A Comparison of Methodologies Incorporating Uncertainties into Power Plant Investment Evaluations

Transcription

1 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 A Comparon of Mehodologe Incorporang Uncerane no Power Plan Invemen Evaluaon Nnghong SUN # Derk Jan SWIDER Alfred VOSS Inue of Energy Economc and he Raonal Ue of Energy Unvery of Sugar Hebruehlrae 49a Sugar Germany # Dpl.-W.-Ing. Nnghong Sun. Tel.: ; Fax: E-Mal: nnghong.un@er.un-ugar.de Abrac Th paper offer a comparon of echnque propoed o deal wh uncerane exng n power yem expanon plannng. Dvere approache developed or appled over he pa wo o hree decade are urveyed and clafed no he convenonal and new one accordng o her predomnan applcaon n he regulaed and lberalzed me. Baed on he curren leraure concluon on he poenal of developng new mehodologe able o mee he requremen of power plan nvemen evaluaon n he comng year are drawn. 1 Inroducon The Uned Kngdom and a a poneer n Europe for beng he fr counry o have underaken he rerucurng of elecrcy marke. Snce hen lberalzaon ha been gradually mplemened n he elecrcy ecor of oher counre. The man objecve purued by he lberalzaon of elecrcy marke o reduce co by ncreang compeon n he wholeale and real ecor where radonal monopole had alway prevaled. Under h new framework power plan nveor have o ake varou addonal concern no accoun n her decon-makng. The mo gnfcan of hee concern he expoure o dvere uncerane boh n relaon o he marke fundamenal and o he raegy of her compeor. Therefore he developmen of mehodologe capable of ncorporang and effecvely handlng relevan uncerane no nvemen evaluaon a new challenge one ha reearcher are akng up. In he nex econ we wll brefly nroduce he mo mporan change on he elecrcy marke brough along by lberalzaon and he major uncerane ha need o be aken no conderaon when plannng new power generaon projec. Change hrough marke lberalzaon We wll decrbe he mo gnfcan change n he elecrcy ndury nce he lberalzaon focung on hree apec: he ownerhp and hu nveor of power plan benchmark for evaluang power plan nvemen projec and regulaory polce degned o guaranee he adequae elecrcy upply. In he pre-lberalzaon me generang ule were moly ae owned and operaed. Wh lberalzaon he elecrcy ecor wa enrely or parly opened o prvae nveor. Pror o lberalzaon he goal n power plan nvemen and operaon wa co mnmzaon. Wh he peneraon of prvae nveor no he marke and ncreaed compeon ha goal wched o prof maxmzaon. In regulaed marke he man concern whle plannng for new capacy wa o offer a uffcen upply. Generaor were no under preure nce all 1

2 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 he co relang o he power upply even hoe co reulng from her adveraral decon could evenually be ranferred o he conumer. Bu wh he marke lberalzaon elecrcy prce are no longer fxed a a prevouly negoaed arff bu e by he marke equlbrum. In oher word generaor have o ake a lo for her own accoun. Elecrcy ha alway been a commody under much more uncerane han oher common one. The grea capal neny and long lead me of mo power plan make even more dffcul o enure an adequae delvery olely dependng on he marke mechanm. For he lberaled elecrcy marke dvere concep are developed o enure yem relably. The mo mporan one are energy only capacy paymen capacy marke and relably conrac [1]. In general no company ha an oblgaon o nve n new power plan. In he cae of horage of generang capacy hee mechanm hould creae ncenve for new nvemen. In he German marke for example he energy only prncple mplemened. Th leave he creaon of nvemen ncenve o he marke. In addon a marke for balancng energy erve o enure hor-erm ecury on an energy and capacy paymen cheme. 1.2 Man uncerane on he regulaed and deregulaed elecrcy marke Relevan uncerane for he power plan nvemen can be dfferenaed beween he one whch all along ex bu dd no really play an mporan role due o he cenraled marke regulaon and he one whch have emerged under he new framework of lberalzaon. Eher on a regulaed or lberalzed marke rucure demand noceably one of he mo unceran facor n he power plan plannng. The long-erm developmen rend of elecrcy demand rongly dependen on varou facor uch a he growh of populaon gro domec produc employmen and o on. The dffculy n properly forecang hee facor and he complexy of analyng her correlaon gnfcanly complcae he deermnaon of he developmen of he demand. Durng he power plan nvemen evaluaon no only he long-erm rend of he demand bu alo he load curve mu be condered. In he hor-erm he load profle preen an obvou perodcal cycle becaue of he rong dependency of he elecrcy demand on he meeorologcal condon. Neverhele n he horcal daa many excepon appeared whch could have hardly been foreeen n me. From boh pon of vew enurng a uffcen power upply or maxmzng prof demand forecang conue one of he key pon n power yem plannng. Uncerane aocaed wh fuel prce were earler no a ubanal concern for power plan nveor nce he ncreaed expene creaed by evenual hgh fuel prce could be reganed hrough rang he elecrcy prce. A menoned above he elecrcy prce on he lberaled marke are e by he upply-demand equlbrum. Therefore a a gnfcan par n he operang expene fuel co wll evenually nfluence he nvemen prof. In he pa few year fuel prce epecally of crude ol have experenced a very hgh degree of volaly (from he horcal low of barely10$/barrel n December 1998 o around 60$/barrel by he me of h wrng). The lack of ranparency on he upply de and dffcule o foreee he demand boh conrbue o he prce nably. Furhermore naural ga whch erve a an mporan alernave reource for ol produc ha for long been prced wh a gh lnk o ol. In h repec volale ol prce would drecly reul n volaly of ga prce. Alhough oher fuel prce how a relavely lower volaly modellng her long-erm developmen ll preen a complex ak. Elecrcy characered a a prce nelac produc nce he regulaed me. Sll now lle elacy of demand o prce can be denfed. Bu converely change n he genera- 2

3 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 ng rucure caued by addon of new capace wll lead o change n he prcng. Behavour of oher uppler make nowaday even more dffcul o foreca he elecrcy prce. The above mple ha n a lberaled envronmen no only he elecrcy prce are e by he marke bu alo he elecon of new generang echnologe ubjec o. Technologcal nnovaon however ha alway been an unpredcable and omeme even accdenal occurrence. Managng rk wh a dverfcaon of he energy mx ha already been aken no conderaon by power plan nveor. Ju lke n regulaed me energy polce relaed o elecrcy marke can mpac he nvemen decon o a grea exen. The nroducon of he greenhoue ga radng yem and he decon o phae ou nuclear power for example ha aroued nene dcuon regardng a neceary change of he energy mx. 1.3 Paper rucure The re of h paper rucured a follow: n econ 2 dvere mehod o evaluae nvemen under uncerany wll be nroduced. They are compared accordng o he dfferen echnque ued o ncorporae uncerane. Secon 3 con of a cae udy evaluang a e power plan nvemen projec hrough he applcaon of hree eleced mehod dcued. The fnal econ analyze he reul and draw concluon abou he rend n he developmen of fuure mehodologe. 2 Comparon of convenonal and new mehod wh her applcaon o power plan nvemen 2.1 Convenonal mehod for he regulaed plannng The leraure urveyed n h paper race back o he md eghe. Snce hen ncorporang uncerane no power plan nvemen evaluaon or power yem expanon plannng ha been gradually aracng he aenon of he planer. Wh he aumpon of perfec foregh parameer uch a power demand fuel prce were formerly condered o feaure a deermnc developmen. In order o acheve a more realc plannng ophcaed mehodologe dealng wh uncerane were added o he exng model ll rerced o meeng he fuure power demand wh a gven relably a mnmum co. In oher word he movaon of ncorporang hee uncerane no he modellng o a grea exen o avod he co penaly from neffcen generang rucure. In he fr par of h econ an nroducon of radonal approache wll be gven. We focu on he one whch durng he regulaed me had been mo commonly dcued n he leraure dealng wh power expanon plannng under uncerane. A farly exenve workng paper of he World Bank [2] ugge clafyng hee approache n he followng hree caegore: () ochac opmzaon () robune analy or rade-off analy and () opon value mehod. In anoher arcle [3] comparng everal olvng mehodologe addree h ue wh a dfferen clafcaon. In he abence of opon value mehod nclude he approach of deermnc equvalen n he dcuon. Wh an n-deph gh n he mehodologcal developmen no dffcul o conclude ha he deermnc equvalen approach preen he fr ep oward ncorporaon of uncerane alhough he way on whch handle he uncerane appeared o be oo mple. The erm opon value derve orgnally from he fnance marke and more pecfc from he ock marke where ued o denoe opporune o ell or buy ock hare. I exenon for power economc 3

4 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 can ll be frequenly found n recen leraure. Hence opon value mehod alo and for a gnfcan ubjec n he reearch of new mehod n h paper. All of hee four caegore are o be decrbed nex. Deermnc Equvalen In he deermnc equvalen approach nvemen plannng formulaed a a radonal lnear opmzaon problem. To keep a clear overvew we mplfy he nvemen plannng problem wh he followng formulaon: Mn { Q } ( fc + oc Q ) () Subjec o l (1.2) Q D 0 Q ρ ( τ + ) τ = 1 (1.3) (1.4) Q 0 (1.5) Where: fc oc 0 l Q D Specfc nvemen co of echnology n me age Specfc operang co of echnology n me age Invemen varable for echnology n me age Exng capace of echnology pror o he plannng horzon Mnmum nvemen capacy of echnology n me age Producon varable for echnology n me age Demand n me age ρ Tme-dependen avalably of echnology n me age Th nend o fnd an opmal power plan nvemen plan n erm of decdng on echnologe nveng me nveng capace a well a operang power plan o a o mee he fuure demand akng no accoun he avalably of he nalled capacy. A he name deermnc equvalen mple acually deal wh deermnc conran. Unceran facor a demand and fuel prce are nally aumed o be conan for each me age. Ther value are o be emaed baed on he currenly be avalable nformaon. Thu he nvemen chedule deermned by he deermnc equvalen only opmal a vewed from he curren me age. In he ucceedng age new foreca are o be aumed. Afer updang he daa nvemen raege from h age wll be agan decded by recalculang he opmzaon problem. Th proce recur ll he end of he plannng horzon. A already poned ou n [3] he deermnc equvalen approach doe no necearly lead o he mo adequae nvemen plan becaue he opmzaon n each age obvouly ju 4

5 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 reaonable for a lmed perod of me. In h conex alhough he deermnc equvalen approach doe no mply a compuaonal complexy uually no able o provde a plauble advce for he long range. Ye mgh be more nereng for he projec whch poe he flexbly o be readjued durng he execuon proce whou reulng n ubanal loe. Robune Analy In general power yem plannng a complex ak whch uually face more han one objecve. In ome cae hee objecve even conflc wh each oher. For example whle amng a a pobly economcal generaon expanon he yem planner mu mulaneouly aure ceran yem relably wh exra capace ha are lef unued for mo of he me. The robune analy approach wa developed o olve uch problem wh mulple objecve. I prncple o fnd a o called robu decon wh a rade-off analy among he conflcng objecve. In [4] h mehodology wa furher exended for applcaon under uncerany. Durng he fr ep of eekng a robu plan all he poble cenaro are ummarzed. The amoun of cenaro depend no only on he nvemen alernave he planner mgh prefer bu alo on he poble fuure ae of unceran facor. Thee cenaro decrbe all he uaon he decon-maker would evenually confron afer he plan carred ou. Furhermore f he uncerane are modeled probablcally a correpondng probably can be calculaed for each cenaro. To avod geng no a caarophc exen rgh from he ar recommended o carefully defne he meanngful plan alernave and relevan nfluencng facor. In addon he objecve purued n he plannng hould be nerpreed wh quanfable funcon e.g. he mnmzaon of he oal co or he maxmzaon of an ndex for he envronmenal compably. Ther value are ubjec o he cenaro pecfc arbue: J ( r) f ( ) = a ( S (2) r j= 1 r j ) Here f r () and for he value of r -h objecve n he -h cenaro from he cenaro e S. Equaon conrbung o compue f r () are ( ) whoe defnon and number J (r are deermned by he objecve. a r j ) Afer he problem formulaon decrbed above he rade-off analy follow. The rade-off analy nend o denfy he be comprome n he e of objecve value. Whou conderng uncerane he mulaed cenaro are dencal o he nvemen alernave. Therefore objecve value of a cenaro can be een a he objecve value of he correpondng nvemen alernave. Accordng o [4] he domnance beween wo alernave can be dfferenaed beween he condonal rc domnance and he condonal gnfcan domnance. The former obaned f he eleced alernave alway ha a beer value han he oher one for each objecve. The laer mean ha he domnan alernave ha a lea one gnfcanly beer objecve value and no gnfcanly wore han he oher canddae. To generalze he obervaon o unceran cae where he occurrence probable are gven rk analy echnque lke Mone Carlo mulaon are appled o calculae he domnance probably of an alernave relave o anoher one. Domnance defnon are alo exended o he rc global domnance and he gnfcan global domnance repecvely wh a predefned probably ay p. 5

6 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 On he ba of he global domnance deermnaon of every wo alernave he decon e rade off curve e and knee e can be exraced. Trade off curve e con of all he alernave whch are no rcly globally domnaed by any oher. A knee e he collecon of all he alernave whch are no gnfcanly globally domnaed by any oher. In he proce of fndng he decon e he nferor alernave are elmnaed. In order o defne he fnal plan ubequenly mporan o analye he decon e by examnng oher addonal queon a robune of he alernave her performance regardng a parcular objecve and her flexbly. Sochac Opmzaon Adaped from he mahemacal programmng he ochac opmzaon approach ha been frequenly appled n mul-age nvemen plannng under uncerany hence alo n power yem expanon plannng. I applcaon uually bae on he cenaro analy whch denfe dfferen ae of he fuure dependng on he poble evoluon of uncerane. The objecve of ochac opmzaon however no o fnd he opmal oluon for each cenaro bu o deermne he decon ha be f all of hem. Therefore h global opmum may no be he deal oluon for ome of hee cenaro bu repreen he be one for he whole e. To llurae he applcaon of he procedure o a power plan nvemen problem we connue akng he mplfed formulaon () a example. Fr we reformulae by addng ochac characerc: Mn { Q } (3.1) Subjec o l p fc + oc Q ) ( (3.2) Q p Q. p D ρ 0 τ + τ = 1 (3.3) (3.4) Q 0 (3.5) In (3.1) he pecfc operang co exended o a cenaro-dependen erm and an occurrence probably p aocaed o he cenaro. In h conex he objecve funcon equal o he expecaon of he ngle cenaro. The formulaon of an nvemen problem n a ochac opmzaon model doe no eem o be very dffcul aumng ha poenal echnologe her echncal performance and evoluon of uncerane a demand and fuel co are gven. Wh he nvolvemen of addonal facor hence ncreang he number of cenaro he complexy of uch problem grow exponenally. Before he appearance of he ophcaed compung echnology avalable oday he greae challenge n applyng h mehodology wa olvng uch problem. Addonally equaon (3.4) complcae he cae by makng mul-age. 6

7 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 In he leraure on he ochac opmzaon approach urveyed he Bender decompoon algorhm [5] appear o be he mo popular nrumen o olve he mul-age ochac problem. The crucal pon of applyng h echnque o ranfer he ngle complex problem no a maer problem and a e of ub problem. [6] ugge dvdng he power plan nvemen problem no an nvemen problem and an operaon problem each repreenng he maer problem and he ub problem repecvely. Soluon va h dvon can be acheved by erave opmzaon. To llurae h concep we replace he formulaon (3) wh (3 ) and (3 ) a followng: Maer problem: Mn Subjec o Sub problem: For each S : l fc (3'.1) (3'.2) 0 (3'.3) Mn Q Subjec o oc Q (3''.1) Q Q Q. D 0 ρ τ + τ = 1 0 (3' '.2) (3' '.3) (3' '.4) Where: Opmal oluon of he maer problem (3') Durng he opmzaon he maer problem (3') o be updaed durng each new eraon. Th done by changng he o called Bender cu θ and he addonal lnear conran aocaed whθ (ee Fgure 1). A convergence e nroduced o conrol he ermnaon of he erave opmzaon proce by examnng he upper bound UB and he lower bound B whch are nally e o he pove and negave nfny. The eraon procedure connue unl he convergence conran fulflled. The cheme of opmzng problem (3) ung he Bender decompoon echnque hown n Fgure 1. 7

8 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 Inalzaon: := 1 (Ieraon number) UB := B := Solve he nal maer problem: Mn fc Subjec o l Inalze he opmal value of he nvemen varable : * : = (Opmal value) Solve he ub problem for each S : Mn Q Subjec o Q : oc Q Q. D ρ τ τ = 0 Q 0 Q v = Q * : q q = Updae he upper bound: 0 + Updae he opmal value of he operaon varable : (Opmal value) (Opmal dual value) UB : = mn{ UB p ( fc + oc Q )} Updae he lower bound: B : = Solve he updaed maer problem: Mn { θ } fc +θ Subjec o l h 0 h θ p ( q ( ρ τ + Q )) τ = 1 h = Updae he opmal value of he nvemen varable : * : = * θ : = θ fc + θ (Opmal value) (Opmal value) Convergence e: ( UB B ) /(1 + B ) TO? no Nex eraon: : = +1 ye Opmal oluon found Fgure 1: Illuraon of opmzng power plan nvemen wh Bender decompoon echnque Thank o he noable progre n compung echnque made n he la decade many ofware capable of olvng large mahemacal programmng problem are now avalable. The dffcul proce of Bender decompoon already embedded n he olver of hee ofware whch can be appled o a properly formulaed problem whou he uer havng o poe dealed knowledge abou he echnque. Such a olver (CPEX) for example provded by he mahemacal programmng ofware GAMS and wa ued o olve he E2M2 model developed n [7] on whch an exemplary calculaon of he cae udy n h paper baed. The Opon Approach Conrary o he mehodology decrbed before he opon approach examne he profably of an nvemen projec and no only co. The erm opon here dffer omehow from orgn on he fnancal marke where an opon an nrumen o proec agan rk. An unexerced nvemen can be een a an opon becaue he opporune for delayng can- 8

9 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 celng and evenually wchng o oher projec are kep alve. However he nvemen hould feaure he rreverbly and he flexbly.e. he ably o wa a defned n [9]. The rreverbly denoe ha he nvemen become valuele f denfed o be unprofable. I expendure whch repreen unk co can no be reganed hrough ellng he equpmen or ung for oher purpoe. In fac h propery ex o a ceran degree n mo cae. The dnc prncple ha dfferenae he opon approach from he radonal ne preen value rule he prcng of he flexbly wh an opon value. Ung h approach nveor expec a reurn whch no only cover he co bu alo he opon value. The ably o wa valuable and omeme can brng grea benef becaue allow obanng more explc nformaon abou he evoluon of unceran facor. Pror o he marke lberalzaon he opon approach wa no commonly appled o he power plan nvemen problem a he oher one. Some reaon are conderable. Frly he way he opon approach evaluae an nvemen.e. accordng o profably no convenonal. Some auhor (e.g. [2]) argue ha he maxmzaon of prof for he prelberalzed power marke hould lead o he ame reul a he mnmzaon of co nce he demand unchanged. Th hypohe however doe no hold for an mperfec marke where he prce are no e by he compeon equlbrum. Anoher reaon could con n he lack of flexbly o delay an nvemen on he regulaed marke. Depe hee unfavorable concern ome bac dea o adap he opon approach n power plan nvemen can ll be denfed. In [9] for example h mehod wa appled o a wo-age nvemen projec whch hould decde wheher o nall one 200-MW coal-fred plan or wo 100-MW ol-fred plan o mee a yearly demand ncreae of 100 MW. Whle aumng he demand ncreae o be known unceran fuel prce are aken no accoun. In h cae he cale compared o he flexbly. Alhough he lager coal plan comple wh he economy of cale nveng n an ol plan n he fr year provde he pobly o wch n oher echnology f he ol prce urn o be dadvanageou. In recen year he opon approach ha araced much more aenon no only n he evaluaon of nvemen problem bu alo n he operaon of power yem. In he nex par of h econ we are gong o dcu h approach once agan h me n he framework of a lberalzed marke. 2.2 New mehod for he lberalzed marke I no very exac o defne he mehod a new one nce hey already exed and were appled n he me before marke lberalzaon. They are een a new n he lgh of he modfcaon and exenon requred o make hem f for he new envronmen. In conra o he power generaon plannng of he regulaed era decon on power nvemen on he lberalzed marke are done baed on he profably raher han on yem adequacy. A ndcaed by he macroeconomc heory he maxmum of ocal welfare could be reached by he prof maxmzaon of each ndvdual marke parcpan. However h docrne only enable under he aumpon of a perfec marke. Some elecrcy marke do no fulfll h prereque depe beng lberalzed. A an example alhough he German marke 100% lberalzed can be beer decrbed a an olgopoly where he four large ule ll poe he domnan poon. On he oher hand elecrcy conumer do no repond o he prce change a much a before. Therefore clacal economc rule may no be uable 9

10 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 for elecrcy marke and upplemenary nrumen hould be developed o provde a ecure power upply. Dcouned Cah Flow Approach The dcouned cah flow (DCF) approach wa nroduced n an OECD repor [15]. I ake uncerane no accoun n a general way n whch a dcoun rae aumed for he emaon of all major co componen. The deermnaon of h dcoun rae bae on an aemen of varou uncerane wh dfferen cenaro. The OECD udy ae ha compane can apply he DCF approach a comparng dfferen echnologe wh predefned nernal arge for reurn on equy. To addonally handle uncerane n revenue he auhor adve o emae anoher dcoun rae for revenue dfferen han he one for co. Baed on he recen updae of an OECD udy [16] a mehodology o calculae he o called Average feme eveled Elecrcy Generaon Co nroduced. The prncple o fnd a reference co of a projec by makng he preen value of oal co equal o he preen value of revenue over he lfeme. Equaon (4) explan h mehodology n he mahemacal conex. T = 0 * T p E I ( 1+ r) = 0 Where: + M + F (1 + r) = 0 (4) * p r E I M F Reference co o be defned Rk-adjued dcoun rae Elecrcy generaon n he year Invemen expendure n he year Manenance expendure n he year Fuel expendure n he year By olvng (4) * p can be calculaed by applyng he followng formula: p T ( I + M * = 0 = T = 0 + F ) (1 + r) E (1 + r) (5) Ung he reference co o emae dfferen nvemen opon offer he calculaon mplcy and he comparon convenence. However he eleced dcoun rae no elf explanaory nce he way how he dcoun rae deermned by ncludng all uncerane no h facor obcure. Furhermore wheher approprae o rea uncerane n each year baed on he ame dcoun rae alo queonable. 10

11 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 Real Opon Approach In econ 2.1 an nroducon for he bac prncple of he opon approach and a prelmnary example of applcaon o he power plan nvemen problem were provded. The adapaon of he fnancal opon for real ae nvemen whch herefore named real opon had been dcued over he la wo decade. I wa however no wdely acceped on he regulaed power marke. Due o he enormou change of marke fundamenal nce he lberalzaon many reearcher have nvolved he real opon approach n her analy of ome apec of he power yem e.g. uly nvemen and un commmen. Boerud e al. [10] deve a model o calculae he opmal power generaon nvemen raegy under boh cenralzed ocal welfare and decenralzed prof objecve. In [11] h model even exended o analyze he effec of nvemen ncenve on he yem adequacy of an elecrcy marke wh he capacy paymen mechanm. Roque e al. [12] deal wh an nereng obervaon on he lberalzed power marke ha ndvdual nveor end o prefer fol fuel echnologe (carbon naure ga) agan nuclear power. They explan h ue by howng he decreae of he opon value of he nuclear echnology wh a rng correlaon beween elecrcy ga and carbon prce. In order o conder he behavor of oher marke parcpan n nvemen decon Muro [13] develop a mehod combnng he real opon approach wh game heory o ncorporae he compeve neracon no nvemen evaluaon. Snce h paper concenrae on he evaluaon of power generaon projec he mehodology developed by Boerud farly repreenave for an applcaon of he real opon approach. He llurae he dfferenaon of he real opon heory from he clacal ne preen value (NPV) mehod wh he dagram of Fgure 2. Ne Preen Value (NPV) I: Invemen co V*: opmal hrehold for nvemen F(V) = N(V) + A(V) F(V) A(V) N(V) I V* Ne Cah flow from Projec V Fgure 2: Illuraon of he dfference beween he real opon approach and he NPV mehod The curve N(V) how he NPV over he range of poenal ne cah flow of he projec. The clacal NPV mehod would ugge nveng a oon a he ne cah flow exceed he nvemen co I. Accordng o he real opon heory hould however no ye be nveed 11

12 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 unl he NPV of he projec exceed he value of he nvemen opon. The opon value F(V) reul from he NPV of he projec plu an addonal value A(V) of poponng he nvemen decon o wa for more nformaon abou fuure rend of uncerane. In h conex decon-makng ung he ac NPV mehod rea he nvemen raher a a now or never ak. In he mul-age model developed n [10] demand he only facor condered a unceran. A long-erm and a hor-erm uncerany are aken no accoun. Furhermore o quanfy he rk averon of he nveor a rk-adjued dcoun rae ued. The model underle he objecve of maxmzng he ocal welfare or he nvemen prof by deermnng he opmal echnology and nvemen mng. To olve h model he ochac dynamc programmng ued for a backward opmzaon. Becaue he dynamc programmng mple a grea mahemacal complexy and doe no belong o he cope of h paper wll no be dcued n deal. The model n [10] unforunaely ha ome lmaon nce he elecrcy marke condered a a ngle-agen yem. Thu he neracon beween dfferen marke parcpan dregarded. I alo aumed ha nveor are purely prce aker. Bu on he compeve power marke elecrcy prce could be nfluenced o a grea exen e.g. when a new large cale power plan become avalable. To ake he mpac of new capace on he elecrcy prce no he model Keppo and u [14] nclude he prce effec n he calculaon of he opon value conderng ha no only he value of he new plan bu alo he value of oher exng plan of he nveor ubjec o marke prce. The value of a real opon can hen be exended o he followng expreon: F(V) = N(V) + A(V) (V) (5) The erm (V) demonrae he lo value due o lowered marke prce beng caued by he nvemen. A mlar concepon can be found n [17] where he auhor defne he value of a company a he compoon of operave raegc real opon and he value of real ae calculaed on he ba of he adoped raegy. A gnfcan advanage poned ou n [9] a well a n [17] ha applyng he real opon approach avod he elecon of a rk-adjued rae. The nvemen evaluaon calculae drecly wh he rk-free rae whle ncludng uncerane wh her ochac profle n he evaluaon proce. Alhough he applcaon of he real opon heory n he power yem preen a ubanal progre n he mehodology developmen bu he ranfer of h concep from he fnance marke frequenly crczed due o he mperfecon of he elecrcy marke and lower lqudy on radng poble. Therefore prcng of a real opon baed on he marke dffcul [18]. Anoher dffculy ndcaed n he acquon of opon-pecfc npu daa a ochac coeffcen decrbng he volaly of he fuel prce developmen. 2.3 Mehod comparon In h par we preen a bref revew of he urveyed mehod by comparng hem accordng o four characerc a lluraed n Table 1. 12

13 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 Sochac Dynamc Analycal Compuaonal complexy Pre-lberalzaon Snce lberalzaon Deermnc Equvalen Robune Analy Sochac Opmzaon Opon Approach Dcouned Cah Flow Approach Real Opon Approach low - - low - hgh very hgh low very hgh Table 1: Comparon of dcued mehod 3 Cae udy for a e projec In h econ he reul of he applcaon of hree eleced approache nroduced n econ 2 o a cae udy are preened. I mporan o noe ha daa ued for h cae udy bacally aumed for an exemplary calculaon and doe no reflec he realy. In h example a company plan o nve n new capace o mee he ncreae n demand n 2 conecuve year wh an expeced conan growh rae of 100 MW n each perod. The wo echnologe avalable for h company o nve n are coal fred or ga fred plan. Due o echncal conran each coal and ga plan can only be bul wh a ne nalled capacy of 200 MW and 100 MW repecvely. Demand and operang co of he coal plan are aumed a ceran. The evoluon of he operang co of ga plan on he oher hand aumed o preen a gven ochac profle durng he plannng perod and a conan growh rae aferward. I alo agreed ha he eleced power plan could be ready for operaon a he begnnng of each year. In order o provde a comparable bae he lfeme and full load hour of boh plan are equally e o 40 year and 5000 hour. A dcoun rae of 10% choen for he followng calculaon. In Table 2 he parameer of he wo plan ype and he developmen of her operang co are preened. The ga prce n hee wo year aumed o be parcularly volale. Capacy Cap [MW] Invemen co fc [Mo. ] Operaon co n bae year [ / MWh] Operaon co growh rae =1 =2 =3 40 Coal fred plan % 5% 5% Ga fred plan Pr 50% : 50% Pr 50% : 50% Pr 50% : -50% Pr 50% : -50% 5% Table 2: Daa of wo canddae echnologe 13

14 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 The ochac profle gven n Table 2 reul n four cenaro for he developmen of fuure operaon co of he ga fred plan: Scenaro Probably p Operaon co of he ga fred plan oc =1 =2 2 [ /MWh] 1 25% % % % Table 3: Scenaro of fuure operaon co of he ga fred plan We fr formulae h nvemen projec n a ochac opmzaon problem amng a he mnmzaon of oal co durng he plannng perod. Mn = 1 = 1 = 1 fc ( Cap 1 u + p oc Q ) (6) Subjec o 2 Q. D = 1 Q Q τ = 1 u τ Cap 0 u {01} Where: u : Bnary decon varable 1 and for he nvemen n he echnology The opmal oluon of h projec baed on he ochac opmzaon ugge an nvemen of a ga fred plan wh 100 MW capacy for each perod wh a oal expene of Mo. durng he plannng perod. Furher we apply he wo approache dcued a he new mehod n he evaluaon of he cae udy projec. Three alernave nvemen plan are predefned and led n Table 4. Alernave 1 ugge an nvemen n 200 MW of capacy wh one coal fred power. Th repec he economy of cale rule. In conra Alernave 2 buld ju he capacy whch requred n each year and chooe a ga fred plan for each perod. Alernave 3 combne boh opon by addng he exac capacy needed for he fr year and a larger cale coal plan for he remanng me. 14

15 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 =1 =2 Coal [MW] Ga [MW] Coal [MW] Ga [MW] Alernave Alernave Alernave Table 4: Conderable nvemen alernave In he fr ep he leveled co mehod appled o evaluae hee hree alernave. The preen value of oal co and he average lfeme leveled generaon co are calculaed: * p [ /MWh] pv oal [Mo. ] Alernave Alernave Alernave Table 5: Calculaon reul wh leveled co mehod Accordng o he comparon n Table 5 Alernave 1 obvouly he mo economcal varan no only regardng average leveled co bu alo he preen value of oal co. For he nex evaluaon we ue he real opon heory o examne agan he hree nvemen alernave. Alernave 1 doe no need o be modfed and he preen value of oal co over he lfeme correpond o he calculaon reul above. Alernave 2 and Alernave 3 wll furher be een a an nvemen opon whch gve he pobly o wa for more nformaon abou he ga prce developmen rend n he econd year. If he ga prce end o be hgher whch would rae he operaon co n he fr year he nveor could wch he decon o a coal fre plan wh lower fuel co or ck o he nal plan of buldng anoher ga plan. Baed on h we can calculae he preen value of h opon wh he followng formulaon: OV = 50 Mo. (7) 40 /MWh MW 5000h 180 Mo ( + 40 = 2 20 /MWh MW 5000 h ) 90 Mo /MWh MW 5000 h 50 Mo ( + 15

16 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 = 455 Mo. 20 /MWh 200 MW 5000 h = 3 20 /MWh MW 5000 h ) -2 The preen value of h opon gnfcanly lower han ha of Alernave 1. Therefore buldng a ga fred plan n he fr year and keepng he opon for he followng year hould be he preferred decon. A he evaluaon reul how he real opon approach aache addonal value o he nvemen flexbly. The coherence beween uncerane and nvemen decon can be quanavely preened by real opon model wh he mplcaon ha he more unceran he fuure he more valuable he opon and he longer he nvemen me wll be delayed [18]. 4 Concluon The mehod dcued n h paper cover he man caegore commonly ued durng he regulaed me and hoe mehod ha are beng exended for her applcaon n he lberalzed marke. The way each mehod ncorporae uncerane no power plan nvemen evaluaon wa decrbed and compared. Through a cae udy he meanng of dealng wh uncerane n he decon makng wa demonraed and wa hown ha could lead o a oally dfferen reul han baed on purely deermnc aumpon. Of all he mehod decrbed n h paper he real opon approach repreen a novel approach wh he ably o quanavely emae he flexbly of choong beween avalable echnologe deermnng nvemen mng and defnng nvemen cale. A hown n h paper mo mehod dealng wh uncerane demand her quanave decrpon. Therefore mehodologe able o precely model he uncerane wll be requred o furher mprove hee mehod and her applcably. On he oher hand hgher accuracy on he decrpon of uncerane may dramacally ncreae he complexy of he decon problem due o he ochac and dynamc propere. Therefore he developmen of mehodologe o denfy he gnfcan nfluencng facor anoher neceary and challengng ak. 16

17 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 Acknowledgemen Th paper preen a reearch whn he ongong projec Energewrchaflche Anforderungen und Inveonenchedungen für neue Krafwerke m lberaleren Mark fnancally uppored by he Sfung Energeforchung Baden-Würemberg Semen AG E. ON Energe AG and MTU Aero Engne GmbH aocaed wh projec KW21: Reearch Nework Power Plan for he 21 Cenury (hp:// Reference [1] Krchen D. and Srbac G. (2004) Fundamenal of Power Syem Economc: [2] Croulla E. O. (1989) Incorporang Rk and Uncerany n Power Syem Plannng Workng Paper of The World Bank [3] Gorenn B. G. Campodonco N. M. Coa J. P. and Perera M. V. F. (1993) Power Syem Expanon Plannng Under Uncerany IEEE Tranacon On Power Syem 8(1): [4] Burke W. J. Merrll H. M. Schweppe F. C. ovell B. E. McCoy and M. F. Monohon S. A. (1988) Trade Off Mehod n Syem Plannng IEEE Tranacon On Power Syem 3(3): [5] Bender J. F. (1962) Paronng procedure for olvng mxed varable programmng problem Numer. Mah. vol. 4: [6] Granvlle S. (1988) Mahemacal Decompoon Technque for Power Syem Expanon Plannng EPRI E-5299 [7] Swder D. J. and Weber C. (2005) The Effec of Sochac Elecrcy Marke Modellng on Emang Addonal Co of Inermen RES-E Inegraon 7h IAEE European Conference Bergen Norway [8] Kalvelagen E. (2003) Bender Decompoon for Sochac Programmng wh GAMS hp:// [9] Dx A.K. and Pndyck R.S. (1994) Invemen under Uncerany Prnceon Unvery Pre: 3-54 [10] Boerud A. Ilc M. D. and Wangeneen I. (2004) Opmal Invemen n Power Generaon Under Cenralzed and Decenralzed Decon Makng IEEE Tranacon On Power Syem 20(1): [11] Boerud A. and Korpå M. (2004) Modellng of Power Generaon Invemen Incenve under Uncerany n beralzed Elecrcy Marke 6h IAEE European Conference Zurch Swzerland [12] Roque F. A. Nuall W.J. Newbery D. M. and de Neufvlle R. (2005) Nuclear Power: a Hedge agan Unceran Ga and Carbon Prce? hp:// 17

18 Preened a he 29h IAEE Inernaonal Conference. Podam Germany June 2006 [13] Muro P.(2003) On Invemen Uncerany and Sraegc Ineracon wh Applcaon n Energy Marke Syem Analy aboraory Reearch Repor A84 Helnk Unvery of Technology Fnland [14] Keppo J. and u H. (2003) Real Opon and A arge Producer: The Cae o Elecrcy Marke Energy Economc 25(2003): [15] OECD/IEA (2003) Power Generaon Invemen n Elecrcy Marke: [16] OECD/IEA (2005) Projeced co of Generang Elecrcy 2005 Updae: [17] Ram A. (2001) De Bewerung von Krafwerknveonen al Realoponen. Hommel U. Scholch M. and Vollrah R. Reale Oponen n der Unernehmenprax. Sprnger Verlag: [18] Müller D. (2005) Inveonenchedung n der Elekrzäwrchaf ene berebwrchaflche Analye. Zechrf für Energewrchaf 29(2005) 1: