Energy Optimization in a Pulp and Paper Mill Cogeneration Facility

Transcription

1 2010 Amercan Conrol Conference Marro Waerfron, Balmore, MD, USA June 30-July 02, 2010 WeB12.6 Energy Opmzaon n a Pulp and Paper Mll Cogeneraon Facly D.J. Marshman, T. Chmelyk, M.S. Sdhu, R.B. Gopalun and G.A. Dumon Absrac Alarmngly low pulp prces n early 2009 lef pulp and paper mlls across Norh Amerca desperae for any way o mprove hn prof margns. One soluon ha connues o gan populary among he ndusry s mproved energy managemen sysems for cogeneraon sysems, whch use seam for wo purposes - o provde hea for he pulpng process, and o generae elecrcy for sale o regonal provders. Ths paper presens an energy opmzaon algorhm for use n a pulp and paper mll cogeneraon sysem. The algorhm s applcable o a number of popular mll confguraons, power sale conracs, and fuel purchasng scenaros. Resuls are presened n he form of wo case sudes. I. INTRODUCTION A cogeneraon or combned hea and power (CHP) sysem produces seam ha provdes hermal energy o hea exchangers and mechancal energy hrough expanson o urbne uns. The urbne uns hen ransfer he mechancal energy o generaors, whch n urn produce elecrcy. The generaon of hea and power whn a sngle facly, as opposed o separae facles, ofen resuls n effcency mprovemens n he range of 10% o 40% [1]. Pulp and paper mlls are excellen canddaes for cogeneraon facles. Large scale seam producon equpmen s already necessary for washng, refnng and dryng sages of he pulpng process, herefore he cos of nsallaon for a cogeneraon facly s sgnfcanly offse. Pulp producon, dependng on he pulpng mehod used, may also yeld wo addonal fuel sources as byproducs - hog fuel and black lquor. Seam producon ha ulzes hese alernave fuels n he place of naural gas or fossl fuels sgnfcanly reduces cogeneraon operang coss. Successful managemen of a cogeneraon facly s by no means sragh forward, bu s a crcal componen of recoverng profs n oday s roubled foresry ndusry. Elaborae plan confguraons resul n complex un co-dependences. Marke-dependen elecrcy prces, whch ypcally flucuae by 200%-300% over he course of a day, make effcen producon schedulng crcal o plan managemen. Mos cogeneraon facles have herefore employed opmzaon algorhms o ad n he process of plan energy managemen. Ths work was suppored by NORPAC Conrols Ld. R.B. Gopalun and D.J. Marshman are wh he Deparmen of Chemcal and Bologcal Engneerng, Unversy of Brsh Columba, Vancouver, BC, Canada gopalun@chbe.ubc.ca, dmarshman@chbe.ubc.ca G.A. Dumon s wh he Deparmen of Elecrcal and Compuer Engneerng, Unversy of Brsh Columba, Vancouver, BC, Canada guyd@ece.ubc.ca T. Chmelyk and M.S. Sdhu are wh NORPAC Conrols Ld., 7500 Wnson Sree, Burnaby, BC, Canada chmelyk@norpacconrols.com, msdhu@norpacconrols.com These algorhms, or energy managemen sysems (EMSs), are responsble for he opmal schedulng of power and hea generaon hrough effcen resource and un operaon managemen. I s mporan o noe ha hese energy managemen sysems are ofen dsnc from un conrollers. The EMS ofen dcaes opmal un sepons, whereas he un conrollers acheve and manan hose sepons. Energy managemen algorhms emerged from subsanal growh n compuaonal auomaon durng he 1970s. Mos early mehods ook advanage of heursc opmzaon algorhms. A summary of several early energy managemen sraeges s provded by Gruhl, Schweppe and Ruane [2]. More recen approaches such by hose by Chen, Tsay & Gow [3], Rajan & Mohan [4], Wllams, Huff & Francno [5], Vaseb, Fesanghary & Bahaee [6], and Sudhakaran & Slochanal [7] ulze one or more well known heursc opmzaon echnques. Chen, Tsay & Gow [3] use an enhanced mmune algorhm, whle Rajan & Mohan [4] use a mehod ha combnes smulaed annealng and evoluonary algorhms. Wllams, Huff & Francno [5] employ a mehod known as he smplex self-drecng evoluonary operaon procedure (SSDEVOP). Vaseb, Fesanghary & Bahaee [6] a harmony search algorhm, and Sudhakaran & Slochanal [7] combne he genec algorhm wh he abu search algorhm o produce a heursc search mehod for a cogeneraon sysem. Rong, Lahdelma, Makkonen, Hakonen & Grunow have conrbued several works on cogeneraon opmzaon mehods; boh heursc [8], [9] and non-heursc [10], [11], mos of whch deal wh power generaon on a larger scale and nvolve mulple plan co-ordnaon. Non-heursc energy managemen soluons were proposed durng he 1970 s and 80 s, bu compuaonal lmaons a ha me led o mpraccal run mes for mos reasonably accurae soluons [12]. Several algorhms n he early 1990s aemped o make use of non-heursc mehods n he form of lnear programmng [13], [14], [15], bu mos of he mehods were oversmplfed. Recen advances n mahemacal ools and compuaonal echnology have made complex onlne calculaons feasble for real applcaons wh cogeneraon sysems. Some mxed neger lnear programmng (MILP) mehods, and dervaons hereof, have been proposed n he works of Arroyo & Conejo [16], Cheng [17], Ferrar-Trecae e. al. [18], and Thorn, Brand & Weber [19]. Ferrar-Trecae e. al. [18] use model predcve conrol (MPC) reformulaon, followed by MILP echnques. Thorn, Brand & Weber [19] propose a Lagrangan relaxaon eraon sep o mprove robusness. Rodrguez-Toral, Moron & Mchell [20] presen a sequenal quadrac programmng mehod, bu noe ha onlne /10/$ AACC 1229

2 feasbly may be problemac for complex sysems. Ths paper presens a non-heursc approach o energy opmzaon for a pulp and paper cogeneraon facly, wh emphass on dversy of applcaon. The oulned approach develops a complex plan model ha can easly be smplfed o represen varous cogeneraon sysem confguraons operang under a varey of condons. Despe he model complexy, he opmzaon problem s convex. The remander of hs paper s organzed as follows: secon 2 oulnes he noaon used n he paper; secon 3 provdes a bref descrpon of he cogeneraon process; secon 4 shows he developmen of he plan model; secon 5 presens he deals of he opmzaon algorhm; wo case sudes are examned n secon 6; and conclusons are presened n secon 7. C c hog c ng c e, g Hn Hou h,j m m m MAX δm MAX n sa n bo n sh n P RV n sup n ur n ven n P q s j max α j β ɛ θ φ II. NOTATION cos of operaon durng perod cos of hog fuel from suppler cos of naural gas cos of elecrcy durng perod naural gas consumpon by boler durng perod un nle seam enhalpy un oule seam enhalpy hog fuel consumpon from suppler j o boler durng perod average seam mass flow rae no un durng perod seam mass flow rae ncrease a pressure relef valve durng perod due o conac wh waer supply durng depressurzaon max seam mass flow rae no un rae of change lm for seam mass flow rae no un over one perod number of sages n urbne number of bolers number of seam headers number of pressure relef valves number of hog fuel supplers number of urbnes number of vens oal number of uns power generaon durng perod plan hea demand a pressure level durng perod avalable hog fuel from suppler j perod ndex whn he opmzaon horzon duraon of an opmzaon perod oal number of perods whn he opmzaon horzon hog fuel energy conen coeffcen from suppler hog fuel combuson effcency un effcency naural gas energy conen coeffcen naural gas combuson effcency III. COGENERATION PROCESS DESCRIPTION Ths work s movaed by several ndusral applcaons n cogeneraon facles across Brsh Columba, Canada, and has herefore been desgned wh a specfc sysem confguraon n mnd. The confguraon schemac, as shown n Fg. 1, conans aspecs from several of he facles, whch have been combned n order o creae a sngle, generc sysem applcable n a number of mlls. The facly s essenally spl no wo dsnc plans separaed down he mddle of Fg. 1, whch share supples of waer and fuel. The sysem feaures a oal of wo recovery bolers and hree power bolers, whch burn he fuel supples n order o generae hgh pressure seam. The recovery bolers use a byproduc from he pulpng process known as black lquor, whch s a hydrocarbon-rch slurry, o hea he waer source a a consan rae. Alernavely, power bolers produce seam a varable raes usng eher hog fuel or naural gas. Hog fuel s also a combusble byproduc from he pulp mll wh a mulch-lke conssency. Naural gas can also be used o provde hea o he bolers, bu s sgnfcanly more expensve han he mll byproduc fuels; hog and black lquor. For hs reason, fuel managemen s crcal o economcally effcen cogeneraon plan operaon. Hgh pressure seam from he power bolers passes hough a hgh pressure header on s way o eher he mll, where s used as a hea source for varous pulpng processes ncludng washng, dryng and refnng; o a urbne un, where expands, roang he urbne, whch powers a generaor producng elecrcy; or o a pressure relef valve (PRV), where descends o a lower pressure and pcks up addonal waer durng de-superheang. Lke any real process, an effcency s assocaed wh each of hese seps o accoun for hea losses. Seam arrves a he medum pressure header afer passng hrough eher he frs sage of he urbne or pressure relef valve. Ths header agan passes seam o he plan, urbne, PRV, or smply vens he seam o he amosphere. The low pressure header s fed by he urbne and PRV, and passes seam o he fnal urbne sage, he plan, or vens. Upon exng he low pressure applcaon he seam has usually condensed back o lqud form, alhough s usually oo ho o be reaed and pumped back o he bolers. A fnal coolng sage s herefore requred. In order o maxmze he economc oupu of such a facly many facors mus be consdered ncludng effcen fuel managemen, desgnaon of un sepons o cusomze seam flow pahs, and power generaon schedulng. Ths ask becomes ncreasngly complex as lmaons are nroduced such as me-dependan power and fuel coss, complex power conracs, lmed fuel supples, and mll hea requremens. Ths paper presens an approach o maxmzng plan profably whle addressng each of hese ssues. The proposed approach nvolves wo major seps; he generaon of a workng plan model, and he use of ha model o formulae an opmzaon problem ha maxmzes profably of plan operaon. The focus, agan, s on ndus- 1230

3 Fg. 1. Pulp and paper mll cogeneraon sysem schemac ral applcaon, so un operaons are approxmaed usng frs order models and un effcences are approxmaed as consan around normal operang condons. Ths allows for he esablshmen of a convex opmzaon problem relang plan operaon o overall profably, wh consrans mposed by varous feaures of he plan model. Snce he opmzaon problem s convex n naure, can be mplemened n an onlne fashon. IV. COGENERATION PLANT MODEL The model has been desgned o represen a relavely complex pulp and paper cogeneraon sysem based on he schemac shown n Fg. 1. The model racks waer enhalpy hroughou he sysem, makng sae changes and fuel combuson easy o represen. The relave complexy of hs process and correspondng model (for a pulp and paper mll) allow for represenaon of smaller facles n he ndusry smply hrough un deacvaon. The energy opmzaon mehod presened here s herefore wdely applcable wh mnmal changes. The characersc behavor of he facly, ha s he nheren relaonshps beween operang coss, power generaon and hea generaon, can be descrbed by a model ha consss of ses of dfferenal and algebrac equaons of varyng levels of complexy [9]. However, several smplfyng assumpons, such as lnearzaon and model order reducon, allow for he developmen of a convex energy opmzaon problem. Ideally, devaon no regons where lneary does no reasonably hold wll be lmed by underlyng conrol mechansms ndependen of he EMS. Valdaon of he lnearzaon assumpons was carred ou usng sx monhs of ndusral operaon daa from a facly very smlar o he one represened n Fg. 1. These daa ncluded a number of monored varables hroughou he sysem such as flow raes, pressures, and emperaures. The prmary, unobserved modelng sae of seam and waer enhalpy was calculaed based on hese daa usng he mehods presened n [21]. Enhalpy flow rae of un operaon npu Fg. 2. Comparson of model oupu and acual oupu over me for several cogeneraon un operaons and oupu sreams were mpored no he MATLAB denfcaon oolbox, and subsequenly f o lnear ransfer funcon models. Measuremens of four mporan varables from four major un operaons and her correspondng predcons are presened n Fg. 2; PRV (op lef), condenser (op rgh), power boler (boom lef), and condensng urbne (boom rgh). The correspondng percenage f values, whch are a quanfcaon of model qualy based on he percenage of he oupu varaon reproduced by he model, range from 55% o 85%. I should be noed ha model qualy would have mproved wh larger order model srucures, bu praccal applcably would have suffered. The resulng ransfer funcons were used o esablsh selec equaly consrans. Un me consans and delays were used o generae consrans resrcng he rae of se pon changes. For furher deals, see he secon on problem formulaon. Due o he assumpon of lneary of ndvdual un models, he rae of elecrcal generaon can be expressed as a lnear funcon of seam flow rae beween each exracon pon whn a urbne a seady sae, as shown n (1). The seady sae operaonal coss are expressed as lnear funcons of fuel flow rae o each boler, as shown n (2). n sa n ur P = =1 j=1 n bo n sup ( C = =1 ( ) ) (ɛ,j H j n Hj ou m j j=1 c hogh,j (1) ) + c ng g (2) V. OPTIMIZATION PROBLEM FORMULATION The prmary objecve of a cogeneraon facly s o generae hea. Ths s especally rue n a pulp and paper mll applcaon, where mos cogeneraon sysems n he ndusry 1231

4 are modfed process heang sysems. For hs reason, he pulp mll and he cogeneraon facly have a maser-slave relaonshp n reference o hea producon. Alhough here may be conracual oblgaons assocaed wh elecrcy producon, here s usually a large degree of flexbly when comes o he rae of power generaon n day-o-day operaon. Therefore, plan hea demand does no appear n he objecve funcon, bu raher as par of a consran. The rae of elecrcy producon, on he oher hand, s a defnng componen of he EMS objecve funcon along wh operang coss. Snce he rae of elecrcy producon from a pulp and paper mll s relavely small compared o overall grd demands, he relaonshp beween power generaon and plan profably s defned by he conracual agreemen beween he cogeneraon facly and a larger regonal power provder. These conracs can be exremely complex n naure, and he sale prcng mehod for elecrcy can vary sgnfcanly from facly o facly. Prces may flucuae wh he marke, makng updaed prcng profles a necessary componen of an effecve EMS; or elecrcy prces may be fxed for an enre year. For hs reason he algorhm horzon, eraon perod lengh, and prcng srucure have no been fxed. The overall objecve of he EMS s o maxmze profably over a gven horzon hrough he coordnaon of ndvdual un operang condons whn he facly. Each un s gven a dsnc sepon for every perod over he course of he horzon, subjec o operaonal consrans such as feasble operaon lms, rae of change lms, and un codependences. Ths plan managemen problem s defned by he overall cos of operaon objecve funcon defned n (3), where P and C are defned as per (1) and (2) respecvely, he nequales n (4)-(6) and he equales such as he mass and energy balances as seen n (7)-(9). More specfcally, (4) represens a lmaon on hog fuel supply over he enre opmzaon horzon, (5) consrans a seam flow rae ṁ o physcally realzable values for un, and (6) s a rae of change lmaon o seam flow hrough un, where δṁ MAX s specfed accordng o a dscrezed form of he un ransfer funcon. (7) and (9) enforce mass balances around a PRV and a pressure header, respecvely. (8) represens an energy balance around boler where seam s poenally produced usng boh naural gas and hog fuel from varous dfferen supplers. s.. max =1 max Mn n bo =1 (C c e, P ) (3) =1 h,j s j j = 1 o n sup (4) 0 m m MAX = 1 o n (5) m 1 δm MAX m m 1+δm MAX = 1 o n (6) ( H P RV1 n m P RV1 = Hou P RV1 m P RV1 ) + m P RV1 (7) ( ɛ bo β ( ) ) n sup j=1 h,j α j + φgθ m ur1 + m P RV1 = H bo ou m bo = 1 o n bo (8) + m P RV1 = qmp + m ur2 Hou ur1 + m P RV2 + m ven2 (9) These equaons represen he general framework for consrans n he overall problem. In order o opmze he process, opmal values for all hog and naural gas fuel combuson raes, and all seam mass flow raes hrough every un whn he sysem mus be chosen. The fnal problem conans max (2n bo n sup + n) opmzaon varables subjec o n sup + max (4n + n bo n sup + 2n sh ) consrans, several of whch may become redundan dependng on he complexy of he sysem a hand. For a mll smlar o he one under nvesgaon n hs arcle, an opmzaon problem over a 24 hour horzon nvolves approxmaely 1000 opmzaon varables subjec o approxmaely 2500 consrans. Despe he large sze of he problem, s convex naure resuls n reasonable soluon mes wh a sandard convex opmzaon ool. The CVX oolbox for Malab by Mchael Gran and Sephen Boyd was used by he auhors of hs paper. VI. STANDARD CASE STUDIES The case sudes presened below are based on real power plan models and power generaon conracs. Un gans, dynamc consrans and mll hea demands have been approxmaed from ses of ndusral daa. Fuel and elecrcy prces have been esmaed based on hsorcal rends. A. Case I: Daly Producon Scheduler The frs case sudy nvolves an hourly opmzaon over a 24 hour horzon. Elecrcy sale prces are assumed o flucuae hourly over he course of he day n a sandard manner accordng o marke demand. Fuel prces are fxed for he day. I s assumed ha an unlmed supply of naural gas s avalable, bu ha he hog fuel supply s lmed. The opmzaon procedure s carred ou assumng hog fuel supples of 0, 30, 50, 75 and 100 merc onnes. Fg. 3 shows he rae of power generaon by he facly for he fve dfferen hog fuel supples. The elecrcy prce profle s also ncluded on a second axs for reference. In he case of no hog fuel avalably, he algorhm has only naural gas o use. Due o he hgh cos of naural gas relave o he sale prce of elecrcy, seam producon s lmed o raes suffcen o sasfy mll hea demands. The pah ha seam follows as descends o sasfy low pressure hea demands depends on he prce of elecrcy a a gven me. When he sale prce s low he algorhm sends seam hrough PRVs, where he seam s conaced wh a waer source as expands. Energy s ransferred o he waer supply, so alhough seam enhalpy s decreased on a per un bass, he mass flow rae s ncreased hrough he PRV. When he sale prce s suffcenly hgh, he seam passes hrough he urbnes nsead, generang power. 1232

5 Fg. 3. Elecrcy producon schedule for lmed hog fuel supples over a 24 hour perod wh hourly marke-based sale prces Fg. 4. Comparson of elecrcy producon schedules for 40 onne hog fuel supply over a 24 hour perod wh hourly marke-based sale prces As hog fuel becomes ncreasngly avalable s used o frs replace naural gas, hen o ncrease seam producon n order o generae more power. Beween he 50 and 75 onne supply profles n Fg. 3, a shf n peak elecrcal generaon s observed. Ths shf represens a decson by he algorhm o aler he plan confguraon by openng a ven n plan 1, and a PRV n plan 2. Seam flowng hrough he PRV s suffcen o sasfy he mll hea demands, so no md pressure exracon s requred from he urbne, and more seam can be forced o he back of he condensng urbne. A smlar suaon s seen n plan 1, where he seam flow rae hrough he urbne uns s resrced by he exhausng capables of he low pressure (LP) lne. Inally, he only oule for seam n he LP lne s he mll hea demand; bu when becomes economcally feasble o open he ven o provde furher exhaus, sgnfcanly more seam can flow hrough he urbnes. These changes ncrease he seam producon and herefore operaon coss, bu he peak sale prces and abundance of cheap fuel make economcally feasble. Ths mehod was compared o an algorhm currenly beng used n a pulp and paper mll n Brsh Columba. The mehod n use essenally nvolved proposng a predefned sepon ncrease and decrease o every sysem varable and relang ha change back o overall mll profably usng a cos funcon. If he change was economcally advanageous (beyond a prese deadband) hen was mplemened, oherwse operaon connued unchanged. The mll usng hs mehod s frequenly faced wh lmed hog fuel supples, makng hs case sudy especally applcable. For he comparson, a 40 onne supply of hog fuel was assumed (agan wh an unlmed supply of naural gas) over he 24 hour horzon, and he same elecrcy prce profle was used. Resuls are presened n Fg. 4. The mehod currenly mplemened begns o force power generaon early n he day, and quckly deplees he supply. The cheap prce of hog fuel relave o he sale prce of elecrcy makes advanageous o force producon (see Fg. 4) despe hn prof margns. There s no consderaon of fuure sale prces, whch predcably peaks n he early afernoon well n excess of he prces early n he mornng. Once he hog supply s depleed, only he more expensve naural gas remans o sasfy mll hea demands for he res of he day, and he algorhm s lef ryng o mnmze losses. The resul s a ne loss of approxmaely $20-40 per MW of elecrcy produced wh naural gas, dependng on he sale prce a he me, whch brngs he overall daly profably of he plan o a ne loss of $ The mehod presened n hs paper explos he sale prce rend by reservng he majory of he fuel supply and only forcng seam producon durng he peak hours. The dfference n performance over he opmzaon horzon s subsanal, as he mehod presened here resuls n a ne prof of $666.81; or n oher words, a oal of $ more han he prevous mehod. Ths amoun may appear o be relavely nsgnfcan for an enre mll, bu amouns o an annual dfference of $473,279. I s also mporan o noe ha he urbne uns n hs case sudy peaked ou a roughly 12 MW, bu uns double and rple ha sze are no uncommon n pulp and paper applcaons. B. Case II: Weekly Producon and Purchasng Scheduler The second case sudy nvolves an hourly opmzaon over a 168 hour perod (1 week). Elecrcy sale prces are assumed o be under conrac a dsnc bu consan peak (hgh) and off-peak (low) values. The peak prce s appled o power generaed beween he hours of 8am and 8pm, and he off-peak prce s appled o power generaed beween he hours of 8pm and 8am, daly. Naural gas s avalable a a fxed prce and n unlmed quany. Hog fuel s avalable from hree supplers, each wh lmed supples a prces rangng from $34.21/T o $56.70/T. The resuls are no surprsng wh one excepon: he power generaon schedule s coordnaed wh he purchasng schedule, makng sraegc long-erm plannng possble where shorsghed decsons would have prevously been made. As a resul, opmzaon consders no only curren fuel prces, bu fuure prces ha wll be pad once he curren sock s depleed. Several oher algorhms, such as he exsng one oulned n he prevous secon of hs paper, use only curren fuel prces o deermne profably. Ths dsncon wll no lkely have any shor-erm mpac, bu may decrease profably over a longer me frame. For 1233

6 Fg. 5. Comparson of elecrcy producon schedules over a seven day perod under a wo er elecrcy sale prce conrac example, a decson ha requres 30% more fuel o ncrease overall profably by 10% would be deemed reasonable by he pre-exsng algorhm, regardless of oher vendor supply prces and quanes. The algorhm presened n hs paper, on he oher hand, may rejec a emporary 10% ncrease n profably n order o make a cheap fuel las 30% longer f he only oher avalable hog fuel s double he prce. Fg. 5 shows he resuls from hs case sudy by comparng he power generaon profles usng he exsng mehod from he prevous case sudy wh he new mehod developed n hs paper. The elecrcy prce profle s also ncluded for reference. Over a one week perod, he exsng mehod produces $41,623 worh of elecrcy a an operang cos of $ 34,556, resulng n a ne prof of $7,067. The new mehod, on he oher hand, produces $34,224 worh of elecrcy a a cos of $24,927, resulng n a ne prof of $9,297. I s evden ha he exsng mehod makes neffcen use of he cheap fuel, and s lef wh only he fnal, more expensve suppler of hog fuel a roughly he 130 hour mark. By nsead raonng he fuel supply for he enre week, he new mehod acheves a susanable level of profably and earns over $2000 more over he one week perod. VII. CONCLUSIONS A praccal energy opmzaon algorhm for use n a pulp and paper mll cogeneraon plan has been developed. The proposed approach s applcable o a wde range of mlls n he ndusry, wh he poenal o address a varey of plan confguraons and power conracs over a flexble horzon. The soluon also addresses he scenaro of mulple fuel supplers and coordnaes purchasng wh producon over he opmzaon horzon. The opmzaon problem s posed n a convex form, and can be solved usng a number of readly avalable convex opmzaon solvers such as CVX oolbox, whch was used for he case sudes presened n hs paper. Due o he convexy of he problem, coupled wh he avalably of effcen algorhms for convex opmzaon, soluon me was no an ssue. REFERENCES [1] R Madlener and C Schmd. Combned hea and power generaon n lberalsed markes and a carbon-consraned world. GAIA - Ecologcal Perspecves for Scence and Socey, 12(2): , [2] J Gruhl, F Schweppe, and M Ruane. Un commmen schedulng of elecrc power sysems. Sysem Engneerng for Power: Saus and Prospecs, [3] Sung-Lng Chen, Mng-Tong Tsay, and Hong Jey Gow. Schedulng of cogeneraon plans consderng elecrcy wheelng usng enhanced mmune algorhm. Inernaonal Journal of Elecrcal Power & Energy Sysems, 27(1):31 38, [4] C Chrsober Asr Rajan and M R Mohan. An evoluonary programmng based smulaed annealng mehod for solve he un commmen problem. Inernaonal Journal of Elecrcal Power & Energy Sysems, 29(7): , [5] Jeffery Wllams, Frederck C Huff, and Peer Francno. Islands of opmzaon: a web-based economc opmzaon ool. Whe paper, Emerson Process Mangemen, [6] A Vaseb, M Fesanghary, and S M T Bahaee. Combned hea and power economc dspach by harmony search algorhm. Inernaonal Journal of Elecrcal Power & Energy Sysems, 29(10): , December [7] M Sudhakaran and S M R Slochanal. Inegrang genec algorhms and abu search for combned hea and power economc dspach. Conference on Convergen Technologes for Asa-Pacfc Regon, 1:67 71, [8] Ayng Rong, Rso Lahdelma, and Marn Grunow. An mproved un decommmen algorhm for combned hea and power sysems. European Journal of Operaonal Research, 195(2): , [9] Ayng Rong, Henr Hakonen, and Rso Lahdelma. A varan of he dynamc programmng algorhm for un commmen of combned hea and power sysems. European Journal of Operaonal Research, 190: , [10] Smo Makkonen and Rso Lahdelma. Non-convex power plan modellng n energy opmsaon. European Journal of Operaonal Research, 171(3): , [11] Rso Lahdelma and Henr Hakonen. An effcen lnear programmng algorhm for combned hea and power producon. European Journal of Operaonal Research, 148(1): , [12] Arhur I Cohen and Vahd R Sherka. Opmzaon-based mehods for operaons schedulng. Proceedngs of he IEEE, 75(12): , [13] K Mosleh, M Khadem, R Bernal, and G Hernandez. Opmzaon of mulplan cogeneraon sysem operaon ncludng elecrc and seam neworks. IEEE Transacons on Power Sysems, 6(2): , [14] Rchard E J Puman, Thomas Allen, John J Novacek, and Frederck G Huff. Opmzaon of a pluraly of mulple-fuel fred bolers usng eraed lnear programmng. Paen , Wesnghouse Elecrc Corp., [15] Guohe Huang, Bran W Baez, and Glles G Pary. A grey lnear programmng approach for muncpal sold wase managemen plannng under uncerany. Cvl Engneerng and Envronmenal Sysems, 9(4): , [16] J M Arroyo and A J Conejo. Opmal response of a hermal un o an elecrcy spo marke. IEEE Transacons on power sysems, 15(3): , [17] Ruoyu Cheng. Decomposon of coordnaon of large-scale operaons opmzaon. Docor of phlosophy n process conrol. deparmen of chemcal and maerals engneerng, Unversy of Albera, Edmonon, [18] Gancarlo Ferrar-Trecae, Eduardo Gallesey, Paolo Leza, Maeo Spedcao, Manfred Morar, and Marc Anone. Modelng and conrol of co-generaon power plans: a hybrd sysem approach. IEEE Transacons on Conrol Sysems Technology, 12(5): , [19] Eva Thorn, Heke Brand, and Chrsoph Weber. Long-erm opmzaon of cogeneraon sysems n a compeve marke envronmen. Appled Energy, 81(2): , [20] M A Rodrguez-Toral, W Moron, and D R Mchell. The use of new sqp mehods for he opmzaon of uly sysems. Compuers and Chemcal Engneerng, 25: , [21] Inernaonal Assocaon for he Properes of Waer and Seam, Lucerne, Swzerland. Revsed release on he IAPWS ndusral formulaon 1997 for he hermodynamc properes of waer and seam, f97 edon,