九州大学学術情報リポジトリKyushu University Institutional Repository

An Analytical Method of Constructing Best-mixedPower Generation Systems Reflecting PublicPreference

Shikasho, NarumiDepartment of Applied Quantum Physics and Nuclear Engineering : Graduate Student

Akasaka, RyoInstitute of Environmental Systems : Contract Researcher

Matsumoto, TatsuyaInstitute of Environmental Systems : Reaserch Associate

Morita, KojiInstitute of Environmental Systems : Associate Professor

他

http://hdl.handle.net/2324/1118

出版情報：九州大学工学紀要. 62 (4), pp.149-164, 2002-12-20. 九州大学大学院工学研究院バージョン：権利関係：

Memoirsof the Faculty of Engineering, Kyush u University, Vol. 62, No. 4, December 2002

AnAnalytical Methodof Constructing Best-mixed Power Reflecting Public Preference

Generation Systems

by

Narumi SHIKASHO Koji

*, Ryo AKAsAKA ** , Tatsuya MATsuMoToMoRITA t and Kenji FuKuDA tt

***'

(Received September 24, 2002)

Abstract

An investigation of energy consumer's preference for the power

generation was performed. It was found that most consumers gavetheir preference te a value `social acceptability' and to `environmental

effect' in constructing the energy system. An analytical method to eval-

uate the best-mixed power generation system to meet the consumer'spreference was developed. It was applied to evaluate each best-mixedsyst' em meeting with a preference of each consumer. The resultingbest-mixed system was largely composed ofthe natural gas fired sys-

tem and the hydraulic power generation system. And the other powerswith disadvantages in terms of the `social acceptability' and/or `envi-

ronmental effect' were hardly introduced. The duality theorem allowed

us to evaluate the marginal cost of consumers' preference. The `social

acceptability' yielded the highest marginal cost, and the `environmental

effect' was the next.

Keywords: Best-mix, Analytical Hierarchy Process, Linear program-

ming method, Duality theorem, Marginal cost

1. Introduction

There are many controversial issues in terms of energy problem. Energy suppliers arenow forced to take into account the environmental effects and the safety at the cost ofless commercial profit. Although they intend to build more nuclear plants, sometimes itis difficult facing to the opposing people who fear the risk of severe accident or the waste

disposal from the nuclear plants. On the other hand, energy consumers expect alternative

natural energy resources such as the solar energy as the main energy resources in the nearfuture. However, at this moment, it is presumed that the natural energy resources are rather

expensive and their technologies are yet immature. Unfortunately, three participants of the

'Graduate Student, Department of Applied Quantum Physics an **Contract Researcher, Institute of Environmental Systems*'" Reaserch Associate, Institute of Environmental Systems tAssociate Professor, Institute of Environmental Systems ttProfessor, Institute of Environmental Systems

d Nuclear Engineering

150 N.SmKAsHo,R.AKAsAKA,T.MATsuMoTo,K.MoRITAandK.FuKuDA

energy society: suppliers, consumers and the government hardly eva}uate uncountable values

ofenergy resources, or the energy externalities because ofcomplexity and variety. Under this

,gituat•ion, arguments on the future energy system among the participants are often confused.

Recently, especially after 1980, in the field of nuclear eng-ineering many subjects about

t•he best-mixed power generation system, or simply the `best-mix' have been discussed rec-ognizing the extemality of nuclear power. In Japan, Mankin et al.i) estimated a gain on

investment for smal}- or middle-scale nuclear reactor in the future, and predicted that itwould be cornpatible with that for large-scale reactor. Ol}kubo et al.2) produced a new

model to simulate the future energy best-mix, and using their model they showed an ad-visability of the nuclear power for the Japanese policy. The authors also evaluatJed theroles of nuclear energy in terms of energy security of this country 3). In other countries,

Afanasiev4) revealed an economical advantage of Russian nuclear power over other types of

powe}' generation using an idea of marginal cost.

After the agreement of the Kyoto Protocol, marginal cost estimations for the reduction

of greenhouse gas emissions have been focused in the field of environmental engineering.Kainuma"") reviewed several economic mode}s to achieve the Kyoto Protecol Standard, and

pointed out that Japan had higher marginal cost to reduce the C02 emissions than othercountries. Yoshida et al.6) proposed new energy model minimizing the power generation cost,

and predict,ed that the marginal cost, to reduce the C02 emissions would become higherdramatically when the growth of nuclear power generation approached to its saturation.Jackson7) compared some technologies for the reduction of greenhouse gas emissions based

on their marginal costs.

HovLTever, few discussions have fbcused on constructing energy system refiecting con-sumers' preference. Thus we have developed a method to know the public preference forvalues by questionnaire8), and to establish the best-mix which refiects the preference9'iO). In

t•his st•udy, applying this method, a survey on energy consumers' preference was conducted,

and the best-mix vv'hich reflects the preference was evaluated. In the analysis, the 1inear

programming algorithm was app}ied; with the duality theorem, marginal costs for various

extemal values were also evaluated.

2. AnalyticalMethod

2.1 Investigationofenergyconsumer'spreference

A questionnaire shown in Fig. 1 examines consumers' preference for the following fivevalues: economical e{IicieRcy, convenience, energy security, environmental effect and social

acceptabi}ity, which are classified by the factor analysis as the essential values regarding

the energy related problems. Except for the ecoRomical efliciency, all of the remaining four

values might be regarded as the ext,ernal values. The questionnaire is composed of tenquestions based on t,he AHP (Analytical Hierarchy Process), a multivalues decision supportmethod designed to make overall ranking table of preference for values; e.g., "Which value

do you regard more important in coristructing the power generation system, economicalefficiency or environmental effect? " All of prefereRces for each value are normalized to be

between O and 1.

Best-mixed Power Generation Systems R eflecting Public Preference 151

Please choose one suitable for your idea.(a) more important than (b) a little more important than (c)

(d) a little less important than (e) less important than

Ql. Economical efficiency is convenience.Q2.Q3.Q4.Q5.Q6.Q7.Q8.Q9.Qlo.

Economical efliciency is

Economical efficiency isEconomical efficiency isConvenience is

as important as

energy security.environmental effect.social acceptability.

Convenience isConvenience isEnergy security isEnergy security is

energy security.environmental effect.social acceptability.

environmental effect.

Environmental effect issocial acceptability

social acceptability.

Fig. 1 Questionnaire to investigate a consumer's preference for values

2.2 Performance of power generation system

In constructing the best-mixed power generation, the following eight systems are em-ployed: oil fired (OIL), coal fired (COA), natural gas fired (LNG), hydraulic (HYD), photo-

voltaic (SOL), light water reactor (LWR), high temperature gas cooling reactor (HTGR),and fast breeder reactor (FBR) power generation systems. An assessment of these systemsis performed in terms of five values described above, and the performance scores of each

system for each value are evaluated. • As shown in Table 1, several specifications related to each value are selected; e.g., capital

cost, maintenance cost and fuel cost are taken to assess the value `economica} eMciency'.Similarly, emissions of C02, SO., NO. and radioactive waste are chosen for assessment of

the value `environmental effect'. The quantitative specifications such as costs or amount of

emissions of exhaust are available from literatures. These are carefully determined referring

the latest publications. However, some qualitative specifications, such as `technologicalmaturity', contained in Table 1 are diflicult to evaluate. To do this, the AHP is applied.

All specifications thus evaluat,ed are weight averaged and summed up to give the per-

formance scOre of values. The weights are also determined by the AHP. The performancescores ofeach system are tabulated in Table 2. These are reduced to the standard deviation

scores, where zero indicates an average. If a score is positive, it is superior to the average

performance, and if negative, it has less performance.

2.3 Linear Programming

Figure 2 illustrates the process to find the best-mix applying the linear programmingmethod (LP)9'iO). The preferences of five values, which vary depending on, examinees, are

the input to LP. The LP searches the solution that minimizes the total cost to construct the

best-mix. The problem is formulated as follows:

152

Tabie 1

N. SmKAsHO, R. AKASAKA,

Values and Specifications

tems

T.

to

MATSUMOTO

evaluate the

K. MoRITA and K. FuKuDA7

performance of power generation Sys-r

[iZil[gE =]I]Capitalcost

Economicalefliciency MaintenancecostFuelcostTechnologicalmaturity

Convenience EnergydensityEasinesstohaBdlethewasteAmountofresource

Energysecurity DistributionofresourceEasinessoffue}storingorself-supplying

C02emission

EnvironmentaleffectSO.emissionNO.emissionRadioactivewaste

HumandamageSystemrisk

SocialacceptabilityLocalagreementPossibilityoflarge--scaleaccident

Table 2 Performancescoresofeightsystems

Economicalefficiency O.388 O.388 O.460 O.191 -2.464 O.465 O.286 O.268

Convenience O.241 -O.339 O.285 O.576 -O.501 -O.279 O.037 -O.020

Energysecurity -- O,861 -O.729 -O.843 1254 1.254 -O.352 -O.352 O.629

Environmentaleffect -O.542 -1.247 -O.114 O.693 O.478 O.242 0.242 O.242

Socialacceptability -O.054 -1.065 O.296 O.035 1.274 -O.140 -O.140 -O.207

8 Minimize x==2czxi, i== 1 8subject to 2Si.ixi2bo' (3'=17'''

zgi

2xz =i i==1 ci }il O (i = 1,•••,8)

where a]i and c;i are the composition an

,5)

d power geReration cost of the system i,

(i)

(2)

(3)

(4)

respec-

,

Best-mixed Power Generation Systems Reflecting Public Preference 153

tively. bo• is the preference for the value ]' , Sio• the performance score of the system i for

value 1'. Only xi is unknown and ci, bj, and Sij are fixed during minimization. The righthand side of Eq.(1) is the total cost to be minimized. Equation(2) imposes a requirement

that a sum ofthe product to the performance score Sio• and the composition xi with respect

to all power generation system should exceed the preference boJ of the value i Each value

of ci is tabulated in Table 3. To solve the LP, the simplex algorithm is adopted.

Performance score of sy stems

Input

Preference of value

Jiii.

LinearProgramming

Output

Composition of systems

Fig. 2 Process to find the best-mixed power generation

Table 3 Powergenerationcostsofeightsystems

Powergenerationcost[yen/kWh]

10.96 10.96 10.23 12.96 40.00 10.17 12.00 12.00

2.4 Dualproblem The duality theorem belongs at the centergives the dual problem formulated as follows:

of the underlying concept of the LP, which

5

O' --1 5 subject to 2Sijy,•+y6Sci (i=1,•••,8) (6) j' --1

yj >-O (]'=1,•••,5) (7) where yo•,the variable in the problem, gives the marginal costs ofthe constraint conditions

of the primal problem.

The implication of the marginal cost (or the shadow price) is very important. Takingthe emission trading as an example, the interpretations ofthe primal problem and its dualare presented below.

Suppose a situation: A new law for the power generation is enacted. To assess the powergenerating system i, the law defines their performance scores for values 1' to yield the score

l54 N.SHiKAsHo,R.AKAsAKA,"I".]vfATsuMoTo,K.MoRyrAandK.FuKuDA

table Si3•, and also defines the regulation of each valute bj•. All of energy suppliers must keep

the guideline written in ]E)q.(2). However, a supplier failirig to the regulation is allowed to

buy a surplus score from other suppliers. A price ofthe score traded can be decided through

a, negotiation between them, and the price is determined from demand and supply.

Suppliers will face the primal problem when they try to minimize the total cost forconstructing the power generation system, however they have to do this with guideline.When a supplier can affQrd to sell his surplus score, the dual problem is arise. With a price

`yi per unit score of value 1' his total benefit is given by Eq.(5). AIthough he shall wish to

be the bellefit as high as possible, Equation(6) determines its upper limit. To let other

suppliers buy his score, the price charged to the performance of a system shou}d not exceed

the power generation cost of the system. Otherwise, other suppliers never buy his score.

According to the duality theorem, the minimized total cost for power generat,ion of abuyer is the same to the maximized total benefit of a seller. Therefore, even though a supplier

decides either to meet all regulations by himself or to buy scores from other suppliers, both

costs are equal.

Furthermore, the comp}ementary slackness condition in the theorem tells us that if abuyer had score over the regulation for a value, the price of the value yields zero. In other

words, if a buyer has just met/ the regulation for a value, that value is priced.

3. ResultsandDiscussions

3.1 Preference

A survey was conducted from October to December in 1999. Figure 3(a) shows theresult of individual preferellce for values obtained from the survey. The abscissa and theordinate are the percentage of examinees and their preference, respectively. Figure 3(b)

shows the result of the averaged preference. A preference O.2 indicates an average. If anexaminee regards that a certain value is more important than the average, its preference is

above O.2,

About 90% of' the examinees thought that the value `social acceptability' was above the

average importance, and the `environmental effect' and `energy g, ecurity' were the next. Few

examinees put, their preference on the `economical ellEiciency' and `convenience'.

3.2 Best-mixedpowergenerationsystem

Figure 4(a) shows the best-mix to accord with examinees' preference evaluated ipdivid-

ually by the procedure described above. The abscissa and the ordinate are the percentageof examinees alld the composition of each power generation system in the best-mix, respec-

tively. Figure 4(b) shows the best-mix averaged. LNG and HYD comprised large part in most ofthe best-mix evaluated for all examinees'preference. This was reasonable because these power generation systems have relativelyhigher performallce scores for the social acceptability as tabulated in Table 2.

Some best-mixes contained small compositions of SOL and LWR. AIthough SOL had thebe$t score for the social acceptability in all systems, its economical score was considerably

lesser than the others. Therefore, it was involved only in the best-mix of an examinee who

regarded the social cft,cceptability as extremely important•. rll]he reason for including LWR

was that it had the average performance for a}1 values.

The best-mix that contained OIL, COA, HTGR and FBR hardl.y appeared. OIL andCOA had few advantages except for economical efficiency and convenience, which were not

Best-mixed Power Generation Systems Reflecting Publ ic Preference 155

thought important much. HTGR and FBR had average performancesLWR, but the lower economical performances were disadvantage.

almost the same as

"--'- Economicalefficiency Convenience "'-'- Environmental effect '- - - Soci al acce

O.6

Energy securitytabilit

O,5

O.4

8:9 O.3

gO9

pt O.2

O.1

'1N. Ns L N II N l" Nt 1 L .-N .-s

L

N

N.- -.---.. -b Ng s- N-....-.- SS-i"e-- N.. - '-N -b-- N N N. . .- -

NN Ns.N A N. '-'---

'NN --.

"N---. -hl . ---

-"` X N sS 'I s k -b 's-t--

o 20 40 60 80 Persentage of examinees (9e)

100

(a)

O.4

O.3

8g

.ts O.2

Ept

O.1

o

ii--ii---------i--i-i--is-----iti-i-i----- 'rrr-i-i--i4Y---thi"-i--i-------'-'-'-rv-'i'-'i-'-'-'-'-'4'-'--'-'-U' -

'le >,.2 o-==og lE•

p!S "trs

8=

.9=o>=oU

hoo-o=m

h•=-5ooen

re

1oE=o

.tc

>=m

69,O,,

,•tS

.b-rl-g- "A'-'

ig .s

(b)

Fig. 3 Preferenceofeachvalue (a)individual (b)averaged

156 N. SmKAsHo, R.AKAsAKA, T. MATsuMoTo, K. A/IoRITA and K. FuKuDA

1-- -- LNG HYDe"e="SOL LWR

g o.s

g:Ysc. O.6

E.9 O.4•=

g•

g o.2

U

x sN -- NN

-lita. "-k"-u- " ."m" - -tae - tu= t 'nt - -ny-M e .-heg - '"k`e. ' m-n - N,

-' hx

. "ljta- .

hx

l

o 20 40 60 80 100

Percentage of examinees(9o)

(a)

o.6 r

O.5E9IS2.,

.IAZ o.4

gt+.di

o o.3:o

•=-F4

o o.2aaOv O.1

o

1

=F

H

OIL COA LNG HYD SOL LWRHTGR FBR

(b)

Fig. 4 Compositionof each system in the best-mix (a) individua} (b)averaged

Best-mixed Power Generation Systems Reflecting Public Preference 157

3.3 Marginalcosts

Figure 5(a) shows the marginal costs of values calculated individually for all examinees'

preferences. The abscissa and the ordinate are the percentage of examinees and the marginalcost ofeach value, respectively. Figure 5(b) showsthe marginal costs averaged. The highest

marginal cost of the social acceptability meant that most examinees approved the highestlevel of expense for the social acceptability. It made this result agreeable that the marginal

costs ofenvironmental effect and energy security follows. As mentioned above, these values

were regarded as important next to the social acceptability. The fact that the marginal costs

of economical efficiency and convenience were consistently zero was also remarkable. This

was interpreted that all examinees were going to spend no expense for these values sincetheir requirements for these values had been already satisfied.

In addition, the term bo•yo• in Eq.(5) represents an examinee's willingness to pay for the

value 2' , since yo• i's the price of the value o' while bo• the amount of the va}ue, which the

examinee demands. And Sijyj in Eq.(6) is a monetary value ofthe value 2' ofthe systemiin terms of the price of electricity.

Figure 6 shows the price of willingness to pay for values averaged. The price for the

social acceptability is the most expensive. Figure 7 shows the monetary value of values of

the systems averaged. LNG and HYD took part in the best-mix since high score for socialacceptability of LNG, energy security and environmental effect of HYD got high appraisals,

respectively. The monetary value of SOL for social acceptability was the highest. But SOL

took only a part ofthe best-mixed power generation system for the reason that the powergeneration cost of SOL was more prohibitive than its value. There were the cases that SOL

took in the best-mix and the other cases LWR did.

Figure 8 and 9 show the preference of an examinee A and his best-mix, respectively.Figure 10 shows his willingness to pay for values. He was willing to pay only for the social

acceptability and the energy security. Figure 11 shows the monetary value of each powergeneration system for value. The energy security of HYD, the social acceptability and the

energy security of SOL were highly evaluated. The SOL, however, did not take part in his

best-mix, since the power generation cost of SOL was more expensive than his appraisal ofthat.

Figure 12 and 13 show the preference of an examinee B and his best-mix, respectively.

Figure 14 and 15 show his willingness to pay for values •and the monetary value of each

power generation system. He was willing to pay only for the social acceptability and theenvironmental effect with very high appraisal ofthe high score ofthe social acceptability of

SOL. By the merit, SOL was called in the best-mix.

4. Conclusions

The primal problem to find the best-mixed power generation system for energy consumers

was discussed. The linear programming approach could solve the problem, and the best-mixwas evaluated individually according to the preference of each consumer. The dual problemthat the duality theorem derived from the primal problem was discussed. A solution of thedual problem gave the marginal costs of values for consumers' preference.

The survey of energy consumers' preference told us that the examinees tended to attach

most importance to the social acceptability, and in their best-mixes the LNG and HYDtook larger part than the others. It was understood from the resulted marginal costs that

most examinees approved the highest expense for the social acceptability. It is regarded

158 N. SHIKAsHo, R. AKAsAKA, rl". MATSUMOTO,K. MoRIrTA and K. FuKuDA

tliat the prices representii}g the `wi

are obtained by the marginal cost.

11ingness to pay7 for values in constructing the best-mix

25sAliii

:20e-

sg 15

-iEi

8Åé 10Hvl

8

gs,ge

E o

Energy security -'---Environmental --• - - Social acceptability

effect

--t - ttp -- -=p w qp -e e e"

,

1

'

s

1

1

1

t

l

ll

----b------nt-e---p-p-----e .- }

, l , ' l } , j n j l I e g , ' e

t

t

I

l

1

20 40

Percentage of

60

exammees

(a)

(9o)

80 100

25

G 202S, i5

g2 lo.s

.EbOts

E5o

-i- -------

'

-

'

ft,9Eo96

pt

Mo=.9

2H..-

o

oo=.O.d

=o>=oU

in .b-

as ts

=opt 8

"eos=o.be

>=m

590-

ts

.b-

S t6o

2

(b)

Fig. 5 Marginal cost for each value (a)indivi dual (b)averaged

Best-mixed Power Generation Systems R eflecting Public Preference 159

7

6

G5Z4fi

YL 3

di 2

1

o

--s--- ,

'

,

,

,

,

,

,

,

,

,

,

,

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,

',

,

,

,

,

,

,'

,

',

,

'

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,

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-

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,

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,

,

,

,

,

,

,

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,

,

,

,

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,,'

,

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,

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,

,

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'

',

,

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,

•- EEi

.2ao=oom

hO:

.9

.O-gg-g

o

oo=o

- !ny-

:o>:ov

hhpa •u

83m8

:.

gEg

•y

di

5s-o-

c-k[j

-a.1--

ooca

h;LÅí.

g8

Fig. 6 Willingness to pay for each value averaged

O Energysecunty rwI]nvironmenta1effect M So cia 1acceptab ility

e.!l

I:3.,

'A

=.9'kl

52'xA

Ys )(

og'5 b8k>hts

.a

gE

30

20

10

o

-- 1 O

-20

-30

. sL " t i--ts ss k"t"' Xli'i

1 N

OIL LNG HYD SOLLWRHTGR

--------l-{l------------------t--+---t-----t-----------t--------t------'-----------------t--t-t----tt4--------ll-l----------i

Fig. 7 Monetaryvalueofeachsystem averaged

160 N. S}m<AsHo, R. AKAs-AKA "I[i. '

]NxlATsuMOTO, K. MoRITA and K. FuKuDA

Q4

O.3

d9

Åít O.2

8-

O.I

o

ft-t

tr---

L---

:.

.t-.1

K.,JEo=o,o

pt

ptoÅë

.9

.OA;•-.

o

8=,9=o>=ov

tz bpt

g. ,6

L2L) 8

esaoE '5: 90"ÅíÅékm

re'o"

oca

h;aÅí

a88

Fig. 8 Preferei}ceofeachvalue(E xammeeA)

O.5

E O.4s.$-

g. o.3

g=

•, O.2'g-•

g8 O.1

o

1i

I

tIrLF •l' l..

L]l l

Lt '} i

; ''' '?f

/g

',a!ca'" L-J

Off- ooA ING HYD SOL LWRmdl FBR

geig. 9 Composition of each system in the best-mix (E xammeeA)

Best-mixed Power Generation Systems Reflecting P ublic Preference 161

O.3

O.25

AI;Ii o.2

MÅ~g o.ls

b•# O.ipt

O.05

o

-.S bEgs, g,

8g

'g

>=o

U

)5 Xge •a

sgm8

:.

g

E5: 90-.g Åé

i;n

pt".-ooca

h:•fg

-q8x

Fig. 10 Willingness to pay for each value (Examinee A)

M Energy security - Social acceptability

s-oi:2.,

ut

:o

•;ct

-o=oua

=oao-oos

!.-.tes

>hts6g

)iil

Giii'M)eil.,

v

3

2.5

2

1.5

1

O.5

o

-O.5

-1

--- 1.5

-2

-2.5

o

Fig. 11 Monetary value of each system (Examinee A)

l62 N. SHIKASHO,R. AKASAKA,rT. MAIisuMoTo. K. '

MoRI7]A and K. FuKUDA

Q5 r i04 V

]llF

8g

.-ko

gl'lil O.2

o3 I

EtL

1 1 i-T.=-

:1!

O.1

o

lL- •

T'rm'- 7

•l i I• l

rw tu 1

F

1

egG. •s

Åítt ,tts

8g

'E21i

grJ

>i )5pa •:.

8Bc:n 31.

es

a;.

==O

't

>=L:.:)

6keotll

G4,'J"

om

x•="-Da-ptovo.v

Fig. 12 Preference ofeach value (Examinee B)

O.7 r f

:o",

E?{

b.

Aoat

o:"."

ono

•=-ms

oc)- Q2aÅë

v

o.6 l----- ll

o.s F'

:O.4 t '" Mrm- lo.3 I

t l iO.1 r-"7rmrmrm E I

Ot i

]tE':

,l='

tT

'

ri1l

'•g-

.t

'

'tt.tttt

L-t

te,'' t

ott ceA ILNG I{YD SOL LWR I-I[GR FBR

Fige 13 Compogition of each syst,em in the best-inix (Examinee B)

Best-mixed Power Generation Systems Refiecting Publ ic Preference 163

5

4

=AZ3S-

•S 2

pt

1

o

g'g

98

;n

xo:o'6u-o

8g

'g>=o

v

hooNo:m

h•. -.

-88

:.

g.•g, g-

cS

h- ;"•g- R

sE 8

Fig. 14 Willingness to pay for each value (Examinee B)

ge Environinental effect - Social acceptability

40Eoor 30ta

g•= 20fi -

/9i, 'g

EV'ls -tog5 -20g: -30

lillli-:-:-::

illll,l,,I,I,II:i:I:I:I:I:i:l•:

}lilil•••il{':'

i,l,ll,ii IINGHYDSOLLWRHrGRlllliiil

Fig. 15 Monetary value of each system (Examinee B)

164 N. SHIKAsHo, R. AKAsAKA, T. MATsuMoTo, K. MoRITA altd K. FuKuDA

References

1)

2)

3)

4)

5)

6)

7)

8)

9)

le)

M. ankin,S.,Sato,O.,Yasukawa,S.and Hayashi,T., Economic Perspective of SMSNRs inthe Energy Market of Japan, NzecZea'r Engineeri'ng a,nd Design, 109,355-363, (1988).

Ohkubo,H.,Suzuki,A.and Kiyose,R., The Mathematical Analysis on an Efficient Use OfEnergy, Journal of .Facult`y of' Engineering, The University of Tokyo, Se.ries B, 36,4,787-

826, (1982).

Fujimoto,N.,and Fukuda,K. TTans. Japan Soc. EneTgy Reso?Lces, 21,5,438,(2000)

Afanasiev,A.A.,Bolshov,L.A.and Karkhov, A.N, Economic Competitiveness of the NewGeneration of NPPs with NP-500 Units in Russia, Nuclear En.gineering and Design,173, 219-227, (1997).

Kainuma,M.,http://www-cger.nies.go.jp/cger-j/c-news/vol1O-4/vol10-4-2.htmlYoshida,Y.,Ishitani,H.and Matsuhara,R., A Study of Systematic Measures for ReducingC02 Emissions, J. Jpn. Soc. SimzLL Technol,., 14, 1, 52-57, (l995).

Jackson,T., Least-cost Greenhouse Planning: Supply Curves for Global Warming, En-erg?.7 Policy, 19, 1,35--46, (1991).

Harada,Y., et. al., Eng. Sci. Rep. Kyzesh?L Univ., 18,4,289,(1997)

Fukuda, K.,Fujimoto,N.,et. al., ibid, 20,1,19

Fujimoto,N.,et. al., Technot. Rep.Ky'ushu Univ.,, 74,3,221