been modeled from forecast and buoy-measured wave data. Ths process has requred the applcaton of a transfer functon,.e. a power 2
matrx to represent the performance of the WEC at Hanstholm ste. In ths way, the records of forecast H m0 and T 02, and buoymeasured H m0 and T 02 along wth the power matrxes have been used to model tme seres data of forecast power producton (P prod ) and buoy-measured P prod, respectvely. Whereas Wavestar provded a power matrx partcularly developed for Hanstholm wave clmate, those for Pelams and Wave Dragon have been down-scaled from [6] to match the predomnant sea states (Table I) and to optmze ther P prod n the study perod. Table II presents the scale factor, man dmensons and the rated power of the three devces, as well as the desgn sea states.e. H m0 and T 02 where they reach full producton, and the operatng lmts of each devce (mnmum and maxmum H m0 and T 02 ). Table II shows Wavestar cuts-off producton n lower sea states than Pelams or Wave Dragon. Fg. 2 presents a comparson between the probablty of occurrence of dfferent sea condtons (defned by the contrbuton n percentage of H m0 and T 02 to the mean wave power) and power producton s dependency on these condtons. Fg. 2 shows that Wavestar has the best correlaton between maxmum P prod and probablty of occurrence of the wave parameter T 02. All power productons presented throughout the study are n terms of percentage of rated power,.e. normalzed P prod. G. Further Assumptons The followng assumptons have been made n the study: - The current delay n the forecast has been dsregarded. At the present tme, and due to the research purpose of ths study, the model delvers the forecast wth 9-hour delay. However, n real mplementaton of the forecast data ths delay can be easly reduced. - WECs P prod dependency on wave drectonalty has been neglected. - Real power producton data from the half scale Wavestar connected to the grd at Hanstholm has not been used n the study. All stated P prod are theoretcal and derved from the power matrxes. - Errors n the buoy acquston system have been dsregarded. TABLE I OCCURRECE OF WAVE PARAMETERS HM0, HMAX, T 02 AD PW AT HASTHOLM THROUGHOUT THE STUDY PERIOD Mean Max <% tme <0% tme <0% tme <% tme Days H m0.4 4.7 0.4 0.7 2.3 3.3 84 407 H max 2.3 8.5 0.7. 3.7 5.8 84 407 T 02 4.7 8.8 3. 3.8 5.7 6.6 84 407 P w (kw/m) 7.4 84.7 0.4.2 5.7 39.7 84 407 TABLE II SCALIG RATIO, DIMESIOS, RATED POWER, DESIG AD OPERATIG SEA STATES FOR PELAMIS, WAVE DRAGO AD WAVESTAR AT HASTHOLM Rato* (λ) Man dmensons* Rated power (kw) Desgn H m0 Desgn T 02 H m0 mn H m0 max T 02 mn T 02 max Pelams :.76 l=02 Ø= 2.3 03 3. 4.6 0.4 4.6 2.5 0 Wave Dragon :.76 l= 96 w=70 960 3 5 0.4 4. 2.6 0 Wavestar :2 --- Ø = 5 600 2.7 4.5 0.5 3 2 3 * Pelams and Wave Dragon scalng ratos are relatve to the Atlantc Ocean and Wavestar s to the orth Sea. l represents length, w wdth and Ø dameter. Fg. 2. Contrbuton, n percentage, of T 02 (a) and (c), and H m0 (b) to the mean wave power at Hanstholm throughout the study perod and normalsed power productons of Pelams (a), Wave Dragon (b) and Wavestar (c) n terms of T 02 (a) and (c), and H m0 (b). Wave Dragon performance s more dependent on the varatons of the wave heght whereas Pelams and Wavestar performances are more dependent on the perod.
III. RESULTS To nvestgate forecast accuracy of the WECs theoretcal power productons the predctablty of the typcal wave parameters s examned frst. Consequently, ths secton presents two sets of results. Frst, the error statstcs obtaned from the comparson of forecast H m0, H max, T 02 and P w and buoy-measured H m0, H max, T 02 and P w. Second, the error statstcs obtaned from the comparson of P prod based on forecast data and P prod based on buoymeasurements of each WEC and a combnaton of all of them. A. Predctablty of Wave Parameters Table III, Table IV, Table V and Table VI show the statstcal parameters, as defned n secton II-D, for H m0, H max, T 02 and P w, respectvely. Forecast accuracy s evaluated for T- hours embracng 0 to hour, 2 to 24 hours, 24 to 36 hours, 84 to 96 hours and 0 to 44 hours. T - hour (h) Mean TABLE III H M0 STATISTICAL PARAMETERS Bas AME RMSE SI unbased CC 0 < 2.44 0.8 0.25 0.3 0.7 0.93 3873 2 < 24.44 0.8 0.27 0.34 0.20 0.9 3849 24 < 36.44 0.7 0.28 0.36 0.22 0.89 3825 36 < 48.44 0.9 0.30 0.40 0.25 0.86 380 84 < 96.44 0.8 0.39 0.5 0.34 0.74 3705 0 < 44.44 0.20 0.35 0.47 0.30 0.80 9053 TABLE VI PW STATISTICAL PARAMETERS T - hour Mean Bas AME RMSE (h) (kw/m) (kw/m) (kw/m) (kw/m) SI unbased CC 0 < 2 7.40.56 2.52 4.64 0.59 0.9 2 < 24 7.4.68 2.79 5.00 0.63 0.90 24 < 36 7.45.49 2.96 5.9 0.67 0.88 36 < 48 7.45.53 3.2 5.70 0.74 0.83 84 < 96 7.46.33 4.7 7.42 0.98 0.68 0 < 44 7.40.74 3.80 6.89 0.90 0.76 The followng fgures present a comparson between forecast H m0 and buoy-measured H m0 durng the most energetc month (/2/200 to /0/20). Fg. 3 llustrates the forecast for a T-hour of 2 hours, Fg. 4 for a T-hour of 36 hours and Fg. 5 for a T-hour of 08 hours. ote the bg waves passng Hanstholm on ew Year s Eve. Fg. 3. H m0 comparson of measured (n red) and 2 hours forecast (n blue) TABLE IV HMAX STATISTICAL PARAMETERS T - hour (h) Mean Bas AME RMSE SI unbased CC 0 < 2 2.35 0.80 0.84 0.98 0.24 0.90 3873 2 < 24 2.35 0.8 0.87.03 0.27 0.88 3849 24 < 36 2.36 0.79 0.86.04 0.29 0.85 3825 36 < 48 2.35 0.82 0.89.09 0.3 0.83 380 84 < 96 2.35 0.8.00.24 0.40 0.70 3705 0 < 44 2.35 0.85 0.97.20 0.36 0.76 9053 Fg. 4. H m0 comparson of measured (n red) and 36 hours forecast (n blue) TABLE V T 02 STATISTICAL PARAMETERS T - hour (h) Mean Bas AME RMSE SI unbased CC 0 < 2 4.7-0.8 0.37 0.50 0.0 0.80 3873 2 < 24 4.7-0.6 0.39 0.52 0. 0.79 3849 24 < 36 4.7-0.7 0.42 0.55 0. 0.77 3825 36 < 48 4.7-0.7 0.44 0.57 0.2 0.74 380 84 < 96 4.7-0.9 0.5 0.67 0.4 0.63 3705 0 < 44 4.7-0.7 0.47 0.62 0.3 0.68 9053 Fg. 5. H m0 comparson of measured (n red) and 08 hours forecast (n blue)
Fg. 6 presents a comparson between forecast T 02 and buoy-measured T 02 and Fg. 7 between forecast based P w and buoy-measured based P w, durng the same month (/2/200 to 4/0/20) for a T-hour of 2 hours. Fg. 6. T 02 comparson of measured (n red) and 2 hours forecast (n blue) Fg. 7. P w comparson of measured (n red) and 2 hours forecast (n blue) The crcles n Fg. 3, Fg. 6 and Fg. 7 show the 3-day perod selected n the next secton to llustrate the evoluton of the power producton for the three devces. These partcular days provde a good representaton of the typcal operatng condtons at the research ste. B. Predctablty of WECs Power Producton Table VII presents the statstcal parameters evaluatng P prod based on forecast data and P prod based on buoymeasurements for each of the selected WECs and for the combnaton of the three of them. The 2 to 36 hours forecast has been consdered. The combned opton reflects the contrbuton of one normalsed unt of each technology. All results presented are non-dmensonal and thus, can be read as percentage of rated power. TABLE VII PELAMIS, WAVE DRAGO, WAVESTAR AD COMBIED ORMALISED P PROD STATISTICAL PARAMETERS THROUGHOUT THE STUDY PERIOD Mean Bas AME RMSE (-) (-) (-) (-) SI unbased Pelams 0.29 0.07 0. 0.5 0.44 90 Wave Dragon 0.28 0.04 0.09 0.5 0.52 90 Wavestar 0.39 0.04 0.5 0.24 0.62 90 Combned 0.32 0.05 0.0 0.4 0.4 90 Fg. 8 to Fg. 0 gve a graphcal representaton of the dfferences between forecast P prod and theoretcal P prod of Pelams, Wave Dragon, Wavestar and the combnaton of the three devces. The graphs cover a 3-day perod (23/2 to 25/2/200). Fg. 8 depcts the 2 hours forecast and Fg. 9 the 36 hours forecast for the power producton of Pelams, Wave Dragon and Wavestar. Fg. 0 llustrates the dfferences of the 2, 24 and 36 hours P prod forecast to the theoretcal P prod for the combnaton of the three devces. For comparson Fg. shows the varaton of the 2 hours forecast H m0, T 02 and P w and buoy-measured H m0, T 02 and P w over ths 3-day perod. ote that buoy-measured H m0, T 02 and P w vary around ther mean values, as shown n Table I. IV. DISCUSSIO Due to the scope of the paper only the results for a T-hour varyng from 2 to 36 hours are dscussed. A. Locaton The results presented n the study are totally dependent on the wave clmate of the chosen locaton. It s expected that a wave clmate characterzed by swell waves wll sgnfcantly mprove the accuracy n the predctons, snce swells are more regular compared to wnd waves. In wnd seas, where the correspondence between waves and wnd patterns reveals to be hgh [7], the short-term forecast errors n wnd are more reflected n wave predctons. B. Predctablty of Wave Parameters ) Sgnfcant wave heght spectral estmate H m0 : Table III shows the error statstcs obtaned from the comparson of forecast H m0 and buoy-measured H m0 for dfferent T-hours. The postve Bas ndcates a prevalent trend where the forecast overestmates the buoy-measured values. Then, an AME larger n magntude than the Bas denotes that also the opposte trend s found,.e. the forecast also underestmates the buoy-measured values, partcularly as T-hour ncreases (Fg. 3 to Fg. 5). RMSE ponts out that 68% of the forecasts are wthn ±0.35 meters of the Mean measured value of H m0,.e..44 meters. A 22% SI unbased llustrates an acceptable dsperson of the dstrbuton. Then, a CC of about 0.9 suggests a hgh correlaton between the two sets of compared values. In bref, results show that the agreement between the 2 to 36 hours H m0 forecast and H m0 buoy-measured data s good. 2) Maxmum wave heght spectral estmate H max : Table IV shows the error statstcs obtaned from the comparson of forecast H max and buoy-measured H max for dfferent T-hours. Although the statstcal results follow the same trend as H m0 the errors are always hgher. These errors are provded by the buoy-measured data. A known dsadvantage of the sphercal buoys (e.g. Datawell Waverder buoy) s that due to the sngle lne moorng, t crcles around the crests of steep waves and thus, does not reach the maxma n the surface elevaton [8].
Fg. 8. P prod based on buoy-measurements (sold lnes) and P prod based on forecast data (dashed lnes), n terms of percentage of rated power of Pelams (n blue), Wave Dragon (n red) and Wavestar (n green) for a T-hour of 2 hours over a 3-day perod (23/2 to 25/2/200). Fg. 9. P prod based on buoy-measurements (sold lnes) and P prod based on forecast data (dashed lnes), n terms of percentage of rated power of Pelams (n blue), Wave Dragon (n red) and Wavestar (n green) for T-hour of 36 hours over a 3-day perod (23/2 to 25/2/200). Fg 0. P prod based on buoy-measurements (sold lne) and P prod based on forecast data (dashed lnes), n terms of percentage of rated power of the combnaton of the three WECs, for a T-hour of 2 hours (dark blue), 24 hours (lght blue) and 36 hours (green) over a 3-day perod (23/2 to 25/2/200).
Fg. 7 llustrates the peaks n P w n comparson to the Mean average value of 7.4 kw/m. Ths dfference explans the hgh value of RMSE and SI unbased. In short, results show that P w forecast derved and P w buoymeasured derved are n good agreement for small P w values but not for larger ones. As a summary, wave parameters predctablty can be consdered accurate for H m0 and T 02, acceptable for H max and for values of P w close to the mean, and not very accurate for larger P w values. Fg. Evoluton of buoy-measured (sold lne) and 2 hours forecast (dashed lne) of H m0 (n blue), T 02 (n red) and P w (n green) over 23/2 to 25/2/200. 3) Zero crossng perod spectral estmate T 02 : Table V shows the error statstcs obtaned from the comparson of forecast T 02 and buoy-measured T 02 for dfferent T-hours. The negatve Bas ndcates a prevalent trend where the forecast underestmates the buoy-measured value. An AME more than twce the Bas denotes that the forecast overestmates the measured values as well. However, both the Bas and AME are small n magntude compared to the Mean. RMSE ndcates that 68% of the forecasts are wthn ±0.55 seconds of the Mean measured value of T 02,.e. 4.7 seconds. The graphcal comparson (Fg. 6) llustrates the small and very acceptable dsperson of the dstrbuton, whch les wthn small bounds (SI unbased of %). The correlaton between forecast and buoy-measured values (CC= 0.77) s lower than for H m0. Ths can be clearly seen n Fg. 6, where the pattern tendences of the buoymeasured values are not strctly followed by the forecasts. In summary, results show that T 02 forecast and T 02 buoymeasurements are n very good agreement but for CC. 4) Wave Power P w : Table VI shows the error statstcs obtaned from the comparson of forecast P w and buoymeasured P w for dfferent T-hours. In ths case, t s mportant to note the relaton of P w wth H m0 and T 02 (Eq.). The errors n H m0 get rased to the power of two and n T 02 to the power of one. The postve Bas reveals the strongest nfluence of H m0. It ndcates that the forecast overestmates the derved buoymeasured value. As happens also n the case of H m0 and T 02, AME s larger than the Bas, so the forecast also overestmates the buoy-measured values. Both Bas and AME are qute large n magntude compared to the Mean. RMSE ndcates that 68% of the forecasts are wthn ±5.2 kw/m of the Mean measured value of P w,.e. 7.4 kw/m. Ths value suggests a qute naccurate forecast; however, t s due to the peaks n P w, whch reaches 85 kw/m at certan perods of tme (Table I and Fg. 7). Smlarly, SI unbased shows 60% to 70% dsperson of the dstrbuton. On the contrary, the correlaton (CC= 0.88) between forecast and buoy-measured values s hgh, nduced by the hgh value of CC for H m0. C. Predctablty of WECs Power Producton ) Pelams, Wave Dragon and Wavestar: Table VII shows the error statstcs obtaned from the comparson of P prod based on forecast data and P prod based on buoy-measurements for the three devces. The fgures llustrate smlar trends n the statstcal parameters of each devce. However, for comparson note the Mean P prod of Wavestar s approx. 7% larger than that of Pelams and Wave Dragon. Forecast accuracy of Pelams P prod and Wave Dragon P prod are comparable. The man dfference s that whereas the SI unbased of Pelams (44%) s better than for Wave Dragon (52%) the relaton between AME and Mean producton favours Wave Dragon (32% versus 40% for Pelams). Then, Wavestar presents larger standard devaton (RMSE= 24% of the rated power) and dsperson (SI unbased = 62% of the rated power), although the Mean normalsed P prod reaches 32% of rated power. Its relaton between Mean and AME (38%) s comparable to the others. For all cases, the postve Bas suggests nfluence of H m0 forecast errors on the power producton calculatons. Then, the AME also ndcates the nfluence from T 02 forecast errors, partcularly for Wavestar. For the three devces, RMSE reveals to be qute hgh, especally compared to the other statstcal parameters. The explanaton s smlar as for P w, t s due to the nfluence of the peaks n the power producton durng fast changng wave condtons and more extreme events (Table I and Fg. 7). Above all, fgures show that predctons of Pelams, Wave Dragon and Wavestar power productons are acceptable. 2) Combned P prod : the last row of Table VII reveals the best forecast occurs when consderng the combned P prod of the three devces. The Bas, RMSE and SI unbased mprove compared to those of each sngle devce. Moreover, not only the statstcal parameters show a more accurate forecast but also a hgh combned Mean P prod. Above all, the combned producton provdes the best compromse between forecast accuracy, as for Pelams and Wave Dragon, and hgh mean producton, as for Wavestar. A good overvew of forecast accuracy of the WECs P prod can be found n Fg. 8 to Fg. 0. To compare these, Fg. shows the evoluton of the 2 hours forecast H m0, T 02 and P w and buoy-measured H m0, T 02 and P w over the same 3-day perod. The three wave parameters oscllate around ther mean values, gvng a qute
real representaton of the typcal sea states at Hanstholm durng a wnter month. Fg. 8 and Fg. 9 llustrate the dfferences between forecast P prod and theoretcal P prod of Pelams, Wave Dragon, Wavestar, for a T-hour of 2 hours and 36 hours, respectvely. The comparson of both fgures shows that the best forecast occurs for a T-hour of 2 hours. Here there are some perods where the predctons concde wth the theoretcal producton. Then, although the errors for the 36 hours forecast are hgher, n any case they exceed 30% of naccuracy. Wave Dragon shows the lowest errors among the three devces and Wavestar the largest. Ths can be explaned due to the more lmted workng condtons of Wavestar compared to Pelams and Wave Dragon (Table II). Fg. 0 depcts the 2, 24 and 36 hours P prod forecast and the theoretcal P prod for the combnaton of the three devces. For most samples the 2 hour forecast s the most accurate. Then, comparng Fg. 8 to the 2 hours forecast combned P prod (Fg. 0, dashed dark blue lne) and smlarly, Fg. 9 to the 36 hours forecast combned P prod (Fg. 0, dashed green lne), t can be concluded that Fg. 0 generally provdes smaller errors than Fg. 8 and Fg. 9. In other words, the combned power producton results n an overall better forecast accuracy. The global mprovement of the statstcal parameters by the combned power output confrms that the response of each WEC to the wave clmate s dfferent. Moreover, a relevant fndng s that the errors n the forecast of the wave parameters H m0 and T 02 do not accumulate but nstead cancel-out when calculatng the power producton of each devce. Ths s a major advantage to take nto account n the short future, where the dfferent solutons proposed for wave energy extracton should be consdered attractve for the electrcty market. To fnalze the dscusson, there are three mportant lmtatons to ths study. Frst, the selected WECs have not been desgned for the typcal wave clmate at Hanstholm but for hgher ones charactersed by longer perod swells, as n the Atlantc Ocean. Therefore, the performances of the devces at ths locaton are dfferent than from those expected at more powerful stes, and thus, ts predctablty mght be compromsed. Moreover, compettve comparsons of the performances of the devces should be avoded and cannot be conclusvely drawn from these results, as the P prod shown are merely theoretcal. The second lmtaton s that the use of three WECs reflects the power producton by those devces, whch embraces dfferent workng prncples, but not all exstng wave energy technologes. The thrd lmtaton s that ths study s not a resource assessment of Hanstholm ste or the orth Sea. The analysed data comprses of a 3-month perod. V. COCLUSIOS Examnng the accuracy of wave energy forecasts plays a major role n the ntegraton of wave energy nto the electrc grd. Wave energy predctablty s related to the electrcty market. Current rules of the Dansh day-ahead market requre the predcton of the followng 2 to 36 hours electrcty generaton. Accordng to ths, the paper has analysed the correlaton of: ) Forecast and buoy-measured wave parameters; ) Forecast based and buoy-measured based normalsed power productons of three WECs; ) Forecast based and buoy-measured based normalsed power productons of a combnaton of the three WECs. The smultaneous and co-located forecast and measured wave parameters at Hanstholm ste, Denmark, durng a noncontnuous autumn and wnter 3-month perod, along wth the power matrces of the devces, have formed the bass of the study. The selected WECs have been Pelams, an offshore floatng heavng and ptchng artculated devce, Wave Dragon, an offshore floatng overtoppng technology, and Wavestar, a near-shore mult-pont absorber. They have been chosen due to ther dfferences n ther workng prncples. Results ndcate an accuracy (n terms of unbased scatter ndex) n the 2 to 36 hours tme horzon forecast of: ) 22%, % and 68% for the wave parameters H m0, T 02 and P w, respectvely; ) 44%, 52% and 62% for the normalsed theoretcal power productons of Pelams, Wave Dragon and Wavestar, respectvely; wth normalsed mean power productons of 0.29, 0.28 and 0.39. ) 4% for the combned normalsed theoretcal power producton of the three devces, wth normalsed mean power producton of 0.32. The noveltes of ths study have been frst, comparng forecast based and buoy-measured based power productons; second, consderng the separated as well as the combned power output of three dfferent WECs, and thrd, locatng the study n the orth Sea waters, an area wth ncreasng nterest on wave energy. Two man conclusons can be drawn from the results: frstly, wave parameters such as H m0 and T 02 can be predcted accurately n the gven energetc sea condtons, and secondly, the combned power producton from dfferent wave energy technologes provdes the best compromse between forecast accuracy and hgh mean power producton. The latter fndng s partcularly mportant at ths stage of development of the wave energy sector: t reveals there wll probably be more than one establshed technology for wave energy utlzaton, t suggests to dversfy R&D grants among the dfferent technologes, t ndcates the strategy to follow wthn energy plannng processes and t provdes a good overvew on the parameters to be mproved to ncrease predctablty of WECs producton.
These conclusons of the paper suggest two further studes. Frst, the examnaton of the predctablty of combnatons of co-located WECs and wnd energy turbnes. Ths wll address the delay between wave and wnd energy and the comparson of the predctablty of both sources. The second study wll examne the error statstcs of the short-term (0-6 hours) forecast, n comparson to the analyzed day-ahead forecast. Ths topc s also of great mportance to TSOs electrc grd operaton. Furthermore, the on-gong prototype tests at Hanstholm can be used to complement the studes by provdng actual power producton data. Last but not least, further mprovement s expected on the knowledge of devce developers about the power producton of ther devces. Ths wll ultmately decrease the uncertanty on the power matrxes and thus, on the predctablty of the actual power to be produced by the devces. evertheless, current rules of the electrcty market may have to change to accommodate larger amounts of renewable sources wthout ncreasng balancng costs. ACKOWLEDGMET The frst author gratefully acknowledges the fnancal support from the European Commsson through the 7th Framework Programme (the Mare Cure Intal Tranng etwork WaveTran2 project, grant agreement number 2544) whch made ths work possble. The authors are also very grateful to Pelams, Wave Dragon and Wavestar, whose nputs to the study have been crucal. Measurements at Hanstholm have been made avalable courtesy of Kystdrektoratet, Denmark. REFERECES [] ord Pool Spot, "The ordc Electrcty Exchange and the ordc Model for a Lberalsed Electrcty Market," ord Pool Spot, Denmark, 2009. [2] EREC, "Mappng Renewable Energy Pathways towards 2020," European Renewable Energy Councl (EREC), 20. [3] IEA, "Innovatve Electrcty Markets to Incorporate Varable Producton," IEA Renewable Energy Technology Deployment, 2008. [4] (20) Pelams webste [Onlne]. Avalable: http://www.pelamswave.com/. [5] (20) Wave Dragon webste [Onlne]. Avalable: http://www.wavedragon.net. [6] (20) Wavestar webste [Onlne]. Avalable: http://www.wavestarenergy.com/. [7] H.C. Soerensen and J. Fernandez Chozas, "The Potental for Wave Energy n the orth Sea," Internatonal Conference on Ocean Energy (ICOE), Span, 200. [8] Ramboll, "Kortlægnng af Bølgeenergforhold den Danske del af ordsøen," Ramboll, Dansk Hydraulsk Insttut, Danamrsk Meteorologske Insttut, 999. [9] Ramboll, "Bølgekraft - forslag tl forsoeg og rapporterng," Ramboll, 999. [0] K. elsen and T. Pontes, "Generc and Ste-related Wave Energy Data," Fnal techncal report, OES-IEA Document o: T02-.., 200. [] L. Marghertn et al., "Avalable wave power n the vcnty of Hanstholm harbor and Dansh Wave Energy Center (DanWEC)," Submtted to Renewable Energy Journal, March 20. [2] M.E. McCormck, "Ocean wave energy converson," John Wley & Sons Inc., 98. [3] (20) Dansh Wave Energy Centre webste. [Onlne]. Avalable: http://www.danwec.com/. [4] (20) DEXA webste. [Onlne]. Avalable: http://www.dexa.dk/ [5] J. Krkegaard et al., "Metocean forecastng for ports and termnals," Port Infraestructure Semnar, The etherlands, 200. [6] ECI, Varablty of UK Marne Resources, Envronmental Change Insttute, Unversty of Oxford, The Carbon Trust, 2005. [7] F. Fusco, G. olan and J.V. Rngwood, "Varablty reducton through optmal combnaton of wnd/wave resources - An Irsh case study," Energy 35, pp. 34-325, 200. [8] L.H. Holthujsen, "Waves n Oceanc and Coastal Waters," Cambrdge, 2007. [9] H. C. Soerensen et al., "Bølgekraftanlæg ved Horns Rev Screenng (Wave energy deployment at Horns Rev Wnd Farm," (partly n Dansh), Copenhagen, 2005. [20] M. Rugbjerg, O.R. Sørensen and V. Jacobsen, "Wave forecastng for offshore wnd farms," 9th Internatonal Workshop on Wave Hndcastng and Forecastng, Canada, 2006. [2] E.D. Stoutenburg,. Jenkns, M.Z. Jacobson, "Power Output Varablty of Co-located offshore wnd turbnes and wave energy converters n Calforna," Renewable Energy, 200. [22] R. Gross, et al., "Renewables and the grd: understandng ntermttency," Energy 60, pp. 3-4. Proceedngs of the Insttuton of Cvl Engneers, 2007.