OPTIMASI POLA OPERASI WADUK SUTAMI MENGGUNAKAN MODEL PEMROGRAMAN LINIER KABUR (FUZZY LINEAR PROGRAMMING)

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1 OPTIMASI POLA OPERASI WADUK SUTAMI MENGGUNAKAN MODEL PEMROGRAMAN LINIER KABUR (FUZZY LINEAR PROGRAMMING) Yso Pryd Abl, Rsp 2, Wdd Soopo 2 ) Mhssw Msr Tkk Pr, Fkuls Tkk Uvrss Brwy, Ml, Jw Tmur, Idos; _ml : [email protected] 2) Dos Jurus Tkk Pr Uvrss Brwy Ml ABSTRAK: Bdu Sum rlk d Ds Krks, Kcm Sumbr Pucu, Kbup Ml. Mf um uuk pdl br, rs, PLTA sbsr 3 x 35 MW d mmuh kbuuh db mmum 56 m 3 /d uuk drh hlr. Pd wl prc, db mmum urb PLTA dlh 25 m 3 /d d db mksmum 5.39 m 3 /d. Dlm us 4 hu, urb hy mmpu mrm db mksmum sbsr 46.9 m 3 /d. Uuk mmprhk produks r lsrk yu d mopmlk ouflow y msuk k urb. Drc muk modl pmrorm lr kbur y dpduk d modl smuls uuk pl kr pol oprs wduk. Dlm k dprolh hsl opms slm hu brup produks r opml sbsr GWh, kurv pur muk r bru d smuls mhslk kdl. % uuk modl d kss. K Kuc : Prorm lr kbur, opms, smuls, pol oprs wduk, wduk Sum. ABSTRACT: Sum Rsrvor s locd Krks Vll, Sumbr Pucu Dsrc, Ml Rcy. Is prmry bfs r for flood corol, rro, powr ro of 3 x 35 MW, d o supply mmum dschr of 56 m 3 /sc for dowsrm ros. Erly o, ws pld h h mmum dschr for h hydropowr urb would b 25 m 3 /sc d h mxmum dschr would b 5.39 m 3 /sc. I s 4 yrs of, h urb hs oly b cpbl of hdl mxmum dschr of 46.9 m 3 /sc. Elcrcy produco c b md by opmz h ouflow h rs h urb. A modl ws dsd us fuzzy lr prormm modl, whch s combd wh smulo modl for rsrvor opr rul prformc vluo. I hs sudy, opmzo of yrs ws obd, h form of opml ry produco of GWh, w rul curv for h rulo of wr surfc lvls, d smuld rsul of % rlbly for h modl d xs mplmo. Kywords : Fuzzy lr prormm, opmzo, smulo, rsrvor opro rul, Sum rsrvor. A. PENDAHULUAN Krss r y rd d Nr k hy dp ds d mcr sumbrsumbr r bru u mopmlk kr ssm. Ar pd wduk y brfus uuk mmbkk r lsrk mrupk sumbr r y prlu dopmlk. Kdl dlm mopmlk kr sbuh ssm rdp vrbl - vrbl y dk dp dpsk d p, mk y rd dlh kdku (ucry) u kkbur (fuzzy). Hl rsbu dp dmodlk d dsrbus probbls d fus ko fuzzy (Loucks, D.P d Bk,E.V, 25: 35). Modl opms pol oprs wduk Sum k drc d muk modl opms prorm lr kbur (fuzzy lr prormm). Hsl solus dpduk d modl smuls dlm mmhm kr drpd oprs wduk. 95

2 96 Jurl Tkk Pr, Volum 6, Nomor, M 25, hlm D mmprhk kods kods ds, mk prmslh dlm sud drumusk sb brku :. Brpkh produks r PLTA Sum mksml y ddp dr hsl opms Prorm Lr Kbur?. 2. Bmkh prbd lps d produks r dr hsl opms Prorm Lr Kbur dbdk d opms Prorm Lr d D Lp? 3. Bmkh prbd hsl smuls hu 29-2brup produks r d kr kdl dbdk kods kss? B. BAHAN DAN METODE B.. U Ssor U ssor dmksudk uuk mu ksbl l vr d r-r dr dr brkl. Pu l vr dr dr brkl dp dlkuk d U-F (Sowro, 995:38): (2.) Apbl hsl pu l vr dk sbl u dk homo brr dr brkl rsbu dk ssor, d dk prlu mlkuk pu sluy, k p sblky k k vr muuk ssor, mk pu sluy dlh mu ksbl dr l r-ry. Pu ksm s l r-r dp dlkuk d muk u- sb brku (Sowro 995: 8): (2.2) B.2. Dsr oprs wduk Sum Wduk Sum dlh wduk y broprs hu/musm. Wduk mmpu r slm db lbh u musm hu d mlpsky pd s db kur u pd musm kmru (Hryd, 2: 27) Volum (u m 3 ) FWL Ds HWL LWL I LWL II Pdl Br Ps Musm Hu Cd Kkr M Poso Musm Kmru Elvs (m) Nop Ju Gmbr. Pol Oprs Wduk Sum Sumbr: Prum Js Tr I, 24 Gmbr 2. Kurv Gbu H-A-V Sumbr: Prum Js Tr I, 24 Produks r dlh prors um y brkmb ps dlm pmf uh r uuk mmur urb lkrk. D mksrs 8-9% r posl uh, PLTA s mrupk sumbr r lsrk y pl fs (Mys,L.W,996:3. 3.3) D krkrsk PLTA wduk Sum, dlh sb brku : Gmbr 3. Khl T Tk Sumbr: Soopo, Wdd. 984 : 38

3 Abl, dkk., Opms Pol Oprs Wduk Sum Muk Modl Pmrorm Lr Kbur 97 (Fuzzy Lr Prorm) B.2. Opms prorm lr kbur Mks : C. bs : C. b ~ ( ɛ N m ), ( ɛ N ) () Gmbr 4. Krkrsk Isls PLTA Sumbr: Soopo, Wdd. 984 : 39 Gmbr 5. Oupu Pr U PLTA Sumbr: Soopo, Wdd. 984 : 4 Hubu r lps db k urb uuk mhslk lsrk brsf o lr, komplks d dk mu. Pdk y dpruk dlh muk prorm lr y dkombs d lok kbur md prorm lr kbur (Fuzzy Lr Prormm). Kkbur dlm hl dlh pd fus bs d pd cr pd k mlh prmslh. Spr pry dr Profsor Zdh yu : Komplkss d kdku brhubu r, smk dk/dl k mlh suu prmslh dlm du y mk smk kbur/dk ls pylsy (S, Zk, 2: ). Pd ksus b ~ ( ɛ N m ) dlh bl kbur y dku fus ko lr : f x b b p x µb (x)= f b x b p p f b p x (2) ) dm x ϵ R. Uuk ms-ms vkor x = (x,x 2,,x ), prm k hu ky, D (x) dm x dlh vrbl bs ( ϵ N m ) pd rumus : D (x) = B ( C. )... (3) Tk dlh hmpu kbur dlm R, d rsy m D dlh o hmpu kbur. Bs bwh dr l opml (Z lowr = Z l ), dprolh d mylsk mslh prorm lr sdr : Mks : Z = c.x Bs :. b ( ϵ N m ), ( ϵ N ) (4) Bs s dr l opml (Z Uppr = Z U ) dprolh d cr y sm d mylsk mslh prorm lr dm p p l b d d b + p : Mks : Z = c.x Bs :. b + p ( ϵ N m ), ( ϵ N ) (5) Kmud l opml hmpu kbur, G dm o hmpu kbur R ddfsk sb fus ko lr G(x) uuk uu brku :

4 98 Jurl Tkk Pr, Volum 6, Nomor, M 25, hlm µg(x)= C. Z U Z Z L L f f f Z C. L C. C. Z Z L U Z Grfk (6) mmbrk fus ko lr y ddp dr prsm (6) uuk uu kbur y dmplk dlm Gmbr 2. Hmpu kbur dlmbk d bs C, dm o hmpu R, ddfsk : µc(x)= ( b p p. f. f b f b p. b. U b p Grfk fus ko lr dr prsm (7) uuk sumbrdy kbur dmplk dlm Gmbr 7. D mbuk forms ds, mslh y ddp dr Prsm () dubh md mslh opms sluy sb brku : Mksmlk : λ Bs : µg(x) λ s.. µc (x) λ m s. x, λ (8) dm :dsffs µg(x) = x mrupk o hmpu fus krkrsk G µc (x) = x mrupk o hmpu fus krkrsk C D r K µg(x) o Z l Z U Dom Gmbr 6. Fus Ko Tuu Sumbr:hp:// Z (6) (7) K D r o µc (x) Gmbr 7. Fus Ko Bs Sumbr:hp:// D muk prsm (6), (7) d (8) dp duls prsm sb brku : Mks : λ Bs : λ (Z u Z l ) cx - Z l, s. λ.p +. b + p ( ϵ N m ). λ,, ( ϵ N ) (9) Dm, λ dlh k kpus/kpk upu dr ko y ly brksr r smp d. Mslh ds sbry mslh uuk mmuk ɛ R spr brku : m D [( ) b.x Dom G] ( x) b + p () Uuk mcp l mksmum dr: mslh uuk mdpk k ( ) y cocok b l fus bs d fus uu pd l dr mksmum. K D µc (x ) r λ o µg(x ) x Gmbr 8. Solus Prorm Lr Kbur Sumbr : hp:// fur=plyr_dlp &v=-zuf3uk6-ui Dom

5 Abl, dkk., Opms Pol Oprs Wduk Sum Muk Modl Pmrorm Lr Kbur 99 (Fuzzy Lr Prorm) B.4. Prumus smuls wduk Sum Adpu bs-bs dr smuls d sums sb brku :. Db Iflow dlh db bul dmbh flow r-r dr wduk Lhor sbsr m 3 /d. 2. Db mmum urb 25m 3 /d d db mksmum 46.9 m 3 /d. 3. Smuls dlkuk d cob-cob Q ouflow PLTA brdsrk Rul Curv hsl opms. 4. Awl smuls dlkuk pd bul Nopmbr y mrupk wl ps wduk Sum. 5. Ar duk sopml muk sh lps y dlkuk dlh lps mksml d dushk dk d spllou. 6. Kbrhsl smuls du dr hu u musm oprs. 7. Korol smuls yu lvs muk r rdh urb dp broprs Produks r hsl dr smuls mrupk pmbd b r hsl dr opms, sh y duk dlh hsl opms. B.4..Ukur kr oprs wduk. Kdl (Rlbly) Kdl mrupk dkor sbrp sr wduk uuk dp mmuh kbuuh y drk slm ms poprsy. Adpu hp prhu :. Tuk umlh d, umlh smuls l d smuls sukss. 2. Kdl.=.(lh.l/lh.d).x% b. Kl (Rslcy) Kl mrupk dkor dlm mukur kmmpu wduk uuk kmbl k kd mmusk dr kd l. Adpu hp prhu :. Hu umlh rss, rr rss,.rr sukss, rr sukss 2. Kl = rr rss/ rr..sukss) *% c. Krw (Vulrbly) Krw dlh bsr dr kl/dfs y ddp dr prbd r kpss wduk d umlh r y dbuuhk, db d umlh r y dbuuhk. Adpu hp prhu :. Hu umlh dfs, hu umlh.kbuuh pd bul l 2. Krw = (lh dfs/lh kb. Bul l) x % B.5. Mod Pl B.5.. Pumpul D D d y dprluk dlm sud dprolh dr Prush Umum Js Tr I, Ml y brlm d Jl Surby No. 2A Ml. Adpu d d y dprluk dlh sb brku :. Db Iflow bul Wduk Sum dr hu 22 smp 23 b. Db Ouflow bul Wduk Sum dr hu 22 smp 23 c. Kbuuh r bul d drh hlr dr hu 22 s/d 23 d. D ks wduk Sum. Pol oprs wduk Sum f. Produks lsrk hu 22 s/d 23

6 Jurl Tkk Pr, Volum 6, Nomor, M 25, hlm B.5.2. Modolo D D Tks Wduk Sum Opms Prorm Lr : - Produks Er - Produks Rls Q bl 2 h : - Qflow - Qouflow - Qhlr Mul U Ssor Y Q PLTA : - Qmks - Qm Idfks Mrumusk Fus Tuu Sr Fus Kdl Modl Mmk Prorm Lr Opms D Solvr Excl Opml? Y Modl Mmk Prorm Lr Kbur Opms D Mlb & Solvr Oupu Opms : - Produks PLTA (kwh) - Ouflow k urb (m3/d) Opms Prorm Lr Kbur : - Produks Er - Produks Rls Hu Er Bk PLTA Tpk Tmpu Awl Hu Lps Mksml PLTA R Rmks? Tdk Hu Tmpu Wduk Akhr Prod Hu Er PLTA Tdk Tdk Smuls Thu 29-2 Produks Er Lsrk PLTA Sum 2 hu U hposs l Prks Fus Tuu (Z) d Fus Kdl D PJT Uuk : - Produks Er - Produks Rls Y RM. RM.2 Tmbh Lps C. HASIL DAN PEMBAHASAN D db dl PJT y dpruk mrupk ol flow y msuk k wduk Sum y brsl dr ouflow Suruh, flow rm bs d rr flow Lhor.. U Sor U ssor dmksudk uuk mu ksbl l vr d r-r dr dr brkl. Pu l vr dr dr brkl dp dlkuk d U-F (Sowro, 995:38): Uuk u ssor duk 2 u hposs yu u F d u T. Adpu hp u F sb brku :. Mhu l F F hu = = Mcr l F dr bl Uuk α = 5% pd dr kbbs dk = dk2 d dk = - = 72- = 7 dr bl dsrbus F mk F bl = Ksmpul Hposs Olh kr F hu < F bl mk l vr muuk bhw kdu klompok d homo u ssor. Apbl hsl pu l vr dk sbl u dk homo brr dr brkl rsbu dk ssor, d dk prlu mlkuk pu sluy, k p sblky k k vr muuk ssor, mk pu sluy dlh mu ksbl l r-ry. Pu ksm s l r-r dp dlkuk d muk u- (sowro 995: 8): Adpu hp u T sb brku :. Mhu l σ 2. Mhu l T T hu = =.5 = Hsl Smuls Kr Pol Oprs Wduk : - Produks Er Lsrk - Kdl Sls Gmbr 9. Drm Alr Sud Sumbr : Hsl Als Sud D Ekss RM.3 3. Mcr l T dr bl Uuk α = 5% pd kdu ss dm muk kolom.975, dm dr bbs = = = 42 mk dr bl dsrbus dprolh l T bl = Ksmpul Hposs

7 Abl, dkk., Opms Pol Oprs Wduk Sum Muk Modl Pmrorm Lr Kbur (Fuzzy Lr Prorm) Olh kr l T hu < T bl mk kdu klompok d brsl dr populs y sm. Apbl dr hsl u F d u T hsly dk mmusk dlkuk u hposs ly spr u Z mu pbl hsly cukup mmusk mk hy kdu u y k dpruk. Mk d y lh du dp dpruk kr sbl scr vr mupu rry u ssor. 2. Opms Prorm Lr Kbur Thp opms prorm lr kbur (plk) d mylsk rlbh dhulu opms prorm lr yu :. Muk Fus Tuu yu mmksmumk ol r shu Mksmumk : Z = E = E+E2+E3+E4+..+E2 2. Muk Fus Bs : - Sm S Smk + S 25 S Rm R Rmk + R 25 R I = R dlm shu - E dm : E = Er lsrk prhu (kwh) = 9.8 x E x R x Hf x N E. = Efss urb ror, bsry.79 R = Rls k urb (m 3 /d) Hf. = T uh fkf (m) TWL = Muk r blk (Tl.wr lvl), l. 79 m HL = Khl (Hd.Loss), bsry 2.85 m = Wku (hour/m) = Er bul N E, E2, E3,E S = Tmpu bul (m 3 ) Sm = Tmp...mmum.(m 3 ) Smk = Tmp.mksmum (m 3 ) S = Prubh.mpu (m 3 ) R Rm Rmk. R I = Ouflow..urb... (m 3 /d) = Rls mmum k urb yu 25 m 3 /d = Rls.mksmum k urb yu 46.9 m 3 /d = Prubh.ouflow (m 3 /d) = Db flow (m 3 /d) 3. Mylsk prorm lr d mmksmumk fus dr uu (Z) muk prorm lr modl Rs (Rsp, 2: 2) d fsls solvr pd xcl. Uuk kods = (λ =) d = (λ=), dm : - Kods = (λ =) mrupk kods opms prorm lr sbry d ddk sb bs bwh (Z Lowr = Z L ) b prorm lr kbur. - Kods = (λ =) mrupk kods opms prorm lr d olrs rvl u d k l prorm lr y fus bsy dlurk (lud) d ddk sb bs s (Z Upr = Z U ) b PLK. dm : λ. = dr.kpus/dr.ko hmpu fuzzy. = rvl brrk dr k 3. Hu l kofs kdl (Po), yu hsl pur dr Z pd s = d Z pd s =. Po = Z U - Z L 4. Gmbr fus ko p p prsm y duk olh Modl Prorm Lr Kbur. 5. Mmbu prsm bru brdsrk po 4 d mcr l λ-cu dp dhu sb λ =. 6. Mylsk prsm uuk mmprolh l λ d Z. 7. Mmsuk l Z k dlm opms uuk mmprolh r prbul. Cooh hsl prhu opms wduk Sum-Lhor Thu 22/23 sb brku :

8 2 Jurl Tkk Pr, Volum 6, Nomor, M 25, hlm Tbl. Opms D Prorm Lr Thu 22/23 Kdl Hsl Opms m 3 /d 6 m 3 m 3 /d 6 m 3 m 3 /d 6 m 3 m m m 3 /d 6 m 3 6 KwH Qmx S Mx Q m Sm Qbuuh Sbuuh El.Mx El.M Eff. Orr Ou Op E. Op S = S - + I - O SO = S - S mx Grv. Bs I S I - O SO TWL 79 HL 3 Bwh m 3 /d m 3 /d m 3 /d m 3 /d 6 m 3 m m 3 /d m m 3 /d 6 6 KwH KwH Bul Iflow S S SO S. Wdk Elv. Qbuuh H O Op H. Op E. Op [] [2] [3] [4] [5] [6] [7] [8] [9] [] [] [2] Ok 25 Nop Ds J Pb Mr Apr M Ju Jul A Sp Ok Jlh Rr Sumbr : Prhu Tbl 2. Opms Lu Bs As Thu 22/23 Kdl Hsl Opms m 3 /d 6 m 3 m 3 /d 6 m 3 m 3 /d 6 m 3 m m m 3 /d 6 m 3 6 KwH Qmx S Mx Q m Sm Qbuuh Sbuuh El.Mx El.M Eff. Orr Ou Op E. Op S = S - + I - O SO = S - S mx Grv. Bs I S I - O SO TWL 79 HL 3 As m 3 /d m 3 /d m 3 /d m 3 /d 6 m 3 m m 3 /d m m 3 /d 6 KwH KwH Bul Iflow S S SO S. Wdk Elv. Qbuuh H O Op H. Op E. Op [] [2] [3] [4] [5] [6] [7] [8] [9] [] [] [2] Ok 25 Nop Ds J Pb Mr Apr M Ju Jul A Sp Ok Jlh Rr Sumbr : Prhu

9 Abl, dkk., Opms Pol Oprs Wduk Sum Muk Modl Pmrorm Lr Kbur 3 (Fuzzy Lr Prorm) Hsl opms d muk prorm lr mhslk r lsrk sbsr Gwh prhu mrupk bs bwh. Bs bwh mrupk prorm lr kr uduk pd ur prorm lr. Opms lu mhslk r lsrk sbsr Gwh prhu mrupk bs s. Bs s dsums buk prorm lr kr mlr ur u dlurk (lud) bsy dr ur prorm lr rsbu. Dr hsl opms prorm lr bs bwh dm = (λ =), d lu opms bs s dm = (λ =) mk dmbrk fus-fus ko dr prsm prorm lr kbur (plk) spr mbr smp d mbr 2 dbwh. D r K o µ = [B.] E = E + E2 + +E2 P =.67 Dom kwh ZLowr =ZL ZUppr =ZU Gmbr. Fus Tuu PLK Sumbr : Hsl Prhu D r K o µ = [B.] P = (E) (E) Gmbr. Fus Bs Bwh Sumbr : Hsl Prhu Dom m 3 /d 6 kwh D r K o µ2 = [B2.] P2 = Dom m 3 /d 2. (E) (E) 6 kwh Gmbr 2. Fus Bs As Sumbr : Hsl Prhu Dr mbr d mbr 2 dp dlh bhw, smk bsr l dom, k mmlk l dr ko y cdru smk kcl. Sh uuk mcr l λcu dp dhu sb λ = -, d : b + p = rus k bs k - D dmk k dprolh buk prsm lr bru u prsm lr kbur sb brku (Kusumdw, 22: 222). Mksmlk : λ d bs : - λ (Z U - Z L ) c.x - Z L - λ p + Ʃ. b + p ( ɛ N m ) - λ, Prumus : # λ ( ) E # λ ( ) + E # λ ( ) + E # λ, E Dsdrhk : #. 67 λ 2E # λ + E # λ + E # λ, E Klk - prs. () r ly posf # λ + 2E = # λ + E = # λ + E = # λ, E Prsm prsm ds dslsk d bu prk luk Mrx Lborory (Mlb) R22 y mrupk sofwr y brbssk fus fus mrks brku.

10 DEBIT INFLOW (M 3 /DET) 4 Jurl Tkk Pr, Volum 6, Nomor, M 25, hlm Gmbr 5. Prbd Produks Rls Sumbr : Hsl Prhu Gmbr 3. Opms Mlb R22 Sumbr : Implms prorm Hsl dr pyls Mlb dlh l λ (dr kpus) sbsr.66 d Z sbsr GWh (rr r prbul prorm lr kbur). Nl Z dklk 2 bul dprolh ol r shu opms prorm lr kbur sbsr GWh. Uuk mdpk r rlss p p bul, ol l Z shu dmsuk sb l cosr d opms solvr. Hsl rkpuls opms slm hu dbdk kss dsk dlm mbr 4 d 5 brku : Dr hsl opms dprolh ol produks r lsrk d rls modl prorm lr kbur lbh bk dr kss. 3. Smuls Pol Oprs Wduk Smuls dlkuk brdsrk Rul Curv hsl opms Modl Rs, dcob-cob lps y mksml d mmprhk pol y dpruk. Smuls muk d y lkp yu hu 29 s/d 2. Dlkuk prbd r pol oprs kss d pol oprs sud brup rfk yu :. Prbd db flow 2. Prbd lvs muk r 3. Prbd volum mpu 4. Prbd db ouflow 5. Prbd hsl oprs wduk d pol oprs rc Db Iflow Wduk Sum Thu Ekss 2 Ekss 2 Ekss 29 S 2 S 2 S Gmbr 4. Prbd Produks Lsrk Sumbr : Hsl Prhu BULAN Gmbr 6. Prbd Db Iflow Sumbr : Hsl Prhu

11 DEBIT OUTFLOW (M 3 /DET) VOLUME ( 6 M 3 ) ELEVASI MAW (M) Produks Lsrk (GWh) Abl, dkk., Opms Pol Oprs Wduk Sum Muk Modl Pmrorm Lr Kbur 5 (Fuzzy Lr Prorm) Elvs Muk Ar Wduk Sum Thu Rc Smuls Ekss 2 Ekss 2 Ekss 29 S 2 S 2 S BULAN Gmb Gmbr 7. Prbd Elvs MAW Sumbr : Hsl Prhu Thu Gmbr 2. Prbd Hsl Oprs Wduk d Pol Oprs Rc Sumbr : Hsl Prhu Volum Wduk Sum Thu Ekss 2 Ekss 2 Ekss 29 S 2 S 2 S BULAN Gmbr 8. Prbd Volum Wduk Sumbr : Hsl Prhu Db Ouflow Wduk Sum Thu 29-2 BULAN 29 Ekss 2 Ekss 2 Ekss 29 S 2 S 2 S Gmbr 9. Prbd Db Ouflow Sumbr : Hsl Prhu Tbl 3. Bs As Rul Curv Bru No Bul Elvs (m) Volum (u m 3 ) Jur Pbrur Mr Aprl M Ju Jul Ausus Spmbr Okobr Nopmbr Dsmbr Sumbr : Prhu Tbl 4. Bs Bwh Rul Curv No Bul Elvs Volum (m) (u m 3 ) Jur Pbrur Mr Aprl M Ju Jul Ausus Spmbr Okobr Nopmbr

12 6 Jurl Tkk Pr, Volum 6, Nomor, M 25, hlm Dsmbr Sumbr : Prhu Gmbr 2. Prbd Rul Curv Bru d Ekss Sumbr : Hsl Prhu D. KESIMPULAN DAN SARAN. Ksmpul Brdsrk hsl sud y lh dlkuk, mk dp dmbl ksmpul sb brku :. Tol produks r mksml hsl opms Prorm Lr Kbur dlh 5,66.66 u kwh u k 27.9 % dr produks kss sbsr 4,47.95 u kwh d lbh.9% dr produks prorm lr sbsr 5,6.59 u kwh. 2. Prorm lr kbur mmpuy ol lps y sm d prorm lr brr lbh fs kr mhslk r y lbh bsr. Efss PLK m3/kwh, PL m3/kwh d Ekss 29.3 m3/kwh 3. Hsl smuls slm 3 hu muk rul curv bru mmlk kr y lbh bk dbdk kods kss kr mhslk r y lbh bsr yu,57.4 u kwh u k 9.4 % dr produks kss sbsr,39.9 u kwh d kdl y sm yu %. Sh dp dsmpulk bhw kurv pur muk r y bru dp duk. 2. Sr. Prorm Lr Kbur (PLK) y duk mrupk bu Prorm Lr d Lok Kbur (Fuzzy Loc) khusus m kkbur (fuzzy) pd sumbr dy d uu ru (crsp) u ss sblh k prsm (Rh Hd Sd/RHS) d hsl y cukup mmusk. Prlu dlkuk pl lbh lu uuk vrs vrs prorm lr kbur spr : sumbrdy kbur d fus uu kbur, kofs sumbr dy kbur, kofs fus uu kbur mupu kombs kmpy. 2. Modl Prorm Lr Kbur dp drpk uuk Pol Oprs Wduk. Nmu pu hrus mmhm prorm lr d lok kbur sh kur prks dbdk modl-modl ul. 3. Pol Oprs Wduk y dlkuk olh Prum Js Tr I dp dkk l. Pk brup, mkk kkur prml d, prluy pu kk pmodl y scr kspls mmpu mrprssk kd poprs ssuuhy. DAFTAR PUSTAKA. Hryd, 2. Sud Als Prp Lok Fuzzy (fuzzy loc) Dlm Prc Pol Oprs Wduk Sum. Skrps Tdk Dpublksk. Ml : Jurus Tkk Pr Fkuls Tkk Uvrss Brwy. 2. Kusumdw, Sr. 22. Als d Ds Ssm Fuzzy Muk Tool Box Mlb. Yoykr : Grh Ilmu. 3. Loucks, D.P., d Bk, E.V. 25. Wr Rsourcs Sysms Pl d Mm. Tur : As Ar Grfch. 4. Mys, L.W Wr Rsourcs Hdbook. USA : McGrw-Hll, Ic. 5. Rsp. 2. Opms Er PLTA d Pur Wduk. Mklh pd Smr Nsol Prorm Msr d Dokor Fkuls Tkk UB (SN-PMD FTUB) K-. Ml : Jurus Tkk Pr Fkuls Tkk Uvrss Brwy.

13 Abl, dkk., Opms Pol Oprs Wduk Sum Muk Modl Pmrorm Lr Kbur 7 (Fuzzy Lr Prorm) 6. S, Z. 2. Fuzzy Loc d Hydrolocl Modl. USA : Tylor d Frcs Group, LLC. 7. Soopo, W Pruh Sdms Wduk Krks Trhdp Produks Lsrky. Skrps Tdk Dpublksk. Ml : Jurus Tkk Pr Fkuls Tkk Uvrss Brwy. 8. Sowro Hdrolo Aplks Mod Ssk Uuk ls D Jld d 2, Bdu : NOVA. 9. hp:// Tl 4 Dsmbr 23, Pukul 2.5 hp:// _dlp&v=-zuf3uk6-ui Tl 8 Ju 24, Pukul 2.