Comparison of Different Techniques for Offshore Wind Farm Reliability Assessment

Transcription

1 6 th Internatonal Worksho on Large-Scale Integraton of Wnd Power and Transmsson Networks for Offshore Wnd Farms Comarson of Dfferent Technques for Offshore Wnd Farm Relablty Assessment Barbers Negra N., Holmstrøm O., Bak-Jensen B., Sørensen P. Abstract -- The ncrease n wnd ower caacty nstalled worldwde has resulted n the necessty to nclude wnd farms n ower system relablty assessment. Esecally, the nstallaton of large offshore unts connected drectly to the transmsson system has created the necessty of accountng for new asects n the analyss. Varous studes have been erformed on the toc and many relevant factors of nfluence have been hghlghted, but a comlete assembly of all factors together has not been consdered yet. Ths aer focuses on the comarson of dfferent aroaches for frequency and duraton relablty assessments of offshore wnd farms. The objectve of the aer s to evaluate the most effcent technque, n order to reresent a wnd farm n the most realstc way and to erform a broad range of studes. Dfferent asects that nfluence the analyss are ncluded n the aer, such as wnd seed varablty and randomness, system comonents, (wnd turbnes, nternal grd cables and connectors to shore) falures and nstallaton layouts. Two man aroaches have been consdered n ths aer: One based on a sequental Monte Carlo smulaton and one based on analytcal methods wth frequency and duraton (F&D) analyss. The latter uses a robablstc aroach to defne mathematcal models of the system elements for calculatng the outut values, whereas the frst model defnes randomly the behavour of each element for a number of samled years and fnal results are evaluated as mean values. The comuted results refer to the yearly outut ower and the caacty factor of the wnd farm: These values, together wth the requred comutaton tme and feasble future studes, are used n order to comare the effcency and strengths of the two technques. Furthermore, the ossblty of dstngushng and evaluatng effects of extreme wnd condtons on the generaton has also been used as a crteron n the comarson. Index Terms -- Offshore Wnd Farm, Power System Relablty, Monte Carlo Smulaton, Analytcal Method, Wnd Seed Tme Seres E I. INTRODUCTION LECTRICITY lays an mortant role n many human actvtes today and the nterest n ensurng safe and secure electrcty suly at reasonable costs has radly Ths work s art of the roject Offshore wnd ower Research related bottlenecks and was funded by Dansh Research Agency ( ), Elsam Engneerng A/S and the Dansh Academy of Wnd Energy (DAWE). N. Barbers Negra s an ndustral Ph.D. wth Elsam Engneerng A/S a art of Dong Energy, Denmark (hone: ; e-mal: nbn@ elsameng.com). O. Holmstrøm s wth Elsam Engneerng A/S a art of Dong Energy, Denmark (e-mal: oho@elsam-eng.com). B. Bak-Jensen s an Assocate Professor at Aalborg Unversty, Denmark (e-mal: bbj@et.aau.dk). P. Sørensen s wth Rsø Natonal Laboratory, Rosklde, Denmark (e-mal: oul.e.soerensen@rsoe.dk). ncreased n the ast 50 years. For ths reason, relablty ssues reresent one of the man asects to consder, when a ower system has to be both lanned and oerated. The term relablty has dfferent defntons, deendng on the urose of the analyss: In a general sense, t ndcates the overall ablty of the system to erform ts functon adequately, for the erod of tme ntended, under the oeratng condtons ntended []. Ths defnton can be aled to ower system analyss: In ths case, the evaluaton may be erformed usng robablstc solutons, whch have evolved n the last 30 years [2]. These aroaches can rovde meanngful nformaton that can be used n desgn, resource lannng and allocaton, as they consder robablstc asects of the system. Two man technques have been develoed so far, analytcal methods and Monte Carlo smulatons, and both solutons can be very owerful wth the roer alcatons. For general uroses, a comlete ower system can be categorsed nto three functonal zones: Generaton, transmsson and dstrbuton. Based on ths classfcaton, a ower system s usually dvded nto three herarchcal levels (HL) for relablty studes [3]: HLI, whch s manly concerned wth assessng the amount of generatng caacty that must be nstalled n order to satsfy the system load; HLII, whch refers both to generaton and transmsson systems and focuses on the comoste roblem of assessng the generaton and transmsson facltes n regard to ther ablty to suly the demanded energy adequately; HLIII, whch adds the dstrbuton segment to the HLII analyss and s usually studed to obtan sutable ndces at actual consumer load onts. Besde these standard analyses, t must be consdered that ower systems have evolved towards a new structure durng the last 5 years [3]. The nstallaton of dstrbuted generaton unts and renewable sources have created a number of new factors to take nto account. In relaton to relablty, these asects have ntroduced elements, such as varablty and randomness of fuel avalablty (e.g. wnd or sun) and control of the generaton managed by rvate oerators, whch nvolves new challenges, that ower system owners have to consder n order to avod roblems durng the normal oeraton of the system [3]. In relaton to wnd generaton, onshore nstallatons have wdely ncreased n the ast 20 years, but many countres have already moved ther nterest to offshore locatons due to the congeston of onshore stes. Offshore nstallatons can rovde

2 6 th Internatonal Worksho on Large-Scale Integraton of Wnd Power and Transmsson Networks for Offshore Wnd Farms 2 an ncrease n roducton due to better wnd condtons of the locaton, however, new drawbacks must be taken nto account. Frst of all, offshore stes can reresent a roblem for rear/mantenance actons durng erods of harsh weather. Furthermore, they are exected to have larger sze than onshore nstallatons, and, due to the varablty of the wnd, ths may cause roblems n ower system oeratons. In the followng lst based on the avalable lterature on the toc, a number of asects that must be consdered n connecton wth wnd farm relablty assessment are hghlghted: ) Smulaton of wnd seed 2) Wake effects 3) Wnd turbne technology 4) Offshore envronment 5) Dfferent wnd seeds n the nstallaton ste 6) Power collecton grd n the wnd ark 7) Correlaton of outut ower for dfferent wnd farms 8) Grd connecton confguraton 9) Hub heght varatons Many of the asects are relevant for both onshore and offshore nstallatons, but some of them (onts 4, 5, 6, 7) have relevance manly n connecton wth offshore condtons, as dscussed n [4] and [5]. In ths aer, two dfferent robablstc technques are comared n order to evaluate the ower system relablty wth the ncluson of a large amount of offshore wnd energy: One technque s based on an analytcal method wth frequency and duraton (F&D) analyss, whereas the other technque s based on sequental Monte Carlo smulaton. Both methods are based on tme-deendent asects (F&D or sequental), as the wnd generaton s charactersed by daly and seasonal varatons. The assessment s erformed by comutng a number of ndces, later resented n ths aer, n order to quantfy the value of the generated energy. Moreover, asects such as the requred comutaton tme, feasble future studes and the ossblty of dstngushng and evaluatng effects of extreme wnd condtons on the generaton are used n order to comare effcency and strengths of the two technques. In secton II of ths aer, the two methods used for the comarson are brefly descrbed, whereas n secton III the analysed system and the comuted results are resented together wth the comarson of the technques. In the last secton, conclusons to the comarson are gven. II. ANALYSED TECHNIQUES As revously mentoned, two methods are comared n ths aer n order to rovde frequency and duraton assessment of offshore wnd farm relablty: One method s based on sequental Monte Carlo smulaton and one method s based on an analytcal aroach wth F&D analyss. Both technques requre dfferent defntons and assumtons n order to erform the evaluatons; however, t s ossble to consder some common asects that are relevant for the resented calculatons. The calculaton erod s chosen equal to year wth hourly ste (.e hours). Comonents of the wnd farm ncluded n the analyss are wnd turbnes, cables of the nternal grd and connectors to shore. All system comonents are reresented by a two-state model,.e. each comonent s ether n full servce or out of servce [2]. Furthermore, for the defnton of the model, each comonent s charactersed by ts falure rate (λ) and ts Mean Tme To Rear (MTTR). In order to translate wnd seeds nto the ower doman, the wnd turbne s charactersed by a ower curve, that can be rovded ether by a manufacture or by a set of equatons, as exressed n [6]. In the resented work, wnd turbne features are based on a Vestas V90-3MW machne. The wnd farm s reresented by assocatng a wnd seed model to the system comonent avalablty descrton. In order to defne the number of wnd turbnes effectvely avalable (.e. number of wnd turbnes connected to the ont of common coulng PCC and n servce), a seudo breadth frst search (PBFS) method s used [7]. Ths aroach roduces the lst of nodes n the wnd farm that are connected to the PCC as outut: If a node s n the lst and an avalable wnd turbne s connected to t, the generaton of the node s added to the total wnd farm outut ower. The use of ths aroach may ncrease the comutatonal tme of the rocess: For ths reason, the PBFS method s utlsed only f, n two followng hours, there s a change n the current wnd farm confguraton (.e. the number of effectvely avalable wnd turbnes changes due to falure/rear of a cable or a connector to shore). Nether comonent overloadng ssues nor wnd farm nternal losses are ncluded n the study. These asects can be comuted by load flow calculatons: They may be relevant for large-scale nstallatons and they must be taken nto account, f the wnd farm s used for HLII analyss. Snce the urose of ths aer s only to evaluate the wnd farm generaton, load flow calculatons are not ncluded n order to avod a huge comutatonal tme. However, some consderatons on ths toc can be found at the end of secton III.B. For the calculaton resented n ths aer, wnd seed measurements are obtaned from 7-year data recorded at the Horns Rev wnd farm locaton, Denmark. Data are recorded wth 0-mnutes average from the 4 May 999 to the 3 May 2006: The amount of data, whch should be equal to , s due to some falures n the measurement equment. Calculatons are erformed by a Pentum 700 MHz and the software used s Matlab, verson 7.. Wth these defntons and the alcaton of the two technques, a wnd farm model s develoed and t can be ncluded n any knd of relablty assessment, such as HLI, HLII or HLIII. In order to erform the comarson of the two methods, a number of ndces that quantfes the wnd generaton are used: ) IWP (Installed Wnd Power) s the sum of the nomnal

3 6 th Internatonal Worksho on Large-Scale Integraton of Wnd Power and Transmsson Networks for Offshore Wnd Farms 3 ower of all the wnd turbnes n the wnd farm; 2) IWE (Installed Wnd Energy) s the roduct of the nstalled caacty and the number of hours n the erod of nterest; 3) EAWE (Exected Avalable Wnd Energy) s the sum of the energes that the comlete number of nstalled wnd turbnes roduces n the erod (no comonent falures are consdered here) as a functon of the wnd seed; 4) EGWEWTF (Exected Generated Wnd Energy Wth Wnd Turbne Falure) s the sum of the energes that the comlete number of nstalled wnd turbnes roduces n the erod ncludng wnd turbne falures; 5) EGWE (Exected Generated Wnd Energy) s the sum of the energes that all effectvely avalable (deendant on comonent falures) wnd turbnes roduce n the erod; 6) CF (Caacty Factor) s the rato of EGWE to IWE. 7) GR (Generaton Rato) s the rato of the ower delvered to the PCC to the ower njecton generated by the wnd farm (.e. avalable ower deendant on the current wnd seed). Moreover, the requred comutaton tme, feasble future studes and the ossblty of dstngushng and evaluatng effects of extreme wnd condtons on the generaton are used as crtera n the comarson. In the two followng sectons, the two technques used n ths aer for the comarson are brefly descrbed hghlghtng ther most relevant asects. A. Analytcal method When an analytcal aroach s used for relablty assessment, the system under analyss s usually reresented by mathematcal models and drect analytcal solutons are used to evaluate a-ror relablty ndces from the models [2]. Ths means that the system s reresented by states and a table s bult wth all the needed F&D nformaton for each state. In ths aer, the wnd seed s analysed consderng the aroach resented n [8]. Wnd seed s a contnuous hyscal henomenon that evolves randomly n tme and sace: Snce each value of tme can be assocated to a random number, a stochastc rocess can be used to model the wnd seed. Thus wnd seed can be consdered as a stochastc rocess wth a contnuous state sace, the wnd seed value (that can be aroxmated as a dscrete state sace), and a contnuous arameter sace, the tme [8]. Fg. : Brth and death Markov chan (λ = transton rate from state to state +; µ = transton rate from state to state -). In order to reresent the wnd seed n a way that consders both robablty and F&D characterstcs of the wnd seed, a brth and death Markov chan (Fg. ) wth a fnte number of states s used [8]. In order to defne the model, the followng assumtons are made [8]: Wnd seed measurements are reresented by a set of wnd seed states. The wnd seed model s statstcally statonary,.e. the stochastc behavour of the wnd seed s the same at all onts of tme rresectve of the ont of tme n focus. The dstrbuton of resdence tmes n a gven state of the brth and death rocess s exonental. The robablty of a transton from a gven wnd seed state to another state s drectly roortonal to the long-term average robablty of the exstence of the new state. Transtons between wnd seed states occur ndeendently on transtons between comonent states. From a gven wnd seed state, only the case of transtons to mmedately adjacent states s consdered. The arameters of the wnd model are calculated from a wnd seed record: Measured values are samled at regular ntervals (e.g. an hour n the resented case) and the data that need to be extracted n order to calculate the model arameters, are the number of transtons from state to j = ± N j and the duraton of the resdence tme n a state before gong to a dfferent state D j (f some transtons occur between nonadjacent wnd seed states, the resdence tme duraton s estmated by a lnear roorton of the samlng tme). State nformaton are calculated as: State robablty = M ws j= M M D ws ws k = j= j D kj State frequency [occ/y] f (2) = N, + + N, Average state duraton [y] d = (3) f where M ws s the total number of wnd seed states. Wth the obtaned data, a fnte state Markov chan wth exonentally dstrbuted resdence tme s generated: The transton rates are calculated as: N λ =, ± (4) ± Ths rocedure requres a small number of arameters to be calculated, but they should be generated from a wnd seed record that s long enough to ensure a good aroxmaton. The total number of states can fnally be groued n order to ()

4 6 th Internatonal Worksho on Large-Scale Integraton of Wnd Power and Transmsson Networks for Offshore Wnd Farms 4 reduce the total number of states and to decrease the comutatonal tme. It must be noted that the wnd seed ranges also can be dvded nto non-equally saced states (.e.: groung states that generate the same outut ower): Ths can reduce the number of wnd seed states and therefore reduce the total number of states n the system. Wth the avalable wnd seed measurements, the wnd seed robablty table used n ths aer s shown n Table I (only few states are resented here), where State ndcates the number of the system state, Wnd Seed ndcates the wnd seed range assocated to the state, Prob s the state robablty, Freq s the state frequency, Dur s the average state duraton, U and Down ndcates the state transton rates resectvely for gong to the adjacent u state and down state. TABLE I WIND SPEED PROBABILITY TABLE State Wnd Seed [m/s] Prob Freq [occ/year] Dur [year] U Down [occ/year] [occ/year] 0-0,5,3E-03 8,7E+00,5E ,04 0,00 2 0,5,5,E-02 8,3E+0,3E ,24 794,24 3,5 2,5 2,6E-02 2,2E+02,2E , ,39 4 2,5 3,5 4,E-02 3,6E+02,E , ,64 8 6,5-7,5 2,0E-02,8E+02,E ,75 552,29 9 7,5-8,5,2E-02,3E+02 9,9E , , ,5-9,5 7,7E-03 8,3E+0 9,4E ,9 6469, ,5-4,5 2,0E-05 4,2E-0 4,8E , , ,5-42,5 2,5E-03 2,E+02,2E-05 0, ,32 When the wnd seed robablty table s known, t s ossble to assocate the wnd farm model to the system comonent avalablty data. For each of the wnd farm states, a vector that ncludes a wnd seed state and the status of each comonent n the system s defned n the followng way [9] [ ws S... S... S ] where ws s the th wnd seed state ( = 43 here), S j s the status of comonent j ( f avalable, 0 f out of servce) and N s the total number of comonents n the system. Assumng e.g. a number of comonents equal to 53 (e.g. 25 wnd turbnes, 25 cables and 3 connectors), each wnd farm state vector has length of 54 and the total number of states s 43x2 53. In order to defne the set of system states, the followng assumtons are made: ) Falure and rear of each comonent are statstcally ndeendent. 2) Two connected system state vectors are dfferent just n one element (.e. t s assumed that the system moves from a state only due to status change of one of ts comonents or change of the wnd seed). 3) Due to the hgh number of states, t s assumed that a maxmum number of three comonents may be out of servce n the same wnd farm state. As for the revous examle, the total number of states s reduced to from 3.87x0 7. j N When the comlete number of state vectors s known, t s ossble to calculate the robablty of each state as: N A N A U com, j Ucom, k (5) z j k = where A and U are the avalablty and unavalablty of comonent j and k, resectvely, N A s the number of avalable comonents n state, N U s the number of unavalable comonents n state and z s the robablty of wnd seed state z of state. Due to assumton 3) t s necessary to normalse all robablty values, n order to have the sum of all state robabltes equal to. State transton rates (measured n [occ/y]) are defned as a vector λ = [ λ j ] (6) that ncludes all ossble transtons λ of state to state j and that has the length of the number of state N that are connected to state. The other F&D arameters are calculated as: State frequency [occ/y] N ( j ) f = λ (7) j Average state duraton [y] d = (8) f All these values must be calculated for an F&D analyss, as they rovde nformaton on the duraton of each event and ts frequency of occurrence. Due to the sze of the roblem, t may be convenent to reduce the total number of states wth an aggregaton rocedure n order to obtan a reresentaton that can be handled more easly n further calculatons. Ths rocess s erformed by aggregatng states wth smlar outut ower n the same new state. In the resented case, t has been chosen to use an aggregaton ste of 5 MW (e.g. states wth generaton between 7,5 and 2,5 MW are aggregated nto the same state) and the outut ower of the new state s calculated by weghtng the outut owers of the orgnal states that are aggregated nto the new state wth ther resectve robabltes. Partcular aggregaton stes are used for the frst two and the last two new states: Orgnal states that generate the exact rated ower and the exact zero ower are aggregated resectvely nto the frst and the last new states. Orgnal states that roduce between the rated ower (excluded) and the rated ower mnus 2,5 MW are aggregated nto the second state, whereas the second last new state s formed by the orgnal states that generate between zero roducton (excluded) and 2,5 MW. Ths rocedure s chosen n order to reduce the aroxmatons of the aggregaton rocess: The

5 6 th Internatonal Worksho on Large-Scale Integraton of Wnd Power and Transmsson Networks for Offshore Wnd Farms 5 total yearly energy generated by the wnd farm s exactly the same wth both comlete and aggregated table. As an examle of ths aroach, consderng a wnd farm wth 53 comonents and a wnd seed table wth 43 states, the assumtons revously mentoned and wth the data resented n secton IV of ths aer, t s ossble to obtan an aggregated table as n Table II. The orgnal states are aggregated nto 8 new states that are charactersed by a set of arameters: State ndcates the number of the system state, Power s the outut ower of the state, Prob s the state robablty, Freq s the frequency of occurrence er year of the state, Fr u/fr down ndcate the cumulatve transton rates of the current state for movng u or down, resectvely, Dur s the average duraton of the state and Energy s the exected energy roduced by the wnd farm n a erod of one year. TABLE II AGGREGATED WIND FARM PROBABILITY TABLE FOR A WIND FARM WITH 53 COMPONENTS. State Power Prob Freq Fr u Fr down Dur Energy [MW] [occ/y] [occ/y] [occ/y] [y] [MWh] 75,00 4,35E-03,8 0, ,50 3,89E , ,77,0E-02 35,23 950, ,50 3,3E , ,96 6,4E-02 53,96 389,97 202,00 4,6E ,9 4 64,93 6,38E-02 27,62 509, ,90 2,35E , ,73 3,50E ,22 387, ,00,7E , ,02 4,0E , ,20 469,60,8E , ,4 4,4E-02 36, , ,40,22E , ,24 5,E , 3868, ,0,20E ,07 9 4,23 4,32E ,5 3934, ,00,9E , ,95 8,46E ,73 49, ,30,6E ,73 28,86,44E-02 26,7 4307,40 450,50,3E , ,4 7,60E-02 67, , ,70,3E ,77 3 8,85 8,7E ,99 459, ,90,E ,29 4 2,98 4,03E , , ,30,2E ,6 5 0,07 8,45E-02 74,79 455, ,00,4E ,94 6 5,9,8E-0 638,9 3029, ,00,85E ,7 7,56 5,77E , , ,90,6E ,90 8 0,00 8,06E-02 22,4 2746,40 0,00 3,64E-04 0,00 It must be exlaned why the resented aggregated transton rates are called cumulatve. Durng the aggregaton rocedure, t must be ket n mnd that, snce all state nformaton are aggregated, t s not ossble to dstngush all transton rates of each new state. For ths reason, two cumulatve transton rates are defned for each new state, one for u states (.e. to states wth bgger generaton) and one for down states (.e. to states wth smaller generaton): Each of these rates reresents the transton rate of the new state for gong to all states wth a bgger (or smaller) generaton. After havng calculated the robablty -agg of the new state as the sum of robablty of all orgnal aggregated states, these cumulatve transton rates are comuted as: N agg N ± λ j j λ ± agg = (9), agg where λ j s the set of transton rates of the orgnal state to other states, N ± s the total number of states wth greater (+) or lower (-) generated ower, s the robablty of state aggregated n state -agg and N -agg s the number of orgnal states aggregated n the new state. The other F&D arameters are calculated wth (7) and (8). B. Monte Carlo smulaton A Monte Carlo smulaton estmates a-osteror relablty ndces by smulatng the actual random behavour of the system, ether n a random or n a sequental way. As revously mentoned, a sequental Monte Carlo technque s used n ths aer n order to evaluate the relablty of an offshore wnd farm. The used method s a standard Monte Carlo smulaton that ncludes: Synthetc generaton of yearly wnd seed tme seres Wnd turbne falures Internal grd falures Connector to shore falures Influence of offshore envronment The smulaton s erformed wth the followng stes ([2]): ) Defnton of wnd farm layout and comonent data 2) Calculaton of the wnd seed robablty table 3) Durng each samled year, a) Calculaton of a synthetc wnd seed tme seres b) Random defnton of the hourly avalablty of each comonent c) Durng each hour, α) Defnton of the effectvely avalable wnd turbne β) Evaluaton of the wnd farm outut ower χ) Calculaton of wnd farm ndces d) Evaluaton of the result accuraces 4) Calculaton of the fnal ndces by average The above-mentoned framework s the standard Monte Carlo smulaton and further nformaton can be found n the avalable lterature (.e. [2]): Therefore, only onts 2 and 3.a wll be exlaned n detal n the next secton. The avalablty of each comonent (ont 3.b) s calculated consderng the data as lsted n Table III of secton III.A and assumng an exonental dstrbuton for both falure and rear resdence tmes, as suggested n [2]. The three assumtons used for the analytcal method (age 4), are not vald anymore n connecton wth the Monte Carlo smulaton: More than three comonents can be out of servce at the same tme and t may be ossble that more than one comonent fals ndeendently durng the same hour. In 3.c.α, the term effectvely means, as revously mentoned, that the wnd turbne s connected to the PCC at the current hour and roduces energy, f avalable. Ths calculaton s erformed wth the descrbed PBFS method. As descrbed n [0], t s necessary to fx some crtera n order to sto the smulaton (3.d). In the roosed method, the followng two solutons are consdered: The ncluson of a maxmum number of samles, n order to avod never-endng smulaton, and a stong crteron. The stong crteron s based on the evaluaton of the coeffcent of varaton [0]

6 6 th Internatonal Worksho on Large-Scale Integraton of Wnd Power and Transmsson Networks for Offshore Wnd Farms 6 calculated for all the system ndces: The ndex wth the hghest coeffcent of varaton s chosen as reference value, and t s comared to a redefned tolerance. The smulaton contnues as long as the tolerance s smaller than the selected coeffcent of varaton. In the resented study, the most crtcal ndex for the stong crteron s EGWE. Fnally the generaton ndces are calculated accordng to the standard Monte Carlo aroach by means of calculatng the averages of all samled results. ) Wnd seed tme seres Snce a new develoed wnd seed generator s defned, more detals about onts 2 and 3.a of the Monte Carlo smulaton framework are gven n ths secton. Two stes are requred for the smulaton of the wnd seed. The frst ste concerns the calculaton of a wnd seed robablty table as dscussed n secton III.A (Table I). The man roblem that occurs when usng one table based on yearly measurements s that some seasonal characterstcs of the wnd seed measurements may be lost and consequentally relevant nformaton for the analyss cannot be used. In ths aer, the roblem s solved by calculatng tables based on monthly nformaton nstead of on yearly measurements. In ths way, 2 monthly wnd seed robablty tables are calculated and used for generatng 2 wnd seed tme seres. These seres are combned and a yearly tme seres that reserves seasonal nformaton s obtaned. After havng develoed the tables, t s ossble to roceed and calculate the random wnd seed tme seres. The current wnd seed can resde n one of the dfferent mutually exclusve states resented n the wnd seed robablty table, and after beng n the current state for a certan amount of tme, t moves to one of the two adjacent states (f the current state s or 43, the wnd seed can move only to the u or down state, resectvely). Snce the henomenon can be descrbed by an exonental dstrbuton [,8] and the transton rates of each state are known, t s ossble to calculate the tme seres wth the followng rocedure: ) Intalsaton of the wnd seed vector ws(h) = ws and the tme varable t = 0. In the case resented here, the ntal wnd seed value s chosen close to the average wnd seed of the measurements (9 m/s). 2) For the generc ste th, two random numbers U and U 2, one for the u transton rate and one for the down transton rate, are unformly generated n the nterval (0,). 3) The Tme To U (TTU) and Tme To Down (TTD) of the current state s evaluated by means of equatons ( U ) h = (0) TTU ln λu ( U ) h = () TTD ln 2 λdown where h s the duraton of the smulaton erod exressed n hours (.e. for one year, h s 8760 hours, for one month of 3 days t s 744 hours), λ u s the u transton rate and λ down s the down transton rate of state ws. The smallest of the two values calculated from (0) and () defnes whch new state the current wnd seed moves to and also how long t wll stay n the current state before movng to a dfferent state (e.g. f TTU < TTD, t s assumed that the current wnd seed goes to the uer state after TTU hours). 4) Vector ws and varable t are udated, so that: t + ws ( t : t ) = ws + (3) = t TTU (2) where (t - : t ) means between tme t - and t (here t s assumed that the wnd seed moves u from the current state). It must be noted that, f t belongs to the same hour of t -, vector ws s not udated, as the wnd enters and leaves the current state durng the same hour. 5) Stes 2-4 are reeated untl t s equal to h. In ths way, a synthetc wnd seed tme seres s obtaned and t can be used for further calculatons n the Monte Carlo smulaton. The man advantage of ths aroach s that the random varaton of the wnd seed s taken nto account and a realstc smulaton can be thoroughly descrbed. The man drawback s the long comutatonal tme needed to evaluate a new tme seres n every samled year. The roblem can be avoded by defnng and storng a set of wnd seed tme seres n advance (.e. before runnng the smulaton) and then callng the seres durng the comutaton: Snce the wnd seed seres wll not be calculated n every samle, the comutatonal tme wll be reduced. For nstance, aroxmately 0 s er samle may be saved by the storage of wnd seed tme seres n the resented case. However, ths rocedure s not used n ths aer. In Fg. 2, three wnd seed tme seres are comared: The measured wnd seed tme seres n year 2004 (a), a synthetc wnd seed tme seres based on a yearly robablty table (Table I) (b) and a synthetc wnd seed tme seres based on the 2 monthly robablty tables (c). It should be noted that, whereas lots a) and c) have smlar seasonal behavours (hgh wnd seed at the begnnng of the year, low wnd seed n the mddle and agan hgh wnd seed durng the last months of the year), lot b) has a comlete random characterstc durng the year, wth hgh and low wnd seed averages dstrbuted durng the year. Ths shows why the wnd seed seasonal characterstc of the wnd seed must be ncluded n a sequental analyss and t justfes the use of monthly robablty tables as smulaton tool n order to reserve some nformaton about the measurements. In the rest of the aer, all used synthetc wnd seed tme seres are obtaned from the 2 robablty tables. In Fg. 3, the average values of dfferent wnd seed tme seres are comared: Mean values of three years of the measurements (year 2000, year 2002 and year 2003), the total average of the measurements, the mean values of 000 samled synthetc wnd seed tme seres, the total average of the 000 samles. The fgure shows that averages of the

7 6 th Internatonal Worksho on Large-Scale Integraton of Wnd Power and Transmsson Networks for Offshore Wnd Farms 7 samles lay between the measurement averages boundares and that the 000 samled year Total Avg (9,27 m/s) dffers from the Total measurement Avg (9,8 m/s) by less than %. Ths roofs that synthetc and orgnal tme seres have the same behavour regardng mean values. If the robablty dstrbuton functon (df) of the tme seres (Fg. 4) s consdered, t should be noted that both measured and synthetc wnd seed tme seres aroxmate Webull dstrbutons. Plots a) and b) refer to measured years 2000 and 2002, whereas lots c) and d) regard two of the 000 synthetc tme seres. III. COMPARISON OF RESULTS Fg. 2: Wnd seed tme seres: a) orgnal measurements (year 2004), b) synthetc wnd seed tme seres based on yearly robablty table, c) synthetc wnd seed tme seres based on 2 monthly robablty tables. A. Analysed System The system analysed n ths aer s an offshore wnd farm wth 25 wnd turbnes, 25 nternal grd cables, 3 connectors to shore and the layout shown n Fg. 5 [] ( x ndcates a wnd turbne, and a lne reresents a cable or a connector). It s assumed that nternal grd cables have the same electrcal characterstcs and same length (700 m) and connectors to shore (between nodes 26-29, and 28-29) have the same electrcal characterstcs and a length of 0 km. Comonent data (λ, MTTR and avalablty) are resented n Table III. Data for wnd turbnes are obtaned from [5], whereas data for cables and connectors come from [4]. The MTTR for cables and connectors s chosen as an average between summer and wnter values [5]. It must be onted out that due to the recent develoment of offshore wnd farms, all data are based on assumtons and not on measurements. Fg. 5: Wnd farm layout used for the smulaton. Fg. 3: Comarson of wnd seed tme seres average values. TABLE III COMPONENT DATA FOR RELIABILITY CALCULATIONS. Nr Falure rate MTTR Avalablty Wnd turbne 25,5 /y 490 h/y 92,0 % Cable 25 0,05 /y/km 440 h/y 99,83 % Connector 3 0,05 /y/km 440 h/y 99,75 % For the analytcal comutaton, the wnd farm s reresented as shown n Table II: It conssts of 8 states and all resented nformaton are used for the calculaton. Fg. 4: Comarson of measured (lot a) and b)) and smulated (lot c) and d)) wnd seed dstrbuton functon. B. Results and Comments The wnd farm generaton ndces are shown n Table IV where also the requred comutatonal tme s ndcated. Only for the Monte Carlo smulaton, the acheved accuracy of the results and the number of smulated samles are ncluded. The last mentoned value, Nr. of samles, reresents the number of samles (= 50 years) that the smulaton has to run n order to obtan the requred accuracy of the results (0,5%). Frst of all, t should be noted that the results resented here do not strctly requre an F&D or sequental calculaton

8 6 th Internatonal Worksho on Large-Scale Integraton of Wnd Power and Transmsson Networks for Offshore Wnd Farms 8 to be obtaned and ths would not justfy the comutatonal effort used for the reresentaton of the two models. However, the am of ths aer s to show how to adot the two robablstc aroaches for evaluatng the wnd farm generaton and whch requrements are needed for addng the wnd farm model nto HLI or HLII analyses. As soon as one of these studes s erformed, t becomes relevant to have an F&D or sequental reresentaton due to the stochastc nature of the wnd: Therefore, the choce of rocedure s exlaned. TABLE IV WIND FARM GENERATION RESULTS Index Unt Analytcal Monte Carlo Method Smulaton. IWP MW IWE MWh EAWE MWh , , 4. EGWEWTF MWh ,6 5. EGWE MWh 2588, ,8 6. CF - 0,393 0, GR - 0,9345 0,9247 Smulaton tme s 637,78 68 Result accuracy % - 0,5 Nr. of samles Index 4 s not calculated accordng to the analytcal method, because, usng state vectors, t s not ossble to dstngush causes of contngency due to sngle comonent falures,.e. t s not ossble to evaluate the wnd farm generaton solely by takng wnd turbne falures nto account. Observng how the wnd farm generaton vares ncludng dfferent comonent falures (ndces 3, 4 and 5), t can be exlaned why the ncluson of nternal grd cable and connector falures may be relevant for the analyss. The dfference between ndex 3 and ndex 4 (only wnd turbne falure taken nto account) s about 7,6% and t s justfed by the avalablty of a wnd turbne (Table III). The dfference between ndces 4 and 5 s about 0,6%, as t can be noted observng the avalablty of the other comonents (Table III). Index CF ndcates the caacty factor of the wnd farm and t s around 39%. Ths value s hgh f comared to onshore nstallatons, but t can be reasonable for offshore stes [2]. Index GR that reresents the generaton of the wnd farm n relaton to ts comonent avalablty, has a value above 92% of the total generaton: Ths can be exlaned consderng the values assumed for the avalablty of each comonent, as shown n Table III. When comarng the ndces obtaned wth the two technques, t must be noted that values are qute close and dfferences vares from 0,4% (CF) to,5% (EAWE). Dfferences can be justfed by the assumtons made, whch roofs that both solutons can be adoted for the evaluaton. From a numercal ont of vew, smlar results can be obtaned. When consderng the comutatonal tme requred by the two methods, t should be noted that the analytcal aroach needs more tme to be comleted manly caused by the huge amount of system states (It s recommended that the comutatonal tme s reduced for a smaller system). On the other hand, the advantage of the analytcal aroach s that most of the tme resources are used for generatng the wnd farm table (Table II) and after the values have been calculated once, the table can be stored and utlsed drectly for further calculatons. Ths observaton s not vald for the Monte Carlo aroach, where the smulaton must be erformed each tme the wnd farm generaton needs to be evaluated. The comact reresentaton of the roblem rovded by the analytcal method has one man drawback n the reresentaton of the zero roducton state (state 8 n Table III). In ths state, three ossble stuatons are ncluded: Wnd seed lower than the cut-n wnd seed, wnd seed hgher than the cut-out wnd seed and comonent falures that cause a full loss of generaton. As these three condtons are aggregated together, t s not ossble to dstngush the dfferent reasons for zero roducton and ths would reresent a relevant reducton n the alcatons of the method, esecally f extreme wnd condtons are to be analysed. A soluton for ths roblem can be found n avodng the aggregaton of the wnd farm table, but ths would result n a table wth many states and ths would exonentally ncrease the comutatonal tme and decrease the ease of handlng the reresentaton. Ths roblem does not occur n the Monte Carlo smulaton, as all system condtons can be dstngushed durng the calculaton. Fg. 6: Probablty dstrbuton functon of ndex EGWE (a) and ndex GR (b). Fnally, consderng the Monte Carlo smulaton, t s ossble to lot the df of each ndex. As an examle of ths, the dstrbuton functon of ndces EGWE (lot a) and CF (lot b) are shown n Fg. 6. The use of these df s can be of hel for redctng the behavour of an ndex and ts frequency of occurrence. In order to consder the ossblty of ncludng the Monte Carlo smulaton n more detaled ower systems, the same calculatons are erformed usng AC load flow. A standard Newton-Rhason aroach s used [3] and t must be comuted durng each hour of the smulaton. As the comutaton of 8760 load flows er samle would ncrease the comutatonal tme consderably, a Power Transfer Dstrbuton Factor (PTDF) s ntroduced for the analyss [3].

9 6 th Internatonal Worksho on Large-Scale Integraton of Wnd Power and Transmsson Networks for Offshore Wnd Farms 9 The PTDF hels to reduce the number of calculated load flows down to aroxmately 40% wth a reducton of comutatonal effort. However, t must be ket n mnd that the PTDF reresents a lnearsaton of the roblem: Therefore, all results are aroxmated. Obtaned ndces are smlar to the one resented n Table IV, e.g. EGWE s reduced to ,8 MWh due to the ncluson of ower system losses n the calculatons. However, the factor that really vares n ths smulaton s the comutatonal tme that ncreases u to 472 s, and the same accuracy (0,5%) s reached after fewer samles (30 n ths smulaton, that means a tme-consumton er samle of 57 s, whereas n the case wthout load flow, the tme-consumton er samle s equal to 24 s). These two asects (ncrease of tme and decrease of number of samles) must be consdered when ncludng load flow calculatons nto relablty evaluatons. IV. CONCLUSIONS In the last years, the ncrease of wnd farm nstallatons has resulted n the necessty to nclude these generaton unts nto ower system relablty assessment. Due to ts stochastc nature, ths technology has created a set of new asects that must be faced n relablty evaluaton. Ths aer focuses on dfferent technques for evaluatng offshore wnd farm generaton for relablty uroses. Two aroaches have been consdered: One based on analytcal methods wth frequency and duraton (F&D) analyss, and one based on sequental Monte Carlo smulaton. By usng these two methods, models for assessng the generaton of the wnd farm ncludng varablty of the wnd seed and system comonent falures are calculated and comared. The comarson s erformed on the base of a number of relablty ndces, the comutatonal tme, the feasblty of future studes and the ossblty of dstngushng the generaton durng extreme wnd condtons. Both methods rovde smlar numercal results and on one hand, the analytcal analyss, after havng beng calculated once, reresents the fastest soluton. On the other hand usng a Monte Carlo smulaton, wnd farm oeratons under extreme wnd condtons can be dstngushed and ndex dstrbuton functons can be obtaned from the comutaton. Both technques can be used for relablty evaluatons of ower systems wth a large amount of nstalled wnd caacty both for HLI and HLII analyses and the choce between them deends on the uroses of the study. V. REFERENCES [] H. Chen, Generatng System Relablty Otmzaton, Ph.D. dssertaton, Det. Elect. Eng., Unversty of Saskatchewan, Saskatoon, Canada, Fall Avalable: htt://lbrary.usask.ca/theses/ (last vst July 2006). [2] R. Bllnton, R.N. Allan, Relablty Evaluaton of Power Systems, 2 nd ed., Plenum Publshng Cororaton, New York, USA, July 996. [3] R. Allan, and R. Bllnton, Probablstc assessment of ower systems, Proceedngs of the IEEE, Vol. 88, No. 2, Feb 2000, [4] G.J.W. van Bussel and M.B. Zaarjer, Relablty, Avalablty and Mantenance asects of large-scale offshore wnd farms, a concets study, Proceedng of MAREC 200, Newcastle, England, 200. Avalable: htt:// (last vst July 2006). [5] A. Sannno, H. Breder, and E. K. Nelsen, Relablty of collecton grds for large offshore wnd arks, n Proc. 9 th Internatonal Conference on Probablstc Methods Aled to Power Systems, Stockholm, Sweden, June -5, [6] R. Bllnton and A.A. Chowdhury, Incororaton of wnd energy converson systems n conventonal generatng caacty adequacy assessment, IEEE Proceedngs-C, Vol. 39, No., January 992, [7] Breadth Frst Search and Deth Frst Search, avalable at htt:// [8] F. Castro Sayas and R.N. Allan, Generaton avalablty assessment of wnd farms, IEE Proceedngs Generaton, Transmsson and Dstrbuton, Vol. 43, No. 5, Setember 996, [9] M. Zhao, Z. Chen, F. Blaabjerg, Relablty evaluaton for offshore wnd farms, Proceedngs of the Ffth IASTED Internatonal, Conference Power and Energy Systems, Benalmadena, San, 5-7 June 2005, [0] M. Ameln, On Monte Carlo Smulaton and Analyss of Electrcty Markets, Ph.D. dssertaton, Det. of Electrc Power Systems, Royal Insttute of Technology, Stockholm, Sweden, [] Burbo Offshore Wnd Farm, nformaton avalable at htt:// [2] T. Ackermann (Edtor), Wnd Power n Power Systems, John Wley & Sons, Chchester, England, [3] L. Söder, Load flow Study and Senstvty Analyss of Power Systems, Det. of Electrcal Power Systems, Royal Insttute of Technology, Stockholm, Sweden, Ncola Barbers Negra receved hs M.Sc. degree n electrcal engneerng n 2005 from the Polytechnc of Turn, Italy. He s currently an ndustral Ph.D. student at Elsam Engneerng A/S a art of Dong Energy, Denmark. Hs secal feld of nterest covers studes related to ower system relablty wth a artcular focus on offshore wnd farm nstallatons. Ole Holmstrøm (M 0) s currently emloyed wth Elsam Engneerng A/S a art of Dong Energy as senor engneer. He has comrehensve exerence n general electrcal engneerng and varous dsclnes wthn analyss of electrcal ower systems. In the last decade he has secalsed n analyss of ower systems usng varous software tools, ncludng advanced comuter modellng and dynamc and transent smulatons. He has artcated n a number of wnd energy rojects concernng desgn of wnd farms as well as analyss of wnd farm grd connecton. He has been nvolved n the develoment of advanced dynamc models of wnd turbnes and has made numerous studes of the mact of wnd ower on ower systems, ncludng all asects from caacty to ower qualty and transent stablty. Brgtte Bak-Jensen (M 88) receved her M.Sc. degree n Electrcal Engneerng n 986 and a Ph.D. degree n Modellng of Hgh Voltage Comonents n 992, both degrees from Insttute of Energy Technology, Aalborg Unversty, Denmark. From she was wth Electrolux Elmotor A/S, Aalborg, Denmark as an Electrcal Desgn Engneer. She s an Assocate Professor n the Insttute of Energy Technology, Aalborg Unversty, where she has worked snce August 988. Her felds of nterest are modellng and dagnoss of electrcal comonents, ower qualty and stablty n ower systems. Durng the last years, ntegraton of dsersed generaton to the network grd has become one of her man felds, where she has artcated n many rojects concernng wnd turbnes and ther connecton to the grd. Poul Sørensen (M 04) was born n Koldng n Denmark, on June 6, 958. He obtaned hs M.Sc. from the Techncal Unversty of Denmark, Lyngby n 987. He was emloyed n the Wnd Energy Deartment of Rsø Natonal Laboratory n October 987, where he s currently workng as a senor scentst and roject manager. Hs man feld for research s ntegraton of wnd ower nto the ower system. He was a member of the IEC workng grou rearng IEC , and s currently a member of the mantenance team MT2. He s also a member of IEA annex XXI on Dynamc models of wnd farms for ower system studes.