A FORMALISM FOR INTEGRATED PRODUCTION AND SITE UTILITY SYSTEM SCHEDULING

Transcription

1 8 h Inenaional Confeence of Modeling and Simulaion - Evaluaion and opimizaion of innovaive ucion sysems of goods and sevices A FORMALISM FOR INEGRAED PRODUCION AND SIE UILIY SYSEM SCHEDULING R. HERY M. AGHA G. HEREUX J.M. LE LANN A. HAI Univesié de oulouse LGC INP-ENSIACE Allée Emile Monso P oulouse Cedex Fance Raphaele.hey@ensiace.f ASRAC: he issue of enegy has emeged as one of he geaes challenges facing he mankind. In he indusial pespecive he developmen of sie uiliy sysem (geneally CHP sysems fo he geneaion and managemen of uiliies povide a gea poenial souce fo enegy savings. Howeve a mase/slave elaionship usually govens his kind of sysem; he managemen of such ype of indusial unis is caied ou in hee sequenial seps: scheduling of he ucion plan esimaion of he uiliy needs and finally scheduling of he CHP based uiliy sysem ae hee asks pefomed. o impove he decision-making pocess his conibuion poposes an inegaed appoach which caies ou simulaneous and isen scheduling of bach ucion plan and sie uiliy sysem. he poposed mehodology elies on discee ime modelling and uses Mixed Inege Linea Pogamg (MILP. Moeove o pemi an efficien and geneic fomulaion of vaious kinds of indusial poblems an exension of he exising famewok RN is developed: he ERN (Exended ask Newok (ERN. he esuls show ha he inegaed appoach leads o bee synchonizaion beween ucion plan and sie uiliy sysem. Hence he inegaed appoach leads o significan educion in enegy coss and decease in hamful gas emissions. KEYWORDS: Sho-em scheduling Uiliy sysem Exended esouce ask Newok (ERN MILP INRODUCION Indusial seco accouns fo one hid of global enegy umpion. A common feaue of indusial pocesses is eliance on fossil fuels as he pimay souce of enegy and a lage pa of he enegy umpion is spen on ucion of uiliies. Uiliy efes o eleciciy seam (a vaious pessue levels ho/cold wae and ho ai. his eliance on fossil fuels as he pimay souce of enegy has huge negaive impac on he envionmen. In his backgound hee is a concenaed effo in scienific wold o find alenaive souces of enegy. oday emphasis is on enewable enegy like wind sola hydogen ec. Howeve even by he mos opimisic assessmens all hese alenaives ae long em soluions. he pojecions of Enegy Infomaion Adisaion (EIA show ha in immediae fuue fossil fuels will emain as pimay souces of enegy. hen along wih finding alenaive enegy souces effos mus be made o seek modus opeandi ha will imize he damage caused by he fossil fuels. Iniiaives like cleane ucion (Kjaeheim 005 and zeo-emissions (Kueh 006 ae impoan appoaches in his egad. Howeve a sho em soluion which has been idenified by IPCC iss in impoving enegy efficiency of indusial pocesses (IPCC 996. his can be achieved by wo means : advancemens in enegy geneaion echnology bu also use of mehodologies such as pocess inegaion. In ha conex his aicle focuses on he developmen of scheduling and ucion planning models dedicaed o he impovemen of he enegy efficiency of indusial pocesses. LIERAURE REVIEW. Scheduling of bach pocesses and enegy managemen he scheduling aspec of he ucion plan has been subjec of exensive eseach. Howeve few scheduling models have been poposed in which he hea inegaion o he managemen of uiliies is explicily aken ino accoun. Egli and Rippin (986 discussed he impoance of uiliy managemen a a bach indusial uni. hey emphasized he need of incopoaing uiliy equiemens while pefog he scheduling of he ucion plan. Kondili e al. (988 developed a mahemaical model o addess he issue of manufacuing plan ucion planning wih he objecive of educing opeaional coss. he cos of enegy was assumed o vay duing he day and enegy umpion was dependen on he naue of he uc manufacued and he equipmen used. he impac of enegy cos was caeed by posiioning enegy cos in he objecive funcion. his iniial model was fuhe enhanced and Kondili e al. (993

2 developed he fis geneic sho-em bach scheduling algoihm. he limied availabiliy of he uiliies was modeled as a scheduling esouce ain. Howeve unlike he esouces classically ideed in he scheduling poblems (pocessing equipmen o manpowe uiliies have special chaaceisics which mus be aken ino accoun. Uiliies ae a moe vesaile esouce which can exis in vaious foms (diffeen pessue seam eleciciy ho wae. Uiliies ae also a esouce which is difficul o soe in is ulimae fom. Some ecen sudies have aken ino ideaion hese peculiaiies of uiliies. Hai e al. (007 pesened an appoach designed o imize he enegy cos of a foundy subjec o he specific povisions elaing o he powe picing and make based saegies fo load shedding. ehdani e al. (007 developed a coninuous-ime scheduling model which included he ains elaed o he ucion availabiliy and umpion of diffeen ypes of uiliies (wae cooling eleciciy and seam. Howeve in all hese appoaches he focus is pimaily on he ucion plan; sie uiliy sysem is eihe oally ignoed o modeled in an aggegaed manne. Some ecen woks have ied o addess his imbalance. Moia e al. (005 developed a dynamic model of sal cysallizaion ucion plan and associaed cogeneaion uni. Finally Zhang and Hua (005 esablished a MILP model fo deeing opimal opeaing poins of an oil efiney ucion pocess coupled wih a cogeneaion uni. Howeve hese models ae specific o he ideed ucion plans and lack he geneic naue which is necessay fo a moe geneal scheduling model.. Using Mixed Inege Linea Pogamg (MILP Seveal excellen eviews in he conex of bach pocess scheduling poblem can be found in Méndez e al. (006 o Floudas and Lin (00. hese eviews clealy poin ou ha duing he las few decades mixed inege linea pogamg (MILP has been mos widely used fo solving he bach pocess scheduling poblem. A vey impoan decision in using MILP is whehe o use discee-ime appoach o coninuous ime appoach. Méndez e al. (006 povided a compaison of boh appoaches. Fis of all he usefulness and compuaional efficiency of coninuous ime appoach eihe using global ime poins o uni specific evens songly depends upon he numbe of ime evens. If a soluion equies a leas N even poins use of fewe poins will esul in subopimal soluions while use of geae poins will esul in significan and unnecessay compuaional effo. Since his numbe is a pioi unknown an ieaive pocess is used wheeas he numbe of even poins is inceased by unil hee is no moe impovemen in objecive funcion. his means ha scheduling poblem needs o be solved a numbe of imes which invaiably leads o long compuaional imes. hen as compaed o hei coninuous ime counepas he discee-ime appoaches usually esul in lage poblem size i.e. geae numbe coninuous and binay vaiables. Howeve hei simple model sucue ends o significanly educe he compuaional ime equiemens when a easonable numbe of inevals is posulaed (aound 00 inevals usually appea as a acable numbe. On he ohe hand he complex naue of he coninuous ime appoaches makes hem useful fo poblems ha can be solved wih educed numbe of even poins (5 poins may be he cuen uppe bound. Finally discee ime models may geneae bee and fase soluions han coninuous ones wheneve he ime disceizaion is a good appoximaion o he eal daa. ased on he above analysis his sudy has adoped discee-ime appoach fo he pupose of poblem fomulaion. In he following secion a deailed analysis of he exising famewoks is caied ou keeping in d he objecive of inegaing he scheduling of sie uiliy sysem wih ha of ucion plan..3 Exising famewoks fo bach pocess scheduling poblems he aim of a geneal scheduling famewok is wo fold: - - fis develop a gaphical pesenaion of he ucion pocess (ecipe and plan opology - hen based on his gaphical pesenaion build up a geneic mahemaical model which can be used o deee he ucion scheduling. Sae ask Newok (SN poposed by Kondili e al. (993 was a majo sep owads developing a univesal sho-em scheduling model fo a bach plan. SN poposed a genealized famewok fo pesening he ucion pocess which was hen used o develop a mahemaical fomulaion applicable o all ypes of bach plans. Panelides (99 poposed ask Newok (RN which is anohe genealized famewok fo pesening he ucion pocess. RN conains moe infomaion abou pocessing equipmen and hei conneciviy an aspec which is no explicily shown in SN. 3 ERN FRAMEWORK 3. Specific feaue of bach indusial unis ased upon he majo concep of SN and RN famewoks he main pupose of he Exended ask Newok (ERN famewok developed in his conibuion is pecisely o enable handling of uiliies in bach ucion scheduling. his secion biefly highlighs he specific feaues of bach indusial uni composed of a bach ucion plan and a sie uiliy sysem Quaniy of available uiliies In he RN famewok uiliies ae assumed o be supplied by independen exenal souces in limied and known quaniies. he geneal assumpion is ha he quaniies of available uiliies ae an. his is a vey esicive assumpion especially if he uiliies ae

3 uced by a sie uiliy sysem. In his case he uiliies ae geneaed in limied and vaiable quaniies. Unlike hei ucion uni counepas some asks in sie uiliy sysems do no uce maeial esouces in fixed a pioi known popoions of bachsize. Fo example seam exacion fom muli-sage ubine depends on he MP and LP seam demand of he ucion uni. he amoun of seam exacion a each ubine sage is vaiable and can ake any value in beween zeo and bounded uppe limi Heeogeneous ucion modes A ypical feaue of some oal pocessing sie is he heeogeneiy of ucion mode whee: Poducion plans ae composed of disconinuous uni opeaions. Sie uiliy sysems ae coninuous pocesses displaying fequen changes in opeaing condiions fom one ime peiod o anohe. Conside a pocess eacion illusaed on he RN pesened in figue. his eacion compleely conves maeial A ino maeial. he duaion of he pocess eacion is h and i can ake place eihe in eaco R (ask o eaco R (ask 3. he HP seam equiemen fo he pocess eacion is 0. ons/h pe kmol of maeial being pocessed. A boile in he sie uiliy sysem is employed (ask o fulfill he HP seam equiemen of he pocess eacion. he Gan cha and he chaaceisic pofiles of he ucion plan and sie uiliy sysem ae epesened in figue. RN epesenaion: Wae Fuel Poducion plan: Reaco Reaco oile 0 0 ime Sie Uiliy Sysem: oile 30 A HP seam 3 ime R 3 R HP seam kmol on/h 5 3 Poducion ecipe Reacion : A Pocess Equipmens: R & R Duaion of ask: h Uiliy demands of he eacion: 0. /h of HP seam fo pe kmol of maeial being pocessed ime ime Figue : Heeogeneiy of ucion modes A ask in ucion plan akes inpu fom feed maeial esouce(s caies ou he ansfomaion pocess houghou he ask duaion and finally delives he uc ino he oupu maeial esouce(s a end of ask. Fo example he eacion ask 3 in eaco sas pocessing 0 kg of maeial A a sa of ime peiod and uces 0 kg of maeial a end of ime peiod 3. heefoe he pocess opeaions of bach ucion plan ae disconinuous and he ypical physical measue is amoun of maeial. Howeve o pefom hese asks he pocessing equipmens equie a coninuous feed of a single o a subse of uiliies (e.g. simulaneous equiemen of seam and eleciciy. his uiliy demand is saisfied by asks in uiliy sysem ha ansfoms insananeously (i.e. wihou any ime delay he inpu uiliy esouces ino oupu uiliy esouces. Fo example o mee he HP seam demand of eaco R (3 /h and eaco R ( /h duing ime peiod 3 he boile (ask sas supply /h of HP seam sa of ime peiod 3 and coninues his supply ill end of ime peiod 3. Hence he pocess opeaions of he sie uiliy sysem ae coninuous (wih muliple opeaing poins and he ypical physical measue is uiliy flows. 3...Dualiy of wae deivaive esouces In an indusial uni he diffeen esouces can be classified ino wo caegoies: he disjuncive esouces and he cumulaive esouces (figue. he cumulaive esouces can hen fuhe be subdivided ino maeial esouces and uiliy esouces. Pocessing equipmens Disjuncive esouces Manpowe Fossil fuels Pimay uiliy esouces s Uiliy esouces Wae deivaive esouces Eleciciy Wae HP MP seam seam Cumulaive esouces LP seam Feeds Exhaus seam Figue : classificaion of esouces Maeial esouces Inemediae ucs Ho /cold wae Finished ucs A difficul poin in he new famewok would be he eamen of he wae deivaive esouces which can be eihe in fom of maeial esouces o uiliy esouces. Essenially all he wae deivaive esouces can be eaed as maeial esouces fo he pocessing asks execued in he sie uiliy sysem since hey cay ou phase ansfomaion fom one phase o anohe phase. heefoe he ambien wae (feed seam a diffeen pessue levels (inemediae ucs and exhaus seam (esidual uc all iue maeial esouces. Howeve he wae deivaive esouces also fulfill he uiliy equiemens of he pocessing asks pefomed in he ucion plan. Hence in his case he wae deivaive esouce acs as uiliy esouce. he pupose of ERN famewok pesened in he following secion is pecisely o inoduce new semanic elemens and o enich he noion of ask ha allows incopoaing he feaues highlighed hee ha is he nonunifom eamen of he esouces he heeogeneous ucion modes and he geneaion of uiliies in limied and vaiable quaniies.

4 3. Semanic elemens he semanic elemens of he ERN famewok and hei elevance ae demonsaed below. 3.. ERN ask nodes: noion of delivey ime he ask node epesens a pocessing opeaion ha umes and/o uces a specific se of esouces. he gaphical epesenaion of he ask node emains he same as used in he RN epesenaion. Howeve a new paamee defined as delivey ime is added o he adiional paamees capaciy hesholds and pocessing ime (figue 3. he delivey ime is a paamee which expesses he elapsed ime beween he aival of feed seam and he delivey of oupu seam. (V k V k p k dd k Figue 3: ERN ask nodes V k : imum bachsize V k : imum bachsize p k : pocessing ime dd k : delivey ime he noion of delivey ime is illusaed in figue. In ha case he pocessing ime and he delivey ime of he eaco ae equal o. In conas he boile ask conves wae ino HP seam by a coninuous pocess. he delivey ime is equal o 0 because he convesion is insananeous and HP seam is supplied houghou he ime peiod. Reaco 0 0 on/h 3 GANCha Flow of HP seam ime (h ime (h he maeial esouces ae aw maeial inemediae and finished ucs ha is umed o uced duing he pocessing opeaion. Uiliy esouce epesens boh wae deivaive esouce and pimay uiliy esouce. he wae deivaive esouces ae all he uiliies ha can be deived fom ambien wae (fo example seam a diffeen pessues ho wae cold wae ec.. he pimay uiliy esouces epesen non deivable uiliies (which can no be diven fom wae like fossil fuel eleciciy ec. he disjuncive esouce node (figue 5b epesens a esouce ha a a given ime can be used by a mos a single pocessing ask. he disjuncive esouces ae nomally pocessing equipmen and manpowe ( R0 C (a Cumulaive esouce node R0 : iniial amoun of esouce C : imum soage capaciy of esouce Figue 5: ERN esouce nodes 3..3 ERN Disjuncive esouce ac name (b Disjuncive esouce node he oiginal RN famewok used he same kind of ac o show ineacion beween he pocessing asks and he esouces. he ERN famewok adops he same pinciple by explicily defining disjuncive esouce ac ha shows he associaion of disjuncive esouce wih he pocessing ask(s. he disjuncive esouce ac gaphically demonsaes he ype and he numbe of diffeen pocessing asks pefomed by a esouce (figue 6. (V k V k p k dd k name (V k V k p k dd k 3 (V k3 V k3 p k3 dd k3 Figue 6: ERN disjuncive esouce ac 3.. ERN maeial flow ac oile 3 3 GANCha ime (h Figue : Noion of delivey ime in ERN famewok 3.. ERN esouce nodes he divesiy of esouce ha needs o be displayed in he ERN famewok makes he gaphical disincion beween cumulaive and disjuncive esouces all he moe necessay. In he ERN famewok he same cicle and ellipse epesenaion exising in RN famewok is adoped. he cumulaive esouce node epesens a esouce ha a a given ime can be shaed by muliple pocessing asks. he cumulaive esouce node can be used o epesen boh maeial and uiliy esouces (figue 5a. In addiion o he concep of adiional maeial fixed flow ac (figue 7a ha aleady exiss in he RN famewok he ERN famewok inoduces he concep of maeial fee flow ac. his ac shown in he figue 7 enables o epesen he opeaion of some asks ha do no uce maeial esouces in fixed and known popoions of bachsize in sie uiliy sysem (e.g. mulisage ubines. x (a Maeial fixed flow ac (b Maeial fee flow ac Figue 7: ERN maeial fixed and fee flow acs 3..5 Uiliy ac he dualiy of wae deivaive esouces ha has been highlighed in he secion 3.. leads o he necessiy of

5 defining a new kind of ac called uiliy ac. his ac enables o epesen he umpion o he ucion of uiliy esouces. In he case of uiliy umpion he paamee uf locaed above he ac pemis o epesen he fixed quaniy of esouce umed wheeas uv epesens vaiable popoion of esouce umed wih espec o he bachsize pefomed by he ask k (figue 8a. Fo example in he case of uiliy ucion he paamee uf and uv locaed above he ac would pemi o define he amoun of uiliy uced by ask k (figue 8b. ( R0 C uf k (V k V k p k dd k uv k uf k k uv (V k V k p k dd k (a Consumpion of esouce by ask k (b Poducion of esouce by ask k Figue 8: ERN uiliy ac ( R0 C he ERN famewok makes use of diffeen acs o claify when a esouce acs as maeial esouce and when i acs as uiliy esouce. his nuance can be explained by eideing he example ha was developed in secion 3... Since he basics of he ERN famewok have been inoduced i is now possible o epesen ERN diagam of he example unde ideaion. In his example he esouces A and wae ae maeial esouces and ae epesened using maeial flow acs. In he same vein he esouce fuel is a uiliy esouce epesened by uiliy esouce ac. In conas he esouce HP seam acs as maeial esouce fo he boile ask and uiliy ask fo eacos R & R. Fo his eason he HP seam is conneced o he boile ask by using a flow ac and o he uiliy ask using he uiliy ac Wae Fuel uf I fuel oile uv fuel A HP seam uf uv &3 HP &3 HP Figue 9: ERN epesenaion of he example developed in secion Resa pecedence ac R 3 R he pocessing equipmen can eihe be in acive sae (execuing a ask o in idle sae. In he fome famewoks i is assumed ha swiching fom he idle o acive sae is insananeous. Howeve in some pocessing equipmen his swiching pocedue equies ideable ime delay and also esuls in incuing addiional coss. A pefec example of such pocessing equipmen is he boile. oile opeaions ae no insananeous and once shudown hey equie a se-up sep o swich fom idle sae o acive sae. Duing his sep boile need o be fed wih fuel bu does no uce seam. o enable he epesenaion of hese peculia se up phase he ERN epesenaion inoduces a new ype of ac called esa pecedence ac (see figue 0. (V k V k p k dd k (V k V k p k dd k Figue 0: ERN esa pecedence ac he diecion of he aow head on he ac ses he ask pecedence. Fo example in he case of figue 0 ask k mus be peceded by esa ask k. 3.3 Mahemaical Model he main advanage of he ERN famewok is is geneic naue which allows developing diec coespondence beween he semanic elemens of he gaphical epesenaion and he mahemaical ains. Hence a complee scheduling model can be developed on he basis of he ERN epesenaion of he indusial uni. his secion invenoies he eniies se which lead o specific ains. 3. Allocaion ains: disjuncive esouce ac Each disjuncive esouce ac linking pocessing ask o he pocessing equipmen leads o he fomulaion of an allocaion ain (figue. (V V p k dd k Figue : Allocaion ains linked o mahemaical fomulaion using disjuncive acs Since he esouces in he ERN famewok ae no eaed in a unifom way he allocaion ains need o be imposed explicily. Equaion ( akes ino accoun full backwad aggegaion. A a given ime peiod a pocessing equipmen j can a mos iniiae one ask opeaion k. Hence i won be available o execue anohe ask fo he duaion of he ask (i.e. duing peiods = p k + ill = + p k. k ' p K j k 0 Wk ' j J.. ( - W k = if a ask k is launched a sa of peiod - W k = 0 ohewise. - p k defines he duaion of he ask k. 3.5 Capaciy ain he geneal epesenaion of a cumulaive esouce node has aleady been given in figue 5. he cumulaive e-

6 souce node displays he iniial amoun of esouce available and he imum soage capaciy of he esouce. his capaciy limiaion is epesened by equaion ( which saes ha he amoun of esouce soed in a esouce should neve exceed is imum soage capaciy. 0 R C R.. ( Whee R k is he amoun of esouce available duing ime ineval and C defines he imum soage capaciy of esouce. 3.6 Pocessing equipmen hough ask node he geneal epesenaion of a ask node is given in figue 3. Equaion (3 epesens he ucion capaciy ains of he pocessing equipmen which limis he amoun of bachsize k ha can be undeaken by a pocessing ask k a ime ineval. he bachsize is bounded by he imum and imum capaciies of he pocessing equipmen. Wk Vk k Wk Vk k K.. (3 k coesponds o he amoun of maeial being pocessed by ask k duing ime peiod Vk defines he imum capaciy of pocessing ask k and Vk defines he imum capaciy of pocessing ask k. 3.7 Cumulaive esouce mass balance Cumulaive esouce node in uiliy sysem can ac simulaneously as uiliy esouce and maeial esouce which is an impoan ideaion when applying mass balance aound esouce node. A esouce node in uiliy sysem no only povides he maeial esouces fo he phase ansfomaion pocess (acing as maeial esouce bu also fulfills he uiliy demands of he pocessing ask (acing as uiliy esouce. As illusaed in figue his esouce can eceive uiliies fom exenal souces as well. he mass balance aound esouce node is capued in he gaphical epesenaion by he use of diffeen acs cog ino and ou of he esouce node. O k O k3 O k UI k7 R ( R0 C I k I k5 he maeial fixed and fee flow acs epesen maeial flow o and fom esouce node (em O sk and I sk he uiliy acs epesen he uiliy exchanges beween cumulaive uiliy esouces cog fom o feeding pocessing asks (ems UO sk and UI sk. he sink and souce acs epesen he esouce puchased and sold o he exenal envionmen (em In s and Ou s Equaion ( epesens he genealized mass balance ha is univesally applicable fo all he cumulaive esouces R kk R UI k kk In O k dd k Ou I k kk kk UO R.. k dd k ( - I k is he quaniy of maeial o maeial flow ino ask k fom esouce a sa of peiod - O k is he quaniy of maeial o maeial flow fom ask k ino esouce a sa of peiod - UI k defines he uiliy flow going ino ask k fom esouce a duing ime peiod - UO k defines he uiliy flow going fom ask k ino esouce a duing ime peiod - In efes o he impo ino he esouce fom an exenal souce a ineval - Ou efes o he expo fom he esouce fom an exenal souce a ineval. he esouce mass balances ae compleed by following addiional ains: he iniial socks R0 ae supposed o be known. R 0 R0 R (5 ounds on he impos and expos of esouce ae given by equaions (6 and (7 Ou Ou Ou R (6 In In In R (7 In and In define he imum and imum impo ino he esouce fom an exenal souce a ineval he demands of each finished uc esouce a ime peiod duing he ime hoizon is supposed o be known. hese demands ae me by using equaions (8 In Ou Ou Ou D R (8 UO k6 Figue : Mass balance aound a esouce node Ou and Ou define he imum and imum expo fom he esouce fom an exenal souce a ineval and D efes o he demand of esouce (finished uc a ime.

7 3.8 ask mass balance In he ERN famewok some ask can uce o ume esouces in a pioi unknown popoions of bachsize. hese popoions ae calculaed hough he esoluion of he opimizaion poblem. Consequenly conay o he RN famewok hese popoions need o be ained by means of mass balance equaions wien fo each ask node. he mass balance aound he ask node is displayed in he gaphical epesenaion by using he fixed and fee flow acs eneing and leaving he ask node (figue 3. R ( C R0 R ( C R0 (V k V k p k dd k R3 ( R0 3 C 3 R ( R0 C R5 ( R0 5 C 5 Figue 3: Mass balances aound ask node Equaions (9 and (0 simply indicaes ha he bachsize of a ask k a ime ineval is equal o he amoun of maeial I sk eneing fom he inpu maeial esouces as well as he amoun of maeial O sk leaving owads he oupu maeial esouces. I k K.. (9 k k k R k O k R k k K.. (0 Fuhemoe he amoun of inpu and oupu flows ino and ou of a ask k needs o be ained. Saing wih he oupus fom he ask hey ae ained by equaions ( and (3. k K R O k k.. ( k k O k k K R.. (3 k k k k is he popoion of esouce uced by ask k wih espec o bachsize pocessed and ks is he popoion paamee fo esouce uced by maeial fee flow ac. In he same vein he following equaions ake ino accoun he maeial leaving he ask k. I k k k k k K Rk.. ( I k k k k K Rk.. (5 k is he popoion of esouce umed by ask k wih espec o bachsize pocessed and k is he popoion paamee fo esouce umed by fee flow ac. 3.9 Poducion/umpion of uiliy esouces Consumpion of uiliy esouce he umpion of he uiliy esouce is displayed in he gaphical epesenaion by a uiliy ac eneing he ask node (figue. ( R0 C uf k uv k (V k V k p k dd k Figue : Uiliy umed by pocessing ask he amoun of uiliy esouce umed by diffeen pocessing asks is quanified by equaion (6. he amoun of esouce UI sk umed by a ask k fom a esouce compises of a an em ufi k and a vaiable em uvi k (is dependen on he bachsize. UI k uf k k W k uv R k K.. k k pk (6 uf is he fixed quaniy of esouce umed by ask k and uv is he vaiable popoion of esouce umed by ask k wih espec o he bachsize Poducion of uiliy esouce he umpion of uiliy esouce is displayed in he gaphical epesenaion by a uiliy ac leaving he ask node (figue 5. (V k V k p k dd k uf k uv k ( R0 C Figue 5: Uiliy uced by pocessing ask As a equence of he execuing pocessing ask ceain pimay uiliies ae also geneaed. he amoun of uiliy esouce (wae diven uiliy esouce and pimay uiliy esouce UO sk uced by a ask k fom a esouce s compises of a an ufo ks and a vaiable em uvo ks (dependen on he bachsize. UO k uf k W k uvo R k K.. k k pk (7 uv is he vaiable popoion of esouce uced by ask k wih espec o he bachsize and fixed quaniy of esouce uced by ask k.. APPLICAION.. Poblem Saemen uf is a Enegy inensive chemical indusial unis usually use onsie uiliy sysem o mee hei uiliy equiemens. Howeve in hese indusial unis emphasis is placed on

8 WES 600 SE A ALM WES 600 SE A ALM WES 600 SE A ALM WES 600 SE A ALM WES 600 SE A ALM manufacuing (ucion schedule while he aspec of opeaional planning of uiliy sysem is lagely ignoed. In his secion he ERN famewok is exploied o demonsae he advanages of an inegaed appoach ha simulaneously undeakes sho-em scheduling of a mulipupose bach plan and opeaional planning of uiliy sysem. Wae Fuel HP seam o he MP seam o he ucion plan ucion plan HPRV MPRV oile LP seam o he ucion plan Ehs muli-sage ubine... Descipion of he bach plan Fuel oile he bach plan opology he ecipe and he uiliy umpion of he bach plan ae pesened on figues 6 and 7 and on able A C P Ehs Pump muli-sage ubine Eleciciy o he ucion plan Figue 8: CHP Plan.. Modeling hough ERN epesenaion D G REACOR REACOR E H REACOR 3 Figue 6: ach plan opology F I REACOR REACOR 5 Reacion R Reacion R C Reacion R3 P A Reacion R Reacion R5 F Reacion R6 P D E Reacion R7 Reacion R8 I Reacion R9 P3 G H Figue 7 : bach plan ecipe asks LP seam MP Seam HP Seam Eleciciy able : Uiliy umpion of bach plan he ucion uni conves hee feeds (A & C ino fou inemediae ucs (HoA inc inc & ImpuE and wo finished ucs (P & P. o achieve his fou pocess equipmens (Heae Reaco Reaco & Sepaao ae used which ume eleciciy seam a high pessue medium pessue and low pessue. hee eacions (R R & R3 can ake place eihe in Reaco o in Reaco.... Descipion of he sie uiliy sysem o uce hese uiliies an onsie Combined Hea & Powe (CHP based uiliy sysem is used (see figue 8. he fuel anks supply fuel o boile which geneaes HP seam. HP seam is conveed ino MP and LP seam by using ubines o by using pessue elease valves. he advanage of using ubine is ha i no only educes pessue bu also simulaneously geneaes eleciciy. P P3 he ERN epesenaion of above menioned indusial uni is shown in figue 9. he ucion uni while he lowe half depics uiliy sysem. he link beween he wo unis is povided by flow of uiliies LP (label MP (label HP (label 3 and ELEC (label. Concening he CHP plan he boile opeaion is insananeous as long as he boile is in acive sae. Howeve once shu down (idle sae boile opeaion is no longe insananeous and he boile needs o go hough a esaing phase. Duing he esa phase he boile umes fuel bu does no uce he HP seam of equied qualiy. Moeove he fuel umpion in a boile is a non linea funcion of amoun of high pessue (HP seam uced caloific value of fuel boile efficiency and he caloific value of fuel boile efficiency and he enhalpy diffeence beween supeheaed seam and feedwae. Fo sake of simpliciy he lineaizaion of he equaion and he ERN modeling of he boile opeaion is no pesened in his aicle bu he eade can find his infomaion abou his aspec in (Agha Resuls o judge he effeciveness of ERN based scheduling model he above menioned example was fomulaed and esolved using sofwae XPRESS-MP elease 008A. On his inegaed appoach he objecive funcion is a cos cieion including he fuel cos and emissions coss. he poblem was solved on an Inel(R Coe(M Duo GHz and.00 G of RAM. A hou planning hoizon is ideed wih he ime inevals divided ino one hou peiods. o esimae he impac of make demand on he opeaional aciviy he bach plan was supposed o wok a 50 o 00 % of imum capaciy. he scheduling of he ucion plan in a classical mase/slave appoach would is in fis calculaing he scheduling of he bach plan by imizing ealiness and hen esablishing he enegy planning of he CHP plan. hus he uiliy equiemen duing a ime peiod is calculaed a poseioi. Conay o his sequenial appoach figue 0 pesens he Gan cha esuling fom he inegaed scheduling of he whole plan. Howeve in he inegaed appoach he asks in ucion plan ae aanged in such a manne ha ha imizes he poenial of he CHP plan. Fo example ide a scenaio

9 LP (00 MP (00 HP (00 3 A (5000 D (5000 Reacion R (0 00 (000 (0 80 J Reaco 0.5 Reacion R 6 ( E (000 7 ( Reacion R 3 (0 50 J3 Reaco 3 8 (0 50 Reacion R C (050 F (050 ( ( Reacion R3 J Reaco Reacion R6 9 ( ( P ( P (0 0 Make Make ELEC (00 G (5000 J Reaco 0.5 Reacion R7 (0 00 (0 80 H (000 J5 Reaco Reacion R8 ( I ( (050 5 (0 80 P3 (0 Make Reacion R9 HP (00 o ucion plan 3 J7 HPRV Expansion o ucion plan J0 o ucion plan MPRV Expansion 5 ( MP (00 8 ( LP (00 oile opeaions J J3 J8 ubine ubine ubine Sage Sage 3 Sage Expansion Expansion Expansion Pumping Wae (0000 Fuel ( ( In MP (00 9 ( S9 ELEC In LP (00 3 Ehs ( ( o ucion plan 33 ( J6 Pump ( In MP (00 30 ( In LP (00 3 ( Ehs (00 Expansion Expansion Expansion J9 ubine Sage J ubine Sage J ubine Sage 3 Figue 9: ERN epesenaion of he bach plan and CHP plan in which duing a specific ime duaion he pocessing asks equied wo diffeen uiliies fo insance LP seam and eleciciy. his can be achieved eihe by geneaing seam and eleciciy sepaaely (expensive opion o using cogeneaion o simulaneously geneae boh seam and eleciciy (cheape opion. Hence in ode o imize he benefis of CHP plan he ucion plan should have as many uiliy cascades (equiemen of a leas wo diffeen uiliies a same ime duaion as possible. Compaed o a classical mase/slave appoach he inegaed appoach hen leads o a educion of cos of 5 o 30 % (depending on he load aio. Finally figue pesens he seams cuves in he mase/slave and sequenial appoaches. Seam cuves ae gaphical epesenaions used o show he vaiaion of seam a diffeen pessue levels in he uiliy sysem wih espec o ime. In he sequenial appoach he uiliy sysem is ideed as a suppo funcion whose ole is o simply follow he scheduling of he ucion plan. his esuls in haphazad and quick vaiaions in he seam cuves. Howeve in he case of inegaed appoach he uiliy sysem scheduling is also aken ino accoun which esuls in smoohing of he seam cuves. his is a vey ineesing poin because his leads o a moe conollable CHP pocess and would also enable o design a CHP plan of educed capaciy.. CONCLUSION We have inoduced a famewok fo he modeling of bach plan composed of disjuncive bu also cumulaive esouce. he main advanage of ERN famewok lies in he fee maeial flow acs.ha allow he oupus fom he ask o be in vaiable popoions of bachsize and on he concep of delivey ime ha allows he uiliy ucion and umpion o be eaed as insananeous pocess heeby ovecog he phenomenon of slack ime ha is a pemanen feaue of he RN famewok.in ha pape he ERN famewok has been applied o he inegaed scheduling of manufacuing uni and uiliy sysem bu his ERN could be used fo ohe uiliies such as wae fo example. Moeove in he poposed ERN famewok hee is a diec elaionship beween gaphical epesenaion and he mahemaical fomulaion. Evey eniy in he gaphical epesenaion coesponds o a se of mahemaical ains. his opens he way fo developmen of a uly geneal pupose scheduling algoihm and sofwae. he pepocesso of he sofwae will ake inpus fom he use develop a gaphical epesenaion of indusial pocess conve auomaically he gaphical epesenaion o he

10 mahemaical ains and in end pesen he esuls in gaphic based pos pocesso. Fuhemoe his sudy is a pa of eseach being conduced a CNRS whose geneal objecive is enegy managemen soluions fo mono and muli-sies. In fuue he discee ime model will be eplaced by a coninuous ime fomulaion. his would enable he poblem o incopoae he impac of bach sizes on he duaion of asks. hen he genealizaion of he appoach o eco-indusial paks is also pojeced. ask ug LP seam ask ug MP seam ask ug MP seam ask ug Eleciciy ask ug LP seam and Eleciciy ask ug MP seam and Eleciciy Figue 0: Scheduling of he whole indusial uni (a Mase/slave appoach REFERENCES Agha M.H. 009 Inegaed Managemen of enegy and ucion: scheduling of bach pocesses and CHP plans PhD hesis INP oulouse ehdani. M.R. Pishvaie and D. Rashchian 007 Opimal scheduling of mixed bach and coninuous pocesses incopoaing uiliy aspecs Chemical Engineeing and Pocessing 6( p Egli U.M. and D. W.. Rippin 986 Sho-em Scheduling Fo muliuc ach Chemical Plans Compues and Chemical Engineeing 0( p Floudas C. A. and Lin X. 00 Coninuous-ime vesus Discee-ime Appoaches fo Scheduling of Chemical Pocesses: A eview. Compues and Chemical Engineeing 8 p Hai A. C. Aigues M. epanie and P. apise 007 Odonnancemen Sous Conaines d'énegie e de essouces humaines ème Congès de la Sociéé Fançaise de Génie des Pocédés. Sain-Eienne (Fance IPCC 996. Inegovenmenal Panel on Climae Change. Climae change 995: he science of climae change. Cambidge: Cambidge Univesiy Pess Kjaeheim G. 005 Cleane ucion and susainabiliy. Jounal of Cleane Poducion 3( p Kondili E. C.C. Panelides and W.H. Sagen 988 A geneal algoihm fo scheduling bach opeaions 3 d Figue : Seam Cuves (a Inegaed appoach Inenaional Symposium Pocess Sysems Engineeing Sydney p Kondili E. C.C. Panelides and W.H. Sagen 993 A geneal algoihm fo sho-em scheduling of bach Jounal of Cleane Poducion 3( p Kueh R. 006 owads a susainable sociey: Unied Naions Univesiy s zeo emissions appoach Jounal of Cleane Poducion 5(3 p Méndez C.A. J. Ceda I.E. Gossmann I. Hajunkoski M. Fahl 006 Sae-Of-he-A Review Of Opimizaion Mehods Fo Sho-em Scheduling Of ach Pocesses Compues and Chemical Engineeing 30 p Moia R.D H.A. Maos C. Fenandes C.P. Nunes and J.M. Pio 005 Dynamic Modelling And Simulaion Of A Cogeneaion Sysem Inegaed Wih A Sal Recysallizaion Pocess Chemical and Chemical Engineeing 9 (6 p Panelides C.C. 99 Unified Famewok Fo he Opimal Pocess Planning And Scheduling CACHE Publicaions. Poceedings of he Second Confeence on Foundaions of Compue Aided Opeaions p Zhang.J. and. Hua 005 Effecive MILP model fo oil efiney-wide ucion planning and bee enegy uilizaion Jounal of Cleane Poducion 5 p