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1 HIERARCHICAL MULTIPLE CRITERIA OPTIMIZATION OF MAINTENANCE ACTIVITIES ON POWER DISTRIBUTION NETWORKS Problm Rprsaion EPDS comprising: Subsaions, primary nworks, scondary, nworks; Fdrs (cabls, lins, pols, auxiliary srucurs); Chrisiano Lyra Clso Cavllucci Fábio Luiz Usbri José Fdrico Vizcaino Gonzálz Opimizaion of Mainanc Aciviis - Modls, Mhods and Applicaions - Gohburg, 0 Dcmbr 2009 Swiching quipms; Procion quipams; Corrcion quipms (volag rgulaors, capacior banks); Tranformrs. Summary Problm Rprsaion Moivaion Problm Rprsaion Mahmaical Formulaion for On Objciv Main Daa and Paramrs Cas Sudis wih a Rfrc Nwork Mulipl Criria Formulaion Hirarchical Mulipl Criria Discussion EPDS dividd in blocks conncd by procion quipms Subsaion Cli Procion Dvic Subsaion Subsaion Scion Moivaion Provid h bs possibli policis for mainanc aciviis a ach local nwork of a larg disribuion company; Allow o dfin h bs allocaion of consraind mainanc budgs; Avoid fins associad o inadqua rliabiliy indics for a group of nworks; Allow o ngocia and jusify mainanc budgs a h various dcision lvls of a disribuion company (including h board). Problm Rprsaion Comms: A cusomr conncd o any load poin rquirs all compons bw himslf and h subsaion o b opraing; Failurs can occur du o aging of compons or du o xrnal acions (r branchs ouching h nwork, for insanc); Corrciv mainanc is prformd afr h failur; Prviv mainanc is prformd bfor h failur (o avoid i).

2 Mahmaical Formulaion for On Objciv Failur ra modl: Mahmaical Formulaion for On Objciv Minimiz prs valu of coss s.. rliabiliy consrains: Rprss h aging of nwork compons and hir chang of sa by h avrag failur ra of h compons; MIN HP i n p x c Failur ra muliplirs opra on h avrag failur ra of nwork compons o modl diffr mainanc acions. s.. max Mahmaical Formulaion for On Objciv Failur ra modl Th failur ra of a compon in priod, afr rciving a mainanc procdur i is compud as follows: Main Daa and Paramrs, failur ra for compon in im ; p, cos of prviv mainanc acions of lvl n on compons ; i c, cos of corrciv mainanc on compons ; Daild informaion abou h nwork opology and locaion of compons. Mahmaical Formulaion for On Objciv Th rliabiliy of h nwork is rprsd by h sysm avrag inrrupion frquc indx - Whr, s N TOTAL s N s - avrag failur ra for scion s, Ns - numbr of cusomrs in scion s, NTOTAL - oal numbr of cusumrs in h nwork. s Rfrc Nwork A small nwork adapd from h liraur (Siihumwa al., 2004), o allow sciiviy analysis wih rspc o iniial condiions of compons and diffr mainanc acions. 7 scions (3 primary, 4 scundary) and 22 nwork compons. Planning horizon of 5 yars.

3 Rfrc Nwork Primary Nwork Scondary Nwork SECTION 4 Compons Transformr Muli-criria Opimizaion 00 clis SECTION SECTION 3 SECTION 6 Dfiniion: Swichs Poss Infrasrucur 5000 clis SECTION 2 Transformr 00 clis Volag Rgulaor Poss Infrasrucur 3700 clis SECTION 5 Transformr 00 clis Poss Infrasrucur 300 clis SECTION 7 Transformr 00 clis procss of simulanously opimizing wo or mor conflicing objcivs subjc o crain consrains. Characrisics: Th goal of muli-criria opimizaion problm is sarching for soluions in which ach objciv has b opimizd o h x ha if w ry o opimiz i any furhr, h h ohr objciv(s) will suffr as a rsul. Yar Nw nwork 0,55 BLOCO SECTION 4 4 Mainanc Lvls No Mainanc Mulipl Criria Formulaion 0,26 Transformr Inspcion 0 0, 0,2 0,3 0,4 0,5 0,6 Prs Maximum 00 clis clis Mainanc BLOCO SECTION Chav Swichs Rligadora s Poss Infrasrucur BLOCO SECTION 3 3 Rgulador Volag Rgulaor d Tsão s Poss Infrasrucur BLOCO SECTION 6 6 s Poss Infrasrucur Considrs wo objciv funcions: Nwork rliabiliy (maximiz) and Mainanc coss (minimiz) clis clis 3700 clis clis 300 clis clis BLOCO SECTION 2 2 Transformr BLOCO SECTION 5 5 Transformr BLOCO SECTION 7 7 Transformr Conflicing objcivs: w mus sarch nondominad soluions (ffici soluions) and associad paro fronir ( rad-off curvs). 00 clis clis 00 clis clis 00 clis clis Prviv Mainanc cos = R$.025,00 Corrciv Mainanc Cos= R$3.475,00 Yar 5 BLOCO SECTION Chav Swichs Rligadora s Poss Infrasrucur 5000 clis clis 0,55 0,55 0 0, 0,2 0,3 0,4 0,5 0,6 Prs Maximum BLOCO SECTION 2 2 Transformr 00 clis clis BLOCO SECTION 3 3 Rgulador Volag Rgulaor d Tsão s Poss Infrasrucur 3700 clis clis BLOCO SECTION 4 4 Transformr 00 clis clis BLOCO SECTION 5 5 Transformr 00 clis clis BLOCO SECTION 6 6 s Poss Infrasrucur 300 clis clis Mainanc Lvls No Mainanc Inspcion Mainanc BLOCO SECTION 7 7 Transformr 00 clis clis Prviv Mainanc Cos = R$5.680,00 Corrciv Mainanc Cos = R$6.204,00 Solv... Mulipl Criria Formulaion MIN MIN s.. HP n max i max p x c

4 Mulipl Criria Formulaion Hirarchical Mulipl Criria Soluion: Diffr mainanc plans for a nwork Elcrical group Nworks Mainanc Plans wih quival qualiy, i.., ffici soluions Manução Inspção Manução Inspção s s s s s s s s s Cos Manução Inspção Mulipl Criria Formulaion Hirarchical Mulipl Criria Solvr: Consrain Mhod powrd by a Hybrid Gic Algorihm (Paulo Ris, 2007) Elcronic copy availabl (in porugus): hp://libdigi.unicamp.br/docum/?cod= Two main propris: Effici soluions a h uppr lvl ar composd of ffici soluions a h lowr lvls; No all combinaions of ffici soluions a h lowr lvls ar ffici soluions a h uppr lvls. Hirarchical Mulipl Criria Rgion A Cos A Rgion B FEC Rgion C Cos B Mainanc plans for a group of nworks Toal Cos Cos C BLOCO 0 Inpu: 5200 clis Nhuma Manução BLOCO 2 BLOCO clis BLOCO 3 BLOCO 4 BLOCO clis BLOCO 5 BLOCO 6 BLOCO clis BLOCO BLOCO 2 BLOCO clis BLOCO 3 BLOCO clis Nhuma Manução BLOCO 5 BLOCO 6 BLOCO clis BLOCO BLOCO 2 BLOCO clis BLOCO 3 BLOCO 4 BLOCO clis Nhuma Manução Hirarchical Mulipl Criria n paro fronirs (on for ach nwork); ach paro fronir populad wih p nondominad soluions. BLOCO 6

5 Hirarchical Mulipl Criria Hirarchical Mulipl Criria Composiions: calcula all possibl soluions and filr p nondominad composiions - p n calculaions; x., p=20 and n=50, p n = ; Compound h paro fronir wo-by-wo prsrving a ach sag p non-dominad soluions (n-)p 2 calculaions. Excuion ims in a Pium Quad- Cor 3.0 GHz, 4 Gb RAM. Nwork A 3m40s; Nwork B 5m6s; Nwork C 29m33s; Composiion of paro fronir 2s. Composiion of paro fronirs Curv Curv 4 Agrgaion of Curvs 2 and 3 Discussion Non-Dominad Non-Dominad Dominad Curv 2 Curv 3 Prooyp wll rcivd by ginrs and uppr lvl dcision makrs (~ 3k lins of cod in Java); Non-Dominad Non-Dominad Can provid informaion for ngoiaion of rliabiliy indics wih h rgulaory agcy (Anl). Hirarchical Mulipl Criria Insanc S of hr ral powr disribuions nworks in Brazil (48247 cusomrs, 634 quipms): Nwork A (453 cusomrs, 765 quipms); Nwork B (8268 cusomrs, 206 quipms); Nwork C (25466 cusomrs, 3488 quipms). Discussion Is h mhodology rady? No. Wha dos i nd? Polish h modl wih inpu from fild ss; Implm procdurs (br, a culur) ddicad o nwork mainanc daa acquisiion for ginring purposs (no only for accouning); Dvlop spcific daa banks o kp rack of quipm sas and mainanc acions; Dvlop spcific inraciv usr inrfacs.

6 Acknowldgm CPFL PAULISTA CPFL PIRATININGA

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