FINANCING OF RADIOACTIVE WASTE DISPOSAL IN THE CZECH REPUBLIC

Transcription

1 FINANCING OF RADIOACTIVE WASTE DISPOSAL IN THE CZECH REPUBLIC Auhors: Mroslav Kucerka, RAWRA Jan Cmburek, consulan o RAWRA Jaroslava Lehneova, RAWRA INTRODUCTION In 1997 n he Czech Reublc came n force a new Aomc Ac he Ac No. 18/1997 Coll., On Peaceful Ulzaon of Nuclear Energy and Ionzng Radaon. Among he oher rovsons he Ac has esablshed new sae olcy n he feld of radoacve wase managemen. A new sae organzaon, he Radoacve Wase Reosory Auhory (RAWRA), whch s resonsble for radoacve wase dsosal, has been esablshed n June The rovsons of he Ac clarfy he relaons beween radoacve wase generaors and sae, and defne exlcly dues of wase generaors. One of her mos moran dues s o cover all exenses for radoacve wase managemen now and n he fuure, ncludng radoacve wase dsosal and decommssonng of nuclear facles. For a cumulaon of fnancal resources from wase generaors, o cover coss on dsosal of her radoacve wase, a secal sae fund - he Nuclear Accoun has been esablshed. To assure suffcen fnancal resources for decommssonng of nuclear nsallaon, her owners are oblged o creae a secal reserve whn her accounng and budge. The exsng radoacve wase reosores shall be ransferred o he Sae ownersh and oeraed by RAWRA no laer han n June RAWRA s resonsble also for admnsraon of leves o he Nuclear Accoun, whch ncludes also develomen of calculaon formula and calculaon of ndvdual leves. The admnsraon of leves and he Nuclear Accoun s regulaed by he governmenal drecve No. 224/97 Coll., where are lad down he basc rovson on relaons beween RAWRA and wase generaors. RAWRA s resonsble for rearaon of a roosal of a new regulaon ha should relace he resen one, afer a ransfer of he reosores no roery of he Sae, and sar of her oeraon under RAWRA. The followng few aragrahs show n bref he new aroach o he leves assessmen n he Czech Reublc whch uses a basc mahemacal aaraus lnear rogrammng. Followng aragrahs are a summary of a revous work called The Mehodology for Calculaon of Leves o he Nuclear Accoun ublshed a he Economc Unversy n Prague as a dloma work, ha was develoed n accordance o needs of RAWRA. The goal of he work s o rovde a basc mehodology for he leves assessmen, ha ncludes a ool for esablshng of some qualave crera and her weghs f needed. For hs urose a self-generang mahemacal model s creaed, whch uses all he nus, creaes a ceran mahemacal algorhm and offers resuls (whch qualy deends on he qualy of he nu daa). THE CASH FLOW IN THE SYSTEM By he sysem are mean all he elemens of organzaon and managemen of he RW dsosal rocess. The fnancng of he whole sysem from he esablshmen ll he ermnaon s ensured by collecng fnancal resources a he nuclear accoun. The nuclear accoun has wo sdes: 1. exendure sde 2. ncome sde

2 The ransfer of fnance o and from wo sdes of he nuclear accoun reresens cash flow n he sysem. On he exendure sde are recorded ransfers from he nuclear accoun exendure, on he ncome sde are recorded ransfers o he nuclear accoun ncome. The goal of he nuclear accoun s o assure suffcen fnancal resources for assurng he rmary funcon of he sysem he safe RW dsosal and acves conneced wh. EXPENDITURE The analyss of exendure sde of he nuclear accoun, he quanfcaon and descron of exendure are he mos moran facors for he exac assessmen of he desred ncome no he sysem and herefore he mos moran facor for he assessmen of he leves. The exendure sde of he nuclear accoun s consued of hese yes of exendure: Non-nvesmen exendure By non-nvesmen exendure are mean he fnancal resources sen on securng he common funcons of RAWRA. Among non-nvesmen belong all fnancal resources essenal for securng he everyday oeraon of reosores (oerang exendure). Invesmen exendure By nvesmen exendure are mean he fnancal resources sen on lanned or unlanned nvesmen rojecs. The mos moran and exensve nvesmen rojec s a consrucon of a underground reosory. Bu here are oher nvesmen rojecs such as nvesmen no modernzng he exsng RW reosores. INCOME Fnancal resources flowng no he sysem reresen he ncome sde of he nuclear accoun. These resources are deosed on he nuclear accoun wh he goal o cover all he necessary exendure. The Aomc law defnes all ossble yes of ncome: a) Fnancal resources obaned from he RW generaors b) Ineres from he nuclear accoun c) Revenue from oeraons on he fnancal marke d) RAWRA ncome e) Subvenons, donaons, grans, ec. For he uroses of he mehodology, everyhng, exce he leves, s called he oher ncome. Income s called he oal ncome (leves + oher ncome). CATEGORIZATION OF RW Before he leves assessmen we need o grou RW no concree RW caegores. For hese concree RW caegores are hen calculaed adequae leves. I s ossble o choose from a wde range of crera (for examle: acvy, half-lfe me, radooxcy, ec.). Afer selecng relevan crera, he model generaes several RW caegores. MODEL FOR LEVIES CALCULATION The model for levy calculaon s suosed o rovde a rce ls, n whch for each RW caegory s deermned he rce for a RW un. The caegorsaon rocess s a rocess, whch combnes acceed

3 crera and creaes RW caegores so ha any generaed RW can belong no one of he caegores. In he model we use: K acceed crera for =1,2,,k k he number of acceed crera Each of he crera dvdes no sub-crera: K j j=1,2,,k k he number of sub-crera n he -h creron for =1,2,,k Afer combnng every creron we ge n RW caegores: n = k = 1 k Each caegory s denfed by a number code. The code s k numbers long and on he -h oson of he code s he concree value of he sub-creron n he -h creron. (a 1 a 2 a 3... a k ) Ths secfc number confguraon s used for wegh assessmen of every RW caegory. WEIGHTS IN THE MODEL There are wo yes of weghs n he model: 1. The crera weghs 2. The RW caegores weghs The crera weghs deermne he morance of he creron and are he base ndcaor for he RW caegores weghs calculaon. The RW caegory weghs deermne he oron of each RW caegory on he oal exendure. The quanfcaon of weghs for crera and sub-crera s a raher comlcaed rocess whch suoses co-oeraon of a large grou of exers n varous felds. Those exers quanfy he wegh of every sngle creron usng varous mehods such as he Saay mehod. Wegh s assgned o every RW caegory. As above every RW caegory s descrbed by s code. Numbers n hs code deermne he value of he concree RW caegory wegh: v(a a a 1 2 k v1w ) = 1a + v w = 1 j = a 1 2 k k v w j + w w k ka k THE ROLE OF TIME IN THE MODEL Tme and s flow lay an moran role n he whole sysem. The dynamcs of he whole rocess s nheren n hese areas: 1. Exendure me dversfcaon Exendure s rregularly dversfed hrough he me. Ths rregulary s caused for examle by hgh nvesmens for he consrucon of he underground reosory. 2. RW roducon me dversfcaon The amoun of roduced RW s changng durng he me. Whn he framework of our sysem he amoun of roduced RW reresens demand for RAWRA servces.

4 3. Income me dversfcaon The oal amoun of fnance flowng no he sysem s deenden on RW roducon, as he RW roducon s he man deermnan of RAWRA ncome. 4. Inflaon Inflaon lays an moran role n devaluaon of he fnancal resources deosed on he nuclear accoun. The me dsharmony n he momen of collecng fnancal resources on one hand and nvesng hese fnancal resources on he oher would lead no gradual decrease of he real value of he fnancal resources. 5. Income from oeraons on fnancal marke The ncome from he nvesmen of free fnancal resources from he Nuclear Accoun kees he real value of he fnancal resources and ncreases her nomnal value. The recen dscusson s wheher he ncome from nvesng wll cover an nflaon only or wll be hgher (he real value of he deosed money wll ncrease) or wll be lower (he real value of he deosed money wll decrease). In hs mehodology verson s used he frs aroach nflaon and nvesmen ncome are he same. 6. Suffcency of he fnancal resources on he nuclear accoun The ereual flucuaon of he economc resul (ncome mnus exendure) s caused by he exendure and ncome me dversfcaon. The condon s ha he whole sysem should be selffnancng. Ths condon means ha here can be no red numbers on he nuclear accoun and he leves should assure. 7. Suffcency of he fnancal resources on he nuclear accoun afer RW roducon ermnaon Because of he me dsharmony beween he laned RAWRA oeraon and RW generaors acves lfeme, s necessary o assure suffcen amoun of fnancal resources on he nuclear accoun. Ths fnal cash balance s essenal for fnancng he sysem, when no longer any leves wll flow o he nuclear accoun. The dynamcs of he whole rocess s dslayed n he followng able. Table I: The dynamcs of he rocess Years RW roducon n RW uns Exendure Income Economc Cash balance T RW 1, - code RW 2, - code RW n, - code N I resul NA 1998 RW 1,1998 RW 2,1998 RW n,1998 E 1998 I 1998 ER 1998 NA RW 1,1999 RW 2,1999 RW n,1999 E 1999 I 1999 ER 1999 NA T RW 1,T RW 2,T RW n,t E T I T NA T Toal ΣRW 1 ΣRW 2 ΣRW n ΣE ΣI ΣER Levy 1 2 n RW, roducon of RW of -h caegory n he year (=1,2,...,n) E oal exendure n he year

5 I oal ncome n he year NA cash balance on he nuclear accoun n he year NA T fnal cash balance on he nuclear accoun n he year T FCB he rce for he dsosal of one RW un n each RW caegory (=1,2,...,n) THE CALCULATION ALGORITHM The goal of RAWRA s o assure suffcen fnancal resources for fnancng he RW dsosal and before of all he consrucon of he new underground reosory. For all hs uroses s requred o cover all he exendure wh ncome. Whereas he whole rocess of fnancng s non-rof we ge he followng equy: TS = z n = 1 T = S E n I, where I = RW, + OI = z =1 RW, = 0, ro =T s,t s +1,...,T E... exendure n he year I... ncome n he year T S... he ermnaon of he sysem T... he ermnaon of all RW generaors The whole roblem of he assessmen of leves o he nuclear accoun can be ransferred on a mahemacal omzng model, whch nus are: The roducon of RW dvded no n caegores n concree years (me seres) RAWRA exendure n concree years (me seres) RAWRA oher ncomes n concree years (me seres) There also derved quanes n he omzng model: RAWRA economc resul n each year (ncome mnus exendure) Nuclear accoun s cash balance (cumulave sum of economc resuls n recen years) As o fulfl he consran of self-fnancng of he whole rocess s necessary o assure suffcen fnancal resources on he nuclear accoun. Ths condon says ha s no ossble o dro he fnancal resources on he nuclear accoun below zero and can be characerzed by he followng consran: NA 0, = z, z +1,...,T NA... he nuclear accoun cash balance Varables of he omzng model are he leves for he RW un for each RW caegory: 1, 2,..., n. LEVIES CONSTRAINTS As above he morance of RW caegory wegh s o deermne he oron of each RW caegory on he oal exendure conneced wh RW dsosal.

6 Table II: The oal oron of he RW caegores on oal exendure RW caegory RW caegory wegh Poron on he oal exendure RW 1 - code v(code) 1 v(code) 1 ΣN RW 2 - code v(code) 2 v(code) 2 ΣN RW n - code v(code) 3 v(code) 3 ΣN Toal exendure n nerval 1998 T ΣN The sum of fnancal resources reresenng he oron of he concree RW caegory on he oal exendure s dslayed n he hrd column of he able. Afer a able ransformaon we ge he followng able whch comrses leves for he RW un n each RW caegory. Table III: Theorecal leves - T RW caegory RW roducon RW caegory wegh Poron on he oal exendure Levy for he RW un - T RW 1 - code RW 1 v(code) 1 v(code) 1 ΣN (v(code) 1 ΣN)/RW 1 RW 2 - code RW 2 v(code) 2 v(code) 2 ΣN (v(code) 2 ΣN)/RW 2 RW n - code RW n v(code) n v(code) n ΣN (v(code) n ΣN)/RW 3 Toal exendure n nerval 1998 T ΣN If we had o analyse he sysem annually, hen we wouldn requre he self-fnancng consran and we could consder T as he fnal values (leves) and so omzng. Unforunaely hese values are only heorecal leves and deermne an nerval for he acual leves levy consrans. The levy consrans are derved from T calculaed n he able above. 1. Inervals D H L lower bound of he nerval for concree levy for =1,2,,n U uer bound of he nerval for concree levy for =1,2,,n I s ossble o calculae he concree values of he lower and uer bounds by dfferen ransformaons of T. Transformaons: absolue The absolue ransformaon ransforms values T by addng or subracng a gven consan from o T. = d, where d 0, D H T, where h = + h, T ( T ) ( 0 ), =1,2,...,n relave The relave ransformaon ransforms values T by mullyng values T by a gven consan.

7 D H = T d, where d = h where h, T, ( 0,1) ( 1 ), =1,2,...,n combnaon of absolue and relave I s ossble o combne ransformaon of T. Table IV: Levy consrans Lower bound - D o 1D o 2D o nd Levy - o 1 o 2 o n Uer bound - H o 1H o 2H o nh D H n D n n H D 1 1 1H 2. Fxed nervals If s needed he nervals can be fxed no ransformaon s needed 3. Combnaon of nervals and fxed leves Some of he RW caegores can have fxed leves and some can have nerval consrans. THE OPTIMIZING MODEL The roblem of assessmen of he leves can be ransferred on a lnear omzng roblem. For hs ransformaon s necessary o defne he objecve funcon, varables and consrans. objecve funcon T n z = RW, + OI MAX = b + 1 = 1 consrans T n T RW, + OI E + FCB = + 1 = 1 = + 1 b b n SCB + RW, + OI E 0, = b +1, b +2,...,T j= b + 1 = 1, =1,2,...,n H, =1,2,...,n D 0, =1,2,...,n varables for =1,2,...,n (where s consraned) The characersaon of he model quanes: RW, RW roducon n a secfc caegory n he year E oal exendure n he year OI... oher ncome n he year FCB desred fnal cash balance on he nuclear accoun SCB... sarng cash balance on he nuclear accoun

8 levy for he RW un n he -h RW caegory U uer bound for he levy n he -h RW caegory L lower bound for he levy n he -h RW caegory T... he acvy ermnaon of all RW generaors b... acual erod (erod n whch s he sysem a he momen) I was necessary o secfy he objecve funcon as maxmze (mnmze) funcon as o be able o aly he means of lnear rogrammng. The bes ways s o maxmze he oal ncome of he fnancal resources flowng no he sysem. I s clear ha maxmzng of he ncome whou any consrans would lead no nfne ncome. Tha s why here are consrans n he omzng model, whch are securng he non-rof rncle (exendure equals ncome n he me nerval). The me nerval ha defnes he me of he exsence of he sysem s z, TS. Ths nerval comrses wo sub-nervals: z, T and ( T, Ts. The equy condon for exendure and ncome n he nerval z, TS s T n T assured by he consran RW, + OI E + FCB, where he exresson on he = b + 1 = 1 = b + 1 rgh sde reresens he exendure of he sysem n he nerval z, TS and he exresson on he lef hand sde reresens he ncome of he sysem n he nerval z, T. Durng he nerval z, T RW generaors erodcally ransfer her leves ono he nuclear accoun. Durng he nerval ( T, s he funcon of he sysem fnanced only by he fnancal resources lef on he Ts nuclear accoun n he year T. The oal sum of he fnancal lef on he nuclear accoun equals FCB (fnal cash balance) and also by he RAWRA oher ncome. z +1 z T T S The sar of nuclear accoun s funcon The erodcal leves udang The acvy ermnaon of all RW generaors The ermnaon of he whole sysem The leves assessmen for he frs erod Income Leves on he nuclear accoun + oher ncome Oher ncome Exendure Invesmen + Non-nvesmen exendure Non-nvesmen exendure Fnancal means on he nuclear accoun The cumulaon of he fnancal means n order o he economc resul - he man deermnan are he fnancal means obaned from he RW generaors The fnal cash balance - FCB decreases by he economc resul n each erod Fgure 1: The me schedule of ncome, exendure and he fnancal resources on he nuclear accoun

9 The amoun of he fnancal resources deosed on he nuclear accoun s deenden on he RAWRA economc resul n each year (ncome mnus exendure). I s clear, from he logc of he roblem, ha amoun of he fnancal resources on he nuclear accoun wll ncrease from he year z (he sar of he nuclear accoun). I wll be ncrease unl he exendure wll oubalance he ncome (hs wll haen n he erod of huge nvesmen no he consrcon of he underground reosory execed round 2030). Afer hs oubalance he fnancal resources on he nuclear accoun wll decrease unl he year T, when he man source of ncome leves wll so. The fnancal resources n he nerval ( T, Ts wll furher decrease from he fnal cash balance (FCB) ll zero. The fnancal resources on he nuclear accoun should no dro below zero n he whole nerval, T. Ths s assured by he consran: n SCB + RW, + OI E 0, = b +1, b +2,...,T. j= + 1 = 1 b z S

10 Consrucon of he new reosory Invesmens no he old reosores Invesmen exendure RAWRA Reosores exendure exendure Non-nvesmen exendure RW generaors New echnologes Energec olces,... Oher facors Planned exendure Planned RW roducon Crera Tme seres Consans Model crera Crera for RW Crera for RW generaors Crera weghs Tme seres Planned exendure Planned oher ncome Planned RW roducon Consans Sarng cash balance Fnal cash balance Consrans for leves Model for leves calculaon Leves (rce ls) Fgure 2: The rocess of leves calculaon THE START OF THE NUCLEAR ACCOUNT FUNCTION The sar of he nuclear accoun funcon should roceed n several relmnary hases, whch goal s o rovde a suffcen amoun of nformaon needed for he assessmen of leves: 1. The defnon of RW caegores 2. The quanfcaon of nu nformaon 2.1. The creaon of he RW generaors daabase 2.2. The quanfcaon of exendure me seres 2.3. The quanfcaon of oher ncome me seres 2.4. The quanfcaon of oher nu nformaon 3. The assessmen of leves for he frs erod 4. The nofcaon of leves

11 THE ADMINISTRATION OF THE NUCLEAR ACCOUNT By he admnsraon of he nuclear accoun s mean he funconng of he nuclear accoun durng he exsence of he sysem. The oeraons conneced wh he funconng of he nuclear accoun: Udang leves on he bass of comarson of he lan and realy The assessmen of sandard rocedures for leves collecon The consrucon of he aymen order for RW generaors The annual schedule for he nuclear accoun funconng (assessmen and leves collecon, roosal for RAWRA exendure for he governmen,...) The collecon of nformaon relevan o he sysem Oher oeraons (for examle he conrollng funcon,...) Inu changes RW roducon Exendure Income FCB Tme horzon Oher changes The quanfcaon of nu changes and udang of nu daa Leves assessmen for he new erod (+1) The common erod The admnsraon of he nuclear accoun The boundary beween he new erod and he common erod - he change of he new erod o he common erod and he leves nofcaon for he common erod Fgure 3: The rocess of annual udang All he oeraons above are very comlex and comlcaed. Esecally he oeraon of udang leves lays a key role and s conneced wh many sub-oeraons. EXPECTED DEVELOPMENT OF THE METHODOLOGY The model offers one ossble look a he subsanal roblem of levy assessmen wh s advanages and dsadvanages.

12 The dsadvanages of hs hlosohy are now n dscusson. Some of he sakeholders requre ha he model should be aled so ha levy s calculaed for each reosory searaely. The nflaon facor and he nflaon mac analyss can be mlemened no he model. A ossbly of a robablsc rsk assessmen mehod mlemenaon s dscussed as well. The success and he recson of he model deend on he qualy of all he nu daa. Therefore, for daa qualfcaon and quanfcaon, exer eams n varous felds (RW classfcaon, accounng, omzng,...) shall be esablshed. REFERENCES 1. The Ac No. 18/1997 Coll., on he eaceful ulsaon of nuclear energy and onsng radaon (The Aomc Ac) 2. The Governmen Resoluon No. 244/1997 on he amoun and manner of aymens by radoacve wase roducers o he nuclear accoun 3. The Ac No. 337/1992 Coll., on he admnsraon of axes 4. M. MANAS, P. FIALA, J. JABLONSKY, The mulcrera assessmen mehods, Insue of Economy, Prague (1997) 5. Inernaonal Aomc Energy Agency: Safey analyss mehodologes for radoacve wase reosores n shallow ground, (Venna 1997) 6. The roosal of The Mehodology for Calculaon of Leves o he Nuclear Accoun, he nernal documen of RAWRA reared by PROSPECTUS ld.(1997)