Abstract. The startup cost is considered as an exponential function of off time of a generating unit and the corresponding equation is:

Transcription

1 Secan generalzed mehod mnmzng he fuel and emssons coss n a power saon of small cogeneraon mulmachnes Inernaonal Conference on Renewable Energy and Eco-Desgn n Elecrcal Engneerng Llle, 3-4 march 11 Fras ALKHALIL*1, Frédérc COLAS* and Benoî ROBYNS*3 Member IEEE * Laboraory of Elecroechncs and Power Elecroncs of Llle, France (LEP) 1, Ars e Méers ParsTech, LEP, Llle, France. Tel: +33 (0) Fax: +33(0) E-mal: fras1@homal.com, frederc.colas@ensam.eu 3 Ecole des Haues Eudes d'ingéneurs, LEP, Llle, France Tel: +33 (0) Fax: +33 (0) e-mal: beno.robyns@he.fr Topcs: Power generaon and eco-desgn Absrac The objecve of hs paper consss n opmzng he fuel consumpon of a power saon of small cogeneraon mulmachnes whle mnmzng generaed polluon (CO and NO x ). Frsly, a sudy carred ou on he sraeges of Economc Dspach was used o solve he un commmen problem, whose man goals s o deermne he opmal schedule of onlne generang uns so as o mee he power demand a mnmum fuel and emsson coss under varous sysem and operang consrans. Ths work was carred ou by Secan mehod combned wh Improved Pre-prepared Power Demand (IPPD) able whch deermnes he un saus nformaon; he opmal soluon s hen acheved by Secan mehod a each power demand for 4 hours. The proposed algorhm was generalzed o 0 uns n a 4 hours un commmen schedule. Fnally, by comparng he resuls obaned by our suggesed mehod wh he resuls of he classcal mehod, we fnd ha he mehod suggesed (Secan) provdes a any hour he beer soluon. 1. Inroducon Un commmen problem (UCP) s he problem of selecng he generang uns o be n servce durng a schedulng perod [1]. The overall problem can be dvded no wo sub problems namely un commmen and economc dspach. The commed uns mus mee he sysem load and reserve requremens a mnmum operang cos, subjec o a varey of consrans. The Economc Dspach Problem (EDP) opmally allocaes he load demand among he runnng uns whle sasfyng he power balance equaons and uns operang lms. The soluon of he (UCP) s really a complex opmzaon problem. I can be consdered as wo lnked opmzaon problems, he frs s a combnaoral problem and he second s a nonlnear programmng problem. The un commmen decson nvolves he deermnaon of he generang uns o be runnng durng each hour of he plannng horzon by consderng sysem capacy requremen. The economc dspach (ED) decson nvolves he allocaon of he sysem demand and spnnng reserve capacy among he operang uns durng each specfc operaon of power. The mehods used o solve he UCP n leraure mnmzed he operang fuel cos. Bu, n hs documen, we used a mulobjecves mehod (fuel and emssons cos) o solve he UCP durng a very shor compung me compared o oher mehods. Ths proposed mehod s he secan mehod combned wh Improved Pre-prepared Power Demand (IPPD) able []. The proposed algorhm was mplemened n MATLAB (R08b Verson). Ths paper s organzed as follows: In Secon., Un commmen problem formulaon s nroduced. Secon.3 addresses he soluon mehodology for UC problem. In Secon 4, Applcaon of he proposed mehod o cenral mulmachnes small cogeneraon s presened. The smulaon and comparson resuls of power sysem wh varous generaor uns are presened n he same Secon.4. Conclusons are fnally gven n he las secon.. Un Commmen Problem (UCP) The objec of un commmen s o decde whch of he avalable generaors should sar-up and shu-down over a gven me horzon so ha he overall operang cos s mnmsed subjec o demand and spnnng reserve consrans [, ]..1. Objecve funcon: The objecve funcon of UC problem s expressed as he sum of fuel cos, he sar up and shu down cos of ndvdual uns for he gven perod subjeced o varous consrans. Mahemacally can be formulaed as follows: n ng F c ( p ) I SU SD (1) mn,,,, 1 1 The sarup cos s consdered as an exponenal funcon of off me of a generang un and he correspondng equaon s: SU SO.1 D.( e ( T off / T down ), () Consderng he fuel cos funcon as a quadrac funcon of real power generaon fg, ED problem can be formulaed as follows: c ( P, ) a b P, cp, (3).. Consrans [], [7]: Dependng on he naure of he power sysem under sudy, The UCP has many consrans such as he power balance, spnnng reserve and he oher consrans ncludng he hermal consrans, fuel consrans and secury consrans. ) 1

2 1) Load balance consran. The real power generaed mus be suffcen enough o mee he load demand and mus sasfy he followng equaon: N P U PD (4) 1,, ) Lms of generang uns. The oupu power of each generang un mus whn s allowable mnmum and maxmum lms. P P P (), mn,,max 3) Spnnng reserve consrans. Spnnng reserve mus be consdered o mee abrup load varaons and unexpeced generang un ouage. I s he oal amoun of power generaon avalable from all uns mnus presen load. N (6) P U PD R 1,max, 4) Thermal consrans. The emperaure and pressure of he hermal uns vary very gradually and he uns mus be synchronzed before hey are brough onlne. A me perod of even 1 hour s consdered as he mnmum down me of he uns. There are ceran facors, whch govern he hermal consrans lke mnmum up me, mn down me and he crew consrans. a) Mnmum up me. If he uns have already been shu down, hen here s a mnmum me before whch hey can be resaed. T T (7) on MU b) Mnmum down me. If all he uns are runnng already, hen hey canno be shu down smulaneously. T T (8) off MD c) Mus run uns. Generally n a power sysem, some of he uns are gven a mus run saus n order o provde volage suppor for he nework..3. Soluon Mehodology of UCP.3.1. Formaon IPPD able [], [7]: The procedure o fnd IPPD able s as follows, 1) Selecon of he Lambda values: Fnd mnmum and maxmum lambda values for all generaors a her maxmum and mnmum oupu power values. ) Arrange all he lambda values n ascendng order. 3) Fnd he oupu power values for all generaors a all lambda values. The generaor consrans are consdered as follows, f,,mn... hen P, 0 For mus run generaors: f,,mn... hen P, P, mn 4) Arrange lambda, powers, and sum powers a lambda n able s known as IPPD able. I gves he nformaon abou all predced power demands and he nformaon of commed uns. ) A specfed power demand, he upper and lower rows of he IPPD able are seleced such ha he power demand a ha hour les whn he IPPD lms. Each column represens he nformaon abou he saus of he generang uns. If any value of column s zero, hen ha correspondng generang uns s off condon and he remanng uns are n on condon. Therefore wh help of he IPPD able, he nformaon of saus of un s s deermned. Whenever he nformaon of commed uns s known, hen he economc dspach s used o fnd he opmal soluon..3.. Secan mehod for EDP[- 6][ 8]: A each power demand over 4 hours, IPPD able gves he nformaon of un saus. Now, he economc dspach s used o fnd he opmal soluon for all forecased power demands over 4 hours. In hs paper, he secan mehod s used o fnd he opmal soluon a each hour. In hs secon, Secan mehod s presened o solve he ED problem. The followng wo seps are nvolved n he proposed mehod. The secan mehod [3-4] s a roo fndng algorhm ha uses a successon of roos of secan lnes o beer approxmae a roo of a funcon. Ths mehod assumes ha he funcon s approxmaely lnear n he local regon of neres and uses he zero crossng over he lne connecng he lms of he nerval as he new reference pon. The nex eraon sars from evaluang he funcon a he new reference pon and hen forms anoher lne. The process s repeaed unl he roo s found. Geomercally, Newon mehod uses he angen lne and secan mehod approxmaes he angen lne by secan lne. The secan mehod has super lnear convergence. I wll converge whn fve eraons f he guess value s correc. To fnd he roo of f(x) =0 n he nerval of (x0, x1) wh whch f(x0).f(x1) <0. xk xk 1 k1 xk f ( xk) (9) f ( xk ) f ( xk 1) 1) The applcaon of Secan mehod for EDP s as follows, he power balance equaon s wren as funcon of lambda. Therefore ng f ( ) P ( ) PD () 1 ) For he secan mehod, he values of x k-1, x k, f(x k-1 ) and f(x k ) are seleced as follows: A specfed power demand, wo rows are seleced from he IPPD able such ha he power demand les whn he SOP lms. These wo rows forms a able known Reduced IPPD (RIPPD) able. Table. 1. Reduced Improved Pre-prepared Power Demand able (RIPPD) ng k1 mn & f ( xk 1) P ( mn) 1 ng k max & f ( xk ) P ( max ) 1 x x PD (11) PD (1) If P volaes he generaor lms, hen se he

3 Fuel flow(bu/ hr LHV) generang lms as follows: a) If P s less han he Mnmum lm of generang un, se P value s zero. b) f P s greaer han he maxmum lm of generang un, se P value s Pmax c) f he operang generang un s mus run generaor hen ha un s always operang n beween he mnmum and maxmum operang range d) From (9), opmal lambda value s evaluaed by secan mehod a requred power demand. The chef advanage of hs mehod s ha converges super lnearly o fnd he roo of he polynomal. 3. Applcaon and smulaon 3.1. Example1 The effecveness of he proposed mehod has been esed on hree gas mcrourbnes (GMT) o solve un commmen problem over 4 hours n order o mnmze he cos of fuel and emssons ISO Paral Load Performance Performance a paral load and ISO amben condons for he Capsone Model C Mcrourbne operang on hgh pressure naural gas fuel s presened n Table.. These values are esmaed from nomnal performance curves. Fg.1 confrms he lnear relaonshp beween power and fuel flow [9]. 1 wa s approxmaely BTU/h. Then BTU= 1/ Wh= Wh =93e-6 kwh. From he base prce ls by Gaz of France n Llle we see ha he cos per kwh of naural gas s abou.97e-, see Table.3. Table.. Paral Load Performance a ISO Amben Condons Power (kw) fuel flow (Bu/ hr LHV) converson fuel flow (kwhr/ hr) Cos of KWhr ( ) Fuel cos ( / hr) e-6,83,97E-0 1, e-6 6,0833,97E-0 1, e-6 9,71,97E e-6 3,839,97E-0 1, e-6 36,04773,97E-0, e-6 39,649,97E-0, e-6 4,493,97E-0, e-6 4,4601,97E-0, e-6 48,64979,97E-0, e-6 1,8737,97E-0 3, e-6,0973,97E-0 3, e-6 8,3113,97E-0 3, e-6 61,184,97E-0 3, e-6 64,476,97E-0 3, e-6 67,6994,97E-0 4, e-6 70,9318,97E-0 4, e-6 74,14696,97E-0 4, e-6 77,07767,97E-0 4, e-6 80,14,97E-0 4, e-6 83,81831,97E-0, e-6 87,049,97E-0, e-6 90,687,97E-0, e-6 93,787,97E-0, e-6 97,997,97E-0, e-6 0,8164,97E-0 6, e-6 4,663,97E-0 6, e-6 7,801,97E-0 6, e-6 111,6601,97E-0 6, e-6 11,47,97E-0 6,89 3 Fgure 1. Lnear relaonshp beween power and fuel flow Table. 3. Base arff n he cy of Llle Tarff Use Indcave annual consumpon Tarff Type Subscrpon Prce (EUR/an) hors CTA Naural Gas Prce (ceur / kwh) dfferen prce levels apply dependng on your common TICGN (ceur / kwh) Base Kchen To 00 kwh bnomal Tarff 33 7,01 Base Tarff n your cy Llle B0 Ho waer, heang small buldngs from 00 o 6000 kwh bnomal Tarff 4,84,97 B1 Heang, ho waer and / or ndvdual Kchen bnomal Tarff 146,4 3,94 0,119 from o 0000 kwh o kwh BI Heang and / or ho waer n he mddle boler, process. bnomal Tarff 146,4 3,94 Draw he curve of fuel cos n erms of power produced, fg.. Fgure. Fuel cos n erms of power produced We fnd he rend lne of hs curve and s quadrac equaon o oban ulmaely he coeffcens of specfc fuel cos of he mcrourbne gas C. Fc(p) = 0,000P + 0,1809P + 1,3 (13) Table. 4. Specfc coeffcens fuel cos for MTG a ( / hr) b ( / kwhr) c ( / kwhr) 1,3 0,1809 0, Exhaus emssons Measuremens of emssons were carred ou by EDF R & D / SPE. These measures relae o he concenraons of exhaus gases: O, CO, CO, and NOx a dfferen operang regmes of he gas mcrourbne C. The resuls of measuremens presened n he able. are expressed on dry gas n ppm measured oxygen reduced o 1% O. Table.. Measuremens resuls of CO and NOx Power (kw) CO (ppm), 39 NOx (ppm) , 4,7 1,4 6,7 3,3 1 9,8 68,6 4, 11,3,, 6,7 8,6 7, 8,3 8, 1,6, 1,6 1,3 To ake no accoun all he emssons and he oxcy of each ype of polluan, we wll use he CO equvalen wll be calculaed by he formula [11]: Equvalen on of a gas = on of Gas * GWP of Gas Where: GWP s he global warmng poenal. We noce ha under 1kW (0% power) mcro-urbne ems a bes, so o mnmze he emssons s advanageous o work n he operang range of around 0% of he mcrourbne capacy[1]. To conver emssons from ppm o mg / kwh, CO emssons (ppm) s mulpled by 1,09 and NOx

4 Equvalen CO( /hr) emssons (ppm) by 9. See he able.6. Table. 6. Emssons n (mg/kwh) for MTG CkW CO (mg/kwh) Nox (mg/kwh), 39, 3 71,6 161,6 74,6 7, 49,9 9,3 9, 9, 7 1,7 4,9 13,1,3,,4 1 1,9 1,4 7, 1,9 14,9 8, 18,3,1 To have he equvalen of CO, we apply hs relaonshp: CO eq (mg/h)=[nox(mg/h)*0+co(mg /h)*1] (14) The CO equvalen n mg/hr s n he able.7 Table. 7. Emssons n (mg/hr) for MTG CkW CO equvalen (mg/hr), 7, 1, 7, 8, Suppose ha he penaly for a gram of CO equvalen s abou 8 (ceur / gram). Fnally, o have he curve of he prce of emssons, we mulply he emssons (g / hr) by he supposed penaly, see Fg.3. I represens he prce of emssons for he MTG C kw and he rend lne wh s quadrac equaon Emssons cos em(p) = 0,031P - 1,9936P + 4, The emsson curve The rend lne Fgure 3. Emsson coss of GMT C. The emssons, expressed by CO equvalens of a mcrourbne, can be modeled hrough a nonlnear funcon em (p, ) as a funcon of power generaed (p, ). The equaon of he rend lne s a quadrac equaon as follow: em P ) * P P (1) (,, *, These emssons are herefore defned by hree specfc coeffcens as shown n Table.7 Table. 8. Specfc coeffcens Emssons for MTG CkW α ( / hr) β ( / kwhr) γ ( / kwhr) 4,93-1,9936 0,031 As we have already seen he cos funcon of operaon (3): The global funcon ha should be sough mmedaely o mnmze by he Secan mehod akes he followng form: f P ) k * C ( P ) (1 k)* em ( P ) (16) global (,,, Where: (k) s a coeffcen whch expresses he objecve funcon o opmze by Secan or Fmncon and whch n hs example akes he followng values: (k=1): when we wan o mnmze he fuel cos alone. (k=0): when we only wan o mnmze emssons cos. k can ake oher values f we search a compromse beween fuel and emsson coss. The reducng of he emsson coss s always a he expense of fuel coss and nversely. Ths las pon s very clear n able.1 for he opmzaon performed by he Secan mulobjeves mehod (k =1, 0.8, 0., 0.3 and zero).the global funcon akes he followng fnal form: f P ) A B * P C P (17) global(,, *, A k * a k * B k * b k * C k * c k * (18) 4 To mnmze hs global funcon we wll use wo mehods of opmzaon: Secan and Fmncon on a small power plan conssng of 3 gas mcrourbnes C. And as we have already noed, we mus choose a pror he value of k wh whch we specfy he objecve of opmzaon. To sar, we chose he exreme values of k [0, 1], hen we observe he evoluon of he fnal cos of fuel and emssons assocaed wh he values beween hese wo exremes. When k = 1, Secan opmzes under he objecve (cos only). The opmzaon resuls are summarzed n he able.9. A glance a hs able we can see ha hs mehod has a selecvy performance of mcrourbnes runnng. When he load s relavely small can be enrely covered by he hrd mcrourbne and, he oher mcrourbnes are smply swched off. When he power demand exceeds he rang of he mcrourbne (3), a handover procedure akes place and he mcrourbne () s brough onlne. When he power demand exceeds he capably of wo mcrourbnes, he mcrourbne (1) s brough onlne o supplemen he power. Ths sraegy gves prory o all mcrourbnes ha are brough onlne necessary, snce he lnear relaonshp beween power and fuel flow. The economc resuls of hs sraegy are evden n comparson wh oher sraeges such as Fmncon. The sraegy followed by Fmncon s o dsrbue he power demand beween he hree mcrourbnes dencally. So Fmncon ses ou all mcrourbnes, whch mples a hgher cos han from Secan sraegy. In addon, Fmncon does no change s dsrbuon by changng he coeffcen k s o say ha hs dsrbuon s a dvson of he power demand on he number of mcrourbnes regardless of he arge se by he coeffcen k. The resuls for any value of Fmncon k = [0, 1] are summarzed n he Table.. Table. 9. Sécan 3 MTG objecve cos k= 1 Hour Demand P(1) P() P(3) Producon Cos Emsson 1 4,4 0 1,4 4,4 6,1 74,86 4, 0 1, 4, 6,6 71,63 3 1, 0 1, 1, 7,6 66,79 4 8, 0 8, 8, 8,9 63,98 60,6 0,6 60,6,1 6, ,7 6,7 66,7 11, ,7 9,7 69,7 11,90 47,8 8 7,7 7,7 1,48 43, ,0 17,0 77,0 13,31 38,83 78,8 18,8 78,8 13,68 37, ,8,8 80,8 14,08 3,7 1 81,8 1,8 81,8 14,8 3, ,8,8 80,8 14,09 3, ,8 18,8 78,8 13,67 37,4 1 7,7 7,7 1,48 43, ,6 3,6 63,6,76 6, ,6 0,6 60,6,1 6, ,7 6,7 66,7 11, ,7 7,7 1,48 43,36 7,8 1,8 7,8 13,07 40,0 1 78,8 18,8 78,8 13,67 37,4 66,7 6,7 66,7 11, , 0 4, 4, 8,0 6, , 0 18, 48, 7, 68,97 Fuel Cos n he end of he day ( ) 68, Emssons cos n he end of he day ( ) 1,9

5 Table.. Fmncon 3 MTG objecve cos k= 1 Hour Demand P(1) P() P(3) Producon Cos Emsson 1 4,43 14,14 14,14 14,14 4,43 8,73 9,83 4,4 1,1 1,1 1,1 4,4 9,18 6,73 3 1, 17,17 17,17 17,17 1,,07 1,0 4 8,1 19,40 19,40 19,40 8,1 11,07 4,6 60,61,,, 60,61 11,43 43, ,66,,, 66,66 1,3 40, ,70 3,3 3,3 3,3 69,70 1,8 38,38 8 7,73 4,4 4,4 4,4 7,73 13,8 36, ,97,66,66,66 76,97 13,94 3,14 78,8 6,8 6,8 6,8 78,8 14,3 34, ,79 6,93 6,93 6,93 80,79 14,3 33, ,6 7,6 7, ,69 33, ,8 6,9 6,9 6,9 80,8 14,4 33, ,79 6,6 6,6 6,6 78,79 14, 34,49 1 7,73 4,4 4,4 4,4 7,73 13,8 36, ,64 1,1 1,1 1,1 63,64 11,89 41, ,61,,, 60,61 11,43 43, ,66,,, 66,66 1,3 40, ,73 4,4 4,4 4,4 7,73 13,8 36,90 7,7,,, 7,7 13,7 3, ,79 6,6 6,6 6,6 78,79 14, 34,49 66,66,,, 66,66 1,3 40,04 3 4, 18,18 18,18 18,18 4,, 48, ,4 16,1 16,1 16,1 48,4 9,6 3,83 Fuel Cos n he end of he day ( ) 98 Emssons Cos n he end of he day ( ) 989,86 When k = 0, Secan opmzes under he objecve (emssons only). The opmzaon resuls are summarzed n he able.11. I may be noed ha hs mehod have a dfferen dsrbuon han when k = 1 so ha he mcrourbne operaes mosly n he range where s effcency s relavely hgh. Ths s he range expanded producon of 18 o kw where as we have already seen ha he mcrourbne pollues less. The mos remarkable resul o be derved from numercal resuls of hese wo exremes of he coeffcen k (0 and 1) s ha he dmnuon occurred n he cos of emssons [1,9-989,46 = 33,47], obaned durng he opmzaon where k = 0, s accompaned by an ncrease n he fuel cos [98,968-68,496 =,47]. Tha s o say ha reducng he cos of emssons s always a he expense of fuel coss and nversely. Ths las pon s very clear n he summary able.1 for he opmzaon performed by he Secan mulobjecves mehod (k = 1, 0.8, 0., 0.3 and 0). Table. 11. Sécan 3 MTG objecve cos k=0 Hour Demand P(1) P() P(3) Producon Cos Emsson 1 4,43 1,0 14,16 13, 4,43 8,8 9,78 4,4 16,01 1,17 14,8 4,4 9,6 6,68 3 1, 17,9 17,19 16,41 1,,1 1,01 4 8,1,04 19,41 18,7 8,1 11,14 4,60 60,61,80,1 19,60 60,61 11,0 43, ,66,7,3 66,66 1,40 40,0 7 69,70 3,68 3,4,78 69,70 1,86 38,36 8 7,73 4,63 4, 3,84 7,73 13,3 36, ,97,98,66,33 76,97 13,97 3,13 78,8 6,7 6,9,99 78,8 14,6 34, ,79 7,19 6,93 6,67 80,79 14,6 33, ,0 7,7 7, ,71 33, ,8 7, 6,9 6,69 80,8 14,6 33, ,79 6, 6,7,97 78,79 14, 34,49 1 7,73 4,63 4, 3,84 7,73 13,3 36, ,64 6 1,,66 63,64 11,9 41, ,61,80,1 19,60 60,61 11,0 43, ,66,7,3 66,66 1,40 40,0 19 7,73 4,63 4, 3,84 7,73 13,3 36,89 7,7,9,6 4,91 7,7 13,78 3, ,79 6, 6,7,97 78,79 14, 34,49 66,66,7,3 66,66 1,40 40,0 3 4, 18,88 18,19 17,47 4,,60 48,4 4 48,4 16,9 16,17 1,33 48,4 9,70 3,79 Fuel Cos n he end of he day ( ) 99 Emssons cos n he end of he day ( ) 989,46 Table. 1. Fuel and emsson coss Objecf foncon Fuel coss( ) Emsson coss ( ) Toal coss ( ) Fuel where k=1 68,496 1,9 1491,416 fuel-emsson where k= ,0047e3 19,7 fuel-emsson where k=0. 96, ,49 187,377 fuel-emsson where k=0.3 98, ,6 187,717 emsson where k=zero 98, ,46 188,48 We ake he hrd column (oal coss) o fnd compromse beween wo goals (fuel and emsson), we fnd ha he coeffcen (k) can ake he value (0,) o acheve hs compromse. Fnally, regardng he compuaon me, s for Secan mehod of abou 0,03788 seconds, whle for fmncon s abou 3,8697 seconds. 3.. Example Anoher approach o solvng he un commmen (UCP) s presened n he leraure [13]. I s based on a marx real-coded genec algorhm (MRCGA) wh new reparng mechansm and wndow muaon. The MRCGA chromosome consss of a real number marx represenng he generaon schedule. Usng he proposed codng, he MRCGA can solve he UCP hrough genec operaons and avod copng wh a subopmal economc dspach (ED) problem. The new reparng mechansm guaranees ha he generaon schedule sasfes sysem and un consrans. The wndow muaon mproves he MRCGA searchng performance. Numercal resuls show an mprovemen n he soluon cos compared wh he resuls obaned from oher algorhms. The exensve sudes have been performed for large-scale power sysem by consderng, 40, 60, 80 and 0 generang un. In hs example, he commmen schedule for 0-un sysem s deermned by Secan, fmncon and MRCGA. Also he resuls of he proposed algorhm were compared n erms of soluon qualy wh convenonal mehods such as Dynamc Programmng, Lagrangan relaxaon mehod, a marx real-coded genec algorhm (MRCGA), Heursc mehods such as genec algorhms (GA), Fmncon, smulaed annealng (SA) and evoluon program (EP). Frsly, he sysem -uns daa and 4-h load demand are shown n he ables.13 and 14. For he -un confguraon, he nal -un sysem daa were duplcaed. The 40 0-un sysems were creaed n he same way. The economc dspach for uns made by he Secan mehod s summarzed n he able. 1, also he economc dspach made by he mehod Fmncon s n he able.16. MRCGA soluons for each sysem are presened n Table.17, wh soluons of oher algorhms. Superory MRCGA s evden, ndcang ha he MRCGA s beer han oher algorhms [13]. On he oher sde, we appled he mehod Secan and Fmncon on hese sysems lsed above and have nsered he resuls n wo new

6 columns n he same comparson able. 18. Takng a look a hs able, we fnd Secan mehod ha has dvded he producon accordng consrans and wh Table. 13. Paramères of uns an addonal gan of fuel cos and sarup. Therefore, hs able economcally valorzes our mehod n he essenal objecve of mnmzng he fuel cos. Table hours load demand Hour load Hour load Table. 1. The resuls of he economc dspach by Secan mehod for uns N uné heure ,18 67, , ,18 67, ,37 7 6,7 87, ,36 8 6,7 87, , , , Table. 16. The resuls of he economc dspach by fmncon mehod for uns hour p1 p p3 p4 p p6 p7 p8 p9 p p11 p1 p13 p14 p1 p16 p17 p18 p19 p demand Cos , , , , , , , , , , , , , , , , , , , , , , , ,98 Execuon me = sec oal cos ,9 Table. 17. The resuls of he economc dspach by MRCGA mehod for uns Hour p1 p p3 p4 p p6 p7 p8 p9 p p11 p1 p13 p14 p1 p16 p17 p18 p19 p Demand ,1 43, ,8 89, ,3 408, ,6 6, , , ,8 7, ,6, ,6 43, ,7 37,6 13,4 14,3, ,6, ,9 7, ,4 19,

7 Compuaon me (sec) , 81,6 19, , 367,1 14, ,3 43, ,4 31, ,3 16, , , ,6 4, , 341, Table. 18. Toal coss obaned wh dfferen algorhms N un LR [4] EP [14] GA1 [4] GA [] ICGA [33] MRCGA fmncon Secan , , , , , Regardng execue me, we ploed he curve (execue me-number of uns) for he hree mehods o compare (Secan, MRCGA [13] and Fmncon) see Fg.4. We can clearly see n he able. 19, ha he execue me aken by he Secan mehod s lower han ha aken by he oher mehods (MRCGA and Fmncon). Table. 19. Execue me for algorhms compared N unes Execue me (sec) for MRCGA Mehod Execue me (sec) for Fmncon Mehod Execue me (sec) for Sécan Mehod Compuaon me (sec) n uns MRCGA Mehod Fmncon Mehod Secan Mehod Fgure 4. Compuaon me comparson 4. Concluson Ths paper has suggesed parcle swarm opmzaon combned wh IPPD able for solvng un commmen problem. Ths work conssed n s enrey n a echncal-economc sudy whose objecve was o mnmze fuel cos and emssons cos of a small cenral cogeneraon mulmachnes conssed of hree gas mcrourbnes. The advanages of Secan mehod are: Showng remarkable robusness and flexbly. The proposed algorhm can oban feasble and sasfacory soluons of dfferen UC problems, regardless of he sysem sze. Avodng solvng he subopmal ED problem n each our, he calculaon speed s ncreased and he execue me are shorened. The proposed generalzed algorhm was appled o 0-un n a 4 h un commmen schedule. The praccal resuls confrm ha he proposed algorhm (Secan mehod) acheves excellen resuls. Inally for all power demands, he un saus s deermned by IPPD able hen he opmal soluon s obaned by secan mehod.. References [1] K.Chandram, Dr. N.Subrahmanyam, M.Sydulu, Naonal Insue of Technology, Warangal, A.P, INDIA Dynamc Economc Dspach by Equal Embedded Algorhm, 4h Inernaonal Conference on Elecrcal and Compuer Engneerng. ICECE 06, 19-1 December 06, Dhaka, Bangladesh. [] F. Alkhall, Ph. Degober, F. Colas and B. Robyns Member, IEEE, «Fuel consumpon opmzaon of a mulmachnes mcrogrd by secan mehod combned wh IPPD able» (ICREPQ 09), Span, Aprl, 09. [3] H.M.Ana Numercal mehods for Scenss and engneers nd ed., 0 Brkhäuser publshers. [4] Press, W. H. Flannery, B. P. Teukolsky, S. A.; and Veerlng, W. T. Secan Mehod, False Poson Mehod, and Rdders' Mehod. 9. n Numercal Recpes n FORTRAN: The Ar of Scenfc Compung, nd Ed. [] C.P.Chang, C.W.Lu and C.C.Lu, Un commmen by Lagrangan relaxaon and genec algorhms, IEEE Trans Power Sys 1 (00) (), pp [6] Carlos A. Hernandez-Aramburo, Member, IEEE, Tm C. Green, Member, IEEE, and Ncolas Mugno Fuel Consumpon Mnmzaon of a Mcrogrd, IEEE ransacons on ndusry applcaons, vol. 41, NO. 3, May/June 0. [7] C.C.A. Rajan, M.R. Mohan and K. Manvannan Neural-based abu search mehod for solvng un commmen problem IEE Proceedngs-Generaon, ransmsson and Dsrbuon, Inda, July 03, pp [8] N.P.Padhy, Un commmen a bblographcal survey, IEEE Trans Power Sys 19 (04) (), pp [9] Capsone Turbne Corporaon, 4004 Rev. D (Aprl 06). Techncal Reference. [] Therry BENOIST, BOUYGUES/e-lab, Maurce DIAMANTINI ENSTA/LMA, Benoî ROTTEMBOURG BOUYGUES/e-lab Relaxaon lagrangenne e flrage par coûs rédus applqués à la producon d élecrcé. Rappor ENSTA, 4 jun 0, p. [11] hp:// [1] C Perurbaons Capsone, rappor EDF R&D. [13] Lyong Sun, Yan Zhang, Chuanwen Jang. A marx real-coded genec algorhm o he un commmen problem Elecrc Power Sysems Research 76 (06) Avalable onlne 1 December 0. 7