1995年度日本オペレーションズ0リサーチ学会 秋季研究発表会 1一団−−5 O T馳eA汀岬口昌正風佳苗①m①『『MZEyDym皿m貢疋『『①即風mmn皿g細 ○ 『①W即Sy＄紬mⅡ》旭mm8mg孤md①炉即叙任昆①mIP『①恥nem＄
ⅢokkaidoUn五verslty Graeme￠IBSON
踊okkaidoUniverslty Ⅲiro叩ki監汀A MokkaidoInst．ofTechnology Ken−ichiNIS附IYAO1503151 MokkaidoUniverslty ∬un‡堰AS正GAWA
proce∬）玩comes仙e minimisadon of弧0頓血ve
軋mc“om where a given sはge，転h鮎a number o一 匹∬ib葛e 町Stem StateS Which 陀餌1t 五m d∝isionrequlrememtCO汀eS卵mdi‡唱tO仙eoperationo叫∝li明．汀
即de陀dd∝ision making皿Sperぬme吼仙emasol血iom 鎚n晩obtained（DPapproac甘l）．meinilialslaleofthis
卯S飴m be de魚med by Equa血n（1）紺dlhe
m血misadon o叫eclive蝕nction cam be defined by
E耶a扇om（2）・me Ope柑timg s旭te乳at s旭ge kis
detemlinedbythedecisionvalue払Whichco汀eSPOnds
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membeFShip免）nClions，We are able to如mulate a
mathemalicaltechniquetoselectthepr（痴rred鮎nclion．
Wehavechosenr∝t卸如1甜餌nct哀0れS如ma血ematic如 Simpticily due to dlelengthyintegTalion calcu）ations
requ壱『e瓜 Ahhough 仙is t∝hmique comsiders 吻
membership免ⅢClions，themathematicalapplicalionis not s＆貢c11y爪1㍑y血00叩，i爪Stead jtis an o蝕prhg of
probabilitylheo町．me gener扇ぬmulais givenim
Equalion（3）．
A恥＄任『風C仕
丁仇is paper presenls a mew 免1Z野 dynanlic
progra‡llmlmgteCh丑Iique曾brsoIvingmll111isl喝edecision problems孟m poⅥ′即町Slem明椚血om．批use＄a爪皿Z町 decision pr∝eSS Called仙e pre∬もrence fhc80r，Which equates抽e ma抽emalicalp陀r如emce orome decision
知れClion willlreSpeCt tO細Oltl即．Toinvesligateils
Validity，五Iwasappliedtolhehydro抽ema且scheduling
probtem，Whicho晩rsanideatapplicalion魚）rdymamic programmmg．Resulls showedlhat this techniqueproducesamoperat．ingbandgiv直mgsolulioni随xibi］ity． Ⅱ。Im加・①』Ⅷ正也岩①m
Mullislagedec孟siommakiれglSaniI叩0拍antp涌Or
pollrer SyStem Opera再0爪 plamm川名 amd 貞sllSua11y
per−brmed by d〉rmamic progr綱Imimg（ロP）．Various
pl卸nlng prOblems exisIsllCh as 仇y伽otller111al
SChedulin臥Ihermaigenera11ng unit mainlenance
SChcdu］ing，eCOnOmica】】oad 朗spalching and11nit
COmm抽Ⅵet−＝1，2】．Ⅲowever，血ese problems a11deal Wilh elementslhat conlain adegreeor川ICertajnfy．7f 餌zzy theoⅣ，Or mOre SpeCi爪cally，血z町me−mbersIlip 餌nclions are used10 repFeSentload and nalural富Iydraulic 爪ows，仙emilnalurally fbllows 仙alttle
lhermaR production cost willalso become a AIZZy
membersllip血ncliollI2】．Fu曲er，itis仙emmecessa呵10
use n．1ZZy malhemalicaltechniques10 COmParelhe
VariollSSlalecosIsJbraglVentimeslagealldtoct100Se
themin云mumcostp飢haccordingty．‡mlhispaper，lhis
ispeTfbrmcdbylheprqPp・eP7CejactorDPlec甘Iniqueandapplied101lle hyd柑th即maⅦ schedulimg proble札
Therefbre，WeCaneXPeCtaLlnaⅡso］utionlh飢willhave aRIZ町ba冨1dfbrreseⅣOirs10rage】el′els． 2。IDe正員s芭①m肝『①疋eSS Manyprob］emsaresuchlhalamu］lislagedccision process雇s陀quiredねroblaimll唱tlleOp11‡ma且operaliom
Ofasystem．OneninpowersyslemopeTaliomplannIng，
lheqptima［qperotioniscostoricnled．‡n caseswheredecisionsalalaterslagedonoiagYbctlheoperalionof
lhesyslematearljerslageslhenlheproblcm（SOlulion Jニーl刷だ腑妙血 〃W，β）＝ （3） Jニ山伺血†ニ両脚 PF（Å，B）denoleslhatlhjsparticularfbrmulacompares AJZZy number B with respect10A to determine A●spreEもrence：ねctor value．This value canlhen be
COmPalTedwithaprenominatedconstrainingvallle，β，tO
deleTminetherelaliveoplin；alityofbolhfunclions．The
mathemalicaldehitionofPisgiveninEquation（4）．−50−
delerminislically．．Wemadetheassumpl）Onlhatitwas nolnecessary10aPPIy afuzzy band tolhe fbrecasted
loaddatabecauseithasonlyasmallerrorwithlimited
Varialion．ConverseIy，thefbrecasted naturalhydraulic innow has a much grcater variationin error due to
COmplicatedwealherconditions．Weapplieda5％band
to these values10 aCCO11nt fbr this uncertainty or
fuzziness．TllepreftrencefhctorconstrainlngValuewas
Set at P＝0．475．Althoughnot shownin this p叩er，it
ShouId be noted that the operatlng band was smaller
thanlhatfbrlhecasewhereP＝0．45，lhusdemonstraling
lheefrbcliveness ofa句ustlnglhisvalue．This has the
errect of further restricting the number of possible
equlValenlcosts and hence reduces the size of the Operalingband．
β≦PJγ〃，堺≦トβ メ＝β
叩，即＜P ；βd （4）
1−β＜メソⅥ，印 ン1＜β
Fronltllisderinilionilcねnbeseenthatβcannolbeset above O．5 aslhis va）ue represenls equality belween membership A）nClions．Ifwe makelhe assumpl10n aS giveninEqualion（5），lhereare4rcsu］1ingderivalives
COrreSpOnding tolhe4coTlnguralions excIuding cases
Wheretllereisnooverlap（noIshowninlhispaper），PJ7印，β）・十P門β，」）＝1 （5）
4．NewFuz町DPApproachn汀
Hydrolherma］Schedu］ing
Formulation of Hvdrothermal Problem
lnthispaper，inordertoinvesligatelhevalidityof thisnewfuzzyDPapproach10111emultislagedecision process it was necessary to choose a simple example
PrOb）em．For this purpose，lhe minimtslng Oflllermal
powcrproducLioncostsfbrasellimeperiodwaschosen
togetherwilh a slng］e hydroelectric power slalion10
provideahydrolhernlalco−Ordinationproblcm．Forlhis plannlngPrOb］em，lheslagesconsis10‖ndividuallime interva】sand theDP melhod todetermine thereseTVOir Water］evcl．Thecorrespondinglllermalproduclioncost mnelionthenb∝OmeSthelbtlowlng：
刑期m〓仙Ⅷ幻0
︵＞DP・S＼−×可〓①＞旦﹂．6≧①Sの巴 0 刀0 4∞ ∝O e∝1∝刀12∝）14〔刀 Timein†ervoIsFig．1Schedulingsolulion
（tnLlowband＝5％LbrP＝0．475）q＝0
（6） C；＝¶㌢・（q￣−＋C仇ト1㈲） （7） Here，Cktislhetota］cost什omll−einilia］timeinten′alto lhe end oflimeinleTValt where ttle Waterlevel（Operalingstale）isdcnncdbyk．Tnaddilion，C（い一1；k，l） islllelransilion cost什om slaleJaltlle end of tlle previouslimeintervalt−110・Statekat
nexllinleiIllen／a】t．
5．NumericalExAmples
TestMbdel
Simulalions were cdrried ollt On tlle fbllowlng
SyStemmOdeltolestlhevalidilyoflhisnewnlell10d・ ＞schedulingperiod＝1year（1456timeinlcrvals） ＞ 2x］00MWgenerators ＞ reseTVOirvolumerange＝0∼1060（tJs．day）： dividedinLo265unitseachof4tlノs．day） i・9−unitl）1ermalgenerali11gSyStCmTestResults
Fig・lglVeSlhesctledulingsolulionobLainedbythe prcftrencefhctorDP technique・Thc2di恥ren11ines denotetheupperand］owerlimitsortheoperalingband wllichwould notexistenlirllleSOlulionwereobtained ‘．ConcIusionsThis paper presented a new approach fbr soIving
multislagedecisionproblemsinpowersystemoperation
Where e］cments containing uncertainty exist．Fuzzy funcriorls and numbers were used to express the
inherent uncertaintyelemenls，・namely，load demand， naluralllydrau］ic flows andlhe corresponding power
geTleralionlevelsandthermalpowerproduclioncosts・
The resulls obtained have an operatlng band which
renects’lhe robustness andI】exibiIity ofthe solulion・Thisallowsthesystemoperatortocarryoutoperalion
withinlhisrangetosuitanyg］VenSCenario．ReftreIICeS
川 C．Huang．etal．：’FuzzyApproachforGeneratorMainl， Schedu＝ng’，EPSRProc．Vol．24，PP．31−38，1992． 【2）J．Hasegawa，et al．：’A Method that Considers
Unce丘ainty・in Power System Planning”（inJapan8Se），
lEEJPowerTech．Meeting，PaPerPE−93−175．1993．
