Dynamical Behavior of Fuel Cost Component in Total Electricity Cost of Nuclear Power Plants with WWER-type Power Units

Transcription

1 Dynamcal Behavor of Fuel Cost Component n Total Electrcty Cost of Nuclear Power Plants wth WWER-type Power Unts A.V. Kryanev 1,2,N.I.Geraskn 2, V.V. Hartonov 2, S.G. Klmanov 2, V.I. Savander 2 1 Laboratory of Informaton Technologes, JINR 2 Moscow Engneerng Physcal Insttute (State Unversty) Abstract The paper descrbes a techncal and economcal analyss of those changes n the fuel component of prme electrcal energy cost, whch are caused by mplementng varous versons of nuclear fuel desgn and nuclear fuel cycle (NFC) schemes on example of WWER-440 power reactors. 1 Introducton At present tme, thrty-one nuclear power unts are under operaton n the Russan Federaton, ncludng ffteen power unts of WWER-type (sx WWER-440 power unts and nne WWER power unts). In addton, thrty-nne Russan nuclear power unts were bult-up abroad (twenty WWER-440 power unts and nneteen WWER-1000 power unts). The Federal Purposeful Program Development of Russan Nuclear Power Industral System n and, n perspectve, up to 2015 was adopted by the Russan Government on October 6, 2006, and the Program set a task for the accelerated deployment of nuclear power plants and upgraded effcency of electrcty generaton at nuclear power plants (NPP) through reducng specfc expenses, for nstance, by reducng fuel cost component n total cost of electrcty generated by NPP (The Federal Purposeful Program, 2006; Strategy for development of Russan nuclear power n the frst half of the XXI century, 2001). In order to mprove effcency of fuel utlzaton and ncrease ts compettveness n the last few years n Russa some new desgn versons of fuel assembles and advanced fuel cycles have been developed and mplemented nto Russan NPP and some Russan-desgn NPP abroad. Transton to new types of nuclear fuel wth ncreased uranum enrchment and new fuel cycles wth ncreased multplcty of refuelngs pursues the 0, fuel and nvestment components (Shevelev, Klmenko, 1996; Economcs of nuclear power ndustry, 2004; Gordeev, 2001; Snev, 1986; Konovalov et al., 2002). When mplementng a new fuel type or an advanced scheme of refuelng, we decrease the fuel component n prme cost of electrcal energy. Under constant cost of the delvered electrcal energy, full economy n the fuel component may be used for ncreasng the nvestment component, and ths can gve an addtonal mpetus to further development of nuclear power ndustry n Russa. The paper presents the followng studes: 1. Techncal and economcal analyss of those changes n the fuel component of prme electrcal energy cost, whch are caused by mplementng varous versons of nuclear fuel desgn and NCF schemes on example of WWER-440 power reactors. 2. Senstvty assessment of the fuel component to the predcted prce varatons. 3. Determnaton of rsk to lose economcal effcency. 2 Statc model A varant of WWER-440 desgn wth well-profled fuel dstrbuton n fuel assembles (average uranum enrchment % 235 U) was adopted as a basc case for further comparatve analyss of fuel utlzaton schemes n power reactors of WWER-440 type. Smlar fuel s beng used 198

2 now n 4-year fuel campagns of NPP Dukovany (EDU3), NPP Mohovce (EMO1) and NPP Bogunce (EBO4). Currently, the second-generaton fuel assembles loaded wth uranumgadolnum fuel (average uranum enrchment % 235 U) have been developed, and they are beng mplemented now nto fuel cycles of WWER-440. These fuel assembles are planned for usng n 5-year fuel campagns of Cola NPP and NPP Dukovany. The fuel component n prme cost of electrcal energy for varous fuel types was calculated for once-through fuel cycle of WWER-440. It means that spent fuel assembles are transported for long-term storage and reprocessng wthout any recycle of resdual uranum and accumulated plutonum. The followng expenses were taken nto account: 1. expenses for natural uranum needed for fabrcaton of the feedng fuel; 2. expenses for converson of natural uranum; 3. expenses for uranum sotope enrchment; 4. expenses for fabrcaton of dfferent fuel assembles for smultaneous loadng nto the reactor core; 5. expenses for SNF management (nterm storage and reprocessng). The fuel component n prme cost of electrcal energy Y (US dollars per MW day) s defned as a rato of the feedng fuel cost 3 (US dollars), ncludng all the expenses lsted above, to full amount of thermal energy produced for the reactor operaton tme between two consecutve refuelngs W (MW days): Y = 3 W. (1) It was assumed that thermal effcency factor for all versons of WWER-440 under consderaton here was of dentcal value. Specfc consumpton of natural uranum M (x) for fabrcaton of one fuel assembly of -th type wth uranum mass m and uranum enrchment x may be calculated from the followng equaton (Gordeev, 2001): M (x) =f(x, y, c) m f(x, y, c) = x y, (2) c y where c, y -fractonof 235 U ( uranum enrchment ) n natural uranum and n uranum waste, respectvely; f(x, y, c)- consumpton factor. The expenses for uranum sotope enrchment are defned by the number of the Separatve Work Unts (SWU) per producton of one klogram of uranum enrched up to x. The number of the SWU depends on uranum enrchment n product and n waste, as t follows from the followng equaton (Gordeev, 2001): ( ERR(x, y) =(2 x 1) ln x ( ) (2 c 1) x y c y ln c 1 c. 1 x ) ( ) +(2 y 1) x c c y ln y 1 y So, total cost of enrched uranum for fabrcaton of the feedng fuel may be calculated by usng the formula: 3 U =(C e + C k ) n M +C R n m ERR, (4) where C e cost of natural uranum (USD/kg U), C k cost of uranum converson (USD/kg U), C R cost of one Separatve Work Unt (USD/SWU), n the number of fuel assembles of -th type. The expenses related wth fabrcaton of fuel assembles and SNF management are proportonal to uranum mass n fuel assembles of any type. So, these expenses may be calculated by usng the followng formula: 3 FA = C zg n m + C X n m, (5) 199 (3)

3 where C zg - cost for fabrcaton of fuel assembles of -th type; C X - cost for storage of spent fuel assembles per one klogram of fuel. The man factor that makes t possble to ncrease fuel burn-up s related wth hgher uranum enrchment n the feedng fuel. Another factors, such as the ncreased multplcty of refuelngs, the lower neutron absorpton n structural materals (by usng thnner wrappers of fuel assembles, for nstance), proper axal dstrbuton of fuel, can lead to the hgher fuel also, but to the less degree. By usng the adopted methodology, the fuel components n prme cost of NPP-generated electrcal energy were calculated for all the ways towards upgradng the fuel utlzaton effcency n power reactors of WWER-440 type. Uranum enrchment n the feedng fuel was vared wthn the range from 3.82% to 5.0%. Multplcty of refuelngs was vared from 4 to 6, ncludng mxed refuelngs. Two versons were consdered for ncreasng fuel load n pellet: removal of central vod cavty from the pellet, elongaton of fuel column n fuel rod on 60 mm. Slght reducng the number of fuel rods n fuel assembly (from 126 to 120) resulted n some larger ptch of fuel lattce. Fuel loadng was profled by usng the lower-enrched uranum n axal blankets (100-mm long). The followng prces at dfferent NFC stages were used n numercal analyss of the varants lsted above: prce of natural uranum - C e =46.0 USD/kg U; prce of SWU - C R =88,0 USD/SWU; prce of uranum converson - C K =7.5 USD/kg U; prce of fuel fabrcaton for all types of fuel assembles - C zg =310 USD/kg U; prce of SNF long-term storage and reprocessng - C X =650 USD/kg U. The results obtaned n the calculatons are presented n Fg. 1 n form of dots on the plane, where average values of fuel burn-up n dscharged fuel assembles are lad on axs of abscssas and the fuel components n prme cost of electrcal energy are lad on axs of ordnates for all the varants. As s seen, the dependence has a non-monotonous nature though general tendency s traced as a lnear recesson of the fuel component wth growth of fuel burn-up. Therefore, these data were treated wth the least square method and presented n Fg. 1 n form of lnear functon. The followng unambguous concluson can be derved from these results: major factor, whch s able to decrease the fuel component n prme cost of electrcal energy, s related wth the utmost possble growth of fuel burn-up, regardless the way we used to succeed t. Indeed, the hgher fuel burn-up, the larger proportonally expenses for natural uranum and uranum enrchment, but expenses for fabrcaton of fresh fuel assembles and expenses for SNF management reduce proportonally to ncreasng fuel burn-up because cost of SNF management, accordng to our assumptons, s proportonal to SNF mass. Comparson of two varants wth maxmal dfference between the values of fuel burn-up may be used here as an llustraton to the concluson. In the varant wth maxmal value of fuel burnup, contrbuton of the expenses for natural uranum and ts sotope enrchment nto the fuel component n prme cost of electrcal energy s equal to about 54%. If fuel burn-up ncreases, the fuel component drops down, and ths decrease may be decomposed onto contrbutons of ndvdual NFC stages. It turned out that the less expenses for natural uranum and ts sotope enrchment contrbute only 23% nto total economy of the fuel component. The less expenses for SNF management gave a man contrbuton nto reducton of the fuel component. 3 Dynamc model Further, we consder dynamc behavor of the fuel component n prme cost of electrcal energy under uncertan condtons of tme-dependent varatons n prce characterstcs of dfferent NFC stages. Dynamc analyss of the fuel component under uncertan prce varatons requres makng 200

4 Fg. 1: Dependence of the fuel components n prme cost of electrcal energy on fuel burn-up n spent fuel assembles a prognoss on tme-dependence of the followng parameters for some gven perod of NPP operaton: the normalzed expenses for fuel fabrcaton and storage at all NFC stages; tarff on electrcal energy and rate of dscount. All the calculatons were carred out under the followng assumpton: tme t takes only dscrete values,.e. t = 0 means a start-up date of the reactor operaton; t = 1 means the end of the frst year of the reactor operaton and so on. Full perod of the reactor operaton s equal to N years (we used N = 20 n our calculatons). Tme-dependent uncertantes of prce characterstcs are expressed here n the followng forms: C j (t) =Cj PRED (t) [1 + ε j (t)], (6) where Cj PRED (t) - the predcted prce value of j-th prce component at tme moment t; ε j (t) - random fluctuaton of approprate prce component n the vcnty of ts predcted value. The varable j corresponds to ndvdual prce components, namely C e - prce of natural uranum; C R - prce of separate works; C k - prce of uranum converson; C zg - prce of fuel fabrcaton for all types of fuel assembles; C x - prce of long-term storage per 1 kg of spent fuel. The dscounted cost of electrcal energy produced for some tme perod from t=0 to t=τ s calculated by the followng formula: W (τ) =W 0 τ t=1 LF (t) C T (t) (1 + r(t)) t, τ =1,..., N, (7) where W 0 annual producton of electrcal energy for NPP operaton at constant level of nstalled power, LF (t) - load factor of nstalled power n year t ; C T (t)- average tarff of electrcal energy n year t, r(t) - rate of dscount. The values presented above were taken as ntal costs at dfferent NFC stages. Intal tarff of electrcal energy was taken as C T (0) = 0.041$/(kwt h). 201

5 Numercal algorthm for evaluatng the dynamc varatons of prces and tarffs foresees a possblty to take nto account the correlatons between vector components of the random fluctuatons n prces and tarffs. The random fluctuatons are defned by the covarance matrx K ε, elements of whch are equal to the dspersons n vector components of the random fluctuaton dspersons (dagonal elements) and co-varatons between couples of vector components (non-dagonal elements) (Kryanev and Lukn, 2006). Acquston of suffcent statstcal nformaton about dstrbutons of specfc expenses at dfferent NFC stages, whch were calculated by formulae (6-7), made t possble to determne rsk for specfc expenses of the fuel component by the followng formula: p(z(τ) Z )=p rsk, (8) where p (Z(τ) Z (τ)) - probablty for element Z(τ) of the fuel component to be larger than the utmost possble value Z,p rsk the gven rsk probablty, whch was used n calculatons, f the random prce fluctuatons took place (usually, standard value of the rsk probablty p rsk = 0.05 s taken n the calculatons). It s assumed n the calculatons that tme s counted out from the date when all fuel assembles of the gven type are loaded nto the reactor core,.e. t = 0. The number of fuel assembles n eff, necessary for refuelng n every calendar year, was calculated by the formula: n eff = 365n /T eff,wheret eff average effectve tme (n calendar days) between two consecutve refuelngs. The growng lnear and pecewse-lnear functons are used n the forecastng models of prce dynamcs: CJ PRED (t) =C J (1 + k J t), (9) where C J - ntal prce at j-th stage of nuclear fuel cycle, k J - coeffcents of lnear or pecewselnear growth of approprate prces. Tme-dependences were calculated for man consttuents of the fuel component for varous values of ntal parameters. Results of the calculatons are presented n Fgs. 2 and 3. The ordnates are the values of the dscounted expenses Y for approprate consttuents of the fuel component. These values were obtaned from the followng nequaltyp (Z(t) Z )=P rsk, where P (Z(t) Z ) - probablty for the specfc dscounted expenses be larger than Z,p rsk the gven rsk value (n the calculatons t was adopted that p rsk = 0.05). Standard devaton of chaotc component n relatve unts was taken as σ = σ(0) = 0.1, and t grew wth tme as the followng functon: σ(t) =σ(0) t 0.5. Several scenaros of prce varatons were consdered for tme perod of years. The frst scenaro, whch may be called neutral, foresees dentcal growth rate for all the prces, ncludng tarffs. It may be antcpated that, under dentcal growth rate of all the prces, the fuel component does not change wth tme. Snce man contrbuton nto reducton of the fuel component s related wth the expenses needed for SNF management, two other scenaros consder dfferent growth rate of the expenses for SNF management n comparson wth the growth rates at other NFC stages. In the second scenaro the growth rate of the expenses for SNF management s lower on 50% than the growth rates at other NFC stages. The thrd scenaro s a drect alternatve to the second one,.e. the growth rate of the expenses for SNF management s hgher on 50% than the growth rates at other NFC stages. In addton, one separate scenaro was consdered, n whch the growth rate of natural uranum prce was substantally hgher than the growth rates at other NFC stages. Results of the calculatons are presented n Fgs. 2 and

6 Fg. 2: Varatons of specfc expenses caused by prce varatons at dfferent NFC stages. 1 all the prces ncrease on 10% per year. 2 prce of SNF management ncreases on 5% per year; prces at the remanng NFC stages ncrease on 10% per year. 3 prce of SNF management ncreases on 15% per year; prces at the remanng NFC stages ncrease on 10% per year Fg. 3: Varatons of specfc expenses caused by prce varatons of natural uranum. 1 all the prces ncrease on 10% per year. 2 the outstrppng growth of natural uranum prce (10% per year n the frst ten years and 30% per year n subsequent years) 203

7 4 Concluson The numercal analyss demonstrates that, under current prce condtons at dfferent NFC stages, ncrease of fuel burn-up s an effectual way to reducng the fuel component n prme cost of NPP-produced electrcal energy. Increase of ntal uranum enrchment leads to proportonal growth of fuel burn-up. However, man contrbuton nto reducng the fuel component s gven by economy of the expenses for fabrcaton of fresh fuel assembles and for spent fuel management. The methodology, whch was used n the study for determnaton of the fuel component n prme cost of electrcal energy produced by WWER-type power reactors, can analyze varous forecastng optons for dynamc prce varatons at dfferent NFC stages, calculate the values for all the consttuents of the fuel component and evaluate rsks and uncertantes of these values. The calculatons demonstrated that, n neutral scenaro (dentcal growth rate for all the prces, ncludng tarffs), the fuel component, normalzed to the tarff rate, remans constant wth tme, despte sgnfcant varatons of partal consttuents occurred. Under the prevalng growth of the expenses for SNF management n comparson wth another NFC stages, the fuel component sharply ncreases. Under relatvely slow growth of the expenses for SNF management, the fuel component sharply drops down. In scenaro wth the prevalng growth of natural uranum cost, tme varatons of the normalzed fuel component become sgnfcantly lower. Ths means that varatons of natural uranum cost, wthn the range under consderaton here, gve practcally no effects on the values of the fuel component. Acknowledgement We would lke to thank Assocate Professor at MEPhI Department of Theoretcal and Expermental Nuclear Reactor Physcs Vladmr Apse for hs work on translatng ths paper. References [1] The Federal Purposeful Program (2006) Development of Russan Nuclear Power Industral System n and, n perspectve, up to Decree No. 605, dated October 6, 2006, was ssued by the Government of the Russan Federaton. [2] Strategy for development of Russan nuclear power n the frst half of the XXI century (2001). Moscow, Cnatomnform. [3] Shevelev Ya.V., Klmenko A.V. (1996). Effectve economcs of nuclear power and nuclear fuel system. Moscow, Russan State Humantaran Unversty. [4] Economcs of nuclear power ndustry (the lecture course) (2004). The tranng manual. Edted by Professor Hartonov V.V. Moscow, MEPhI. [5] Gordeev B.K. (2001). Introducton to economcs of nuclear fuel cycle. Moscow, Cnatomnform. [6] Snev N.M. (1986). Economcs of nuclear power ndustry. Moscow, Energoatomzdat. [7] Konovalov V.F., Vorobev A.I., Glushkov A.N., Kozhn V.M. (2002). Corporatve management of Russan nuclear power system. Publshng House Graal. [8] Kryanev A.V., Lukn G.V. (2006). Mathematcal methods for processng of uncertan data. Moscow, Nauka. 204