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 Accepted author manuscrpt, peer revewed verson 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: January 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 day-ahead electrcty markets. 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 forecast horzon, the accuracy n the predctons (n terms of scatter ndex) of the sgnfcant wave heght, zero crossng perod and wave power are 22%, % and 74%, respectvely; and the accuracy n the predctons of the normalsed theoretcal power outputs of Pelams, Wave Dragon and Wavestar are 37%, 39% and 54%, 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 markets, grd ntegraton, power output, predctablty, wave energy. I. ITRODUCTIO As wave converson technologes approach the commercal stage, t s necessary to nvestgate some of the ssues ahead the ntegraton of wave power nto the electrc grd. Above all, the paper focuses on the role of wave energy predctablty wthn 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 hours 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 waves 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). Corrected verson of June 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20
The objectve of ths study s to provde some ntal ndcaton on the extent the power productons from WECs can be predcted 2 to 36 hours ahead for day-ahead markets. Moreover, waves forecasts play also a major role n the operaton of WECs. It allows estmatng and evaluatng future power productons of a 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, examnng wave parameters predctablty; second, comparng forecast based and buoy-measured based theoretcal power productons; thrd, consderng the separated as well as the combned power outputs of three dfferent WECs, and fourth, 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 wave parameters and of forecast accuracy of 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 long term mean energy flux s estmated at 7 kw/m at water depths of 7 meters comng prmarly from West-orth-West and West drecton, and the 0 years desgn wave heght 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..5 km offshore and at 7 m water depths (coordnates 8.582 E, 57.35 ). Fg. depcts the wave 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 buoymeasurements 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 peak 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 tmes 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, Aprl, 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, t s sutable to defne the wave resource by the sgnfcant wave heght H s and the zero crossng perod T z. These parameters have been approxmated by H m0 and T 02, 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, 8.9 kw/m, s hgher than the mean annual wave power, 7 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 wave at Hanstholm n ths perod. P wave (power per unt of crest wdth) has been calculated accordng to the wave power densty formula: Corrected verson from July 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20
P wave ( W / m) gh 6 2 m 0 C where C g s the group velocty, defned by: 2kd gte C ( m / s) tanhkd g 2 snh2kd 2 k (m - ) = 2π/L s the wave number L = g*t e 2 /(2π)* tanh(kd) s the wave length For Hanstholm the followng values have been consdered: ρ salt water = 027 kg/m 3 represents the water densty consderng an average water salnty concentraton of 33 ppm and an average water temperature of 7 C. g = 9.82 m/s 2 represents the gravty acceleraton d = 7.5 m represents the water depth T e =.2T 02, represents the energy perod. The equalty s true assumng a Person-Moskowtz spectral shape [0]. 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. A new wave energy test ste named DanWEC, the Dansh Wave Energy Centre [2] has been establshed, where a :2 scale model of Wavestar and a :5 scale model of Dexa Wave [3] are currently deployed. These prototype tests can complement the present study by provdng actual power producton data. On the other hand, the wave 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 Wave forecasts have 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 [4]. The forecast reaches 5 days nto the future, s calculated every 2 hours and provdes half-hour records of the man wave parameters wth 2 decmals resoluton. 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 wth 2 decmals resoluton. 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 wave and buoy-measured P wave, respectvely. A varable has been ntroduced nto the study to compare the forecasts 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 g s calculated and the buoy measures the correspondng parameters. E. Qualty ndces Verfcaton of forecast data aganst buoy-measured data can be quantfed by the qualty ndces 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 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) The mean of absolute dfference or MAE s defned as: ( MOD OBS MAE ) 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: SI unbased Mean 2 ( MOD OBS Bas ) 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 MOD)( OBS MOD) 2 ( OBS 2 Mean) Mean) 2 Corrected verson from July 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20
F. Wave converters Pelams, Wave Dragon and Wavestar To take advantage of the varablty of the wave 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 (P prod ) 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 matrx that represents the performance of the WEC at Hanstholm. 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 of forecast P prod and buoymeasured 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 [5] 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 peak 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. Throughout the study the power productons of the three WECs are gven as percentages of peak power,.e. as normalzed or non-dmensonal values. TABLE I OCCURRECE OF WAVE PARAMETERS HM0, HMAX, T 02 AD PWAVE 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 3.7 87 457 H max 2.4 8.5 0.7. 3.8 6.0 87 457 T 02 4.7 8.8 3. 3.8 5.7 6.7 87 457 P wave (kw/m) 8.9 98.6 0.4.3 9.6 58.4 87 457 TABLE II SCALIG RATIO, DIMESIOS, PEAK POWER AD DESIG AD OPERATIG SEA STATES FOR PELAMIS, WAVE DRAGO AD WAVESTAR AT HASTHOLM Rato* (λ) Man dmensons* Peak 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 00 3. 4.6 0.4 5 2.5 0 Wave Dragon :.76 l= 96 w=70 000 3 5 0.4 5 2.6 0 Wavestar :2 --- Ø = 5 600 2.5 3.4 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. (a) (b) (c) Fg. 2. Contrbuton, n percentage, of T 02 and H m0 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)-(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. Corrected verson from July 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20
G. Further Assumptons - The current delay n the forecast has been dsregarded. At present, due to the research purpose of ths study, the model delvers the forecast wth 9-hour delay. In real mplementaton of forecast data ths delay can be reduced. - Errors n the buoy acquston system have been dsregarded. - WECs power producton dependency on wave drectonalty has been neglected. - Real power producton data from the half scale Wavestar operatng at Hanstholm have not been used n the study. All stated power productons are theoretcal and derved from the power matrxes. III. RESULTS To nvestgate forecast accuracy of 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 wave and buoy-measured H m0, H max, T 02 and P wave. Second, the error statstcs obtaned from the comparson of P prod based on forecast data and P prod based on buoy-measurements of each WEC and of a combnaton of them. A. Predctablty of Wave Parameters Table III to Table VI show the qualty ndces, as defned n secton II-D, for H m0, H max, T 02 and P wave, 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) TABLE III HM0 QUALITY IDICES THROUGHOUT THE STUDY PERIOD Mean Bas MAE RMSE SI unbased CC 0 < 2.5 0.9 0.25 0.32 8% 0.94 405 2 < 24.5 0.9 0.27 0.34 20% 0.9 399 24 < 36.5 0.7 0.29 0.37 22% 0.89 3967 36 < 48.5 0.8 0.30 0.40 25% 0.86 3943 84 < 96.5 0.8 0.40 0.54 35% 0.72 3847 0 < 44.5 0.20 0.36 0.48 30% 0.79 4527 T - hour (h) TABLE IV HMAX QUALITY IDICES THROUGHOUT THE STUDY PERIOD Mean Bas MAE RMSE SI unbased CC 0 < 2 2.4 0.82 0.85 0.99 23% 0.92 405 2 < 24 2.4 0.82 0.87.02 25% 0.90 399 24 < 36 2.4 0.80 0.86.04 28% 0.87 3967 36 < 48 2.4 0.82 0.89.08 30% 0.85 3943 84 < 96 2.4 0.80.00.25 40% 0.69 3847 0 < 44 2.4 0.85 0.97.20 36% 0.77 4527 T - hour (h) TABLE V T 02 QUALITY IDICES THROUGHOUT THE STUDY PERIOD Mean Bas MAE RMSE SI unbased CC 0 < 2 4.7-0.7 0.36 0.49 0% 0.8 405 2 < 24 4.7-0.6 0.38 0.5 0% 0.80 399 24 < 36 4.7-0.7 0.42 0.55 % 0.77 3967 36 < 48 4.7-0.7 0.43 0.56 % 0.75 3943 84 < 96 4.7-0.20 0.5 0.68 4% 0.62 3847 0 < 44 4.7-0.8 0.47 0.62 3% 0.68 4527 TABLE VI PWAVE QUALITY IDICES THROUGHOUT THE STUDY PERIOD T - hour Mean Bas MAE RMSE (h) (kw/m) (kw/m) (kw/m) (kw/m) SI unbased CC 0 < 2 8.8.96 3.5 6.42 69% 0.9 2 < 24 8.8.94 3.33 6.28 68% 0.90 24 < 36 8.9.62 3.59 6.70 73% 0.86 36 < 48 8.9.58 3.88 7.26 80% 0.82 84 < 96 8.9.6 5.3 9.68 08% 0.64 0 < 44 8.9.8 4.62 8.82 97% 0.75 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 2/2/200 and on ew Year s Eve. Fg. 3. H m0 comparson of measured (n red) and 2-hour forecast (n blue) Fg. 4. H m0 comparson of measured (n red) and 36-hour forecast (n blue) Corrected verson from July 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20
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. Fg. 5. H m0 comparson of measured (n red) and 08-hour forecast (n blue) Fg. 6 presents a comparson between forecast T 02 and buoy-measured T 02 and Fg. 7 between forecast based P wave and buoy-measured based P wave, 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-hour forecast (n blue) Fg. 7. P wave comparson of measured (n red) and 2-hour 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 productons for the three devces. These days provde a good representaton of the typcal operatng condtons at the research ste. B. Predctablty of WECs Power Producton To evaluate power productons predctablty normalzed qualty ndces are used, whch are normalzed n terms of peak power (Table II). They are ndcated by an at the begnnng of the parameter (.e. Bas, MAE, RMSE). Table VII presents the qualty ndces evaluatng P prod based on forecast data and P prod based on buoy-measurements TABLE VII PELAMIS, WAVE DRAGO, WAVESTAR AD COMBIED ORMALISED P PROD QUALITY IDICES THROUGHOUT THE STUDY PERIOD Mean Bas MAE RMSE SI unbased Pelams 0.33 0.08 0. 0.4 0.37 90 Wave Dragon 0.33 0.04 0.09 0.3 0.39 90 Wavestar 0.44 0.04 0.5 0.24 0.54 90 Combned 0.37 0.05 0. 0.4 0.36 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 wave and buoy-measured H m0, T 02 and P wave over ths 3-day perod. ote that buoy-measured H m0, T 02 and P wave 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 on predctablty of wave parameters and power productons are dependent on the wave clmate of the chosen locaton. A wave clmate characterzed by swells wll sgnfcantly mprove the accuracy n the predctons, snce swells are more regular compared to wnd seas. In a wnd sea, where the correspondence between waves and wnd patterns reveals to be hgh [6], 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, a MAE 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..5 meters. Corrected verson from July 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20
Fg. 8. P prod based on buoy-measurements (sold lnes) and P prod based on forecast data (dashed lnes), n terms of percentage of peak 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 peak 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 peak 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). Corrected verson from July 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20
A 22% SI unbased llustrates an acceptable dsperson of the dstrbuton. Then, a CC of 0.89 suggests a hgh correlaton between the two sets of compared values. In bref, results show that the agreement between H m0 forecasts 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. Errors for H max forecastng are always hgher than for H m0, although the qualty ndces follow the same trend.. These errors may be 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 [7]. In ths case, t s mportant to note the relaton of P wave wth H m0 and T 02. 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, MAE s larger than the Bas, so the forecast also underestmates the buoy-measured values. Both Bas and MAE are qute large n magntude compared to the Mean. RMSE ndcates that 68% of the forecasts are wthn ±6.8 kw/m of the Mean measured value of P wave,.e. 8.9 kw/m. Ths value suggests an naccurate forecast; however, t s due to the peaks n P wave, whch can reach up to 99 kw/m at certan perods (Table I and Fg. 7). Smlarly, the SI unbased shows a 75% dsperson of the dstrbuton. On the contrary, the correlaton (CC= 0.86) between forecast and buoy-measured values s hgh, nduced by the hgh CC of H m0. Fg. 7 llustrates the peaks n P wave n comparson to the Mean average value of 8.9 kw/m. Ths dfference explans the hgh value of RMSE and SI unbased. In short, results show that P wave forecast derved and P wave buoy-measured derved are n good agreement for small P wave 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 wave close to the mean, and not very accurate for larger P wave values. C. Predctablty of WECs Power Producton Fg. Evoluton of buoy-measured (sold lne) and 2-hour forecast (dashed lne) of H m0 (blue), T 02 (red) and P wave (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. A MAE more than twce the Bas denotes that the forecast also overestmates the measured values. However, both the Bas and MAE 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 wave : Table VI shows the error statstcs obtaned from the comparson of forecast P wave and buoymeasured P wave for dfferent T-hours. ) Pelams, Wave Dragon and Wavestar: Table VII shows the error statstcs obtaned from the comparson of normalsed P prod based on forecast data and normalsed P prod based on buoy-measurements for the three devces. The fgures llustrate smlar trends n the qualty ndces of each devce. However, for comparson note the normalsed mean producton of Wavestar s approx. 7% larger than that of Pelams and Wave Dragon. Forecast accuracy of Pelams and Wave Dragon producton are comparable. The man dfference s that whereas the SI unbased of Pelams (37%) s better than for Wave Dragon (39%), the MAE favours Wave Dragon (9% versus % for Pelams). Then, Wavestar presents larger standard devaton (RMSE= 24%) and dsperson (SI unbased = 54%), although the normalsed mean producton reaches 44% of peak power. Hence, MAE (5%) s comparable to the others. In the three cases, the postve Bas suggests an nfluence of H m0 forecast errors on the power producton calculatons. The MAE also ndcates the nfluence from T 02 forecast errors, partcularly for Wavestar. For the three devces, RMSE reveals to be hgh, especally compared to the other error statstcs. The explanaton s smlar as for P wave, 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). Corrected verson from July 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20
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 producton of the three devces. The Bas, RMSE and SI unbased mprove compared to those of each sngle devce. Moreover, not only the qualty ndces show a more accurate forecast but also a hgh combned mean producton. 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 wave and buoy-measured H m0, T 02 and P wave over the same 3-day perod. The three wave parameters oscllate around ther mean values, provdng a 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 and 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-hour forecast are hgher, they do not 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-hour forecast combned P prod (Fg. 0, dashed dark blue lne) and smlarly, Fg. 9 to the 36-hour 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 error statstcs 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 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 been desgned for more energetc wave clmates than at Hanstholm Therefore, the performances of the devces at ths locaton are dfferent than from those expected at more powerful stes, and thus, ther predctablty mght be compromsed. Moreover, comparsons among the performances of the devces should be avoded and cannot be conclusvely drawn from these results, as the power productons 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 converson technologes. The thrd lmtaton s that ths study s not a resource assessment of Hanstholm ste nor of the orth Sea. ote the analysed data comprse 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. Waves 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 accuraces (n terms of unbased scatter ndex) n the 2 to 36 hours forecast horzon of: ) 22%, % and 74% for the wave parameters H m0, T 02 and P wave, respectvely; ) 37%, 39% and 54% for the normalsed theoretcal power productons of Pelams, Wave Dragon and Wavestar, respectvely; wth normalsed mean power productons of 0.33, 0.33 and 0.44. ) 36% for the combned normalsed theoretcal power producton of the three devces, wth a normalsed mean power producton of 0.37. The noveltes of ths study have been frst, examnng wave parameters predctablty; second, comparng forecast based and buoy-measured based power productons; thrd, consderng the ndvdual as well as the combned power output of three dfferent WECs, and fourth, locatng the study n the orth Sea waters, an area wth ncreasng nterest on wave energy. Corrected verson from July 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20
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, "Revew on avalable nformaton on waves n the DanWEC area, (DanWEC Vækstforum 20)," DCE Techncal Report o. 35, Aalborg Unversty, 202. [2] (20) Dansh Wave Energy Centre webste. [Onlne]. Avalable: http://www.danwec.com/. [3] (20) DEXA webste. [Onlne]. Avalable: http://www.dexa.dk/ [4] J. Krkegaard et al., "Metocean forecastng for ports and termnals," Port Infraestructure Semnar, The etherlands, 200. [5] ECI, Varablty of UK Marne Resources, Envronmental Change Insttute, Unversty of Oxford, The Carbon Trust, 2005. [6] 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. [7] L.H. Holthujsen, "Waves n Oceanc and Coastal Waters," Cambrdge, 2007. [8] H. C. Soerensen et al., "Bølgekraftanlæg ved Horns Rev Screenng (Wave energy deployment at Horns Rev Wnd Farm," (partly n Dansh), Copenhagen, 2005. [9] M. Rugbjerg, O.R. Sørensen and V. Jacobsen, "Wave forecastng for offshore wnd farms," 9th Internatonal Workshop on Wave Hndcastng and Forecastng, Canada, 2006. [20] 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. [2] R. Gross, et al., "Renewables and the grd: understandng ntermttency," Energy 60, pp. 3-4. Proceedngs of the Insttuton of Cvl Engneers, 2007. Corrected verson from July 202 of the paper wth the same ttle presented at the European Wave and Tdal Energy Conference, EWTEC, 20