TECHNICAL REPORTS SERIES No. 5

Introduction to the

Methods of

Estimating Nuclear Power

Generating Costs

V E ? ) INTERNATIONAL ATOMIC ENERGY AGENCY • VIENNA 1961

INTRODUCTION TO THE METHODS OF

ESTIMATING NUCLEAR POWER GENERATING COSTS

The following States are Members of

the International Atomic Energy Agency

AFGHANISTAN ALBANIA ARGENTINA AUSTRALIA AUSTRIA BELGIUM BRAZIL BULGARIA BURMA BYELORUSSIAN SOVIET SOCIALIST REPUBLIC CAMBODIA CANADA CEYLON CHILE CHINA COLOMBIA CONGO ( Léopoldville) CUBA CZECHOSLOVAK SOCIALIST REPUBLIC DENMARK DOMINICAN REPUBLIC ECUADOR EL SALVADOR ETHIOPIA FINLAND FRANCE FEDERAL REPUBLIC OF GERMANY GHANA GREECE GUATEMALA HAITI HOLY SEE HONDURAS HUNGARY ICELAND INDIA INDONESIA IRAN IRAQ

ISRAEL ITALY JAPAN REPUBLIC OF KOREA LUXEMBOURG REPUBLIC OF MALI MEXICO MONACO MOROCCO NETHERLANDS NEW ZEALAND NICARAGUA NORWAY PAKISTAN PARAGUAY PERU PHILIPPINES POLAND PORTUGAL ROMANIA SENEGAL SOUTH AFRICA SPAIN SUDAN SWEDEN SWITZERLAND THAILAND TUNISIA TURKEY UKRAINIAN SOVIET SOCIALIST REPUBLIC UNION OF SOVIET SOCIALIST REPUBLICS UNITED ARAB REPUBLIC UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN

IRELAND UNITED STATES OF AMERICA VENEZUELA VIET-NAM YUGOSLAVIA

The Agency's Statute was approved on 26 October 1956 at an international conference held at United Nations headquarters, New York, and the Agency came into being when the Statute entered into force on 29 July 1957. The first session of the General Conference was held in Vienna, Austria, the permanent seat of the Agency, in October, 1957.

The main objective of the Agency is "to accelerate and enlarge the contribution of atomic energy to peace, health and prosperity throughout the world".

© I A E A , 1961

Permission to reproduce or translate the information contained in this publication may be obtained by writing to the International Atomic Energy Agency, Kaerntnerring 11, Vienna I, Austria.

Printed by the IAEA in Austria November 1961

I N T R O D U C T I O N

T O T H E

M E T H O D S O F E S T I M A T I N G N U C L E A R P O W E R

G E N E R A T I N G C O S T S

TECHNICAL R E P O R T SERIES

No. 5

I N T E R N A T I O N A L A T O M I C ENERGY A G E N C Y

K A E R N T N E R R I N G , V I E N N A I, A U S T R I A

1 9 6 1

INTRODUCTION TO THE METHODS OF ESTIMATING NUCLEAR POWER GENERATING COSTS IAEA, VIENNA, 1961

STl/DOC/lO/5

FOREWORD

One of the ma in s t a tu to ry r e s p o n s i b i l i t i e s of the In te rna t iona l Atomic Ene rgy Agency i s the development of n u c l e a r power f o r p e a c e f u l p u r p o s e s .

Success ive r e s o l u t i o n s of the G e n e r a l Confe rence of the In te rna t iona l Atomic Energy Agency 1-2-3) have r e - e m p h a s i z e d the i m p o r t a n c e a t tached to th i s sub jec t by the M e m b e r Sta tes and s t r e s s e d the need f o r spec i a l a t tent ion to the r e q u i r e m e n t s of l e s s - d e v e l o p e d c o u n t r i e s .

The d i s c h a r g e of th i s r e spons ib i l i t y inc ludes t h r e e c a t e g o r i e s of ac t iv i t i e s :

(1) The col lec t ion and d i s semina t ion of t echn ica l and cos t in fo rmat ion on power r e a c t o r s .

(2) The development of methods for the evaluat ion and use of th is in-f o r m a t i o n .

(3) Appl icat ions to spec i f i c c a s e s tud ies which may be r e q u e s t e d by M e m b e r S ta tes .

With r e g a r d to cos t i n fo rma t ion , the Agency expec ts f r o m t i m e to t i m e to p r e p a r e documents containing a su rvey of the l a t e s t data on power r e a c t o r c o s t s , and two such documents have been i s sued 4 - 5 ) . The p r e s e n t r e p o r t p r e -p a r e d by the Agency with the guidance and a s s i s t a n c e of a pane l of e x p e r t s f r o m M e m b e r S ta tes , the n a m e s of whom will be found at the end of th i s r e p o r t , r e p r e s e n t s the f i r s t s tep in the me thods of cost evaluat ion.

The main ob jec t ives of the r e p o r t a r e :

(1) The p r e p a r a t i o n of a fu l l l i s t of the cost i t e m s l ikely to be encounte red so that the p r e l i m i n a r y e s t i m a t e s fo r a given n u c l e a r power s y s t e m can be r e l i ed upon in deciding on i t s economic m e r i t s .

(2) A su rvey of the me thods c u r r e n t l y used f o r the e s t ima t ion of the gen-e ra t ing cos t s of the power p roduced by a nuc l ea r s ta t ion .

The su rvey i s intended f o r a wide audience ranging f r o m e n g i n e e r s to public o f f i c ia l s with an i n t e r e s t in the p r o s p e c t s of nuc l ea r power . An a t t empt has t h e r e f o r e been made to r e f r a i n f r o m deta i led t echn ica l d i s c u s s i o n s in o r d e r to make the p r e s e n t a t i o n eas i ly unde r s t andab le to r e a d e r s with only a v e r y g e n e r a l knowledge of the p r i n c i p l e s of nuc l ea r eng ineer ing .

The de t e rmina t ion of gene ra t ing cos t s f o r a s ingle n u c l e a r s ta t ion i s , of c o u r s e , only a f i r s t s tep in the evaluat ion of the m e r i t s of n u c l e a r power . If the n u c l e a r s ta t ion i s ope ra t ed within a power s y s t e m , a c o m p a r i s o n between the r e s p e c t i v e c o s t s of a n u c l e a r and a conventional power plant will be r e q u i r e d . F u r t h e r , if a count ry con templa t e s an expanding nuc l ea r power p r o g r a m m e , the ind i rec t co s t s to the whole nat ional economy should be taken into account and ba lanced aga ins t p o s s i b l e a l t e r n a t i v e s . T h e s e p r o b l e m s of s y s t e m and nat ional cos t ing , a r e , however , so complex that they c l ea r l y d e s e r v e s e p a r a t e s tud ies .

!) Assistance to Less-developed Countries, GC(II) /RES/27, 8 Oct. 1958. 2) Assistance to Less-developed Countries with the production of Nuclear Power, GC(III) /RES/57, 8 Oct. 1959. 3) Studies on Nuclear Power Costing, GC(IV)/RES/86, 6 Oct. 1960. 4 ) The Development of Nuclear Power, Review of Nuclear Power Costs, GC(IV) 123, 22 Aug. 1960, Vienna. 5 ) Nuclear Power Costs. A review by the Secretariat, GC(V) /INF/38, 13 Sept. 1961, Vienna.

It should be s t r e s s e d that the advisabi l i ty of developing n u c l e a r power p lan t s cannot be a s s e s s e d solely in t e r m s of t h e i r economic compe t i t i venes s . While a c o m p r e h e n s i v e cos t a n a l y s i s mus t p r e c e d e any dec is ion , the advantage of n u c l e a r power can only be judged in the light of i t s e f f ec t s on the whole economy. T h e s e consequences which v a r y f r o m country to country cannot be eas i ly r educed to f i g u r e s . Most impor t an t among t h e m a r e : a pos s ib l e speed-up of s c i en t i f i c and technologica l p r o g r e s s , the impac t on the i n d u s t r i a l and c o m -m e r c i a l s e c t o r s , and the poss ib i l i ty of indus t r i a l i z ing r e m o t e a r e a s lacking loca l fue l r e s o u r c e s .

Nothing but an ove ra l l view of the p r o b l e m will su f f i ce to make a s a t i s -f a c t o r y evaluat ion of the m e r i t s of n u c l e a r power . Nor should we lose s ight of the fac t that while n u c l e a r e l ec t r i c i t y may not be ful ly compet i t ive today, it will be so in the fut i i re and that once th i s s t age has been r e a c h e d it will soon b e c o m e a m a j o r s o u r c e of p o w e r .

November 1961 D i r e c t o r G e n e r a l

CONTENTS

I. Int roduct ion 9

II. Station Cons t ruc t ion Cos t s 11

III. Nuc lea r Fue l Cos t s 17

IV. Opera t ion , Maintenance and Other Cos t s 24

V. The De te rmina t ion of Genera t ing Cos t s 28

Acknowledgements 35

Appendices

I. Cost I t ems f o r a N u c l e a r Power Station 37

II. Nuc lea r Fue l Cyc les 42

III. Opera t ion , Maintenance and P e r s o n n e l 49

IV. Typica l E x a m p l e s of the Cost of Genera t ing E l e c t r i c i t y in Nuc lea r P o w e r Stat ions 51

V. P r e s e n t Worth Method 69

I. INTRODUCTION

Coun t r i e s endeavour ing to m a k e a p r e l i m i n a r y a s s e s s m e n t of the cost of n u c l e a r power under t he i r spec i f i c condit ions a r e usual ly faced with two c a t e -g o r i e s of d i f f i cu l t i e s in i n t e r p r e t i n g publ ished cos t f i g u r e s and applying t h e m to t he i r spec i f i c condi t ions .

On the one hand, the cost data may be incomple te o r p r e s e n t e d in such global f o r m as to make t he i r evaluat ion diff icul t ; on the o the r , the gene ra t ing c o s t s d e t e r m i n e d on the b a s i s of t he se data a r e computed th rough d i f f e ren t p r o c e d u r e s which may not a lways have g e n e r a l appl ica t ion .

In p r inc ip l e , the e s t ima t ion of the gene ra t ing cost of n u c l e a r power is subs tan t ia l ly s i m i l a r to that of conventional e l e c t r i c i t y . In both c a s e s the p u r -pose is to d e t e r m i n e a u n i t - g e n e r a t i n g - c o s t on the b a s i s of the c o s t s i n c u r r e d fo r the cons t ruc t ion , fue l l ing , and opera t ion and ma in t enance of the p lant . How-e v e r , while co s t s may in both c a s e s be c l a s s i f i ed unde r s i m i l a r b road head ings , the complexi ty of the r e a c t o r types , the unique f e a t u r e s of n u c l e a r fue l and the g e n e r a l lack of expe r i ence in the opera t ion of power r e a c t o r s m a k e the p r o b l e m of power cos t ing m o r e complex f o r nuc l ea r than for convent ional s t a t ions .

B e f o r e p roceed ing to cons ide r t he se ques t ions in s o m e deta i l , it may be worthwhile to look b r i e f l y at the t h r e e c a t e g o r i e s of n u c l e a r power c o s t s and the methods used to e s t i m a t e n u c l e a r genera t ing c o s t s .

1. P lan t cons t ruc t ion

The unit cap i ta l cos t of nuc l ea r power s ta t ions i s l a r g e r than that of con-vent ional p lan t s and al though th is d i spa r i ty is being n a r r o w e d , it i s unl ikely to be en t i re ly r e m o v e d in the f o r e s e e a b l e f u t u r e .

This cost v a r i e s with the type, locat ion and s i ze of the r e a c t o r . F u r t h e r -m o r e , the r a t e of va r i a t i on of cost with s i z e i n c r e a s e s rap id ly in the low power r a n g e . Thus , while the r a t i o of the cap i ta l c o s t s of a nuc l ea r and of a con-vent ional s ta t ion may be of the o r d e r of 2 in the 200 MW r a n g e , it may r i s e to 3 or m o r e in the 20 MW a r e a , at the p r e s e n t t i m e .

Lack of expe r i ence , development expenses , o v e r - d e s i g n , r e s t r i c t e d t r a d e in r e a c t o r components and conse rva t i ve sa fe ty p rocau t ions account for t he se r e l a t ive ly high c o s t s in the ea r ly y e a r s . Substant ia l sav ings will a c c r u e with accumula t ing e x p e r i e n c e a s wi tnessed by the example of c o u n t r i e s which have developed a s u c c e s s i o n of power r e a c t o r s of a given type. On the o ther hand, s o m e r e a c t o r s y s t e m s at an ea r ly s tage of development o f f e r the poss ib i l i ty of achieving an output subs tan t ia l ly h igher than the o r ig ina l r a t i n g by us ing i m -proved fue l c o r e s over the l i fe of the r e a c t o r , thus lower ing the unit cap i ta l cos t , provided adequate a l lowance h a s been m a d e f r o m the beginning f o r the i n c r e a s e d power output.

2. Fue l

The p r o m i s e of n u c l e a r power l i e s e s sen t i a l ly in the ach ievemen t of fue l c o s t s subs tan t ia l ly lower than those of convent ional s t a t i ons , which will o f f se t the h igher cap i ta l c o s t s i n c u r r e d . Although much has a l r e a d y been done in th i s f ie ld , addi t ional sav ings in eve ry ca tegory of fue l c o s t s a r e l ikely to be achieved in the n e a r f u t u r e . Th i s will be achieved a s a r e s u l t of abundant suppl ies of

9

u r a n i u m , the pos s ib l e u s e of r e a c t o r - p r o d u c e d f i s s ionab le m a t e r i a l s such as p lu tonium and u r a n i u m 233, d e c r e a s e d f ab r i ca t ion cos t s of . fue l e l e m e n t s due to s t anda rd i za t i on , l a r g e batch product ion , complet ion of the a m o r t i z a t i o n of the s e m i - e x p e r i m e n t a l f ab r i ca t i ng f ac i l i t i e s a s well a s b e t t e r u t i l iza t ion of nuc l ea r fue l s in the r e a c t o r p e r m i t t i n g the ach ievement of a g r e a t e r amount of energy p e r unit weight of fue l dur ing i t s r e s i d e n c e in the c o r e .

It should be pointed out that the unique f e a t u r e s of nuc l ea r fue l give r i s e to t echn ica l and cos t ing p r o b l e m s without p a r a l l e l in convent ional s t a t ions . The inves tmen t in fue l i s many t i m e s l a r g e r in the c a s e of a nuc l ea r s ta t ion . Thus , a c o a l - f i r e d s ta t ion will need to keep a s tock of coal ava i lab le to p reven t shu t -downs in the event of de l ivery de lays . A t h r e e months coal supply would amount to about one ton /KW of capaci ty o r in the o r d e r of $5 to 20/KWe depending upon the p r i c e of coa l . In the c a s e of nuc lea r r e a c t o r s the to ta l va lue of the working s tock of fue l p lus the r e a c t o r c h a r g e can amount to ten t i m e s as much .

F u r t h e r m o r e , the fue l cost p e r unit of power p roduced is much m o r e sen -s i t ive to v a r i a t i o n s of plant s i z e fo r nuc lea r than fo r convent ional power . Thus , fo r r e a c t o r s in the 10 MWe r a n g e the to ta l fue l cost p e r kWh may be subs t an -t ia l ly h igher than that of the s a m e r e a c t o r type in a l a r g e s i z e .

In addi t ion, the spent fue l f r o m a nuc l ea r r e a c t o r is of p o s s i b l e value f o r the f i s s i l e m a t e r i a l it con ta ins . T r a n s p o r t and p r o c e s s i n g of th is fue l will in-volve cos t s which mus t be ba lanced agains t the c r e d i t s which may f inal ly be r e c e i v e d .

3. Opera t ion and ma in t enance

The novelty of n u c l e a r power s t a t ions and the hea l th and safe ty p r e c a u t i o n s n e c e s s a r y f o r t he i r opera t ion demands a conse rva t ive app roach . Th i s m a k e s f o r h igher opera t ion and ma in t enance cos t s than f o r convent ional p lan t s of s i m i l a r output. But the accumula t ion of opera t iona l expe r i ence p r o m i s e s r educ t ions in th i s i t e m . The s a m e c o m m e n t appl ies to the cost of damage to p r o p e r t y and of t h i r d - p a r t y l iabi l i ty i n s u r a n c e .

4. Gene ra t ing cos t s

The p r o b l e m of e s t ima t ing the genera t ing cost and espec ia l ly i ts fue l cos t component has been deal t with d i f fe ren t ly in nuc l ea r l y - advanced coun t r i e s , pa r t ly b e c a u s e of the d i f f e ren t condit ions under which nuc l ea r fue l is m a d e ava i l ab le and of the d i f f e r e n c e s in r e a c t o r and fue l t ypes . All me thods a im , however , at p r o p e r l y a l loca t ing to the uni ts of energy p roduced , a l l expend i tu res connected with the r e a c t o r plant and p a r t i c u l a r l y with i t s fue l . P rov ided that the e s t i m a t e s of cons t ruc t ion and fuel l ing expendi tu res a r e comprehens ive ly and c l e a r l y l i s t ed , it i s p o s s i b l e to d e t e r m i n e the gene ra t ing cost of a nuc l ea r power plant within qui te n a r r o w l imi t s under the condi t ions s ta ted fo r i t s ope ra t ion .

The next t h r e e c h a p t e r s will deal with the p r o b l e m s a r i s i n g under the above t h r e e c a t e g o r i e s of c o s t s , while Chapte r V and the r e l evan t appendices will out l ine the c u r r e n t me thods of genera t ing cost ca lcu la t ions and cons ide r the l im i t a t i ons to which they may be sub jec t .

10

II. STATION CONSTRUCTION COSTS

1. Int roduct ion

"Station cons t ruc t ion c o s t " m e a n s the to ta l cos t of building a power s t a t ion . It inc ludes not only the d i r ec t cost i t e m s fo r s i t e , m a t e r i a l s , equipment and ins ta l la t ion , but a l so a s s o c i a t e d cos t s f o r s ta t ion des ign , i n t e r e s t on cap i ta l dur ing cons t ruc t ion , commiss ion ing , f e e s and working cap i ta l , which a r e c o m -monly r e f e r r e d to a s ind i rec t or d i s t r ibu t ive c o s t s . In making e s t i m a t e s p r i o r to cons t ruc t ion , con t ingenc ies m u s t be c o n s i d e r e d . Lega l f e e s , patent r i g h t s , p r o f i t s , and roya l t i e s or r e c o v e r y of r e s e a r c h and development expenses may a l so have to be included. The s ta t ion cons t ruc t ion cos t is a l so commonly r e -f e r r e d to a s the "Capi ta l c o s t " or "Plant co s t " . As def ined h e r e it exc ludes both the in i t ia l and subsequent fue l c o s t s .

While cos t i n fo rma t ion i s ava i lab le on many g o v e r n m e n t - s u p p o r t e d n u c l e a r r e a c t o r s , t h e s e data a r e of l imi ted u s e f o r the a s s e s s m e n t of the p robab l e cos t of a n u c l e a r power s ta t ion cons t ruc t ed and ope ra t ed sole ly f o r the c o m m e r c i a l product ion of e l ec t r i c i t y , p a r t i c u l a r l y fo r a spec i f i c locat ion in ano ther coun t ry . The p r i m a r y i n t e r e s t of many coun t r i e s contempla t ing the u s e of n u c l e a r power is to know the cost of a r e a c t o r now or in the i m m e d i a t e fu tu re , a s s u m i n g m a x i m u m u s e of domes t i c r e s o u r c e s , r a t h e r than to a s c e r t a i n cos t s which have been i n c u r r e d for r e a c t o r s dur ing the development s t age . Ideally, th i s could only be achieved by a thorough engineer ing ana ly s i s fo r the spec i f i c appl ica t ion and by a rev iew of t e n d e r s fo r r e a c t o r s of def ini te spec i f i ca t i ons .

D i s c r e p a n c i e s can a r i s e with r e g a r d to cons t ruc t ion cos t s b e c a u s e the s a m e i t e m s a r e not included in al l da ta . Var ia t ions occu r r e g a r d i n g such i t e m s a s aux i l i a ry bui ldings and s e r v i c e s , i n t e r e s t dur ing cons t ruc t ion , con t ingenc ies , f e e s , f ield supe rv i s ion and ins ta l la t ion , a d m i n i s t r a t i o n c h a r g e s , and o ther in-d i rec t ove rhead c h a r g e s . T h e r e f o r e , a deta i led breakdown, suf f ic ien t to p e r m i t the ident i f ica t ion of spec i f i c cons t ruc t ion i t e m s is impor t an t p a r t i c u l a r l y when cons ide r ing the poss ib i l i ty of domes t i c supply. It would f ac i l i t a t e c o m p a r i s o n of va r ious n u c l e a r power s ta t ions if a c o m p r e h e n s i v e l ist ing1) of cons t ruc t ion c o s t s w e r e in te rna t iona l ly a g r e e d upon.

2. Breakdown of cons t ruc t ion c o s t s

In s o m e coun t r i e s , p a r t i c u l a r l y t he se whe re e l e c t r i c power supply e n t e r -p r i s e s a r e subjec t to gove rnmen ta l r egu la t ions , t h e r e a r e l ikely to be spec i f i c s y s t e m s of accounts under which cons t ruc t ion cos t s mus t be l i s ted a f t e r c o m -plet ion of the p r o j e c t . In the United Sta tes of A m e r i c a , fo r ins tance , the F e d e r a l P o w e r C o m m i s s i o n u s e s a u n i f o r m s y s t e m of accounts f o r e l e c t r i c u t i l i t i e s 2 )

under t he i r j u r i sd i c t ion . Some modif ica t ion or addit ion to exis t ing accounts may be n e c e s s a r y to cover i t e m s p e c u l i a r to nuc l ea r p l an t s . This type of a c -counting i s main ly u t i l ized dur ing and a f t e r cons t ruc t ion .

P r i o r to cons t ruc t ion two types of eng inee r ing -cos t b reakdowns may be cons ide r ed . In one the m a j o r i t e m s of cost a r e grouped by the funct ions they

Work is underway in the United States of America to develop a detailed listing of all cost items of nuclear power plants.

2) Uniform System of Accounts, Federal Power Commission, effective 1 Jan. 1961.

11

p e r f o r m , i . e . conta inment (building and s t r u c t u r e s ) , p roduct ion of heat ( r e ac to r plant equipment) , t r a n s f e r of heat ( s t eam genera t ing equipment) , conver s ion of hea t ( e lec t r i c i ty gene ra t i ng equipment ) 1 ) . The i t e m s of cost can then be f u r t h e r subdivided a s to m a t e r i a l s o r equipment , l abour or ins ta l la t ion , and overhead c h a r g e s . The second type of eng ineer ing cost breakdown inc ludes the m a j o r cos t i t e m s by the type of c o n t r a c t o r p e r f o r m i n g the work, i . e . building and civi l works , plant and equipment , mechan ica l and e l e c t r i c a l work, and design and eng ineer ing .

Appendix I g ives a desc r ip t i on and breakdown of cons t ruc t ion cost i t e m s fo r a n u c l e a r s t e a m - g e n e r a t i n g plant fo r the product ion of e l e c t r i c i t y . This b r e a k -down i s ba sed main ly upon the funct ional c r i t e r i o n and is des igned to a s s i s t in the p r e l i m i n a r y evaluat ion of the cos t data ava i lab le in the l i t e r a t u r e , or f r o m r e a c t o r m a n u f a c t u r e r s of d i f f e ren t r e a c t o r types . It will a s s i s t in the p r e -p a r a t i o n of r e q u e s t s f o r f u r t h e r cost in fo rmat ion and in a n a l y s e s of the cos t i t e m s which might be p r o c u r e d local ly .

Account No. 2 l i s t s cons t ruc t ion i t e m s which fa l l unde r the c ivi l works ca t ego ry . In many coun t r i e s they would involve mos t ly loca l labour and d o m e s t i c a l l y - p r o d u c e d m a t e r i a l s . Accounts No. 3 and 4 cover the r e a c t o r and i t s a s s o c i a t e d equipment a s well a s the hea t t r a n s f e r equipment . The highly-spec i a l i z ed i t e m s of t he se two c a t e g o r i e s will usual ly be avai lable only in the n u c l e a r l y - m o s t - a d v a n c e d coun t r i e s and c o s t s of spec ia l ly qual i f ied p e r s o n n e l would be r e q u i r e d f o r ins ta l la t ion and supe rv i s ion . Accounts No. 5 and 6 on the o the r hand cover i t e m s which a r e e s sen t i a l ly ident ica l to t h e s e r e q u i r e d for a convent ional s t e a m e l e c t r i c s ta t ion . Spare p a r t s a r e included under the spec i f i c accoun t s .

Some of t he se cost i t e m s ca l l fo r addi t ional c o m m e n t s .

A. Land and land r i g h t s

The se lec t ion of a s i t e fo r a r e a c t o r is inf luenced by many economica l and t echn ica l f a c t o r s and the cos t of land, which may be in the o r d e r of a few d o l l a r s p e r ki lowatt , p lays a r e l a t ive ly m i n o r r o l e . On the o ther hand, the quest ion of the d i s t r ibu t ion and densi ty of populat ion and indus t ry i s of c o n s i d e r a b l e i m -p o r t a n c e . The p r e l i m i n a r y invest igat ion r e g a r d i n g the s i t ing of a r e a c t o r , p a r -t i cu l a r ly that r e l a t i ng to the f i r s t such r e a c t o r in a country can be a s igni f icant cost i t e m and would be included under Account 8. 1 Engineer ing , Design and Inspec t ion .

T h e r m a l power s t a t ions can of ten be located n e a r e r the e l ec t r i c i t y demand c e n t r e al though they a r e r e s t r i c t e d by the n e c e s s i t y to t r a n s p o r t l a r g e quant i -t i e s of fue l and by the avai labi l i ty of cooling water supp l i e s . F o r a n u c l e a r power s ta t ion t h e r e a r e in addit ion safe ty r egu la t ions which at p r e s e n t spec i fy that the plant should be built away f r o m densely populated a r e a s .

The a r e a of land or "exclus ion a r e a " r e q u i r e d fo r a n u c l e a r power s ta t ion i s usua l ly l a r g e r than for a convent ional t h e r m a l power s ta t ion of s i m i l a r capa -c i ty . E m p i r i c a l r e l a t i o n s h i p s have been developed re l a t ing the s i z e of the ex-c lus ion a r e a to the many f a c t o r s involved in es tab l i sh ing s t a n d a r d s f o r sa fe ty p u r p o s e s and for i n s u r a n c e c o v e r a g e . T h e r e a r e , however , no u n i f o r m i n t e r -na t iona l s t a n d a r d s appl icable to the si t ing of power r e a c t o r s .

1) In the United States of America the heat transfer portion of the plant is grouped with the other components in the reactor plant equipment.

12

At p r e s e n t only g e n e r a l r u l e s a r e used in evaluat ing r e a c t o r sa fe ty and the r e q u i r e m e n t s of the exclus ion a r e a . However , expe r i ence is being gained in the des ign, cons t ruc t ion and opera t ion of n u c l e a r p lan ts r e su l t i ng in the development of c e r t a i n p a t t e r n s of p r a c t i c e d i r e c t e d t owards min imiz ing the h a z a r d potent ia l of such f ac i l i t i e s , which will r e s u l t eventual ly in m o r e f i r m c r i t e r i a and s tand-a r d s . A br ief s u m m a r y of the f a c t o r s r e l a t ing to the locat ion and des ign of nuc l ea r power p lan t s i s given by Bi les and Beck1) and c r i t e r i a ha s r e c e n t l y been publ ished in the United Sta tes F e d e r a l R e g i s t r y fo r g e n e r a l c o m m e n t .

B. Site p r e p a r a t i o n and s t r u c t u r e s

Site p r e p a r a t i o n and i m p r o v e m e n t . The l a r g e r a r e a r e q u i r e d fo r a nuc l ea r plant usua l ly r e s u l t s in ex t ra o f f - s i t e works fo r a c c e s s r o a d s , t r a n s m i s s i o n l ines and cooling wa te r suppl ies . The inves tmen t cap i ta l r e q u i r e d fo r such works cannot be e s t i m a t e d in any g e n e r a l m a n n e r but mus t be e s t i m a t e d sepa -ra t e ly fo r each spec i f i c locat ion. The r a r i t y of su i tab le s i t e s may thus lead to grouping of s e v e r a l r e a c t o r s on the s a m e s i t e . F o r a mul t i -un i t plant p r e p a r a -tion i s of ten c a r r i e d out fo r the whole s i t e when the cons t ruc t ion of the f i r s t unit c o m m e n c e s .

R e a c t o r bui lding. R e a c t o r conta inment may be an i n t eg ra l p a r t of the r e a c t o r bui lding. The n e c e s s i t y and d e g r e e of conta inment is a funct ion of r e a c t o r type, and r e a c t o r - h a z a r d s evaluat ion and regu la t ion . Conse rva t ive design ca l l s f o r p r o v i s i o n s to guard agains t the m a x i m u m c red ib l e acc ident which might be env isaged . F o r r e a c t o r s with coolants under high p r e s s u r e th i s r e q u i r e s l a r g e conta inment of such s i z e and s t r eng th a s to contain the poss ib l e sudden r e l e a s e of a l l s t e a m and g a s e s . F u r t h e r , it may r e q u i r e thick c o n c r e t e b iological shie ld ing aga ins t r ad ia t ion f r o m r e l e a s e d f i s s i on p r o d u c t s . The method of s u p p r e s s i o n of s t e a m vapour in an adjoining wa te r r e s e r v o i r i s used in one r e a c t o r c u r r e n t l y unde r cons t ruc t ion in the United Sta tes of A m e r i c a . This and o ther p r o c e d u r e s will be r e v i s e d in the light of f u r t h e r expe r i ence and should r e s u l t in min imiz ing conta inment c o s t s .

C. R e a c t o r and aux i l i a ry equipment

R e a c t o r . The types of r e a c t o r s c u r r e n t l y in u se , o r being buil t , have a wide r a n g e of design t e m p e r a t u r e , p r e s s u r e , and m a t e r i a l r e q u i r e m e n t s s ig -ni f icant ly a f fec t ing c o s t s . The s i ze and weight of the v e s s e l may i m p o s e spec ia l t r a n s p o r t and cons t ruc t ion c o n s i d e r a t i o n s . F u r t h e r r e q u i r e m e n t s fo r r a d i o -g raph ic examina t ion and s t r e s s a n a l y s i s , and r e s t r i c t i v e spec i f i ca t ions of m a t e r i a l , t o l e r a n c e s and other design f e a t u r e s will s igni f icant ly a f fec t c o s t s .

Fue l handling equipment . Th i s cost i t e m will depend upon the des ign and the expected fue l m a n a g e m e n t . F o r a l l r e a c t o r s it i s n e c e s s a r y to p rov ide c h a r g e - d i s c h a r g e equipment , and f o r r e a c t o r s which a r e capable of being r e -fue l led under load th i s equipment will need expensive p r e s s u r i z e d and fue l -cooling s y s t e m s .

Rad ioac t ive was te t r e a t m e n t and d i sposa l equipment . The ma in s o u r c e of such was te will be the plant equipment which i s used f o r pu r i f i ca t ion of the coolant a n d / o r m o d e r a t o r . Was tes will cons i s t of contamina ted f i l t e r s , spent

Biles, M. B. and Beck, C • K. "Some Safety Matters relating to Small Nuclear Power Plants", SMRl/33, IAEA, Vienna, Austria.

13

ion exchange r e s i n s , di lute and concen t ra t ed liquid was t e s , l abo ra to ry w a s t e s , r ad ioac t i ve clothing and too ls . The t r e a t m e n t of the liquid was t e s may include the following: f i r s t l y , hold-up to p e r m i t s h o r t - l i v e d r ad ioac t ive decay and, secondly, condensat ion s t o r a g e or r i v e r d i s cha rge ; demine ra l i za t ion of low leve l r ad ioac t i ve waste ; and concent ra t ion of high leve l r ad ioac t ive was te and d i s c h a r g e to s t o r a g e . Some p rov i s ion may be m a d e for concen t ra t ion and r a d i o -ac t ive was te d i sposa l by an outs ide p a r t y .

In s t rumen ta t ion . The in s t rumen ta t ion r e q u i r e d f o r a n u c l e a r s ta t ion i s m o r e expens ive than that of a conventional p lan t . Ins t rumenta t ion i s r e q u i r e d fo r r e a c t o r sa fe ty and con t ro l , r ad ia t ion moni to r ing , and coolant pur i ty con t ro l . An impor t an t v a r i a b l e design i t e m is that of detect ion and con t ro l of fue l e lement f a i l u r e and bu rn -up . The d e g r e e of con t ro l n e c e s s a r y will a f fec t the inves tmen t for i n s t r u m e n t a t i o n . In the c a s e of r ad ia t ion moni to r ing i n s t r u m e n t s the need i s not inf luenced by economic cons ide ra t i ons but by the neces s i t y to a s s u r e m a x i m u m safe ty f o r p e r s o n n e l agains t e x c e s s i v e rad ia t ion exposu re .

Mode ra to r and coolan ts . T h e s e m a t e r i a l s mus t mee t s t r ingen t c h e m i c a l and nuc lea r pur i ty r e q u i r e m e n t s and for some of t h e m such a s he l ium, b e r y l l i u m and heavy wa te r t h e r e may be p r o b l e m s of supply. In s o m e c a s e s the cost of f ab r i ca t ion and ins ta l la t ion will need to be cons ide red in addit ion to the p r i m e cost of the r aw m a t e r i a l . In o ther c a s e s spec i a l equipment mus t be ins ta l led fo r the r e m o v a l of degrada t ion p roduc t s f o r m e d by i r r a d i a t i o n and fo r con-ta ining an expens ive coolant such as he l ium or heavy w a t e r .

The equipment f o r the m o d e r a t o r c i r cu i t , n o r m a l l y included under i t e m 3. 8 of Appendix I could a l t e rna t ive ly be included under i t em 4 . 2 if the m o d e r a t o r a l so ac ted a s coolant .

D. F o s s i l fue l s t e a m s u p e r h e a t e r

Most r e a c t o r s p roduce s t e a m of lower g r a d e than convent ional s t e a m s ta t ions (but a constant improvemen t i s being r e c o r d e d a s wi tnessed by the continuously h igher s t e a m c h a r a c t e r i s t i c s in the s e r i e s of ga s - coo l ed n a t u r a l u r a n i u m s ta t ions built in the United Kingdom). Some r e a c t o r des igns , f o r economic o r p r a c t i c a l r e a s o n s , t h e r e f o r e , p rov ide fo r u s e of f o s s i l - f u e l or nuc l ea r s u p e r h e a t . The cost of the f o s s i l - f u e l l e d s u p e r h e a t e r would be included under Account 5. 0 and would include the cos t of fue l s t o r a g e , f i r i ng equipment and a s s o c i a t e d equipment . This i t e m i s l i s ted s e p a r a t e l y to p e r m i t an a s s e s s -ment of the n u c l e a r and non -nuc l ea r por t ions of the p lant .

E . Assoc ia t ed cos t s

Engineer ing design and inspec t ion . This r e p r e s e n t s the cost of the p r e -l imina ry inves t iga t ions , the design work n e c e s s a r y b e f o r e the s ta t ion could be buil t , the inspect ion c a r r i e d out by the p r i m e c o n t r a c t o r s and inc ludes the f e e s of any s p e c i a l i s t s or consu l t an t s .

Ind i rec t cons t ruc t ion c o s t s . T h e s e include c o s t s that do not have a def in i -t ive r e l a t i on to any spec i f i c phys i ca l f e a t u r e of cons t ruc t ion work, and at the conclus ion of the work a r e appor t ioned to the phys ica l i t e m s on s o m e equi table b a s i s . They include publ ic r e l a t i o n s and enqu i r i e s , g e n e r a l s i t e a d m i n i s t r a t i o n and f ield supe rv i s ion , p u r c h a s i n g , p e r s o n n e l , s ecu r i t y accounts , hos te l and m e d i c a l s e r v i c e s and the cos t of expendable cons t ruc t ion such as t e m p o r a r y s e r v i c e s of a l l k inds , welders ' booths , cons t ruc t ion equipment , too ls and sup-p l i e s such a s power , wa te r and c o m p r e s s e d a i r .

14

I n t e r e s t dur ing cons t ruc t ion . This i t e m c o v e r s the cos t of money i m m o -bi l ized b e f o r e the plant s t a r t s opera t ing . The to ta l i n t e r e s t cha rge dur ing con-s t ruc t ion will depend upon the r a t e of i n t e r e s t and the t i m e d i s t r ibu t ion of out-l ays which a r e involved.

Contingency. Most cos t e s t i m a t e s include a contingency fo r u n f o r e s e e n deve lopments such a s r i s i n g p r i c e s o r changes in des ign dur ing cons t ruc t ion a s well a s unexpected snags me t dur ing cons t ruc t ion . T h e s e may r a n g e through f a i l u r e of plant unde r t e s t , d i f f icul t foundation condi t ions , labour t roub le s and acc iden t s . Such-con t ingenc ies a r e ve ry diff icul t to e s t i m a t e and will have to be r e v i s e d in the light of e x p e r i e n c e . As m o r e and m o r e n u c l e a r p lan t s a r e buil t , e s t i m a t e s of ac tua l co s t s should become m o r e a c c u r a t e and the contingency consequent ly r e d u c e d .

3. P r e l i m i n a r y a s s e s s m e n t of s ta t ion cons t ruc t ion c o s t s

Exis t ing ava i l ab le data may r e q u i r e ad ju s tmen t f o r de t e rmin ing the cos t s of a nuc l ea r power p lant in a spec i f i c s i tua t ion . T h e s e a d j u s t m e n t s f a l l in t h r e e ma in c a t e g o r i e s :

(1) Ad jus tmen t of the cos t of an expe r imen ta l o r p ro to type plant in o r d e r to obtain the cost of a plant des igned and ope ra t ed f o r the p r i m e p u r p o s e of gene ra t ing power under c o m m e r c i a l condi t ions .

(2) Adjus tmen t of cos t f r o m country to country and s i t e to s i t e taking into account the pos s ib l e sav ings in civi l works , on the one hand, and the addi t ional t r a n s p o r t c o s t s i n c u r r e d fo r the ma in p i e c e s of equipment , on the o ther hand.

(3) Ad jus tmen t of the cost f o r poss ib l e va r ia t ion in s i ze , the g e n e r a l design being the s a m e .

Even a p r e l i m i n a r y a d j u s t m e n t of the data pe r t a in ing to a p ro to type power r e a c t o r to obtain the cos t of a r e a c t o r producing c o m m e r c i a l power r e q u i r e s a c a r e f u l a n a l y s i s of both cost and techn ica l data and would give at mos t an o r d e r of magni tude . The inc lus ion of l a r g e r e s e a r c h and development expendi tu res and of the cos t of s p e c i a l r e s e a r c h f ac i l i t i e s may subs tan t ia l ly i n c r e a s e the pro to type cost in c o m p a r i s o n with an indus t r i a l plant of s i m i l a r des ign . No l e s s impor tan t i s the poss ib i l i ty of an i n c r e a s e d power output with the s a m e or s l ightly d i f f e ren t c o r e and consequent ly of lower unit i nves tmen t c o s t s . This f e a t u r e which has no c o u n t e r p a r t in convent ional plant ca l l s fo r a c a r e f u l examinat ion of f u t u r e po ten t i a l i t i e s of a plant of a given des ign . In p a r t i c u l a r if it i s expected that i m p r o v e m e n t s in fuel e l ement p e r f o r m a n c e may r e s u l t in achieving g r e a t e r output f r o m a given c o r e it might be d e s i r a b l e to make su i t -able p rov i s ion in the o r ig ina l des ign for heat t r a n s f e r and g e n e r a t o r equipment capable of handling the l a r g e r output. A deta i led technologica l and economic ana lys i s will be r e q u i r e d to d e t e r m i n e the m e r i t s of such design changes .

The ex t rapo la t ion of co s t s f r o m one country to ano ther mus t n e c e s s a r i l y involve a cos t breakdown, f o r i n s t ance along the l ines of Appendix I, and s e p a r a t e a d j u s t m e n t s f o r a l l m a j o r cos t i t e m s . It should be pointed out that while a c c u r a t e ex t rapo la t ions can only be m a d e by expe r t s with a c o m p r e h e n s i v e knowledge of condit ions both in the country of or ig in and the country w h e r e the p lant i s to be bui l t , f i r s t app rox ima t ions to d e t e r m i n e the advisabi l i ty of f u r t h e r deta i led s tud ies can r ead i ly be achieved and will p robably be a s a c c u r a t e a s the b a s i c data on which they a r e b a s e d . In any f ina l a n a l y s i s a v e r y de ta i led breakdown of the cos t s of the v a r i o u s i t e m s of a n u c l e a r plant of a spec i f i c des ign is ne -c e s s a r y .

15

Ext rapo la t ions of c o s t s as a funct ion of s i z e should be made with e x t r e m e caut ion. The e m p i r i c a l f o r m u l a s o m e t i m e s used in convent ional engineer ing p r a c t i c e accord ing to which the r a t i o of to ta l inves tment cos t s is equal to the r a t i o of plant capac i t i e s to the 0. 6th power can only s e r v e a s a ve ry rough guide in the c a s e of nuc l ea r p lan ts within a l imi ted r a n g e .

Some c o u n t r i e s may be i n t e r e s t e d in r e a c t o r s producing low g r a d e s t e a m for i n d u s t r i a l p u r p o s e s . F o r t he se r e a c t o r s it should be c l e a r that spec ia l cos t s tud ies would be r e q u i r e d in each spec i f i c c a s e . Apar t f r o m the obvious dif-f e r e n c e s due to the a b s e n c e of t u r b o - g e n e r a t i n g equipment and r educed s t e a m condi t ions the poss ib i l i ty of s o m e heat s t o r a g e would p e r m i t the design of a r e a c t o r with to ta l capac i ty below peak r e q u i r e m e n t s .

16

III. NUCLEAR F U E L COSTS

1. In t roduct ion

The p r e s e n t t r e n d t o w a r d s lower nuc l ea r fue l co s t s is expected to continue f o r s o m e t i m e a s a r e s u l t of cons tant improvemen t in fue l p e r f o r m a n c e , lower o r e p r i c e s and d e c r e a s e s in f ab r i ca t ion and p r o c e s s i n g c h a r g e s . N e v e r t h e l e s s s o m e s p e c i a l cos t p r o b l e m s a r i s e f r o m :

(1) The v a r i e t y of the f i s s ionab le m a t e r i a l s which may be used e i ther alone o r in combinat ion with wide ly-vary ing f lexibi l i ty and p e r f o r m a n c e and the complex cyc l e s which they may undergo;

(2) The n e c e s s i t y of complex f ab r i ca t ion of the fue l b e f o r e it can be used in a r e a c t o r , and of spec i a l p r ecau t ions and expensive t r a n s p o r t a f t e r it has been i r r a d i a t e d ;

(3) The d i f f e ren t t echn ica l and f inanc ia l condi t ions under which t he se m a t e r i a l s may be m a d e ava i lab le by the p roduc ing coun t r i e s ;

(4) The cons ide rab l e inves tment in the fue l immobi l i zed in a power r e a c t o r . While n u c l e a r fuel cyc l e s may be quite complex and c l a s s i f i e d in many

d i f fe ren t ways, they a l l r e s t e s sen t i a l ly on the u s e of one of the t h r e e f i s s i o n -able m a t e r i a l s u r a n i u m - 2 3 5 , p lu tonium or u r a n i u m - 2 3 3 . The f i r s t of t he se can be ut i l ized e i the r as it o c c u r s in n a t u r a l u r a n i u m or in h igher concen t ra t ions r e q u i r i n g an i so tope s e p a r a t i o n p lant , while the l a t t e r a r e e s sen t i a l ly r e a c t o r -p roduced .

Accord ing to the b a s i c feed m a t e r i a l r e q u i r e d fo r a r e a c t o r opera t ion nuc l ea r fue l cyc l e s may be c l a s s i f i e d a s fol lows:

(1) N a t u r a l u r a n i u m feed . The bas i c feed m a t e r i a l i s n a t u r a l l y - o c c u r r i n g u r a n i u m . The p lu tonium produced i s not r e c y c l e d but sold, s t o r ed or b u r i e d .

(2) U r a n i u m - 2 3 5 - e n r i c h e d u r a n i u m feed . The bas i c r e q u i r e m e n t s a r e n a t u r a l u r a n i u m , and an isotopic s epa ra t i on p lan t . The plutonium p r o -duced i s not r e c y c l e d but sold or s t o r e d .

(3) T h o r i u m feed . The bas i c feed is n a t u r a l l y - o c c u r r i n g t h o r i u m . How-e v e r , s ince it conta ins no f i s s ionab le m a t e r i a l s it mus t be mixed with u r a n i u m - 2 3 5 , p lu tonium or u r a n i u m - 2 3 3 f o r i t s u t i l izat ion in a r e a c t o r .

(4) P lu ton ium f e e d s . The f eeds under t h e s e cyc l e s a r e r e a c t o r - p r o d u c e d plutonium, u t i l i zed a lone o r with u r a n i u m .

The above fue l cyc l e s a r e d i s c u s s e d and schema t i ca l ly shown in Appendix II, P a r t s 1 - 4 , r e s p e c t i v e l y .

Under p r e s e n t fue l technology, i n d u s t r i a l power r e a c t o r s o p e r a t e o r will o p e r a t e with (1) n a t u r a l u r a n i u m , (2) u r a n i u m - 2 3 5 - e n r i c h e d u r a n i u m , or (3) uranium-235 with t h o r i u m a s t h e i r in i t ia l fue l , al though plutonium or uran ium-233 a r e burned p a r t i a l l y as they a r e f o r m e d in the r e a c t o r and thus con t r ibu te to the o v e r a l l p e r f o r m a n c e . Fue l cyc le c o s t s , ba sed upon the u s e of t h e s e m a t e -r i a l s , a r e f a i r l y well e s t ab l i shed , and f o r s o m e types in c e r t a i n loca t ions a r e a l r eady lower than f o s s i l - f u e l c o s t s . Reduct ions in p r i c e s quoted by fue l manu-f a c t u r e r s a r e expected, due to a fa l l in the p r i c e of u r a n i u m c o n c e n t r a t e s , in-c r e a s e d fue l product ion and i m p r o v e m e n t s and s impl i f i ca t ion in fue l e lement des ign .

17

On the o ther hand, the u t i l iza t ion of p lu tonium and u r a n i u m - 2 3 3 is s t i l l in the e x p e r i m e n t a l s t age . The p r e s e n t va lues have been es tab l i shed upon t he i r u se in t h e r m a l , r e a c t o r s in c o m p a r i s o n with that of u r a n i u m - 2 3 5 . F u r t h e r , the cos t of fue l e l emen t s containing t h e s e m a t e r i a l s i s e x t r e m e l y u n c e r t a i n .

In a l l the fue l cyc les the fue l ha s to be f a b r i c a t e d and a s s e m b l e d b e f o r e being in t roduced in the r e a c t o r and may have to be t r a n s p o r t e d and r e - p r o c e s s e d a f t e r i r r a d i a t i o n if the r e c o v e r y of i ts f i s s i l e contents a p p e a r s economic . The condi t ions unde r which n u c l e a r fue l i s p r o c u r e d v a r y . F o r example , n a t u r a l u r a n i u m can be obtained f r o m s e v e r a l coun t r i e s in the f o r m of m e t a l o r c o m -pounds, or f ab r i ca t ed fue l e l e m e n t s . Enr i ched u r a n i u m may be l eased or p u r -chased , a s the hexaf luor ide f r o m the United Sta tes Governmen t , which does not p rov ide fo r f ab r i ca t i on . The s y s t e m of c r e d i t s fo r the i r r a d i a t e d fue l a l so v a r i e s as indicated in the next sec t ion .

2. Main fue l cyc le cost p a r a m e t e r s

The economic and t echn ica l p a r a m e t e r s de te rmin ing nuc l ea r fue l c o s t s may be broad ly grouped in the following c a t e g o r i e s :

(1) The cos t of f a b r i c a t e d fue l a s cha rged in the r e a c t o r . (2) The amount of fue l in the r e a c t o r . (3) The fue l b u r n - u p ( e x p r e s s e d in m e g a w a t t - d a y s p e r unit weight of fue l

f o r fue l of low en r i chmen t and a tom p e r cent b u r n - u p for highly en-r i ched fue ls ) which may be covered by g u a r a n t e e s on the in tegr i ty of the fue l and i t s r eac t iv i ty up to s ta ted i r r ad i a t i on l eve l s .

(4) The value of the spent fue l d i scha rged f r o m the r e a c t o r l e s s p r o c e s s i n g and t r a n s p o r t a t i o n cos t s (or in the c a s e of fuel e l e m e n t s which a r e not p r o c e s s e d , the cos t of t h e i r s t o r a g e and u l t ima te d i sposa l ) .

(5) The fue l schedul ing which d ic ta tes the amount of f r e s h fue l r e s e r v e held in s t o r a g e , the hold-up t i m e of i r r a d i a t e d fue l e l e m e n t s in the cooling pond, the method of approach to equ i l ib r ium, and the shuff l ing of fue l in the r e a c t o r .

(6) The t h e r m a l ef f ic iency of the plant which d e t e r m i n e s the n u m b e r of uni ts of e l e c t r i c energy which one unit of heat will p roduce .

(7) The cost of money or the r a t e (or r a t e s ) of i n t e r e s t which, b e c a u s e of the l a r g e amounts of money immobi l i zed in nuc l ea r fue l , p l ays a much m o r e impor t an t p a r t than in the c a s e of conventional p l an t s .

(8) The plant f a c t o r of the n u c l e a r s ta t ion which a f f e c t s the fuel to a l a r g e r extent than in a convent ional plant b e c a u s e of the r e l a t ive ly l a r g e value of the fue l immobi l i zed in the r e a c t o r , in r e s e r v e and in cooling.

(9) The plant l i fe may a l so be a r e l evan t fue l cost p a r a m e t e r s ince , under s o m e s y s t e m s the f i r s t r e a c t o r loading may be pa r t i a l ly or ful ly a m o r -t ized a f t e r the en t i r e l i fe of the nuc l ea r ins ta l la t ion . Some of t he se i t e m s ca l l fo r addi t ional c o m m e n t s .

A. Cost of r e a c t o r fue l At the p r e s e n t t i m e , f i r m r e a c t o r fue l p r i c e s have been publ ished only by

the United Kingdom and the United Sta tes of A m e r i c a , but o ther coun t r i e s such a s Canada have given quota t ions on n a t u r a l u r a n i u m fue l to both domes t i c and fo re ign c u s t o m e r s . All publ i shed p r i c e s a r e subjec t to r e v i s i o n f r o m t i m e to t i m e .

The United Kingdom Atomic Energy Authori ty will quote a p r i c e f o r a spec i f i c fue l packed and de l ive red f r e e on boa rd ship at a B r i t i s h po r t .

18

In Canada p r i v a t e m a n u f a c t u r e r s a r e p e r m i t t e d to p u r c h a s e n a t u r a l u r a n i u m compounds on the open m a r k e t and conver t t h e m into r e a c t o r fue l . The manu-f a c t u r e r in t u r n may se l l the nuc l ea r fuel in a n o r m a l c o m m e r c i a l m a n n e r .

The United Sta tes Atomic Energy C o m m i s s i o n l e a s e s or s e l l s en r i ched or n a t u r a l u r a n i u m at a publ i shed schedule of p r i c e s fo r d i f f e ren t e n r i c h m e n t s . ^ It does not , however , c a r r y out f u e l p r e p a r a t i o n and f ab r i ca t i on f o r c o m m e r c i a l r e a c t o r o p e r a t o r s , t he se s e r v i c e s being prov ided by p r i v a t e m a n u f a c t u r e r s . These c o s t s m u s t be consol ida ted to obtain the cost of the f a b r i c a t e d fue l cha rged into the r e a c t o r .

Domes t i c o p e r a t o r s in the United States of A m e r i c a to whom the fue l is l eased at p r e s e n t mus t make pe r iod i c paymen t s to the c o m m i s s i o n f o r (a) the lo s s in va lue of the fue l a s it i s i r r a d i a t e d and a s i ts en r i chmen t d e c r e a s e s and (b) the u s e of u r a n i u m , unde r t he i r cont ro l and to which the gove rnmen t has r e t a ined t i t l e , p r e s e n t l y computed at 4 3/4% p e r y e a r on the va lue of the u r a -n ium dur ing the pe r iod f o r which the payment is m a d e . In the c a s e of fo re ign o p e r a t o r s the en r i ched u r a n i u m may be sold and the moda l i t i e s of payment va ry with each individual c a s e . Thus , in the United S ta tes - E u r a t o m a g r e e m e n t the u r a n i u m i s e i the r to be l e a s e d or pu rchased under a d e f e r r e d payment plan.

When the u r a n i u m i s m a d e avai lable a s hexa f luo r ide and a l l i n t e r m e d i a t e s t eps leading to the comple ted fue l e lement a r e the r e spons ib i l i t y of the fuel f a b r i c a t o r o r of the r e a c t o r o p e r a t o r , the e s t i m a t e of to ta l fue l e lement cos t mus t be m a d e by the fue l u s e r on the b a s i s of ava i lab le in fo rmat ion f r o m f a b r i c a t o r s and o ther s o u r c e s . In the fabr ica t ion of a fue l e l ement , n a t u r a l o r enr iched u r a n i u m will f i r s t have to be conver ted into a su i tab le c h e m i c a l f o r m and f ab r i ca t ed into the shape r e q u i r e d , such a s mach ined m e t a l b a r s o r dense oxide p e l l e t s . The f ab r i ca t ed u r a n i u m will then have to be clad with a m a t e r i a l such a s "Magnox", s t a i n l e s s s t ee l , z i r con ium, o r a lumin ium, and then t e s t ed , sea led and a s s e m b l e d into comple te fue l e l e m e n t s . In the c o u r s e of t h e s e o p e r a -t ions , c h a r g e s of 1 to 2% of va lue of the o r ig ina l u r a n i u m may be m a d e by the p r o c e s s o r f o r l o s s e s while r e j e c t s and s c r a p s have been e s t ima ted at 8 to 10%. The ex t r a m a t e r i a l n e c e s s a r y to cover l o s s e s and r ecyc l ing may t h e r e f o r e be included in the amount or ig ina l ly p u r c h a s e d or l e a s e d . If d i f fe ren t f i r m s c a r r y out the v a r i o u s ope ra t i ons , t h e r e may be t r a n s p o r t and i n s u r a n c e c h a r g e s fo r the m a t e r i a l p a s s i n g between the va r ious s t a g e s .

B. Fue l e l emen t p e r f o r m a n c e and g u a r a n t e e s

The cost of power gene ra t ion f r o m a n u c l e a r fue l is c r i t i ca l ly dependent upon the fue l p e r f o r m a n c e or bu rn -up , that i s , the amount of heat obtained f r o m a given weight of nuc l ea r fue l b e f o r e d i s c h a r g e f r o m the r e a c t o r .

The fue l b u r n - u p i s l imi ted by two f a c t o r s , r e ac t i v i t y and in tegr i ty . The f i r s t a r i s e s f r o m the n e c e s s i t y of having a suf f ic ien t amount of f i s s i onab l e m a t e r i a l s to main ta in c r i t i c a l i t y f o r plant ope ra t ion . The second is d e t e r m i n e d by the m e c h a n i c a l and c h e m i c a l damage s u f f e r d by the fue l e l ement a s a r e s u l t of rad ia t ion exposu re .

Ave rage fue l e lement e x p o s u r e s quoted fo r p r e s e n t fue l s and based on expe r imen ta l data a r e 3 MWd/kgU fo r unal loyed u r a n i u m m e t a l , and between 10 and 20 MWd/kgU f o r u r a n i u m oxide. The expe r i ence which will shor t ly be -come ava i lab le f r o m r e a c t o r s now opera t ing , and those soon to be opera t ing , will y ie ld p r e c i s e data on the t r e n d of the n u c l e a r fue l exposure .

1) Recently revised and reduced price schedule effective in July 1961.

19

In many c a s e s it will be p o s s i b l e to r e d u c e the r i s k due to uncer ta in ty of fue l p e r f o r m a n c e by obtaining f inanc ia l g u a r a n t e e s f r o m the m a n u f a c t u r e r s . The g u a r a n t e e s which a r e given may v a r y but the following will ind ica te what may be ava i lab le .

In typica l b u r n - u p g u a r a n t e e s the fuel m a n u f a c t u r e r s will w a r r a n t , in e f fec t , tha t a spec i f i ed a v e r a g e amount of heat energy will be obtained b e f o r e fue l f a i l u r e n e c e s s i t a t e s the d i s c h a r g e of fue l e l e m e n t s . The types of f a i l u r e may be one or both of the following which may be i n t e r r e l a t e d :

(1) Mechanica l o r c o r r o s i o n f a i l u r e of the e l ement which i m p e d e s coolant flow or p e r m i t s suf f ic ien t f i s s ion p roduc t s to be r e l e a s e d in the coolant to r e q u i r e fue l e lement r e m o v a l .

(2) L o s s of nuc l ea r r eac t iv i ty , r equ i r i ng r e p l a c e m e n t of the spent fue l with f r e s h fue l b e f o r e the ave rage guaran teed l i f e t ime is r e a c h e d . The m a n u f a c t u r e r may , however , r e s e r v e the r ight to have the fue l r e -a r r a n g e d in o r d e r to a t t empt to a t t a in the gua ran teed b u r n - u p . The g u a r a n t e e may apply to the bu rn -up of a fue l e lement o r to the a v e r a g e fo r the c o r e ; a l so l e s s robus t fue l e l e m e n t s might be exchanged f o r m o r e robus t ones . The f inancia l r e spons ib i l i t y of the gua ran to r is in mos t c a s e s l imi ted to fue l f abr ica t ion c o s t s , p r o - r a t e d in a c c o r a n c e with b u r n - u p achieved to that gua ran teed , and may include shipping c h a r g e s . The net fue l cost p e r unit of e l ec t r i c i t y g e n e r a t e d may a l s o be gua ran t eed . The ava i lab le g u a r a n t e e s , however , do not extend to o the r c o s t s which might be i n c u r r e d such a s l o s s of power r e v e n u e s r e s u l t -ing f r o m r e a c t o r shut-down because of fue l f a i l u r e .

F i r m p r i c e quotat ions can be obtained f r o m m a n u f a c t u r e r s and p r o c e s s o r s f o r mos t of the f ab r i ca t ion and s c r a p r e c o v e r y s t eps and t he se usual ly include gua ran teed y ie lds and spec i f i ca t i ons . A second c o r e at a r e d u c e d p r i c e to r e -p l a c e faulty fue l might a l so be provided .

C. Value of i r r a d i a t e d fuel

The value of the f u e l d i scha rged f r o m the r e a c t o r i s the va lue of the f i s s i l e and f e r t i l e m a t e r i a l s in the i r r a d i a t e d e l e m e n t s l e s s the cost of t r a n s p o r t and i n s u r a n c e of the i r r a d i a t e d fue l and the cost of i ts p r o c e s s i n g . If r e - p r o c e s s i n g i s not cons ide red , s t o r a g e or d i sposa l cos t s will be i n c u r r e d .

T r a n s p o r t and i n s u r a n c e of fue l . T r a n s p o r t and i n s u r a n c e c h a r g e s f o r new and spent fue l m u s t be e s t i m a t e d or de t e rmined for each spec i f i c r e a c t o r s i tua -t ion. The shipping of new u n i r r a d i a t e d fue l is r e l a t ive ly s imple and the t r a n s -po r t c h a r g e s will be s i m i l a r to those fo r n o r m a l goods . Usually the fue l is i n s u r e d at n o r m a l r a t e s aga ins t l o s s o r damage in t r a n s p o r t . However , b e c a u s e of c r i t i ca l i t y cons ide ra t ion spec i a l packing c o n t a i n e r s may be r e q u i r e d . T h e s e may be p u r c h a s e d or l e a s e d by the suppl ie r of the fue l .

The t r a n s p o r t of the i r r a d i a t e d fuel d i s cha rged f r o m a r e a c t o r is a much m o r e compl ica ted p r o b l e m . Despi te a t h r e e or four mon ths ' "cool ing" pe r iod to allow the decay of s h o r t - l i v e d f i s s ion p r o d u c t s , the spent f u e l i s highly r a d i o -ac t ive and if the cladding i s r u p t u r e d , e i ther in the r e a c t o r o r dur ing d i s c h a r g e , t h e r e may be f i s s i on p roduc t contaminat ion on the outs ide of the fue l . In addit ion, t h e r e is heat gene ra t ion f r o m the r ad ioac t ive f i s s ion p roduc t s so that it i s e s s e n t i a l to u s e robus t con t a ine r s with thick shie lding, often with spec i a l cooling a r r a n g e m e n t s and with s p e c i a l sea l ing p r e c a u t i o n s . As an example , in the c a s e

20

of spent fue l e l e m e n t s f r o m the g a s - c o o l e d r e a c t o r s of the United Kingdom:, con-t a i n e r s weighing s o m e 45 to 50 tons a r e n e c e s s a r y to t r a n s p o r t spent fue l con-ta ining about two tons of u r a n i u m , which may involve spec ia l handling c h a r g e s and cons ide ra t ion of handling f ac i l i t i e s . Min imum t r a n s p o r t c h a r g e s will only r e s u l t f r o m the mos t c a r e f u l opt imizat ion of fue l l ing schedu les and t r a n s p o r t a r r a n g e m e n t s . When studying the t r a n s p o r t of r ad ioac t ive m a t e r i a l s in g e n e r a l , it i s e s s e n t i a l to e n s u r e that the l a t e s t shipping r u l e s a r e compl ied with. R e -cent ly , t h e r e has been a g e n e r a l t ightening up of such shipping r u l e s and the whole p r o b l e m is at p r e s e n t under rev iew by such o rgan iza t ions as OECC and E u r a t o m .

Spent fue l p r o c e s s i n g . The impor t an t components of the cos t of p r o c e s s i n g spent fue l , us ing the c u r r e n t solvent ex t rac t ion p r o c e d u r e , a r e :

(1) The cost of the s epa ra t i on of the i r r a d i a t e d fue l into the n i t r a t e s of the f i s s ionab le o r f e r t i l e m a t e r i a l s (the United Sta tes of A m e r i c a has e s t ab l i shed a daily p r o c e s s i n g c h a r g e which includes the cost of r e m o t e d i s a s s e m b l y of the fue l and the d i sposa l of the f i s s ion p roduc t s ; a cha rge is a l so m a d e for the cost i n c u r r e d f o r plant c l ean-ou t ) ;

(2) The cost of conver s ion of p lu tonium or u r a n i u m - 2 3 3 n i t r a t e s into a f o r m su i tab le f o r c r ed i t (into m e t a l fo r c r ed i t fo r p lu tonium by the United Sta tes of Amer i ca ) ;

(3) The cos t of conve r s ion of r e c o v e r e d u r a n i u m n i t r a t e into u r a n i u m hexaf luor ide fo r r e t u r n to the i so topic s e p a r a t i o n plant ;

(4) T r a n s p o r t co s t s between p lan t s if t he se a r e not included in o ther c h a r g e s .

(5) The l o s s e s of the u r a n i u m and plutonium during the p r o c e s s i n g .

The value of f e r t i l e and f i s s i l e m a t e r i a l in spent fue l . T h e r e a r e d i f f e ren t a r r a n g e m e n t s fo r r ece iv ing c r e d i t s fo r f e r t i l e and f i s s i l e m a t e r i a l in the i r r a -diated fue l d i s cha rged f r o m the r e a c t o r . In the c a s e of the United Kingdom Atomic Energy Author i ty a c r ed i t i s given fo r the d i scha rged fue l e l emen t , and in the c a s e of the United Sta tes Atomic Energy C o m m i s s i o n a c r e d i t i s given fo r the f i s s i l e and f e r t i l e m a t e r i a l s of def in i te spec i f ica t ion and c h e m i c a l f o r m which a r e s e p a r a t e d f r o m the i r r a d i a t e d fue l e l emen t .

The United Kingdom Atomic Energy Authori ty will r e p u r c h a s e i r r a d i a t e d fue l de l ive red to a B r i t i s h p o r t . The p r i c e , which is sub jec t to negot ia t ion, o f f e r s a c e r t a i n amount of g u a r a n t e e on fue l p e r f o r m a n c e in that it v a r i e s accord ing to the i r r a d i a t i o n which the fue l has r e c e i v e d .

The United Sta tes of A m e r i c a will r e p u r c h a s e p r o c e s s e d u r a n i u m - 2 3 5 and p lu tonium and u r a n i u m - 2 3 3 accord ing to a publ ished p r i c e schedu le . The pos s ib l e va r i a t i ons in the value of plutonium and of u r a n i u m - 2 3 3 a r e indica ted in Appendix II.

D. Fue l managemen t

The m a n a g e m e n t of the fuel in the r e a c t o r is of v i ta l i m p o r t a n c e in ach iev -ing m i n i m u m fue l c o s t s . The f a c t o r s of i m p o r t a n c e a r e the method of fue l p r o -c u r e m e n t , the r e s e r v e s of fue l r e q u i r e d which would be inf luenced by how read i ly new fue l could be p r o c u r e d and by the u t i l iza t ion of the r e a c t o r , the method used to ach ieve equ i l ib r ium condit ions; the m a n n e r in which the fue l is scheduled th rough the r e a c t o r , the handling of the fue l a f t e r r e a c t o r d i s c h a r g e , and the p e r m i t t e d level of f i s s ion produc t r e l e a s e due to fue l e lement f a i l u r e s .

21

The methods of fue l l ing r e a c t o r s a r e by (a) continuous c h a r g e - d i s c h a r g e , (b) pe r iod i c r e p l a c e m e n t of a por t ion or zone of a c o r e loading, and (c) pe r iod ic r e p l a c e m e n t of a comple te c o r e loading. Fue l m a n a g e m e n t may a l so involve cha rg ing fue l of vary ing en r i chmen t , and shuff l ing o r r e a r r a n g i n g t he fue l within the c o r e . While a l l s c h e m e s a r e designed to ach ieve b e t t e r p e r f o r m a n c e and lower fue l cos t s , the sav ings r e a l i z e d m u s t b e ba lanced agains t the cos t s in-c u r r e d for compl ica ted c h a r g e - d i s c h a r g e m a c h i n e s , o r the u se of fue l of vary ing e n r i c h m e n t . F u r t h e r , f r equen t shut-down for r e fue l l i ng or r e shuf f l ing the fue l in the c o r e may r e s u l t in added cos t s due to d e c r e a s e d plant ava i lab i l i ty . The methods of fuel l ing a r e d i s c u s s e d f u r t h e r below.

The continuous c h a r g e - d i s c h a r g e method is being used c o m m e r c i a l l y in the ga s - coo l ed , g r a p h i t e - m o d e r a t e d r e a c t o r s and the heavy wa te r - coo led and m o d e r a t e d r e a c t o r s a l so a r e designed to ope ra t e in th is m a n n e r . F o r i t s in i t ia l opera t ion the r e a c t o r may be brought to an equ i l ib r ium condition by continuous r e p l a c e m e n t of the f i r s t f ue l cha rge s t a r t i ng a l m o s t f r o m the t ime the r e a c t o r f i r s t o p e r a t e s . In th is c a s e th is f i r s t fue l cha rge will be on a v e r a g e only half i r r a d i a t e d . T h e r e a f t e r cha rge and d i s c h a r g e is continued at a s teady r a t e , the fue l being i r r a d i a t e d up to the m a x i m u m poss ib l e va lue . At the end of the u se fu l l i fe of the r e a c t o r , it will be shut down and the fue l c h a r g e r emoved fo r p r o -c e s s i n g . Th i s l as t fue l cha rge , l ike the f i r s t cha rge , will, in the absence of s p e c i a l a r r a n g e m e n t s , have been only i r r a d i a t e d to about half of the a v e r a g e b u r n - u p leve l .

In the above p r o c e d u r e the m a x i m u m i r r a d i a t i o n of the c e n t r e of a fue l e l ement channel may be s ignif icant ly d i f fe ren t f r o m that of the a v e r a g e . To i m p r o v e the fuel u t i l iza t ion the r e a c t o r can be designed with a n u m b e r of fue l e l e m e n t s in each channel , and a f t e r they have achieved about one-half of the p e r m i t t e d i r r a d i a t i o n , the e l e m e n t s in a channel would be r e a r r a n g e d , the c e n t r e going to the end and the end e l emen t s to the c e n t r e . This r e s u l t s in an i n c r e a s e in the a v e r a g e i r r a d i a t i o n of the fuel d i scha rged and hence b e t t e r fue l economy. To improve f u r t h e r fue l u t i l iza t ion, r e a c t o r s with continuous c h a r g e -d i s c h a r g e and m u l t i - f u e l e l emen t s in each channel , have been des igned i n c o r -po ra t ing a counter flow movement of fue l in a l t e r n a t e channels which r e s u l t s in max imiz ing the exposu re of the fuel d i s cha rged .

The methods of fue l l ing in which a comple te zone, o r c o r e is r e p l a c e d pe r iod ica l ly a r e used in o rgan ic and water r e a c t o r s of the p r e s s u r e v e s s e l type . Fuel l ing by r e p l a c e m e n t of a comple te c o r e a f t e r deplet ion of the ava i lab le r eac t iv i ty l eads to l a r g e var ia t ion in the exposure level over the c o r e , and hence s o m e economic l o s s due to incomple te u t i l iza t ion of the fue l e l e m e n t s .

By r e a r r a n g i n g the fue l e l e m e n t s dur ing the cyc le , o r by ini t ia l ly loading the r e a c t o r with m u l t i - e n r i c h m e n t fue l , the fue l cos t can be r educed . F u r t h e r i m p r o v e m e n t in the fue l cyc le can be achieved by zone charg ing in which, fo r example , the fuel f r o m the c e n t r e zone is d i scha rged , fue l in the i n t e r m e d i a t e zones moved rad ia l ly inward , and new fue l cha rged in the outer zone. This r e s u l t s in a h igher power ra t ing (and hence lower unit cap i ta l plant inves tment ) , lower en r i chmen t , and f e w e r con t ro l r o d s . Sti l l f u r t h e r advantages a r e obtained by using the above s c h e m e and m u l t i - e n r i c h m e n t loading. Other modi f i ca t ions a r e the u s e of seed ( f i s s i l e m a t e r i a l ) and blanket ( fe r t i l e m a t e r i a l ) a r r a n g e m e n t s , o r spiked co re (d is t r ibut ion of seed through the blanket) . Studies have indicated that spiked c o r e s a p p e a r economical ly compet i t ive with a zoned c o r e .

22

B e c a u s e of the i m p o r t a n c e of the fuel l ing of a r e a c t o r , de ta i led ca lcu la t ions a r e c a r r i e d out to endeavour to d e t e r m i n e the fuel l ing s c h e m e which g ives the bes t r e s u l t . Cons ide r ab l e e f fo r t i s being d i r ec t ed to i m p r o v e the economics of the fuel l ing cyc le , but the m a x i m u m poss ib l e i r r ad i a t i on l eve l s and bes t fue l l ing p r o c e d u r e will only be known when power r e a c t o r s have been in ope ra t ion fo r s e v e r a l y e a r s .

23

IV. OPERATION, MAINTENANCE AND OTHER COSTS

1. Int roduct ion

This ca tegory of cost inc ludes al l o ther c h a r g e s not covered in the p rev ious two c h a p t e r s under cap i ta l and fue l . Normal ly , a s in the c a s e fo r conventional power s ta t ions , it inc ludes only what is r e f e r r e d to as opera t ion and main tenance c o s t s but in the c a s e of n u c l e a r p lan ts may include c h a r g e s fo r make up of heavy water or o ther spec i a l coolants , th i rd pa r ty l iabi l i ty i n s u r a n c e , t axes , and o ther co s t s not a l loca ted to cap i ta l and fue l . T h e s e cos t s (conveniently e x p r e s s e d a s annual c o s t s p e r kilowatt of r a t e d power output) and the cap i t a l cos t s and fue l c o s t s f o r m the b a s i s f o r the de te rmina t ion of the cost of e l ec t r i c i t y genera t ion which is t r e a t e d in the next chap t e r . Taxes and p r o p e r t y i n s u r a n c e a r e a l so ment ioned in th i s sec t ion , although in some c a s e s such as that of the United Sta tes of A m e r i c a they a r e handled as p a r t of the annual cap i ta l cha rge r a t e . The cos t s under th is ca tegory c o m p r i s e only about ten to f i f t een pe rcen t of the cos t of e l ec t r i c i t y power gene ra t ion . N e v e r t h e l e s s , once cap i ta l ha s been ex-pended in the cons t ruc t ion of a nuc l ea r power s ta t ion, sav ings in the cos t of power can only be e f fec ted in th is a r e a and in that of fue l c o s t s . They a r e , t h e r e f o r e , of g r e a t i m p o r t a n c e to s ta t ion managemen t .

2. Opera t ion and ma in tenance cost

Appendix III, P a r t 1 g ives an example of the breakdown of opera t ion and ma in t enance c o s t s . Staff r e q u i r e m e n t s , m a t e r i a l s and ma in tenance a r e b r i e f ly rev iewed in the following sec t i ons .

A. Staff r e q u i r e m e n t s

T h e r e can be cons ide rab l e va r i a t ion in the r e q u i r e m e n t s of the staff fo r the opera t ion of a nuc l ea r s t a t ion . This will va ry with f a c t o r s such a s type and s i z e of r e a c t o r , the d e g r e e of spec ia l i za t ion of the r e g u l a r s ta f f , the avai labi l i ty of h igh ly-sk i l l ed outs ide staff f o r spec ia l ma in tenance , and the g e n e r a l p r a c t i c e s and po l ic ies of unions and power au tho r i t i e s . As an example , s e v e r a l s e r v i c e s , such as f i lm badge p r o c e s s i n g , handling of contaminated clothing, i n s t r u m e n t ca l ib ra t ion and r ad io -b io log i ca l ana lys i s can a l so be dealt with by the r e g u l a r s taff of the nuc l ea r s ta t ion or may be p e r f o r m e d under outs ide c o n t r a c t .

Since opera t ing data for nuc l ea r s ta t ions a r e l imi ted , it i s usua l to e s t i m a t e the total staff r e q u i r e d to run the power s ta t ion e i the r by analogy with o ther s i m i l a r ins ta l l a t ions or by inspect ion of the s ta t ion des igns and deciding spec i f i c jobs . The cos t ing of the staff may be done individually if wage r a t e s a r e known o r on a global b a s i s by c o m p a r i s o n with known cos t s .

Superv is ion c h a r g e s may tend to be h igher than in convent ional power s t a t ions both on account of qual i f ied s u p e r v i s o r s commanding high s a l a r i e s and b e c a u s e of the l a r g e r n u m b e r of d i v e r s e sk i l l s r e q u i r e d , fo r example , in n u c l e a r engineer ing and heal th phys i c s .

The p r o f e s s i o n a l staff will have to be appointed s e v e r a l y e a r s b e f o r e the s ta t ion s t a r t s opera t ing at power and the t r a in ing cos t s a r e h igher than c o r r e -sponding c o s t s fo r convent ional s ta t ion s ta f f , al though the l a t t e r a r e by no m e a n s negl ig ible in view of the i n c r e a s i n g complexi ty of conventional s t e a m p lan t s .

24

Conse rva t i ve p r a c t i c e s , lack of l o n g - t e r m expe r i ence , and need of c e r t a i n spec i a l i zed sk i l l s will n e c e s s i t a t e a somewhat l a r g e r staff then fo r a conven-t ional s t e a m power s ta t ion . An example of the type of s taff r e q u i r e d fo r a n u c l e a r s ta t ion i s given in Appendix III - P a r t 2.

B. M a t e r i a l s

The r e q u i r e m e n t s of n o r m a l m a t e r i a l supp l ies , such as lubr ica t ing o i l s , s p a r e p a r t s and c h e m i c a l s fo r wa te r t r e a t m e n t may be based on those of con-vent ional power s t a t ions . Some types of n u c l e a r power s t a t ions , however , r e q u i r e spec i a l m a t e r i a l s such a s heavy wa te r , sod ium, o rgan ic l iquids o r he l ium to ac t a s coolants a n d / o r m o d e r a t o r s . The cos t of in i t ia l c h a r g e s of such m a t e r i a l s would be included in the s ta t ion cos t , however , any m a k e - u p r e q u i r e d would be included under th is ca tegory of cos t .

Coolants a r e a f f ec t ed by i r r a d i a t i o n , and t h e r e f o r e r ecombina t ion and pur i f i ca t ion s y s t e m s a r e r e q u i r e d to m i n i m i z e l o s s e s and rad ia t ion h a z a r d s . D e s i g n e r s of i n d u s t r i a l r e a c t o r s will need to s t r i k e a ba lance between the cos t of spec i a l con ta inment fo r coolant c i r c u i t s , the cos t of pu r i f i ca t ion p l an t s , the amount of decompos i t ion or p o l y m e r i z a t i o n - p r o d u c t s a l lowable in the s y s t e m , and the va lue of the m a k e - u p m a t e r i a l saved .

C. Main tenance

The cos t of main ta in ing the convent ional equipment of a n u c l e a r power s ta t ion will be r ead i ly a s s e s s e d by r e f e r e n c e to ma in tenance cos t s of con-vent ional power s t a t i o n s . By es t ima t ing the ma in t enance c o s t s of the n u c l e a r por t ion of the s ta t ion one has to cons ide r that ma in t enance may be n e c e s s a r y in r ad ioac t ive a r e a s , on r a d i o a c t i v e equipment , or by r e m o t e con t ro l . F u r t h e r , t h e r e may be decontamina t ion c o s t s .

Cos t s may a l so be i n c r e a s e d b e c a u s e the high inves tment of the n u c l e a r plant m a k e s it economica l ly impor t an t to c a r r y out the ma in t enance work with a m i n i m u m of shut -down of the p lan t . Thus , of ten a c o n s i d e r a b l e amount of o v e r t i m e o r addi t ional staff might be n e c e s s a r y . F ina l ly , the s t a n d a r d s of ma in t enance m u s t be v e r y high which again m a k e s f o r c o s t s h ighe r than those in a convent ional s ta t ion .

3. O the r c o s t s

A. R e p l a c e m e n t of s p a r e p a r t s

M a j o r s p a r e p a r t s would be covered under the in i t ia l s ta t ion c o s t s . They would include c r i t i c a l r e a c t o r components o r spec i a l i t e m s which would be dif f icul t to obtain, and which a r e kept to a s s u r e aga ins t u n f o r e s e e n f a i l u r e . However , t h e r e would a l s o be expendable i t e m s which would be expected to be r e p l a c e d pe r iod ica l ly within the p l a n t ' s l i fe such a s con t ro l r o d t ips , a s s e m b l y channe ls , g r aph i t e s l e e v e s , pumps , va lves , and m e t e r s . An annual ope ra t ing a l lowance should be m a d e fo r the l a t t e r i t e m s , which in the United Sta tes of A m e r i c a ' s p r a c t i c e i s r e f e r r e d to i n t e r i m r e p l a c e m e n t c o s t s .

B. T h i r d p a r t y l iabi l i ty and p r o p e r t y i n s u r a n c e

In o r d e r to c o v e r the potent ia l th i rd p a r t y l iabi l i ty in the event of a n u c l e a r accident at the p lant o r dur ing fue l t r a n s p o r t a t i o n , i n s u r a n c e compan ie s have f o r m e d pools and have m a d e a r r a n g e m e n t s f o r r e - i n s u r a n c e and c o - i n s u r a n c e .

25

One of the p recond i t ions fo r those a r r a n g e m e n t s i s a l so the ha rmoniza t ion of l ega l r u l e s appl icable in c a s e of a nuc l ea r acc ident s ince the cos t of i n su rance does not depend only on the sa fe ty c r i t e r i a and the potent ia l r i s k of a plant but a l so on the legal n o r m s governing c l a i m s fo r compensa t ion . Nuc lea r acc iden t s may have t r a n s - n a t i o n a l impl ica t ions (depending, e . g . on amount and p lace of damage , nat ional i ty of c l a iman t , in t e rna t iona l supply con t r ac t s ) which often may n e c e s s i t a t e mul t ip le i n s u r a n c e coverage f o r one and the s a m e r i sk 1 ) and thus r a i s e the u l t ima te cos t of nuc l ea r power .

An in te rna t iona l convention on civi l l iabi l i ty fo r n u c l e a r damage has been e labora ted by the European Nuc lea r Energy Agency (ENEA) of OEEC and a d r a f t convention on the s a m e sub jec t has been p r e p a r e d by the Agency2) . The fundamenta l p r i n c i p l e s embodied in both convent ions that may be re levan t to the cost of i n s u r a n c e a r e :

(1) Absolute l iabi l i ty for nuc l ea r damage; (2) Channel l ing of l iabi l i ty to the o p e r a t o r of a n u c l e a r ins ta l la t ion with

v e r y r e s t r i c t e d r igh t of r e c o u r s e ; (3) L imi ta t ion of l iabi l i ty in amount and in t ime ; (4) Concent ra t ion of su i t s in s ingle ju r i sd ic t ion ; (5) Obligation to main ta in f inancia l s ecu r i t y up to l iabi l i ty m a x i m u m .

States a r e f r e e to p r e s c r i b e the type of f inanc ia l s ecu r i t y r e q u i r e d and may p rov ide p a r t o r al l of the r e q u i r e d f inanc ia l s e c u r i t y . The OEEC Convention s t i pu la t e s in addit ion that i n s u r a n c e p r e m i u m s and compensa t ion shal l be f r e e l y t r a n s f e r a b l e . The p r inc ip l e of channell ing t r a n s p o r t l iabi l i ty to the o p e r a t o r obvia tes the n e c e s s i t y for s u p p l i e r s and t r a n s p o r t e r s to t ake out i n s u r a n c e and

.. consequent ly may r e s u l t in lower t r a n s p o r t a t i o n cos t s and lower p r i c e s f o r equipment and ins t a l l a t ions .

The high potent ia l t h i rd pa r ty l iabi l i ty in the event of a n u c l e a r acc ident often m e a n s that it i s not poss ib l e to obtain c o m m e r c i a l i n s u r a n c e cove rage fo r the ful l l iabi l i ty . Al te rna t ive ly , the p r e m i u m s r e q u i r e d in the ea r ly days may be h igher than they would be if m o r e s t a t i s t i c a l in fo rmat ion w e r e ava i lab le . One method of a s s u r i n g p ro tec t ion of the public without undue burden on o p e r a t o r s of nuc l ea r ins ta l l a t ions is f o r the government to p rov ide s o m e or a l l of the f inanc ia l s ecu r i t y , e. g. by under tak ing , at no, or at only a nominal , c h a r g e to the r e a c t o r o p e r a t o r , to indemnify h im fo r l iabi l i ty i n c u r r e d above the amount covered by i n s u r a n c e .

P r o p e r t y i n s u r a n c e which r e p r e s e n t s a much s m a l l e r cos t than th i rd pa r ty l iabi l i ty , i s , however , h igher than in conventional p lants and th i s gap i s unl ikely to be br idged in view in p a r t i c u l a r of the p r o b l e m s of r ad ioac t ive contaminat ion which may a r i s e fo r a n u c l e a r s ta t ion .

C. T a x e s

Government -owned e n t e r p r i s e s a r e not no rma l ly subjec t to t axes al though in s o m e c a s e s nomina l c h a r g e s m a y b e levied so as to p rov ide paymen t s to loca l au tho r i t i e s in l ieu of loca l t a x e s . P r iva t e ly -owned e n t e r p r i s e s , on the o ther hand, a r e sub jec t to t axes which can be quite complex and which na tu ra l ly v a r y f r o m country to country both in amount and method of appl ica t ion. Taxes may be

^ For a detailed examination of the legal problems involved see "International Problems of Financial Protection against Nuclear Risk", Havard Law School, 1959.

2 ) See document GOV/INF/47/Add. 1.

26

levied on both the p r o p e r t y o r a s s e t s and on income . The widely va ry ing nat ional p r a c t i c e in th i s f ie ld call* f o r spec i f i c a n a l y s i s in each c a s e , and will not be d i s c u s s e d in th i s r e p o r t .

D. Working Capi ta l

Allowance mus t be made f o r the t i m e lag between r e c e i p t s of r e v e n u e s and expend i tu res i n c u r r e d f o r the p u r c h a s e of fuel 1 ) and o ther opera t ing suppl ies a s f o r the payment of wages and s a l a r i e s . In s o m e s y s t e m s th i s t akes the f o r m of a working càp i t a l c h a r g e .

l ) Fabrication only if it is leased.

27

V. THE DETERMINATION OF GENERATING COSTS

1. In t roduct ion

The main i t e m s of co s t s of building and opera t ing a nuc l ea r powér plant and t t ieir a d j u s t m e n t s to spec i f i c condit ions have been d i s cus sed in the p rev ious s e c t i o n s . The p r o b l e m of de t e rmin ing fo r the energy produced a unit cost p e r ki lowatt hour which will a c c u r a t e l y r e f l e c t the s e r i e s of i r r e g u l a r out lays in-c u r r e d at d i f fe ren t t i m e s for the cons t ruc t ion , fuel l ing and opera t ion of the r e a c t o r i s the subjec t of the p r e s e n t chap te r . Some of t he se out lays , a s fo r in-s t ance s ta t ion cons t ruc t ion c o s t s , a r e known with r e l a t i v e a c c u r a c y , o t h e r s , such a s f u t u r e fue l c o s t s , a r e much m o r e diff icul t to e s t i m a t e . N e v e r t h e l e s s , any a t t empt at e s t ima t ing to ta l genera t ing cos t s r e q u i r e s f o r e c a s t s about the f u t u r e , and the unce r t a in ty a f fec t ing ce r t a i n input data does not de t r ac t f r o m the n e c e s s i t y of us ing a s logical and c o m p r e h e n s i v e a method a s poss ib l e , applying it , if n e c e s s a r y , to d i f fe ren t f o r e c a s t s of f u t u r e fue l p r i c e s in o r d e r to obtain a r a n g e within which genera t ing cos t s may be r ea sonab ly expected to fa l l . Th is is e spec ia l ly impor t an t in view of the expectat ion of lower nuc l ea r fue l c o s t s in the n e a r f u t u r e .

A c c u r a t e gene ra t ing cost f i g u r e s for a s ingle plant will p e r m i t an economic c o m p a r i s o n of two r e a c t o r s with d i f fe ren t capi ta l , fue l and opera t ion and m a i n -t enance cost s t r u c t u r e s provided they a r e expected to p e r f o r m roughly the s a m e s e r v i c e s over the s a m e pe r iod of t i m e within the s a m e power s y s t e m . They should not be used i nd i s c r im ina t e ly for convent ional v e r s u s n u c l e a r power c o m p a r i s o n s . Nuc lea r r e a c t o r s will usual ly be in t roduced within power s y s t e m s whose whole opera t ion will be a f fec ted by the i r a p p e a r a n c e and the d e t e r m i n a -tion of the t r u e cos t to the s y s t e m of opera t ing a nuc l ea r s ta t ion mus t involve an economic a n a l y s i s of the s y s t e m as a whole over a pe r iod of y e a r s b e f o r e a s ign i f ican t conclus ion on the economic m e r i t s of the n u c l e a r plant can be m a d e . Hence the p r a c t i c e of compar ing genera t ing cos t s of a convent ional and a nuc l ea r s ta t ion at the s a m e plant f a c t o r which is expected to r e m a i n constant over t he i r l ives r e s t s on an a s sumpt ion whose validity mus t be ca r e fu l l y checked f o r each spec i f i c c i r c u m s t a n c e . But even with a c l e a r recogni t ion of t hese l imi ta t ions , the t r a n s f o r m a t i o n of a complex s e r i e s of capi ta l and fue l expendi tu res into a s ing le f i g u r e fo r the cost of energy r e m a i n s an opéra t ion based on explici t o r t ac i t a s s u m p t i o n s , s o m e common to conventional and nuc lea r power cos t ing but o t h e r s a r i s i n g f r o m the spec i f i c f e a t u r e s of nuc l ea r s t a t ions . In p a r t i c u l a r the unique f e a t u r e s of nuc l ea r fue l na tura l ly give r i s e to spec ia l cos t ing p r o b l e m s .

The r e l a t i ve ly l a r g e amount of money t ied in the in i t ia l fue l inventory is one of t h e m . Another is the quest ion of accounting c o r r e c t l y f o r the v a r i a b l e fue l expend i tu re s and c r e d i t s i n c u r r e d dur ing the f i r s t y e a r s b e f o r e the m a x i -m u m a v e r a g e i r r a d i a t i o n level is r e ached fo r the fue l d i scha rged f r o m the r e a c t o r as well a s dur ing the las t y e a r s p r eceed ing shut down. Fue l consump-tion c o s t s fo r t h e s e y e a r s will d i f f e r f r o m consumpt ion cos t s fo r equ i l ib r ium y e a r s . Th i s va r i a t i on may or may not be s igni f icant accord ing to the length of p r e - e q u i l i b r i u m and p r e - s h u t down t i m e s but i t s ex i s tence a s well a s the poss ib i l i ty of v a r i a t i o n s in o ther cos t ing p a r a m e t e r s such a s cos t of fue l and p lant f a c t o r dur ing the r e a c t o r ' s l i fe w a r r a n t s the grouping of genera t ing cos t d e t e r m i n a t i o n me thods into two c a t e g o r i e s : the s teady s t a t e me thods and the p r e s e n t wor th me thod . . .

28

2. The s teady s t a t e me thods

Although d i f fe r ing f r o m country to country in t he i r p r a c t i c a l appl ica t ion , t h e s e me thods have a common f e a t u r e which may s e r v e as t h e i r def ini t ion. They a l l s t a r t with equ i l ib r ium condit ions when the a v e r a g e i r r a d i a t i o n of the fue l d i s cha rged f r o m the r e a c t o r has r e a c h e d i t s r a t e d value . The fuel cost is then ad jus t ed in va ry ing ways to make a l lowance fo r co s t s i n c u r r e d dur ing the non-equ i l ib r ium pe r iod .

F o r the sake of c l a r i t y the capi ta l , fue l and opera t ion and ma in t enance components of genera t ing cost a r e cons ide red s e p a r a t e l y .

A. The cap i ta l cos t component

This is the p a r t of the gene ra t ing cost which mus t r e f l e c t a s a c c u r a t e l y a s p o s s i b l e al l the capi ta l i nves tmen t s which have been m a d e in the p lant . Although the p r inc ip l e of i t s de t e rmina t ion i s the s a m e a s f o r convent ional p l an t s , the u n c e r t a i n t i e s a f fec t ing the expected l ives of the nuc l ea r i t e m s and the c o r r e -sponding v a r i a t i o n s of r e s u l t s may of ten ca l l fo r spec i a l a t ten t ion .

The m a i n s t eps of the de t e rmina t ion of the cap i ta l cos t component may be s u m m a r i z e d as fol lows:

(1) The to ta l cap i ta l cos t p e r ki lowatt ins ta l led at the t i m e of s t a r t - u p is d e t e r m i n e d by to ta l l ing a l l capi ta l cost i t e m s , adding a c h a r g e f o r i n t e r e s t dur ing cons t ruc t ion which m a k e s a l lowance fo r the fac t that p r o g r e s s i v e p a y m e n t s a r e to be made b e f o r e the plant s t a r t s ac tua l ly producing power and dividing by the net e l e c t r i c power of the p lan t . T a x e s , i n s u r a n c e and m i s c e l l a n e o u s c h a r g e s which a r e s o m e t i m e s t r e a t e d a s cap i ta l co s t s a r e dealt with s e p a r a t e l y and not cove red in th is sec t ion .

(2) An annual r a t e of i n t e r e s t i s applied to th is cap i ta l cos t to ta l .

(3) A deprec ia t ion c h a r g e i s computed by de t e rmin ing the annual amoun t s of money which if se t a s i de each y e a r and y ie ld ing compound i n t e r e s t will add up at the end of the l ife of the plant to the to ta l cap i ta l cos t ini t ia l ly i n c u r r e d . In economic s tud ies the s o - c a l l e d s inking fund method is a lmos t u n i v e r s a l l y used in which the annual amoun t s a r e r e q u i r e d to be equal and a s s u m e d to yield i n t e r e s t which is annually compounded. Under t he se condi t ions , the deprec ia t ion c h a r g e i s equal to the o r ig ina l

i i s the i n t e r e s t r a t e and n the plant l i fe e x p r e s s e d in y e a r s . The value of th i s f ac to r can eas i ly be found in any annuity t ab le .

(4) The to ta l annual cap i ta l cos t component i s then obtained by adding the annual i n t e r e s t c h a r g e to the deprec ia t ion c h a r g e and dividing by the n u m b e r s of ki lowatt h o u r s p roduced dur ing the y e a r . If X i s taken to r e p r e s e n t th i s cha rge , C n the to ta l unit cap i ta l cost (ad jus ted fo r i n t e r e s t dur ing cons t ruc t ion) and h the equivalent n u m b e r of h o u r s of fu l l power annual u t i l iza t ion then,

Th i s p r o c e d u r e ha s the m e r i t of r e l a t i v e s imp l i c i ty . I ts p r a c t i c a l appl ica t ion i s , however , not without i t s p r o b l e m s . Without en te r ing

cap i ta l cost mul t ip l ied by a sinking fund f a c t o r equal to i w h e r e (1 + i ) n - l

29

h e r e into the ques t ion of se lec t ing a su i tab le r a t e of i n t e r e s t fo r the cos t ing of cap i ta l p r o j e c t s in g e n e r a l and power p lan ts in p a r t i c u l a r , it should be c l ea r l y r e c a l l e d that cost and f inancing ana lys i s involve two s e p a r a t e c a t e g o r i e s of p r o b l e m s which should both be cons ide red but not confused .

Th i s appl ies e spec ia l ly to the deprec ia t ion of cap i ta l i t e m s which mus t be kept c l e a r l y d is t inc t f r o m the amor t i za t i on of the loans which may have been i n c u r r e d fo r t he i r p u r c h a s e . The t e r m s of r epaymen t of the loans may or may not be de t e rmined by the expected l ives of the i t ems of equipment they s e r v e d to f inance but the deprec ia t ion c h a r g e s mus t be .

This l a s t r e q u i r e m e n t m a k e s fo r spec i a l p r o b l e m s in the c a s e of n u c l e a r power p l an t s . Even in conventional s ta t ions plant l i fe is a decept ively s i m p l e f i gu re contingent on economic obso l e scence at l ea s t as much as on t echn ica l w e a r - o u t and d e t e r m i n e d by averag ing , but at l e a s t it r e s t s on a body of pa s t expe r i ence . In the c a s e of nuc l ea r p l an t s , however , t h e r e is s t i l l uncer ta in ty on the behaviour of r e a c t o r m a t e r i a l s unde r i r r a d i a t i o n although s a m p l e e x p e r i m e n t s have given p r o m i s i n g r e s u l t s .

A va r i e ty of me thods have been devised to cope with th is s i tua t ion . Some coun t r i e s d e p r e c i a t e s e p a r a t e l y the d i f fe ren t p a r t s of t he i r p lan ts us ing a v e r y c o n s e r v a t i v e assumpt ion f o r the l i fe of the n u c l e a r c o m -ponent of the o r d e r of 15 to 20 y e a r s and then add toge the r the d i f f e r en t deprec ia t ion c h a r g e s obtained, while o the r s s imply take f o r the whole plant an a v e r a g e l i fe of the o r d e r of 20 to 25 y e a r s which i s lower than that of a convent ional s t a t ion . It should be pointed out, however , that the f i r s t p r o c e d u r e a s s u m e s that by the end of i t s l i fe the r e a c t o r will be r e p l a c e d by an ident ica l unit and that no modi f i ca t ions due to devel -opment in des ign and economic obso le scence would be r e q u i r e d f o r the t u r b o - g e n e r a t i n g equipment .

Under t he se condi t ions, the bes t way a p p e a r s to compute deprec ia t ion c h a r g e f o r s e v e r a l a s s u m e d l ives , say 15, 20 and 25 y e a r s thus ob-ta ining a r a n g e of pos s ib l e va lues within the e x t r e m e s of which the dep rec i a t ion c h a r g e and the capi ta l cos t component may be expected to fa l l .

B. The fue l cos t component

The n e c e s s i t y of main ta in ing a l a rge and cost ly fue l inventory , whose va lue p e r ki lowatt of capac i ty may exceed that of the r e s e r v e s tock -p i l e of a coa l plant by a f a c t o r of ten, the r ece ip t of c r e d i t s fo r i r r a d i a t e d e l e m e n t s , the p r o b l e m s of fue l e l emen t , cooling and t r a n s p o r t , a l l combine to make the ques t ion of n u c l e a r fue l cos t ing r a t h e r complex . As a m a t t e r of fac t , the p r e s e n t d i f f e r e n c e s in the me thods of fue l cycle cos t ing used in the ma in r e a c t o r -ope ra t ing c o u n t r i e s a r e e s sen t i a l l y due l e s s to t h e o r e t i c a l cons ide ra t i ons than to the p r a c t i c a l condi t ions under which the f i s s i l e m a t e r i a l i s made ava i lab le to r e a c t o r o p e r a t o r s in d i f f e ren t coun t r i e s and to the types of r e a c t o r s used .

Outl ine of method used in the United Kingdom. In the c a s e of the United Kingdom, the fue l is sold in the f o r m of f ab r i ca t ed e l e m e n t s at a c e r -ta in negot ia ted p r i c e and the used fue l e lement r e p u r c h a s e d accord ing

30

to an a g r e e d schedule of p r i c e s depending upon the i r r a d i a t i o n they have r e c e i v e d .

In th i s c a s e the de t e rmina t ion can then be b roken down a s fol lows:

(1) A fue l consumpt ion cost is de t e rmined by taking the d i f f e r e n c e between the cos t of the new fue l e l ements de l ive red to the o p e r a t o r and the c red i t f o r i r r a d i a t e d e l emen t s (net of t r a n s p o r t cost) and dividing th is d i f f e r e n c e by the n u m b e r of kilowatt h o u r s of e l ec t r i c i t y p roduced by the fue l .

Thus , if Cf is the p r i c e p e r k i l og ram of f a b r i c a t e d fue l , C^ the net c r ed i t a f t e r an a v e r a g e i r r ad i a t i on of b megawat t days p e r k i l o g r a m and e the t h e r m a l e f f ic iency of the plant the fue l consumpt ion cos t p e r ki lowatt hour of e l ec t r i c i t y produced will be

Y i =

C f - C i 24 000 eb

(2) A fue l inventory cost is de t e rmined by mult iplying the va lue of the fue l immobi l i zed in the c o r e , in r e s e r v e and in cooling and t r a n s p o r t a t i o n channels by the appl icab le i n t e r e s t r a t e . The r e s u l t i s then divided by the to ta l n u m b e r of ki lowatt h o u r s p roduced annually to yield an inven-tory c h a r g e p e r kilowatt hou r .

Thus , if the to ta l c o r e loading i s denoted by LQ , the annual throughput by L a , and the f r a c t i o n s of annual throughput kept in r e s e r v e and cool-ing by k ^ L a and kgL^, the plant capaci ty by P and the annual n u m b e r of h o u r s of equivalent opera t ion by h, the inventory cost will be:

Y o = [ c f ( L 0 + k l L & ) + C ^ L J

2 Ph

(3) If fue l r e p l a c e m e n t begins a lmos t immed ia t e ly a f t e r s t a r t - u p and con-t inues unti l f ina l shut -down the fue l of the f i r s t c o r e loading will be i r r a d i a t e d to only about one half of the r a t e d m a x i m u m i r r a d i a t i o n . The s a m e appl ies to the l a s t r e a c t o r loading. The heat va lue of one c o r e will t h e r e f o r e be lost over the l i fe of the r e a c t o r and m u s t be a m o r t i z e d . Consequent ly a fue l amor t i za t ion cost p e r k i lowat t -hour is se t a s ide such that :

C f L o i Y 3 = Ph (1 + i ) n - l ,

(4) The to ta l fue l cos t component i s obtained by adding toge the r the t h r e e cos t s ment ioned above:

Y = Y 1 + Y 2 + Y 3

Outline of the method used in Canada. The Canadian fue l cyc le cos t ing i s a good example of the way in which the t echn ica l f e a t u r e s of a r e a c t o r na tu ra l ly sugges t the mos t su i tab le s y s t e m of cos t ing .

The n a t u r a l u r a n i u m - f u e l l e d , heavy wa te r - coo led and m o d e r a t e d r e a c t o r s planned by Canada a r e c h a r a c t e r i z e d by high fue l bu rn -up , i r r a d i a t e d fue l d i s c a r d and loading and unloading under power .

31

As a r e s u l t of the l a s t f e a t u r e and a l a r g e in i t ia l e x c e s s r eac t iv i ty , the r e a c t o r can o p e r a t e at the beginning of i t s l i fe without the in t roduct ion of new fue l fo r a length of t ime equal to about half the r e s i d e n c e t i m e of new fue l unde r equ i l ib r ium condi t ions . In o ther words about half of the value of the f i r s t c h a r g e is r e c o v e r e d through power s a l e s b e f o r e f r e s h fue l i s needed . F u r t h e r m o r e , a f r e s h fue l inventory osc i l la t ing between t h r e e and s ix mon th ' s fue l consumpt ion is main ta ined at the r e a c t o r s i t e .

Under t h e s e condi t ions, the fuel cost component is de t e rmined in the following way:

(1) A fue l consumpt ion cost is de t e rmined as in the p rev ious c a s e except that no value is a t tached to the i r r a d i a t e d fue l .

(2) Since about one half of the value of a r e a c t o r fue l c h a r g e i s r e c o v e r e d in the in i t ia l months of opera t ion b e f o r e f r e s h fue l is in t roduced only the r e m a i n i n g one half cha rge of fue l r e m a i n s as an i n - c o r e fue l in-ven to ry . The c u r r e n t Canadian p r a c t i c e is to a m o r t i z e one half of the in i t ia l fue l c h a r g e and although th is may tu rn out to be somewhat low, the ef fec t of th i s on fue l cos t s is ve ry s m a l l .

(3) A fue l inventory cost i s obtained by applying the i n t e r e s t r a t e to one half of the value of the fue l in the r e a c t o r and to the value of the a v e r -age f r e s h fue l r e s e r v e .

Outl ine of the method used in the United S ta tes . Under the United Sta tes s y s t e m , in which the fue l is made ava i lab le in the f o r m of u r a n i u m hexa f luo r ide , the following condit ions apply:

(1) A schedule of p r i c e s fo r u r a n i u m of d i f fe ren t d e g r e e s of en r i chmen t , suppl ied in the f o r m of hexaf luor ide , publ ished by the United Sta tes Atomic Energy C o m m i s s i o n is used .

(2) The u r a n i u m i s l e a s e d to the domes t i c r e a c t o r o p e r a t o r and a c e r t a i n l e a s e c h a r g e (at p r e s e n t 4 3/4%) i s levied on i ts va lue at pe r iod ic i n t e r -va l s (say every s ix months ) .

(3) All the ope ra t ions r e q u i r e d to t r a n s f o r m UF 6 into f a b r i c a t e d fue l e l e m e n t s a r e the r e spons ib i l i ty of the r e a c t o r ' s o p e r a t o r which con-t r a c t s fo r t h e m with p r i v a t e compan ies .

(4) The o p e r a t o r pays a deplet ion c h a r g e equal to the d i f f e r e n c e between the in i t ia l and f ina l u r a n i u m values as l i s ted by the USAEC schedule of c h a r g e s f o r enr iched u r a n i u m .

(5) The cos t of the c h e m i c a l p r o c e s s i n g of the i r r a d i a t e d fue l e l e m e n t s and of the conve r s ion of the contained u r a n i u m into hexaf luor ide will be e f fec ted by the US AEC accord ing to a c e r t a i n schedule of c h a r g e s .

(6) P lu ton ium m e t a l is bought by the US AEC at a s ta ted p r i c e (at p r e s e n t $12 p e r g r a m ) a c h a r g e is made f o r the t r a n s f o r m a t i o n into m e t a l (at p r e s e n t . 50 p e r g r a m ) .

(7) Dur ing a l l t h e s e ope ra t ions al lowance mus t be made fo r u r a n i u m and p lu tonium l o s s e s .

Under t h e s e condi t ions the a l locat ion of t he se cos t s to the kilowatt h o u r s p roduced will involve the s e p a r a t e computa t ions of a s e r i e s of components ; a

32

fue l l e a s e cha rge , a fue l deplet ion cha rge , a f ab r i ca t ion cha rge , a c h e m i c a l p r o c e s s i n g cha rge , a u r a n i u m convers ion cha rge , a p lu tonium conver s ion c h a r g e , a p lutonium c red i t , and shipping c h a r g e s . F u r t h e r m o r e , the t i m e p e r i o d s over which p a y m e n t s a r e to be made under t he se va r ious headings a r e a l so of s o m e impor t ance in the f inal computa t ion . R a t h e r than to go into the de ta i l s of th i s computat ion in the p r e s e n t chap te r , the r e a d e r is r e f e r r e d to Appendix IV P a r t 3.

C. Opera t ion , ma in tenance and o ther cost components

The r a n g e of i t e m s cove red in this ca tegory have a l r eady been d i s c u s s e d in Chap te r IV. The i r co s t s can be e x p r e s s e d at l eas t fo r p u r p o s e s of p r e l i m i n a r y ca lcu la t ions as an annual c h a r g e p e r ki lowatt ins ta l l ed , because the p a r t of the opera t ion and ma in tenance cost which v a r i e s with plant u t i l iza t ion is a r a t h e r s m a l l f r a c t i on of the to ta l and is r e l a t ive ly insens i t ive to plant f ac to r changes .

The co r r e spond ing gene ra t ing cos t component , Z, is t h e r e f o r e obtained by adding the annual c h a r g e s ment ioned above and dividing by the number of h o u r s of equivalent u t i l iza t ion , thus

Z h

where Y. Aj i s the s u m of the annual c h a r g e p e r ki lowat t .

3. The p r e s e n t worth method

The p r e s e n t worth method o f f e r s a g e n e r a l and s y s t e m a t i c a l approach to the p r o b l e m of a l locat ing a s e r i e s of i r r e g u l a r cos t s to the uni ts of a continuous output. F u r t h e r m o r e , if the s a m e economic or t echn ica l p a r a m e t e r s such a s fue l co s t s o r plant f a c t o r a r e expected to v a r y over the l i fe of the ins ta l l a t ion , and if t he se va r i a t i ons can be a c c u r a t e l y f o r e c a s t the method y ie lds a p r o p e r l y weighted a v e r a g e fo r the genera t ing cos t . Commonly used in va r ious coun t r i e s for economic a n a l y s e s and applied in F r a n c e to n u c l e a r power cost s tud ies th i s method c o n s i s t s in:

(1) P r e p a r i n g a t i m e tab le l i s t ing y e a r by y e a r o r , if n e c e s s a r y , q u a r t e r by q u a r t e r , a l l capi ta l , fue l , opera t ion , ma in tenance and o the r ex-pend i tu r e s and c r e d i t s connected with the opera t ion of the r e a c t o r dur ing i ts whole l i fe a s well a s the amounts of energy it i s expected to g e n e r a t e .

(2) De te rmin ing a cha rge p e r kilowatt hour which will make the p r e s e n t wor th value of the to ta l energy expected to be gene ra t ed by the r e a c t o r equal to the p r e s e n t worth value of a l l expend i tu res and c r e d i t s at the t i m e when the r e a c t o r s t a r t s opera t ing at power .

(3) If the following nota t ions a r e u sed : Ej = expend i tu res in j th y e a r , Cj = c red i t in j th y e a r , Hj = energy gene ra t ed in j th y e a r , t = number of y e a r s f r o m the f i r s t outlay connected with the plant to

the date of f i r s t power opera t ion , n = n u m b e r of y e a r s f r o m f i r s t power opera t ion to plant shut down, i = annual r a t e of i n t e r e s t , G = unit gene ra t ing cos t ,

33

the following equation appl ies :

Z _ ( l + i ) 3

j= - t G =

— (1 + i )3 j = l

A m o r e deta i led desc r ip t ion and a s imp le example of appl icat ion of the p r e s e n t wor th method to r e a c t o r s with v a r i a b l e p a r a m e t e r s a r e given in Appendix V.

4. S u m m a r y

The p r o c e d u r e s c u r r e n t l y used for the de te rmina t ion of genera t ing cos t s which have been outl ined under the g e n e r a l heading of s teady s t a t e me thods have been developed on the b a s i s of nat ional fue l p r o c u r e m e n t s y s t e m s and condi-t ioned to s o m e extent by r e a c t o r types . When applied to condit ions s i m i l a r to those f o r which they w e r e or ig ina l ly intended they yield r e s u l t s whose a c c u r a c y i s m o r e than suf f ic ien t in view of the uncer ta in ty of s o m e of the b a s i c input cost da ta .

N e v e r t h e l e s s whenever complex fuel cyc les occur , or the approach to equ i l i b r ium is r e l a t ive ly long, o r f u t u r e va r i a t i ons of r e l evan t cost ing p a r a -m e t e r s can be accu ra t e ly f o r e c a s t , the p r e s e n t worth s y s t e m a p p e a r s su i tab le b e c a u s e of the c o m p r e h e n s i v e and s y s t e m a t i c way with which it i s poss ib l e to deal with s e r i e s of expend i tu re s , c r e d i t s and p roduc t ion- f lows s p r e a d i r r e g u -l a r ly ove r t i m e .

34

A C K N O W L E D G E M E N T S

The following e x p e r t s f o r m e d an Cos t ing" .

CHAIRMAN F . Ippolito Nat ional C o m m i t t e e fo r Nuc lea r

Energy Italy

MEMBERS M. Dayal Depa r tmen t of Atomic Ene rgy India

A. F o r c e l l a Nat ional C o m m i t t e e for N u c l e a r

Ene rgy Italy

L. F o r g o Nat ional Atomic Energy

C o m m i s s i o n Hungary

J . G a u s s e n s F r e n c h Atomic Ene rgy C o m m i s s i o n F r a n c e

J . L . G i l l ams United Kingdom Atomic Energy

Author i ty United Kingdom

E. K i r k h a m U. S. Atomic Ene rgy C o m m i s s i o n United Sta tes of A m e r i c a

S. Miyake Tokyo E l e c t r i c P o w e r Company Japan

M. Nagayasu Kansa i E l e c t r i c P o w e r Company Japan

in te rna t iona l pane l on "Nuclear P o w e r

J . L . Olsen

Canadian G e n e r a l E l e c t r i c Company Canada M. Quoiani South Ital ian Atomic Energy Society Italy

I. Wivstad State P o w e r Board of Sweden

OBSERVERS

H. Hardung-Hardung OEEC F r a n c e

F . H i n t e r m a y e r Assoc ia t ion of E l ec t r i c i t y Works of

A u s t r i a UNIPED and WORLD POWER

CONFERENCE

H. Michae l i s EURATOM Belg ium

S. P i t t o r i Nat ional C o m m i t t e e fo r N u c l e a r

Energy Italy

R . Scal l ie t EURATOM Belg ium

P . Sevet te Economic C o m m i s s i o n fo r Europe Switzer land

SECRETAR I AT

R . K r y m m

Economic and Techn ica l A s s i s t a n c e Divis ion (IAEA)

G. P e t r e t i c

Economic and Techn ica l A s s i s t a n c e Division (IAEA)

F . P i k i e r Divis ion of R e a c t o r s (IAEA)

35

A P P E N D I X I

COST ITEMS FOR A NUCLEAR POWER STATION

PART 1. - Ident i f icat ion and desc r ip t ion of s ta t ion cos t s

Desc r ip t ion of funct ional account

LAND AND LAND RIGHTS Includes a l l land cons ide red n e c e s s a r y fo r plant opera t ion , p r iv i l ege acquis i t ion , employee housing, r e - l o c a t i n g r o a d s , te lephone and power l i ne s .

SITE PREPARATION AND STRUCTURES. (Including only a l l c ivi l works with building s e r v i c e s , but not equipment . )

Site p r e p a r a t i o n and i m p r o v e m e n t . Grad ing , su r f ac ing , r o a d s , r a i l -ways, s e w e r s , pa rk ing a r e a s , s idewalks , fencing, a c c e s s r o a d s and r a i l w a y s .

Underground ducting. Civi l works i t e m s f o r s t e a m , e l e c t r i c c ab l e s , was te . Equipment not included in th i s i t e m .

Cooling wa te r intake and d i s c h a r g e . Civil work p a r t without equip-ment .

R e a c t o r bui lding. Excavat ion , foundat ions , s t r u c t u r e , insula t ion, inc ludes conta inment s t r u c t u r e .

T u r b i n e - g e n e r a t o r s and auxi l ia ry bui ld ings . T u r b i n e - g e n e r a t o r building, was te d i sposa l , ma in t r a n s f o r m e r s ta t ion , pumping s ta t ion , spent fue l s t o r a g e if not included in r e a c t o r bui lding.

Other bui ld ings . All a d m i n i s t r a t i o n bui ldings , such as o f f i ces , l a b o r a t o r i e s , w o r k - s h o p s , s t o r e house .

Building s e r v i c e s . P lumbing , heat ing, l ighting, a i r condit ioning, vent i la t ing, e l e v a t o r s , f i r e p ro tec t ion , if not included in accounts 2 .4 , 2. 5, and 2 . 6 .

R e m a i n d e r . Loca l communica t ions , s igna l and ca l l s y s t e m s , r ad io equipment , s e r v i c e wa te r t r e a t m e n t and m i s c e l l a n e o u s .

REACTOR AND AUXILIARY EQUIPMENT

R e a c t o r . Vesse l , s u p p o r t s , t h e r m a l and biological shie lding, sh ie ld cooling, c o r e s t r u c t u r e excluding fue l e l e m e n t s , d r ive m e c h a n i s m for con t ro l and sa fe ty r o d s .

R e a c t o r cooling, hea t ing and aux i l i a ry s y s t e m s . E m e r g e n c y shu t -down cooling, p r e - h e a t i n g s y s t e m s , sa fe ty in jec t ion .

37

Account No. Desc r ip t ion of funct ional account

3i 3 F u e l handling equipment . C r a n e s , loading and unloading m a c h i n e s , spec i a l too ls , con t a ine r s and r a c k s , spent fue l cooling equipment , shipping c a s k s and c a r s , t e lev is ion , spec ia l l ighting.

3 . 4 Rad ioac t ive was te t r e a t m e n t and d i sposa l . Exchange t o w e r s , f i l t e r s , heat exchange r s , c o n d e n s e r s , e v a p o r a t o r s , pumps , c o m p r e s s o r s , piping, a i r dilution s y s t e m - expendable tanks not included. (Does not include p r i m a r y coolant pur i f i ca t ion equipment given under 4 .2 ) .

3. 5 Ins t rumenta t ion of r e a c t o r and aux i l i a ry e q u i p m e n t . R e a c t o r cont ro l , sa fe ty and rad ia t ion moni tor ing s y s t e m s . B u r s t fue l e lement de tec -tion equipment included.

3. 6 M o d e r a t o r . If d i f f e r en t f r o m coolant including cladding if any.

3 .7 R e f l e c t o r . If d i f fe ren t f r o m m o d e r a t o r .

3 . 8 Modera to r c i r cu i t and components . If o ther than coolant . Includes a l l components of the m o d e r a t o r and ine r t gas c i r cu i t if any, p u r i f i -cat ion, r ecombina t ion s y s t e m s .

3 . 9 R e m a i n d e r . M a j o r i t e m s , such a s l a b o r a t o r y equipment fo r r e a c t o r opera t ion .

3 . 10 Spare p a r t s . M a j o r i t e m s not included above. Would include spec ia l n u c l e a r components not r ead i ly ava i lab le and which b e c a u s e of t he i r s ign i f i cance a r e l i s t ed s e p a r a t e l y .

4. PRIMARY CIRCUIT HEAT EXCHANGERS AND AUXILIARY EQUIPMENT I t ems in th i s ca t egory include a l l equipment f r o m r e a c t o r outlet and inlet p a r t s (excluding i t e m s under 3 . ) to and including the main s t e a m g e n e r a t o r s .

4. 1 P r i m a r y r e a c t o r coolant equipment . Tanks , s t o r a g e , vapour con-t a i n e r s , p r e s s u r i z i n g and re l ie f s y s t e m s , vents and d r a i n s , ine r t gas c i r cu i t ; inc ludes n e c e s s a r y biological shie lding.

4. 2 P r i m a r y coolant supply and t r e a t m e n t p lant . Make-up s y s t e m s , pur i f i ca t ion , r ecombina t ion , t anks , pumps , piping, va lves , h e a t e r s , c o r r o s i o n con t ro l , sampl ing s y s t e m . Includes ini t ia l cooling supply. However , in the c a s e of expens ive coolants such a s heavy w a t e r , it may be d e s i r a b l e to l is t the coolant supply s e p a r a t e l y f o r p u r p o s e s of cost account ing .

4. 3 S team genera t ion p lan t . S team g e n e r a t o r s , ma in va lves and pumps on p r i m a r y and seconda ry s ide , with n e c e s s a r y piping and aux i l i a ry equipment to t u rb ine stop valve .

4. 4 Ins t rumen ta t ion of the p r i m a r y c i r c u i t . Cont ro l of hea t t r a n s f e r and s t e a m genera t ion s y s t e m , cont ro l , piping and tubing.

5 STEAM SUPERHEAT EQUIPMENT (Non-nuclear)

6 FEED-WATER CIRCUIT AND ELECTRICAL GENERATING SYSTEM í

38

Account No.

6 . 1

6 . 2

6 . 3

6 . 4

6 . 5

6. 6

6 .7

7

8.

8. 1

8. 2

8. 3

8. 4

8. 5

Desc r ip t ion of funct ional account

F e e d - w a t e r c i r c u i t . F e e d - w a t e r pumps and h e a t e r s , f l a sh t anks , va lves and piping.

T u r b i n e - g e n e r a t o r and a u x i l i a r i e s . T u r b i n e - g e n e r a t o r and i n t eg ra l a c c e s s o r i e s , such as s top va lves , r e g u l a t o r s , piping, g e n e r a t o r c o o l e r s , e x c i t e r s , f i r e ext inguishing, gland s e a l wa te r s y s t e m , vacuum p r i m i n g s y s t e m .

C o n d e n s e r s and condense r wa te r s y s t e m . Wate r supply faci l i t ies^ wate r t r e a t m e n t , s c r e e n s , pumps , c o n d e n s e r s , a i r r e m o v a l equip-ment , piping.

Intake wa te r plant equipment . Intake wa te r supply, pu r i f i ca t ion , t r e a t m e n t , h e a t e r s , pumps , piping, va lves , t anks , sampl ing .

Ins t rumen ta t ion and con t ro l . F o r i t e m s under 6.

Auxi l ia ry e l e c t r i c a l and mi sce l l aneous power plant equipment . Swi tchgear , swi tchboard , p ro t ec t i ve equipment , c ab l e s , power and con t ro l wir ing , s ta t ion s e r v i c e equipment , ma in and aux i l i a ry power t r a n s f o r m e r s , e m e r g e n c y power , a l l e l e c t r i c a l equipment up to the high vol tage t r a n s m i s s i o n l ine.

Spare p a r t s . Ma jo r i t e m s not included in above.

MISCELLANEOUS EQUIPMENT Misce l l aneous c r a n e s and hoist ing equipment , c o m p r e s s e d a i r and vacuum cleaning s y s t e m s , c e n t r a l lubr ica t ing s y s t e m , l a b o r a t o r y , t e s t and wea the r i n s t r u m e n t s , c leaning equipment , workshop equip-ment , f i r e ext inguishing equipment .

ASSOCIATED COSTS

Engineer ing , des ign, and inspect ion. P r e l i m i n a r y inves t iga t ions , des ign, inspec t ion , consu l tan t s .

Indi rec t cons t ruc t ion c o s t s . G e n e r a l a d m i n i s t r a t i o n , f ie ld s u p e r -vis ion, f ie ld engineer ing , pu rchas ing , p e r s o n n e l , s e c u r i t y , t e m p o -r a r y s t r u c t u r e s , expendable and m i s c e l l a n e o u s cons t ruc t ions , t e m -p o r a r y r o a d s , r a i l w a y s , f ences , o f f i ces , shops , ut i l i ty s e r v i c e s , power , s t e a m , c o m p r e s s e d a i r , cons t ruc t ion equipment and tools , cons t ruc t ion c l ea r i ng accounts , med ica l s e r v i c e .

C o m m i s s i o n i n g . Inspect ion and accep t ance t e s t s and all s t a r t - u p cos t s , such a s s a l a r i e s and o ther expenses , to the t i m e of a c c e p t -ance .

Misce l l aneous f e e s . Includes legal f e e s and r o y a l t i e s of pa ten t s , in-s u r a n c e dur ing cons t ruc t ion . C o n t r a c t o r ' s f e e s o r p r o f i t s to be in-cluded in ins ta l led c o s t s of spec i f ic i t e m s .

I n t e r e s t dur ing cons t ruc t ion . Cost fo r funds r e q u i r e d f o r c o n s t r u c -tion up to fu l l power opera t ion . To be based on a l l cap i ta l a s r e -qu i r ed up to fu l l power opera t ion .

39

Account No. Desc r ip t ion of funct ional account

8 .6 Contingency. Funds r e q u i r e d to guard agains t u n f o r e s e e n develop-m e n t s such as f a i l u r e of plant unde r tes t o r diff icul t foundat ions , labour p r o b l e m s , a cc iden t s .

40

PART 2

SUMMARY OF BREAKDOWN OF STATION CONSTRUCTION COST - EXCLUDING FUEL

Account No.

Identification *

Material or equipment Foreign Domestic

Transport cost Foreign Domestic

Taxes Installation cost

Foreign Domestic Total installed cost Foreign Domestic

1. Land and land rights

2. Site preparation and structures

3. Reactor and auxiliary equipment

4. Primary circuit heat exchangers and auxiliary equipment

5. Steam superheat equipment

6. Secondary circuit and electr. generating system

7.

8.

Miscellaneous equipment

Associated costs

Total

Includes necessary spare parts

A P P E N D I X I I

NUCLEAR F U E L CYCLES

PART 1 - N a t u r a l u r a n i u m feed

As shown in F ig . 1, t h e r e a r e t h r e e ma in s t ages to the fue l cyc le :

(a) The p r e p a r a t i o n and f ab r i ca t ion of the fue l . F o r p r e s e n t r e a c t o r s th is inc ludes the m a n u f a c t u r e of high pur i ty u r a n i u m m e t a l or oxide f r o m o r e c o n c e n t r a t e s o r u r a n i u m s c r a p and the f ab r i ca t ion of the fue l e l e m e n t s .

(b) The m a n a g e m e n t and ut i l iza t ion of the fue l in the r e a c t o r . (c) The p r o c e s s i n g of the spent o r i r r a d i a t e d fue l to s e p a r a t e p lu tonium

f r o m the i r r a d i a t e d u r a n i u m and the f i s s ion p roduc t s , o r the d i sposa l o r s t o r a g e of the i r r a d i a t e d fue l . Recycl ing of p lu tonium i s , however , not cons ide red h e r e , but d i s c u s s e d in P a r t 4 of th is appendix.

N a t u r a l u r a n i u m r e a c t o r s a r e of cons ide rab l e i m p o r t a n c e b e c a u s e of t he i r l e s s e r dependence upon the s o u r c e of fue l supply and the lower cos t s f o r the f a b r i c a t e d fue l , hence , the i n t e r e s t in the ga s - coo l ed g r a p h i t e - m o d e r a t e d r e a c t o r fue l led with "Magnox" clad, n a t u r a l u r a n i u m m e t a l , fo r which t h e r e is e s t ab l i shed opera t ing expe r i ence , and the heavy wa te r r e a c t o r fue l led with z i r c o n i u m clad , n a t u r a l u r a n i u m oxide, f o r which expe r i ence i s being obta ined.

While t h e r e a r e o ther r e a c t o r types which could ope ra t e on th i s fue l cyc le the above a r e the only ones of c u r r e n t c o m m e r c i a l i n t e r e s t . The n a t u r a l u r a n i u m , g a s - c o o l e d , g r a p h i t e - m o d e r a t e d r e a c t o r is r e s t r i c t e d to opera t ing on the m e t a l fo r which the fue l b u r n - u p is me ta l l u rg i ca l l y l imi ted . The heavy wa te r m o d e r a t e d r e a c t o r on the o ther hand can ope ra t e on u r a n i u m oxide, thus , achieving high fue l b u r n - u p s , and hence , ve ry low fue l co s t s but i n c u r r i n g in-c r e a s e d inves tmen t and opera t ing c o s t s .

E x a m p l e s of the cost of power genera t ion us ing th is cycle a r e given in Appendix IV - P a r t 1 and 2.

PART 2 - U r a n i u m - 2 3 5 - e n r i c h e d u r a n i u m feed

F ig . 2 shows a g e n e r a l fue l cycle fo r a r e a c t o r ut i l iz ing n a t u r a l u r a n i u m feed whose u r a n i u m - 2 3 5 content ha s been enr iched , c o m m e r c i a l l y in a d i f fus ion p lant , a l though o ther i so tope s e p a r a t i o n me thods , such as the c e n t r i f u g e - m e t h o d , might have f u t u r e c o m m e r c i a l appl ica t ion . This fue l cyc le c o n s i s t s of four ma in s t ages : '

(a) The e n r i c h m e n t of the u r a n i u m - 2 3 5 content of n a t u r a l u r a n i u m which i s in the f o r m of the hexa f luo r ide p r e p a r e d f r o m o r e c o n c e n t r a t e s , u r a n i u m s c r a p ; o r the u r a n i u m en r i chmen t of u r a n i u m hexa f luo r ide p r e p a r e d f r o m i r r a d i a t e d fue l e l e m e n t s .

(b) The conve r s ion of the enr iched u r a n i u m hexaf luor ide , f o r p r e s e n t power r e a c t o r s , into m e t a l , o r into oxide or c a r b i d e in dense f o r m , and the f a b r i c a t i o n into fue l e l e m e n t s , o r fue l a s s e m b l i e s .

42

Uranium extraction and purification

Ore or scrap

Uranium supplier Oxide or metal ingot

Fuel element fabrication Finished fuel e lement

Storage

R E A C T O R

Cooling

Plutonium for

credit, sale

Fuel re -processing

/ \

Waste disposal or storage for systems where spent fuel is not processed

\7 Fission Products

to waste disposal, storage, or processing

Depleted uranium to waste, storage,

or sale

Fig-1 NATURAL URANIUM FUEL CYCLE

for credit or sale to waste disposal, storage, processing recycled

Fig. 2 URANIUM-235-ENRICHED FUEL CYCLE

44

(c) The m a n a g e m e n t and ut i l iza t ion of the fue l in the r e a c t o r . (d) The p r o c e s s i n g of the spent or i r r a d i a t e d fue l to s e p a r a t e the p lu ton ium

and u r a n i u m f r o m the f i s s ion p r o d u c t s . B e c a u s e of the high r e s i d u a l va lue of the f i s s i l e m a t e r i a l in the spent fue l , it m u s t be r e c o v e r e d f r o m the f i s s i on p r o d u c t s f o r the economic opera t ion of th i s cyc l e .

R e a c t o r s , m o d e r a t e d and cooled, with m a t e r i a l s such a s light w a t e r , o r o rgan ic l iquids , o r u t i l iz ing fue l e l emen t s clad with m a t e r i a l s such a s s t a i n l e s s s t e e l r e q u i r e en r i ched fue l f o r t h e i r opera t ion , The r e a c t o r s of c u r r e n t c o m -m e r c i a l i n t e r e s t ope ra t ing on th i s cycle a r e the p r e s s u r i z e d and boil ing light wa te r r e a c t o r s and the organ ic m o d e r a t e d and cooled r e a c t o r s . The f i r s t two types a r e fue l led with u r a n i u m oxide to ach ieve high b u r n - u p of fue l , and c lad with z i r c o n i u m or s t a i n l e s s s t e e l . In the c a s e of the o rgan ic r e a c t o r s , u r a n i u m m e t a l al loy and oxide clad in a lumin ium a r e being inves t iga ted . The g a s - c o o l e d and heavy wa te r r e a c t o r s , and o ther types under development will a l so be o p e r -a ted on th i s cyc le .

While the u s e of en r i chmen t tends to i n c r e a s e fue l and f ab r i ca t ion c o s t s , it p e r m i t s a wide choice of s t r u c t u r a l , a n d fue l m a t e r i a l s , which can r e s u l t in compensa t ing cos t r e d u c t i o n s . Thusv i n c r e a s e d fue l b u r n - u p can be ach ieved , and m o r e ' compac t c o r e s ope ra t ing at h igher t e m p e r a t u r e s and spec i f i c power can be des igned . This can r e s u l t in ove ra l l r educ t ion of the cap i t a l c h a r g e s . As in the c a s e of the n a t u r a l u r a n i u m fue l cyc le , the en r i ched fue l cyc le mus t be evaluated not by i t s e l f , but in the light of i t s ove ra l l e f fec t upon the cos t of power gene ra t i on .

An example of the cost of power genera t ion us ing th i s cyc le i s given in Appendix IV - P a r t 3.

PART 3 - T h o r i u m feed

The fue l cyc le us ing t h o r i u m a s the feed m a t e r i a l i s shown in F i g . 3. Be -c a u s e n a t u r a l l y - o c c u r r i n g t h o r i u m contains no f i s s ionab le m a t e r i a l , it mus t be used with u r a n i u m - 2 3 3 , p lu tonium, or u r a n i u m - 2 3 5 in r e a c t o r s . The advan tages of th i s type of fue l cyc le a r e the poss ib i l i ty of b r eed ing m o r e f i s s i l e m a t e r i a l than i s consumed , and the poss ib le ' a ch i evemen t of long- l ived fue l . However , the t h o r i u m - u r a n i u m - 2 3 3 cyc le i s at an ea r ly s t age of deve lopment . The fac t that u r a n i u m - 2 3 3 i s not r ead i ly avai lable m e a n s that the cyc le mus t be in i t ia ted us ing u r a n i u m - 2 3 5 o r p lu tonium in o r d e r to obtain suppl ies of u r a n i u m - 2 3 3 .

In c o n t r a s t to the u r a n i u m fue l cycle , the t h o r i u m cyc le i s compl ica ted by u n d e s i r a b l e s ide r e a c t i o n s that occur during i r r a d i a t i o n . One r e s u l t s in the product ion f r o m the t h o r i u m of the 7 0 - y e a r - u r a n i u m - 2 3 2 which has decay p r o -ducts giving g a m m a - e m i t t e r s of g r e a t e r than 2 MeV and subsequent p r o c e s s i n g p r o b l e m s . Another i s the r e l a t ive ly long h a l f - l i f e (27 d) of p r o t a c t i n i u m - 2 3 3 the p r e c u r s o r of u r a n i u m - 2 3 3 , which n e c e s s i t a t e s long ho ld -ups to ach ieve high y ie lds of u r a n i u m - 2 3 3 .

T h o r i u m fue l ha s been t e s t ed in expe r imen ta l r e a c t o r s , and s e v e r a l in-d u s t r i a l r e a c t o r s will be opera t ing with th is cyc le .

While sol id and homogeneous t h o r i u m - f u e l l e d r e a c t o r types a r e at p r e s e n t under inves t iga t ion , only the so l id - fue l l ed r e a c t o r s a r e being opera ted f o r the i n d u s t r i a l p roduct ion of power . This is the light w a t e r - m o d e r a t e d and cooled r e a c t o r fue l led with t h o r i u m oxide, mixed with highly en r i ched u r a n i u m and clad with s t a i n l e s s s t e e l . This fue l , a f t e r d i s cha rge f r o m the r e a c t o r , will be p r o -c e s s e d to s e p a r a t e a m i x t u r e of u r a n i u m - 2 3 5 and o the r u r a n i u m i so topes . It will

45

Start-up and make-up U233 , Pu or U235

\ / l z

Thorium supply

Iz

U23ä , Pu or U235

for recycle, credit or sale

Fuel preparation n

Fission products to waste disposal,

storage, or processing

Thorium Recycle, storage

or discard

Fig. 3 THORIUM FUEL. CYCLE

46

be n e c e s s a r y to u s e th is m i x t u r e with a su i tab le m a k e - u p of f i s s i l e m a t e r i a l to o p e r a t e th i s f u e l cyc le e f fec t ive ly . It is noted that the CNEN organ iza t ion of Italy i s cons ide r ing the cons t ruc t ion of a pilot plant f o r the p r o c e s s i n g and f ab r i ca t ion of i r r a d i a t e d t h o r i u m fue l . Tho r ium m e t a l and c a r b i d e a l so a r e being s tudied fo r fue l l ing sod ium cooled t h e r m a l r e a c t o r s .

The r e fue l l i ng of r e a c t o r s us ing t h o r i u m fue l s while analogous to those us ing n a t u r a l o r u r a n i u m - 2 3 5 - e n r i c h e d f u e l s , i s m o r e complex and will un-doubtedly r e q u i r e r e m o t e fue l f ab r i ca t ion f o r i t s economic u t i l i za t ion .

While a p r i c e f o r u r a n i u m - 2 3 3 has been publ ished, and s e v e r a l r e a c t o r s will o p e r a t e on the t h o r i u m - u r a n i u m - 2 3 5 cycle , t h e r e i s l i t t le opera t ing in fo rma t ion ava i lab le a s ye t on the economic value of r e a c t o r f u e l s containing t h o r i u m . Hence, at p r e s e n t , only t h e o r e t i c a l cos t a n a l y s e s can be c a r r i e d out.

P A R T 4 - P lu ton ium f eeds

Under th i s ca t egory a r e the va r ious pos s ib l e cyc les us ing the r e a c t o r by-produc t plutonium,- e i the r a lone or with u r a n i u m a s a f e r t i l e m a t e r i a l .

All u ran ium- fue l cyc les p roduce plutonium, whether they a r e based on n a t u r a l o r en r i ched u r a n i u m . In s o m e c a s e s , notably in the CANDU type of n a t u r a l heavy wa te r r e a c t o r us ing u r a n i u m dioxide fue l , it i s p lanned to give the fue l e l e m e n t s a lengthy i r r ad i a t i on , without intention of r e c o v e r i n g the p lu tonium. In o ther c a s e s , the u r a n i u m fuel may be r e - p r o c e s s e d a f t e r i r r a d i a -t ion, and the p lu tonium r e c o v e r e d . Since plutonium i s a po ten t ia l fue l fo r f u t u r e r e a c t o r s , c r ed i t f o r the i r r a d i a t e d fue l e l emen t s may then be a l lowed for in the genera t ing cos t . It may be expected that the plutonium will have a va lue r e l a t e d to that of o ther ava i l ab le f i s s i l e m a t e r i a l s . The value a t t r ibu ted to p lutonium is now usua l ly se t a l i t t le below the c u r r e n t value of u r a n i u m - 2 3 5 , on account of i t s c o m p a r a t i v e wor th to the neu t ron economy of a t h e r m a l r e a c t o r and the e x t r a f ab r i ca t ion c o s t s needed to handle a m o r e r ad ioac t ive m a t e r i a l . The p r e -c i s e value of the p lu tonium would of c o u r s e depend on the i r r a d i a t i o n it had r ece ived dur ing p roduc t ion . Higher levels of i r r a d i a t i o n give r i s e to h igher i so topes of p lu tonium, s o m e of which have a d v e r s e e f f e c t s , in d imin ish ing the r eac t iv i ty (at l e a s t in t h e r m a l r e a c t o r s ) , o r in i n c r e a s i n g handling p r o b l e m s .

T h e r e a r e s e v e r a l ways in which the r e c o v e r e d p lu tonium might be used in r e a c t o r s . The lack of ope ra t iona l expe r i ence m a k e s i t , however , p r e m a t u r e to a t t empt to ident i fy in th i s r e p o r t the spec ia l p r o b l e m s of cos t ing methodology which a r e involved. Two m a i n plutonium fue l cyc l e s can be d is t inguished , a p a r t f r o m the u se of p lu tonium with t ho r ium which ha s been ment ioned under P a r t 3 of th i s appendix.

A. The p l u t o n i u m - u r a n i u m t h e r m a l r e a c t o r cyc le

P lu ton ium may be used ins tead of u r a n i u m - 2 3 5 in any of the r e a c t o r s y s -t e m s d e s c r i b e d under n a t u r a l o r enr iched u r a n i u m fue l c y c l e s . The plutonium may be loaded a s a s e p a r a t e fue l in what i s known a s "spik ing" , or may be mixed in with the u r a n i u m . The f o r m e r method f ac i l i t a t e s the d i sposa l of p lu -tonium whenever the n o n - f i s s i l e i so topes have built up to an extent which would cut r eac t iv i ty to an u n d e s i r a b l e level al though it ha s s o m e opera t iona l d i s -advan tages . Detai led cos t ing would depend on which method was u sed . Work on the burning of p lu tonium in th i s way i s in p r o g r e s s in s e v e r a l c o u n t r i e s , notably in the United Sta tes Hanford P lu ton ium Recyc le R e a c t o r .

47

B. P lu ton ium burn ing in f a s t r e a c t o r s

Th i s method o f f e r s the h ighes t convers ion f a c t o r achievable in any r e a c t o r s y s t e m with potent ia l ly v e r y low fue l c o s t s . In c o n t r a s t to the s i tuat ion in t h e r m a l r e a c t o r s , a l l i so topes of the plutonium would be f i s s i l e , and th i s could give a d i s t inc t advantage ove r u r a n i u m - 2 3 5 . Many d i f fe ren t types of p lu tonium fue l , arid of p lu tonium fue l loading, can now be envisàged . The mos t common loading a s s o c i a t e s the p lu tonium with n a t u r a l u r a n i u m in a c e n t r a l c o r e , which i s then s u r r o u n d e d by a blanket of n a t u r a l o r depleted u r a n i u m . Convers ion r a t i o s in e x c e s s of unity a r e expected , so that t h e s e r e a c t o r s a r e of ten known a s " b r e e d e r s " . F a s t r e a c t o r e x p e r i m e n t s a r e a l r e a d y in opera t ion in s e v e r a l c o u n t r i e s and m a j o r p lu tonium loadings a r e p lanned.

Each method of u t i l i za t ion would fo rma l ly def ine a va lue f o r p lu tonium and f o r that m a t t e r a value f o r u r a n i u m - 2 3 5 , and in g e n e r a l each value would be d i f f e r en t . The value would be defined by compar ing the genera t ing cos t s of the p lu ton ium-fue l l ed r e a c t o r with that of the compet ing power s o u r c e . The value would thus be a f fec ted by the cap i ta l cos t , the fue l f ab r i ca t ion cos t , the fue l p e r f o r m a n c e and o ther economic f e a t u r e s of the p lu ton ium-burn ing r e a c t o r . Thus , it i s not yet p o s s i b l e to p red i c t with any a c c u r a c y what the value of p lu tonium would b e . T h e r e i s no expe r i ence of l a r g e - s c a l e p lutonium fue l f ab r i ca t i on , and l i t t le e x p e r i e n c e of the behav iour of such f u e l s in power r e a c t o r s . Substant ia l p r o g r a m m e s of plutonium r e s e a r c h and development have been launched in s e v e r a l c o u n t r i e s , and m o r e in fo rma t ion may t h e r e f o r e be expected within the next few y e a r s .

48

A P P E N D I X I I I

OPERATION, MAINTENANCE AND PERSONNEL

PART 1 - Example of a breakdown of the cos t s fo r opera t ion and ma in tenance and o ther co s t s

Opera t ions M a t e r i a l Labour

Opera t ion supe rv i s ion and engineer ing R e a c t o r and aux i l i a ry equipment Cooling a n d / o r m o d e r a t o r s y s t e m ,

coolant and water (including make-up) Cont ro l and in s t rumen ta t ion Fue l handling S team genera t ion , s t e a m and f eed -

water c i r cu i t , s t e a m expenses Heal th sa fe ty and moni to r ing Waste d i sposa l E l e c t r i c p lant , e l e c t r i c expenses P u r c h a s e d power Misce l l aneous Ren ts

Tota l ope ra t ions

Maintenance

Supervis ion and engineer ing S t r u c t u r e s and s i t e R e a c t o r plant equipment

R e a c t o r and aux i l i a ry equipment Cooling a n d / o r m o d e r a t o r s y s t e m Contro l and in s t rumen ta t ion Fue l s t o r a g e and handling

S team gene ra t ion , s t e a m and f e e d - w a t e r c i r cu i t Waste d i sposa l equipment Maintenance of e l e c t r i c p lant :

P r i m e m o v e r s and g e n e r a t o r s A c c e s s o r y e l e c t r i c equipment

Maintenance m i s c e l l a n e o u s power plant equipment

Tota l ma in t enance Other Cos t s

In su rance ^ 2) Taxes 2) Misce l l aneous

Tota l o ther co s t s

Tota l annual ope ra t ing c o s t s

1) Includes third party liability and property insurance. 2) In some countries property insurance and taxes are included as part of the annual capital charge rate.

49

P A R T 2

NUCLEAR POWER STATION STAFF

A P P E N D I X I V

TYPICAL EXAMPLES OF THE COST OF GENERATING ELECTRICITY IN NUCLEAR STATIONS

Introduct ion

E x a m p l e s of the ca lcula t ion of the cost of e l ec t r i c i t y gene ra t ion f o r a nuc l ea r s ta t ion in the United Kingdom, Canada, the United S ta tes of A m e r i c a a r e p r e s e n t e d in P a r t s 1, 2 and 3 r e s p e c t i v e l y . Some modi f i ca t ions in the p r e -senta t ion and t r e a t m e n t of data was n e c e s s a r y to highlight d i f f e r e n c e s .

It should be emphas i zed that the examples given in this appendix f o r : (1) a n a t u r a l u r a n i u m , ga s - coo l ed r e a c t o r in the United Kingdom, (2) a n a t u r a l u r a n i u m , heavy wa te r r e a c t o r in Canada; and (3) a u r a n i u m - 2 3 5 - e n r i c h e d , p r e s -s u r i z e d wa te r r e a c t o r in the United States of A m e r i c a can in no c a s e be used for an economic c o m p a r i s o n of the t h r e e r e a c t o r types . The cost and t echn ica l data f r o m which unit gene ra t ing cos t s a r e der ived a r e pu re ly i l l u s t r a t i v e and do not n e c e s s a r i l y c o r r e s p o n d to the p r e s e n t condi t ions . Moreove r s o m e i t e m s for which no in fo rmat ion was r ead i ly ava i lab le in the country concerned , a s f o r in-s t ance n u c l e a r l iabi l i ty i n su rance , were omi t ted in s o m e c a s e s and included in o t h e r s . F u r t h e r m o r e , the d i f f e ren t a s sumpt ions fo r cost of money ( ra te of i n t e re s t ) , l i fe of the p lant , and schedule and t e r m s of fue l p u r c h a s e s would make any a t t empt at c o m p a r i n g genera t ing cos t s of the d i f fe ren t s y s t e m s en-t i r e ly m i s l e a d i n g .

A c o m p a r i s o n of r e a c t o r types would r e q u i r e a s t andard iza t ion of a s s u m p -t ions and opera t ing and t echn ica l p a r a m e t e r s which it i s not the p u r p o s e of th is appendix to unde r t ake . It i s r a t h e r designed to show the ma in outl ine of the ca lcula t ion of gene ra t ing c o s t s under the spec i f i c condit ions of the t h r e e coun-t r i e s c o n c e r n e d and to show the appl icat ion of the p r e s e n t wor th app roach to one of the t h r e e c a s e s . The va r i a t ions in the cos t ing f a c t o r s appl ied in the United Kingdom, Canada and the United Sta tes of A m e r i c a fo r the examples ci ted a r e s u m m a r i z e d in Tab le I V - 4 . 1.

P A R T 1 - Calcula t ion f o r the n a t u r a l u r a n i u m cont inuous ly- fue l led r e a c t o r based upon a p r o c e d u r e commonly p r a c t i s e d in the United Kingdom

The p r o c e d u r e which i s d e s c r i b e d below can be used to d e t e r m i n e the cost of e l ec t r i c i t y gene ra t ion r ead i ly f r o m the b a s i c cost in fo rmat ion which i s p r e -sented in (a) $ /kWe f o r the s ta t ion inves tment , (b) $ /kgU for the f a b r i c a t e d fue l , and f o r the i r r a d i a t e d fue l va lue , and (c) $ /kWe p e r y e a r for the opera t ion and ma in tenance and o ther c o s t s . Since the cos t of e l ec t r i c i t y obtained is dependent upon the spec i f i c ope ra t ing and cost p a r a m e t e r s taken, the f o r m u l a e a r e p r e -sented in a f o r m to p e r m i t a r e ady evaluation of the va r i a t i ons in cos t s which would occu r due to changes in t h e s e p a r a m e t e r s .

The t h r e e components of cost a r e given a s I t ems 1, 2 and 3.

I t em 1, the cap i ta l cos t component i s based upon amor t i z ing the ini t ia l s ta t ion cos t , us ing the s inking fund method.

51

I t em 2, the fue l cost component , c o m p r i s e s : (a) A fue l consumpt ion cos t equal to the d i f f e r ence of unit va lues of the

f ab r i ca t ed f r e s h fuel cha rged and the i r r a d i a t e d fuel d i s cha rged divided by the n u m b e r of k i lowa t t -hour s p roduced , during an equ i l ib r ium fue l cycle .

(b) A fuel inventory cost equal to the annual i n t e r e s t on the value of the fue l immobi l i zed in the r e a c t o r , in r e s e r v e and in cooling divided by annual k i lowat t -hour product ion .

(c) A fue l amor t i za t i on cos t equal to the annual s inking fund r e q u i r e m e n t for the deprec ia t ion of the value of the f i r s t c o r e to whatever sa lvage value is a t tached to the las t charge , divided by annual energy p roduc-t ion. (In th i s p a r t i c u l a r example the sa lvage value of the las t c o r e is a s s u m e d to be z e r o . )

I t em 3, on opera t ion and ma in tenance , is s e l f - e x p l a n a t o r y . It will be noted that in making this cost calcula t ion the equivalent annual

n u m b e r of h o u r s of fu l l power opera t ion i s a s s u m e d constant throughout the l i fe of the fac i l i ty .

The bas i c cost and opera t ing p a r a m e t e r s n e c e s s a r y f o r the calcula t ion a r e p r e s e n t e d in Table IV-1. 1 and the cost ca lcula t ions a r e shown in Table IV-1. 2.

TABLE i v - 1 . l

OPERATING AND COSTING PARAMETERS

A. Operating parameters

1. Station capacity (nominal)

Symbols Unit Example A. Operating parameters

1. Station capacity (nominal) P kWe 550 x 103

2. Net station efficiency e 0 .32

3. Reactor fuel loading

4 . Annual fuel throughput

Lo _ P h ( 1 0 ' 3 )

a 24eb

kg U

k g U

596 x 103

167.3 x 103

5. Annual equivalent hours of full power operation h hr 7010

6. Mean irradiation of fuel discharged at equilibrium b mWd/kg U 3

7. Pre-reactor supply of fuel (in storage)

^ mths 3

8. Post-reactor stock of spent fuel (in cooling)

tC mths 3

9. Assumed l i fe of station n y r 20

B. Costing parameters

1. Total capital cost of station C n $ / kWe 340

2. Cost of fresh fabricated fuel at station C f $ / kg U 4 9 . 1

3. Value of fuel discharged from the reactor which has received equilibrium irradiation C i 2 / k g U 13 .4

4 . Mean value of final charge at shutdown C i ¡ 5 / k g U 0

5. Interest rate i p .a . 0 .055

6. Sinking fund rate

7. Operating and maintenance cost

s = i ( l+ i ) n -1

A o

p .a .

¡S/kW p . a .

0.0287

\ 7 8. Other costs ( insurance royalties etc. ) A ' o $ / k W p . a . J

1 ) Net value at station: #14/kg U credit for spent fuel element less #0 .6 /kg U for transport to processor.

52

TABLE IV - 1 . 2

COMPUTATION OF GENERATING COST

Formula Example Result mills/kWh

1. Capital cost C n ( i + s) 103

h (340) (0.0837) 103

7010 4 .06

2. Fuel cost (a) Consumption

C f - ci

24 eb 35.7

(24)(0. 32) (3) 1 .55

(b) Inventory [ c f < v K > + c i K ] i l 0 3

to

[49.1(596 + ̂ - x 167.3)+ 1 3 . 4 ( ^ . x 167. 3)](0. 055) 103

(550) (7010) 0 .45

(c) Amortization CfLgS 108

Ph (49.1)(596)(0. 0287) 103

(550) (7010) 0 .22

Sub-total Items a + b + c 2 .22

3. Operation and maintenance and

(Aq + A'O) 10s

h (7) 103

7010 1 .0 other costs

(7) 103

7010

4. Total generating cost Items 1 + 2 + 3 7 .28

ai oo

PART 2 - I l l u s t r a t i ve ca lcula t ion f o r a n a t u r a l u r a n i u m - f u e l l e d , heavy w a t e r - c o o l e d and m o d e r a t e d r e a c t o r based upon the p r o c e d u r e used

in Canada

Although the Canadian p r o c e d u r e is in p r inc ip l e s i m i l a r to the United King-dom method, t h e r e a r e however s o m e points of d i f f e rence :

(1) With r e g a r d to the cap i ta l cos t component , s ince the l ives of the r e a c t o r of the heavy wa te r and of the r e m a i n d e r of the plant a r e a s s u m e d to be d i f fe ren t , s e p a r a t e annual c h a r g e s a r e computed for each one of t h e m and then added t o g e t h e r . (2) With r e g a r d to fue l , s ince about one-half of the value of a r e a c t o r fue l c h a r g e i s r e c o v e r e d in the in i t ia l months of opera t ion b e f o r e f r e s h fue l is i n t ro -duced only the r e m a i n i n g one-half cha rge of fue l r e m a i n s a s an i n - c o r e fue l inventory . At the end of the plant l i f e t ime the equivalent of approx imate ly one half of a fue l cha rge i s not r e c o v e r e d . In te res t mus t be paid on the i n - c o r e fue l inventory and a sinking fund mus t be es tab l i shed to r e c o v e r the cost of the un-burn t fue l in the c o r e at the end of the plant l i f e t ime . The c u r r e n t Canadian p r a c t i c e i s to cap i t a l i ze one half of the in i t ia l fue l cha rge , and although th is may t u r n out to be somewhat low, the effect of th is on fue l cos t s i s ve ry s m a l l . F u r t h e r m o r e , no a l lowance i s m a d e f o r the va lue of the i r r a d i a t e d fuel which i s at p r e s e n t cons ide red a s was te m a t e r i a l nor fo r the cost of i ts s t o r age or d i sposa l . *

Tab le s IV-2. 1 and 2. 2 give a s u m m a r y of the a s s u m e d c h a r a c t e r i s t i c s of a 203 MW plant and of the s t eps involved in computing i t s gene ra t ing c o s t s .

54

TABLE IV - 2 . 1

Symbols Unit Example

A. Operating parameters

1. Station capacity P kWe 203 x 103

2. Net station efficiency e 0 .29

3. Reactor fuel loading Lo kg U 49 .9 x 103

4. Annual fuel throughput La k g U 21.0 x 103

5. Annual equivalent hours at full power operation h hr 7010

6. Mean irradiation of fuel at equilibrium b mWd/kg U 9 .75

7. Pre-reactor supply of fuel (in storage) ls mths 4 . 5

8. Heavy water inventory kgD 2 0 189 x 103

9. Assumed lives

a) Heavy water n i yr 40

b) Reactor and fuelling equipment n2 yr 15

c) Conventional plant n3 yr 30

B. Costing parameters

1. Cost of reactor and fuelling equipment c r g / k W e 29 .6

2. Cost of heavy water c w g / k W e 60 .2

3. Cost of remainder of plant C c Í / kWe 311

4 . Cost of fresh fabricated fuel at station Cf g / k g U 75

5. Value of irradiated fuel discharged c i ¿ / k g U 0

6. Operating and maintenance cost A o g / k W p .a . 6 .3

7. Heavy water make-up cost A w jg/kW p . a . 0 . 7

8. Insurance and reserve Ar g / k W p .a . 1 .0

9. Interest rate i p . a . 0 .045

10. Sinking fund rates

a) Heavy water s i p . a . 0 .0094

b) Reactor and nuclear equipment S2 p .a . 0 .0481

c) Remainder of plant S3 p .a . 0 .0164

55

TABLE IV - 2 . 2

CALCULATION OF GENERATING COST

1. Capital costs

(a) Heavy water

(b) Reactor component

(c) Remainder of plant

Formula

C w ( i + S l ) 1 0 3

h

C r ( i + s 2 )10 3

h

C c ( i + s 3 )10 3

h

Example

(60.2) (0 .0544) 103

7010

(29,6) (0 .0931)10 3

7010

(311) (0 .0614)10 3

7010

0 .47

0 .39

2 .72

Result mills/kWh

Sub-total Items a + b + c 3 .58

2. Fuel costs

(a) Consumption Cf /24eb (75) / (24) (0 .29) (9 .75) 1 .11

(b) Inventory „ , Lo h , . i 10 C f ( 2

+ 1 2 L a ) Ph

3

75 [ 4 9 ' 9 , 4 , 5 <"\ m l ( 0 ' 0 4 5 ) ( 1 ° 3 )

2 12 1 (203) (7010) 0 .08

(c) Amortization

Sub -total

¿CfL 0 s 3 1 0 3 / P h

Items a + b + c

1 (75) (49.9) (0.0164) (103) 2 (203) (7010)

0 .02

1 .21

3. Operation and maintenance

and other costs

(a) Operation and maintenance

(b) Heavy water make-up

(c) Insurance and contingency reserve

Sub -total

A0 103

h Aw 103

h Ar 103

h

Items a + b + c

(6 .3) 103

7010 (0 .7) 103

7010 (1 .0) 103

7010

0.90

0.10

0 .14

1 .14

4. Total generating cost Items 1 + 2 + 3 5 .93

P A R T 3 - Calcula t ion f o r an enr iched u r a n i u m r e a c t o r based upon a p r o c e d u r e commonly p r a c t i s e d in the United S ta tes of A m e r i c a

The cost ca lcu la t ions which follow a r e pa t t e rned on the p r o c e d u r e given in r ecen t United S ta tes nuc l ea r power cos t s t ud i e s . However , b e c a u s e t h e s e s tud ies a r e ba sed upon the spec i f i c method of cost account ing used in the United States of A m e r i c a and upon condi t ions governing the supply, f ab r i ca t i on , and r e - p r o -ces s ing of fue l , the p r e s e n t a t i o n was modif ied to p e r m i t a m o r e r eady e x t r a -polat ion of the cost of e l ec t r i c i ty genera t ion by an enr iched r e a c t o r to condit ions outs ide the United Sta tes of A m e r i c a .

As has been d e s c r i b e d in the text , at the p r e s e n t t i m e , the o p e r a t o r of a r e a c t o r fac i l i ty which i s fue l led with enr iched u r a n i u m , mus t be concerned with m o r e than jus t the p u r c h a s e of f a b r i c a t e d fue l which is fed into the r e a c t o r and the r ece ip t of c r e d i t s f o r the fue l d i s c h a r g e f r o m the r e a c t o r . To s impl i fy the gene ra t ing cost ca lcula t ion , the p r e sen t a t i on has been made in t h r e e s ec t i ons .

The f i r s t dea l s with the g e n e r a l p r o b l e m of the de t e rmina t ion of gene ra t ing cos t s a s s u m i n g that the ma in cost components of the fue l cyc le have a l r eady been ca lcu la ted and a r e de t e rmined f r o m es sen t i a l l y the s a m e type of b a s i c cost in fo rmat ion as f o r the p rev ious examples in th is Appendix. In p a r t i c u l a r , it u s e s a s i ts s t a r t i n g data the to ta l cost of f ab r i ca t ed fue l a s at the r e a c t o r s i te and the to ta l net va lue of the fue l d i scha rged at the t ime of sh ipment (that i s the to ta l value of the deple ted u r a n i u m and of the contained p lu tonium minus t r a n s -po r t , p r o c e s s i n g , s e p a r a t i o n and convers ion cha rges ) . The opera t ing and cos t ing p a r a m e t e r s a r e given in Table I V - 3 . 1 and the cost ca lcula t ion in Table IV-3. 2.

The second and th i rd dea l with the ca lcula t ion of the component co s t s in-c u r r e d dur ing f ab r i ca t ion and a r e shown in Tab les IV-3 . 3 and 3 . 4 . The com-ponent co s t s i n c u r r e d during the r e - p r o c e s s i n g of i r r a d i a t e d fue l a r e shown in Tab les IV-3. 5 and 3 . 6 .

The t h r e e components of cos t a s given in Table IV-3. 2 a r e (1) the cap i ta l c h a r g e s , (2) the fue l c h a r g e s , (3) the opera t ion and ma in tenance c h a r g e and o ther c h a r g e s .

I tem 1. The cap i ta l c h a r g e c o n s i s t s of two p a r t s (a) the cha rge fo r the cost of money and deprec ia t ion of the cap i ta l i nves tmen t s i m i l a r to the o ther examples , and (b) a cha rge f o r t a x e s ( income and p rope r ty ) and p r o p e r t y i n s u r a n c e . The i n s u r a n c e fo r th i rd pa r ty nuc l ea r l iabi l i ty i s not included but given under I tem 3.

I tem 2. The fue l c h a r g e c o n s i s t s of (a) a fue l consumption c h a r g e based upon the value of the f ab r i ca t ed fue l r e c e i v e d at the r e a c t o r s i t e and the to ta l net value of spent fue l sh ipped, and (b) a fuel inventory cha rge based on the l e a s e of u r a n i u m at annual r a t e of 4 3/4% of i ts value, which would not n e c e s s a r i l y be appl icable outs ide the United Sta tes of A m e r i c a . It will be noted that t hese two i t e m s a r e somewhat s i m i l a r to the co r re spond ing c h a r g e s f o r the n a t u r a l u r a n i u m r e a c t o r s cons ide red in P a r t s 1 and 2 of th is Appendix, but that they do not provide f o r the c o s t s i n c u r r e d in achieving equ i l ib r ium and for the i m m o -bi l izat ion of the funds r e q u i r e d fo r the f ab r i ca t ion of the fue l . The las t point is covered by a working cap i ta l cha rge to be explained below.

I tem 3. Opera t ion and ma in tenance c h a r g e and o ther c h a r g e s .

Under th is ca t egory f o r the s ake of convenience a r e included such i t ems a s th i rd pa r ty nuc l ea r l iabil i ty i n s u r a n c e , i n t e r i m r e p l a c e m e n t s and working capi ta l , the las t of which ca l l s f o r some spec i a l c o m m e n t s .

57

The t ime lag between the expendi tu res f o r the opera t ion and fuel l ing of the r e a c t o r and the col lect ion of r e v e n u e s f r o m the energy it p rov ides , which any s y s t e m of account ing m u s t al low f o r , i s cove red spec i f ica l ly by a working cap i t a l i t e m in the United Sta tes p r o c e d u r e . It has been empi r i ca l ly de t e rmined that under the a v e r a g e condit ions under which p a y m e n t s a r e made and r e v e n u e s r e c e i v e d by a United Sta tes public ut i l i ty , an amount equal to 60% of the cos t of f ab r i ca t ing a whole c o r e (but excluding the u r a n i u m fuel) p lus 2. 7% of. a l l annual c h a r g e s except t a x e s and i n s u r a n c e would in g e n e r a l be adequate fo r th i s p u r -pose . It should be c l e a r l y unders tood that th i s p rov i s ion i s m a d e on the b a s i s of spec i f i c United Sta tes condit ions and that i t s va lue would v a r y subs tan t ia l ly f r o m country to count ry , depending in p a r t i c u l a r upon the t e r m s under which f a b r i c a t -ed fue l is obtained and power r e v e n u e s a r e co l lec ted .

As in the p rev ious examples of this Appendix, the p lant f a c t o r , u r a n i u m c h a r g e and o ther pos s ib l e c h a r g e s which may v a r y dur ing the l i fe t i m e of the r e a c t o r a r e cons ide red cons tan t . Hence, the fue l ca lcula t ion which ha s been given does not r e f l e c t the d i f f e r e n c e s in cost i n c u r r e d by d i f f e ren t r e a c t o r types in achieving equ i l ib r ium fuel condi t ions .

58

TABLE IV - 3 . 1

OPERATING AND COSTING PARAMETERS

Item Symbols Unit Example

A. Operating parameters

1. Station capacity P kWe 270 x 103

2. Net station efficiency e - 0.27 3. Reactor fuel loading Lo kgU 50 x 103

4. Annual fuel throughput La kgU 24 .4 x 103

5. Initial enrichment Eo %u235 3 .0 6. Final enrichment % %u235 2 .0 7. Plutonium production Pu g /kgU 7 .0 8. Annual equivalent hours of full power operation h hr 7010 9. Mean irradiation of fuel at equilibrium b mWd/kg U 12

10. Pre-reactor supply of fuel (in storage) ts mths 4 n - Post-reactor stock of spent fuel (in cooling) te mths 3 12. Assumed life of station n yr 30

B. Costing parameters

1. Total capital cost of station c n g / k W e 275

2. Cost of fresh uranium fuel U f 0/kgU 281 3> 3. Cost of fabrication Uf $/kgU 107 3) 4 . Cost of fresh fabricated fuel at station C f = Uf + u'f $ / kg U 388 3> 5. Value of uranium discharged at equilibrium (corrected

U; )5 /kgU 155 4)

for losses during irradiation, processing and conversion) 1 )5 /kgU

6. Net total value of processed fuel discharged at equilibrium (value of uranium discharged and plutonium obtained

Ci g / k e U 172 4) net of all charges and discounted to the time of ship- 1 " ' O 172 4)

ment to processor) 7. Interest rate on uranium fuel if p .a . 0 .0475 8. Cost of money for other than fuel (interest e t c . ) i p . a . 0 .06

9. Sinking fund rate i

s ( l+ i ) n -1 p . a . 0 .013

10. Annuity rate a = i + s p .a . 0 .073 11. Taxes and nuclear property insurance charge rate 2) X p . a . 0.067 12. Total capital charge rate a + x p . a . 0 .14 5) 13. Nuclear Liability insurance rate A1 $ / kW p . a . 3 14. Working capital charge rate Awe g /kW p . a . 2 s) 15. Operation and maintenance cost (excluding fuel) A 0

jS/kW p . a . 5 16. Interim replacements Ar = 0 .3%Cn $ / kW p . a . 0 . 8 7)

kg U expressed as kg U charged to reactor. 2} Taxes and insurance. Excludes third party nuclear liability. 3) See Table I V - 3 . 4 . 0 See Table I V - 3 . 6 . 5) The total annual capital charge rate given is merely illustrative; it varies from 6 to 15%p.a. , depending

upon the financing and taxes. 6) Computed figure; the annual charge is estimated to consist of 60% of the cost of fabrication of the initial

core plus 2 .7% of the total annual operating expenses (excluding depreciation and taxes). 7) This charge is usually included as part of the capital charge rate (0.3% p . a . ) .

59

OS O TABLE IV - 3 . 2

CALCULATION OF GENERATION COST

Formula and Example Result

mil ls /kWh

1. Capital costs C n (a + x) 103

h (275) (0.14) 103

7010 5.50

2. Fuel costs

(a) Consumption c f - q (388 -172)

2 .78 (a) Consumption 24 eb (24)(0.27)(12)

2 .78

(b) Inventory [ { ( U f + U i ) L0 + (U f J + Uj — ) L a ] i f 103

(b) Inventory

[¿(281 + 155) 50 x 103

Ph

+ (281 x-jj + 155 x l l ) 2 4 . 4 x 1 0 3 ] (0 .0475) (10 3 ) 0 .35

(270 x l O 3 ) 7010 0 .35

Sub-total Items a + b 3 .13

3. Operation and maintenance and other costs

Ao103

(a) Operation and maintenance Ao103

(5) 103

0.71 (a) Operation and maintenance h 7010

0.71

(b) Liability insurance, interim replacement working capital

( A 1 + A r + A w c ) 1 0 3

h

(3 + 0 . 8 + 2) 103

7010 0 .83

Sub-total Items a + b 1 .54

4. Total generating cost Items 1 + 2 + 3 + 4 10.17

TABLE IV - 3 . 3

FUEL PREPARATION AND FABRICATION CHARGES

A. Operating and cost parameters Symbol Unit Value Charge 2 / k g U

1. Transit from UF6 supplier to fuel conversion site to d 30 Ro 1.50

2. Fuel preparation it 30 )

3. Transit to fuel element fabricator ^ t i 0 I Bpf 90 2)

4 . Fuel fabrication tf 30 )

5. Transit to scrap recovery from fuel conversion ts 0 - -

6. Transit to scrap recovery from fabricator t»" 30 1.50

7. Scrap recovery 1 S 60 Rs 10

8. Transit from scrap recovery to UF6 supplier * m c s ti 30 R T 1.50

9. Transit from fabricator to reactor operator l2 tt 30 Rr 1.50

10. Cost of uranium feed as UF. O - - Uf 281

11. Interest on uranium i f °¡0 p. a. 4 .75 - -

12. Interest charge other than on uranium

13. Amount uranium procured

14. Losses during preparation and fabrication

i 1

F " ( 1 - l p f - s )

Ipf

°]o p . a . kgU/kg charged %of F

6

1 .11

2

15. Scrap material produced during preparation and fabrication %of F 8

16. Losses during scrap recovery 1 s %of s 5

^ Fuel preparation, fuel element fabrication, and scrap recovery from conversion assumed to be done at same site.

Includes fuel preparation and fabrication.

TABLE IV - 3 . 4

CALCULATION OF FUEL PREPARATION AND FABRICATION COST

Formula and Example $ / kg U Charged

B. Cost calculations

1. Uranium inventory

Interest charges on uranium value during transit from UF6 supplier, during fuel preparation and fabrication, and during scrap recovery

[ t 0 + t p f + ( t s - + t | + t p s ] F U f i f / 3 6 5

r , (1 .11) (281) (0.0475) [30 + 60 + (30 + 60 + 30) (0 .08)] v 4 . 0 4

2. Shipping charges

Charges on fuel shipments from UF6 supplier, and to and from scrap recovery plant

[ R 0 + R - s + R » s ( l - l s ) ] F

[l. 5 0 + ( l . 50){0.08) +1 . 50 (0 .08) (0 .95) ] 1 .11 1 .92

3. Uranium losses

Losses incurred during fuel preparation and fabrication, and scrap recovery

[ i p f + Is"] FUf

[ 0 . 0 2 + (0.05) (0 .08 ) ] (1.11) (281) 7 .49

4. Scrap recovery RssF

(10) (0.08) (1.11) 0 .89

5. Preparation and fabrication

(Breakdown of charges for fuel preparation fuel assembly, materials etc. not indicated) Rpf

90

6. Total cost at fabrication site f (Items 1 through 5) 104.34

TABLE IV - 3 . 4 (cont'd)

Formula and Example $ / kg U Charged

7. Total cost of fabricated fuel as received at reactor site

(a) Fabrication cost at fabrication site f ( Item 6 ) 104.34

(b) Uranium inventory in transit to reactor site U f t 2 i f / 3 6 5

(281) (30) (0.0475) / 365 1.10

(c) Fabrication inventory in transit to reactor site ft2i / 3 6 5

(104) (30) (0 .06) / 3 6 5 0 .51

(d) Shipment of fabricated fuel to site Rr 1.50

(e) Total fabrication cost at reactor site U f = a + b + c + d 107

( f ) Uranium fuel value Uf 281

(g) Total fabricated fuel cost C f = U f + Uf 388 ^

!) As purchased from supplier; lease charge during fabrication included in Item 7 a .

TABLE IV - 3 . 5

FUEL RE-PROCESSING CHARGES AND/OR CREDITS

A. Operating and cost parameters Symbol Unit Value Charge ? / k g U

1. Transit from reactor operator to processor t3 d 30 R t 16

2. Processing batch Lr kgU 0 . 2 5 L o = 1 2 . 5 x l 0 3 R i 17 1)

3. Hold-up and clean-up cost factor g - 1 .65 2)

4 . Processing to nitrates tr d 40 R r = R i g (17) (1.65) = 28

5. Plutonium production Pu g /kgU 7

6. Value of plutonium as metal v m * / g 12 v m = v m P u 7 x 12 = 84

7. Conversion of UNH to UF6 tr d 20 R r 5 .6

8. Conversion of Pu N to metal tr" d - 3 ) R r 7 x 1 . 5 0 = 10.50

9. Transport from processor to UF6 supplier d o 4 )

10. Loss of uranium during extraction ! U 1o 1

11. Loss of uranium during conversion 1Û °lo 0 . 3

12. Loss of plutonium during extraction *pu % 1

13. Loss of plutonium during conversion Vu % 1

14. Uranium discharged at equilibrium E f < y o U 235 2 v u 160

15. Interest on uranium value discharged i f °/o p . a . 4 . 7 5

16. Interest on other than fuel i % p . a . 6

^ Charge based upon $17000 daily rate in plant capable of processing 1000 kg/d; excludes charges for handling and clean-up.

8 x 103

,2) Equal to 1 + - — : where the processing batch is greater than 8 x 10 3 /kg U and lj is the shrinkage in uranium weight due to irradiation estimated ( 1 - li ) Lr

as 1.06 b + Pu = (1.06) (12) + 7 = 20 g / k g U or 0 . 0 2 .

3) Processing time included in tj. , item 7.

4) Uranium processor and UF6 supplier considered to be at same site.

TABLE I V - 3 . 6

FUEL RE-PROCESSING CHARGES AND/OR CREDITS

B. Cost calculations Formula and Example $ / kg U charged to reactor

1. Net value of fissile fuel

(a) Net value of uranium

Value discharged corrected for losses during irradiation, processing and conversion

ui = ( i - i u - r u ) ( i - i i ) v u

(0. 987) (0. 98) (160)

154. 8

<b) Net value of plutonium

Value discharged corrected for loss in processing and conversion

( l - l p - ] ¿ ) ( l - l i ) V m

(0.98) (0.98) (84)

80.7

Sub-total Items a + b 235.5

2. Processing charges

(a) Uranium inventory

Interest charges on uranium value during extraction, conversion and transit to UF6 supplier for credit

i f ( t r + t ' r ) ( l - 1 ^ , ^ 3 6 5

(0. 0457)(40 + 20) (0. 98) (160) /365 1 .2

(b) Processing and conversion

Charges for extraction from fission products plus con-version of UNH to UF6 and PuN to metal

[R r + R- ( 1 - y + Rp ( l - ]pU ) ] (1-Ü)

[28. 0+ 5. 6(0.99) + 10. 5(0. 99)] (0. 98) 43. 1

Sub-total Items a + b 44. 3

3. Net value of processed fissile fuel V ( Items 1 minus 2) P

191. 2

Value of spent fuel at time of shipment from reactor site (credit available to reactor operator)

(a) Value of processed fuel discounted to time of shipment by reactor operator

(b) Uranium inventory during transit from reactor site to processor

(c) Shipping charge from reactor site to processor

(d) Net value to processor

V - 3 . 6 (cont'd)

Formula and Example £ / k g U charged to reactor

V P 1+ ( t s + t r + t'r+ t4) i / 365

191.2 191.2 1 + ( 3 0 + 40+ 20+ 0 ) ( 0 . 0 6 ) / 3 6 5 1 .015

i f V 1 " 1 ! ) V u

188.4

365

(0.0475) (30) (0. 98) (160) 0. 6 365

Rt(l- l i )

(16) (0.98) 15.7

Cj = a - (b + c) 172

PART 4

TABLE I V - 4 . 1

SUMMARY OF DIFFERENCES IN COSTING FACTORS USED IN DIFFERENT COUNTRIES FOR THE EVALUATION OF ELECTRIC GENERATING COSTS

1. CAPITAL COST FORMULA REMARKS

United Kingdom

C n a 103

h

Annuity factor, a, for depreciation and interest computed on basis of an average plant life of 20 years. C n capital investment in # / kWe, and h is the equivalent full power hours of operation per year.

Canada ( C w 3 l + C r a 2 + C c a 3 ) 1 0 3

h

Annuity factors a l t a2, and a3 computed on basis of 40, 15 and 30 years for: investment in heavy water, C w ; reactor portion, C r ; and conventional portion of plant, C c , respec-tively.

United States of America C n ( a + x) 103

h

Annuity factor; a + x, computed on basis 30 years average plant life, and where x designates the annual charge rate for taxes and property insurance.

2. FUEL COST

United Kingdom C f - C i CCf ( Lo+ IT La) + q J f L a] i l o 3 + c f L o s 1 q 3

24 eb 4 Ph

Fuel consumption charge based upon the (1) difference in value between the fabricated fuel, C f, charged and C ^ discharged for the reactor plus (2) fuel inventory charge for fuel in reactor, in storage, and cooling, plus (3) a charge for the initial fuel loading amortized over the plant life.

h equivalent hours at full power operation p. a. P power (kWe) e thermal efficiency (°¡o)

b burn-up (MWd/kgU L 0 reactor loading (kg U) L a annual throughput (kg U) t s fuel in storage (mths)

t c fuel in cooling (mths)

TABLE I V - 4 . 1 (cont'd)

2. FUEL COST FORMULA REMARKS

Canada C f [ ¿ C f ( L 0 + J i La) i +

i C f L o s ] l 0 3

" Same as for United Kingdom procedure, but where the value of the discharged fuel C¡ is taken as zero, and only i of the initial fuel charge is amortized over the life of 30 years and subject to interest. 24 eb + Ph

" Same as for United Kingdom procedure, but where the value of the discharged fuel C¡ is taken as zero, and only i of the initial fuel charge is amortized over the life of 30 years and subject to interest.

United States of America C f - C i [ i t U f + U O L o + UFN-La + U I J La] if 103

Same as for the United Kingdom procedure but where the inventory charge is applied only on the average value of the uranium in the reactor, in storage and in cooling; the uranium is leased and not purchased and the cost of carry-ing fabrication inventory is considered as part of a working capital, as shown under Item 3 below.

24 eb Ph

Same as for the United Kingdom procedure but where the inventory charge is applied only on the average value of the uranium in the reactor, in storage and in cooling; the uranium is leased and not purchased and the cost of carry-ing fabrication inventory is considered as part of a working capital, as shown under Item 3 below.

3. OPERATION AND MAINTENANCE AND OTHER COSTS

United Kingdom (Afi+ An) 103

h

AQ is the annual charge for operation and maintenance per kilowatt of output sent out, and Aq is the unit annual charge for liability insurance, royalties, etc.

Canada (A 0+ Ar + A w ) 1 0 3

h

No charge applied for liability insurance. A unit annual charge A w is taken for heavy water losses and Ar for in-surance and reserve.

United States of America ( A 0 + A 1 + A r + A w c ) 1 0 3

Unit annual charges for liability insurance, A¡; interim replacement, Ar; and working capital, A w c . The latter item is to provide funds for current operations, for fuel

United States of America h fabrication inventory, and other expenditures prior to re-

ceipt of revenues. Property insurance has been accounted for in the annuity factor under capital costs.

A P P E N D I X V

PRESENT WORTH METHOD

PART 1 - G e n e r a l outl ine of the p r e s e n t wor th method

The p r o b l e m of a l loca t ing to a unit of f ina l output the i r r e g u l a r s e r i e s of out lays and c r e d i t s extending over the l i fe of a p roduc ing fac i l i ty is of c o u r s e not new or spec i f i c to n u c l e a r p o w e r . In many o the r eng ineer ing f i e lds it has been s u c c e s s f u l l y tackled by r e s o r t i n g to the s o - c a l l e d p r e s e n t wor th method . I ts main p u r p o s e is to in t roduce the t ime e lement in the cos t p i c t u r e in a s y s -t ema t i c fash ion and i t s so le a s sumpt ion i s that an amount of money, a, today will be worth a (1 + i ) n in n y e a r s f r o m the date of r e f e r e n c e , w h e r e i i s the r a t e of i n t e r e s t (or the cos t of money) expected to p r e v a i l dur ing th i s p e r i o d . On that b a s i s , any i r r e g u l a r s equence of payment , P p P 2 . . . . P n , (or c r ed i t s ) m a d e (or r ece ived) in f u t u r e y e a r s 1, 2, 3, . . . n, has a p r e s e n t worth value:

P w

P 1 P 2 P n (1 + i) + (1 + i ) 2 + (1 + i ) n

3 = -n

which can be s u m m e d up a s P w P

3 (1 + i)3

3 = 1

while any s e r i e s of p a y m e n t s m a d e dur ing m y e a r s b e f o r e the date of r e f e r e n c e will have a p r e s e n t worth va lue P w such that 1)

3 = m

P w = P j d + i) + P 2 ( l + l ) 2 + p m ( l + i ) m = P . ( l + i)3

3 = 1

F u r t h e r m o r e , s i m p l e a l g e b r a will show that th i s p r e s e n t wor th value i s a l s o equivalent to a r e g u l a r annual s e r i e s of ident ica l p a y m e n t s s p r e a d over n y e a r s

each payment being equal to p = P w 1 - (1 + i) •n

1) If positive exponents are used for years preceeding the date of reference and negative exponents for years follow-

j = n

ing it, the general formula Pw = ^ Pj (1 + i)J may be used.

j = m

69

Thus the p r e s e n t worth method p e r m i t s t r a n s f o r m i n g an i r r e g u l a r se t of v a r i -able amoun t s of money s e p a r a t e d by vary ing t i m e i n t e rva l s e i the r into an equiva-lent to ta l a t one point of t i m e or into an equivalent se t of equal annual amounts s p r e a d un i fo rmly over the pe r iod c o n s i d e r e d .

In the m o s t g e n e r a l c a s e of a r e a c t o r expected to ope ra t e with v a r i a b l e p a r a m e t e r s ove r i t s l i fe th i s de t e rmina t ion involves t h r e e s u c c e s s i v e s t eps :

1. A point of t i m e r e f e r e n c e would be s e l e c t e d . It could for ins tance be the date when the r e a c t o r i s f i r s t ope ra ted at fu l l power .

2. The p r e s e n t worth of a l l expend i tu res and c r e d i t s should be computed at th i s point .

3. The p r e s e n t wor th of a l l the uni ts of energy expected to be produced by the r e a c t o r if they w e r e cha rged at the u n i f o r m cos t to be de t e rmined is ca lcu la ted at the s a m e point . In th is p r e s e n t worth e x p r e s s i o n the gene ra t ing cos t a p p e a r s t h e r e f o r e a s an unknown.

4. The p r e s e n t worth of a l l expend i tu res and c r e d i t s connected with the opera t ion of the r e a c t o r i s then equated to the p r e s e n t wor th of a l l the energy it i s expected to p roduce and the gene ra t ing cos t of the unit of energy is obtained f r o m th is equat ion.

An example will s e r v e to i l l u s t r a t e the p r o b l e m .

PART 2 - Example of appl ica t ion of the p r e s e n t worth method to a United Kingdom power r e a c t o r

To i l l u s t r a t e the p r e s e n t wor th method , a n a t u r a l u r a n i u m g a s - c o o l e d r e a c t o r with t echn ica l and cos t c h a r a c t e r i s t i c s iden t ica l to t hose l i s ted in the United Kingdom example of P a r t 1 of Appendix IV was a s s u m e d to ope ra t e under the following condi t ions:

1. The r e f e r e n c e date at which a l l p r e s e n t wor th equivalents a r e ca lcu la ted i s the date at which the s ta t ion begins to o p e r a t e at fu l l power .

2. P l a n t f a c t o r 90% dur ing the f i r s t ten y e a r s , 70% dur ing the l a s t ten y e a r s .

3. P a y m e n t f o r the s ta t ion is a s s u m e d to be m a d e two y e a r s ahead of the date of fu l l power opera t ion which i s the mid-po in t of an a s s u m e d des ign and cons t ruc t ion t i m e of four y e a r s .

4. P a y m e n t f o r the f i r s t c o r e and f r e s h fue l r e s e r v e i s made one y e a r p r i o r to fu l l power ope ra t ion .

5. P a y m e n t s f o r fue l annually consumed a r e made at the beginning of each y e a r s t a r t i n g f r o m the date of f i r s t power opera t ion and c r e d i t s f o r the s a m e amount of i r r a d i a t e d fue l a r e r e c e i v e d a y e a r a f t e r d i s c h a r g e .

6. The fue l in the l a s t c o r e ha s no sa lvage va lue . 7. The c h a r g e s f o r the power p roduced annually a r e a s s u m e d to be r e -

ce ived at the end of each y e a r .

D For this simplified illustration all computations have been carried out on an annual basis. It goes without saying that a sub-division in smaller" units ••of time such as quarters or months maybe desirable in which the interest rate would of course be adjusted accordingly.

70

TABLE V - 2 . 1

PRESENT WORTH COMPUTATION

Nature of operation Amounts (106 gf)

Time or times of occurence (yrs)

Present worth coefficients

Total present worth value (10 s $)

I. PAYMENTS AND CREDITS (1) (2) (3) (4) = (1) x (3)

A. Payment for station 168 -2 1 .113 187.0

B. Payment for first core 31 .5 - 1 1. 055 33 .2

C. Payment for fuel consumed

a. First ten years 9 .25 p.a. 0 to 9 7 .95 73 .5 ('• 2 •y • J

b. Next ten years 7 .18 p.a . 10 to 19 4 .65 33.4 J

D. Credits for irradiated fuel

a. First ten years - 2 . 5 2 p.a. 1 to 10 7 .55 - 1 9 . 0 b. Next ten years - 1 . 9 6 p.a . 11 to 20 4 . 4 1 -8 .6

E. Credit for reserve -2. 32 20 0 .34 -0 .8

F. Payments for operation and maintenance 3. 85 p. a. 0 to 19 12.6 4 8 . 5

Total I Items A through F 347.2

II. VALUE OF THE ENERGY PRODUCED2)

A. First ten years 4 . 3 4 G p. a. 1 to 10 7. 55 32.8 G B. Next ten years 3 .37 G p. a. 11 to 20 4 . 4 1 14.9 G

Total II Items A + B 47 .7 G

III. GENERATING COST (mills/kWh) Total I = Total II, or G = 347.2

7 .27 Total II, or G = 47 .7 7 .27

0 Time of full power operation is taken 2) Value given in dollars is equal to the

the annual charges are assumed to be

as time zero.

cost of energy charged, G, in mills/kWh levied at the end of each year.

divided by 103 mil ls / % times number of kilowatt-hours produced per annum;

The computa t ions may then be s u m m a r i z e d in Table V-2 . 1. Some s i m p l i f i -ca t ions have been made in the p r e s e n t a t i o n . In p a r t i c u l a r u s e was made of the f o r m u l a

1 1 , 1 ' = 1 - (1 + i ) - n ., 1 + i (1 + i)'¿ " ' ' (1 + i ) n i

which y ie lds immed ia t e ly the p r e s e n t wor th value of a s e r i e s of n equal annual p a y m e n t s .

It will be seen that the r e s u l t of 7. 27 m i l l s / k W h obtained for the gene ra t ing cos t i s p r a c t i c a l l y iden t ica l with the 7. 28 m i l l s / k W h obtained by the method given in Table IV-1. 2 fo r the s a m e r e a c t o r opera t ing at 80% load f ac to r dur ing i t s l i f e . The r e l a t ive ly s i m p l e and continuous fue l cyc le of the r e a c t o r accounts f o r the c l o s e n e s s of the approx ima t ion .

,It should be noted that the t i m e s of the va r ious paymen t s and r e c e i p t s were chosen to s imp l i fy the p r e s e n t a t i o n . The genera t ing cost f i gu re i s of c o u r s e s ens i t i ve to va r i a t i ons of t he se t i m e s and each c a s e should be dealt with in the light of i t s own spec i f i c condi t ions . Thus if ins tead of a s s u m i n g paymen t s for f u e l consumed and expend i tu res f o r opera t ion and ma in tenance to be made at the beginning of each y e a r while power r e v e n u e s a r e co l lec ted only a y e a r l a t e r , it was a s s u m e d that both opera t ions would on an ave rage occur at the y e a r ' s mid-po in t , the gene ra t ing cost would be reduced by approx imate ly 0. 3 m i l l s .

72