Applied Soft Computing

Transcription

1 Appled Soft Computng (2) 4 46 Contents lsts avalable at ScenceDrect Appled Soft Computng journal homepage: wwwelsevercom/locate/asoc Soft computng based optmzaton of combned cycled power plant start-up operaton wth ftness approxmaton methods Ilara Bertn, Matteo De Felce, Alessandro Panncell, Stefano Pzzut ENEA, CR Casacca, Va Angullarese 3, Roma, Italy artcle nfo abstract Artcle hstory: Receved 2 May 2 Receved n revsed form 3 November 2 Accepted 28 February 2 Avalable onlne 9 March 2 Keywords: Combned cycle power plant Evolutonary algorthm Fuzzy logc Process optmzaton Ths paper descrbes an applcaton of fuzzy-logc and evolutonary computaton to the optmzaton of the start-up phase of a combned cycle power plant We modelled process experts knowledge wth fuzzy sets over the process varables n order to get the needed cost functon for the genetc algorthm (GA) we used to obtan the optmal regulatons Due to the obvous mpossblty to test the resultng nputs on the real plant we used a complex software smulator to evaluate the performance of the solutons In order to reduce the computatonal load of the whole procedure we mplemented for the genetc algorthm a novel ftness approxmaton technque, cuttng by 98% the number of ftness evaluatons, e software smulator wth respect to a genetc algorthm wthout ftness approxmaton Moreover, solutons found by our methods remarkably mproved the solutons gven by the plant operators 2 Elsever BV All rghts reserved Introducton Combned cycle power plants (CCPP) are a combnaton of a gas turbne and a steam turbne generator for the producton of electrc power n a way that a gas turbne generator generates electrcty and the waste heat s used to make steam to generate addtonal electrcty va a steam turbne For such plants, one of the most crtcal operatons s the start-up stage because t requres the concurrent fulflment of conflctng objectves (for example, mnmse pollutant emssons and maxmse the produced energy) The problem of fndng the best trade-off among conflctng objectves can be arranged lke an optmzaton problem Ths class of problems can be solved n two ways: wth a sngle-objectve functon managng the other objectves, lke thermal stress, as constrants, and wth a mult-objectve approach At present, the problem of CCPP start-up optmzaton has been tackled n the frst way usng smulators As example, n Ref [] through a parametrc study, the start-up tme s reduced whle keepng the lfe-tme consumpton of crtcally stressed components under control In Ref [2] an optmum start up algorthm for CCPP, usng a model predctve control algorthm, s proposed n order to cut down the start-up tme keepng the thermal stress under the mposed lmts In Ref [3] a study amed at reducng the start-up tme whle keepng the lfe-tme consumpton of the more crtcally stressed components under control s presented Correspondng author E-mal address: matteodefelce@eneat (M De Felce) In the last decade the applcaton research of fuzzy set theory [4] has become one of the most mportant topcs n ndustral applcatons In partcular, n the feld of ndustral turbnes for energy producton, t has been manly appled to fault dagnoss [5,6], sensor fuson [7] and control Partcularly, n the last area n Ref [8] t s proposed a fuzzy control system n order to mnmze the steam turbne plant start-up tme wthout volatng maxmum thermal stress lmts In Ref [9] t s presented a start-up optmzaton control system whch can mnmze the start-up tme of the plant through cooperatve fuzzy reasonng and a neural network makng good use of the operatonal margns on thermal stress and NO x emssons In all the reported examples t s clear that the global start-up operatons are not optmsed Therefore, n ths work we propose an approach based on fuzzy sets n order to overcome the exposed drawbacks Thus, for each sngle objectve we defne a fuzzy set and then we properly combne them n order to get a new objectve functon takng nto account all the operatonal goals We appled ths method to a large artfcal data set of dfferent start-up condtons and we compared the best soluton we found wth the one gven by the process experts Our dea s to use an evolutonary algorthm n order to optmse the whole start-up process, ths because EA wll offer an easy and adaptable way to fnd an optmum n a complex functon wthout the need of a deep knowledge of the process Ths knd of algorthms are able to self-learn the trend of the objectve functon and seek for the best solutons n few steps compared wth other optmzaton algorthms In order to let the EA to work fne, we need to defne a unque functon that can represent the state of our process, consderng a lot of varables (consumpton, emssons, tme, etc) and /$ see front matter 2 Elsever BV All rghts reserved do:6/jasoc2228

2 I Bertn et al / Appled Soft Computng (2) mergng them n a representatve value For ths reason we have used a fuzzy set based ftness functon whch allows us to group many varables nto a sngle value EAs, as stochastc technques, need an hgh number of evaluatons of the ftness functon n order to fnd the optmal soluton and when the functon s expensve (computatonally or economcally), as n real-world applcatons, t could be approxmated to reduce the number of tme-consumng calls, see Ref [] for a survey about ths knd of approach Evolutonary algorthms have already been appled to the combned cycles power plants optmzaton An applcaton of an evolutonary algorthm to the mnmzaton of the product cost of complex combned cycle power plants s proposed n Ref [] where both the desgn confguraton (process structure) and the process varables are optmzed smultaneously Ref [2] apples an evolutonary algorthm to optmze the feedwater preheatng secton n a steam power plant from a thermodynamc vewpont A power plant desgn problem s analyzed n Ref [3] and the optmzaton, concernng techno-economc aspects, s carred out through multobjectve evolutonary algorthms Our man contrbuton s the applcaton of soft computng methods to the global start-up optmzaton of such plants wth a method for reducng the computatonal load of the optmzaton process Ths paper s organzed as follows Secton 2 ntroduces the optmzaton problem, descrbng the start-up phase and the nvolved parameters Secton 3 descrbes the fuzzy sets modellng of the problem descrbed n the prevous secton Descrptons of the EAs approaches, wth and wthout the approxmaton method, are gven n Sectons 4 and 5 and the results are presented n Secton 6 Secton 7 provdes some concludng remarks 2 The combned cycle power plant start-up optmzaton problem Gas and steam turbnes are an establshed technology avalable n szes rangng from several hundred klowatts to over several hundred megawatts Industral turbnes produce hgh qualty heat that can be used for ndustral or dstrct heatng steam requrements Alternatvely, ths hgh temperature heat can be recovered to mprove the effcency of power generaton or used to generate steam and drve a steam turbne n a combned-cycle plant Therefore, ndustral turbnes can be used n a varety of confguratons: Smple cycle (SC): a sngle gas turbne producng power only Combned heat and power (CHP): a smple cycle gas turbne wth a heat recovery heat exchanger whch recovers the heat n the turbne exhaust and converts t to useful thermal energy usually n the form of steam or hot water Fg Combned cycle power plant start-up operaton Combned cycle (CC): hgh pressure steam s generated from recovered exhaust heat and used to create addtonal power usng a steam turbne The last combnaton produces electrcty more effcently than ether gas or steam turbne alone because t performs a very good rato of transformed electrcal power per CO 2 emsson CC plants are characterzed by hgh effcency and possblty to adapt operaton to dfferent load condtons but they are an hghly complex system whch need the avalablty of powerful processors and advanced numercal solutons to develop hgh performance smulators for modellng purposes 2 Start-up phase The start-up schedulng dagram s shown n Fg From zero to tme t (about 2 s) the rotor engne velocty of the gas turbne s set to 3 rpm From tme t to t the power load s set to MW and then the machne keeps ths regme up to tme t 2 All ths ntal sequence s fxed From tme t 2 to t 3 (about 36 s) the machne must acheve a new power load, the ntal set pont load ndcated as X, set pont whch has to be set optmal and then the machne has to keep ths regme up to tme t 4 The tme lag t 4 t 3 s varable and s another varable to optmze, here called X 2, and durng ths nterval the steam turbne starts wth the rotor reachng the desred velocty Then the turbnes have to reach at tme t 5 the normal power load regme (27 MW for the gas turbne) accordng to two load gradents whch are varable dependng on the machne; the gradent for both, compressor and steam rotors, are the last optmzaton varable that we should use: X 3 and X 4 The sequence for that procedure s that frst steam turbne grow up wth X 4 gradent, then the turbne rotor can grow up followng the X 3 gradent Table Process nput and output varables Input varables Varable Meanng Operatng range Unt measure X Intermedate power load set pont [2, 2] MW X2 Intermedate watng tme [75,,] s X3 Gas turbne load gradent [, 2] MW/s X4 Steam turbne load gradent [, 2] %/s Output varables Varable Meanng Operatng range Unt measure Y Start-up tme [,7, 29,46] s Y2 Fuel consumpton [53,, 23,33] Kg Y3 Energy producton [645 8, ] KJ Y4 Pollutant emssons [224, 3258] Mg s/n m 3 Y5 Thermal stress [8, 3939]

3 42 I Bertn et al / Appled Soft Computng (2) 4 46 Table 2 Fuzzy sets Fuzzy set Membershp functon ( F ) Varable Weght (w ) t c Goal F sgmod Y 2 8, Mn F2 sgmod Y2 8 6,2 Mn F3 Sgmod Y Max F4 sgmod Y Mn F5 sgmod Y Mn F x 4 F x 5 F x 9 F F Fg 2 Fuzzy sets dagram Fg 3 Dagram of the ftness model In Table we report the process control varables (nput) and the output varables to be montored Therefore, the problem we are tacklng has four nputs and fve outputs and n order to optmse the overall start-up operatons, the followng objectves need fulfllng (Fgs 2 5): Mnmse startup tme (Y) 2 Mnmse fuel consumpton (Y2) 3 Maxmse energy producton (Y3) 4 Mnmse pollutant emssons (Y4) 5 Mnmse thermal stress (Y5) In Fg 6 a dagram wth the correlaton between each par of objectves s shown, some lnear relatons are vsually evdent, eg between fuel consumpton (Y2) and energy producton (Y3) Fg 4 Example of the proposed approxmaton method: ftness value of requested pont (square) s computed nterpolatng the ftness value of ts neghbours (r 2 and r 3), e all the ponts below the RANDOM THRESHOLD (T random ) radus The grey space s the part of the soluton space where ftness value s computed randomly T dstances represents DISTANCE THRESHOLD 3 Fuzzy sets defnton In order to allow a process of optmzaton through a black-box technques such as evolutonary algorthms, we need to defne a unque numercal quantty that can evaluate the whole process of start-up, gvng an ndex of how the gven confguraton s effectve, n harmony wth the desred trend of the output values The computed quantty wll be used as a ftness value for our ndvduals n the evolutonary envronment In collaboraton wth process experts, we frst defned the sngle fuzzy sets (see Table 2) over the output varables (see Table and Fg 2) and we composed them n order to get a cost functon rangng n the range [, ] Therefore, we got an ndex representng the global start-up performance For every membershp functon, each lnked to one of the process output, we used sgmod membershp functons wth two parameters c and t: sgmod(x) = + exp(c x/t) These functons are used smply as they are, f we wsh to maxmze the value, or used n a complementary mode, f we wsh to mnmze the output The resultng fuzzy output has the followng Table 3 GA parameters Parameter Value Populaton sze 2 Mutaton rate 5 Mutaton ampltude () Crossover rate 9 Tournament pool sze 2 Max number of generatons Target ftness value 83 ()

4 I Bertn et al / Appled Soft Computng (2) ftness (a) GA: Dstrbuton of ftness values generatons (b) GA: Dstrbuton of number of generatons ftness (c) GA wth Ftness Approxmaton: Dstrbuton of ftness values generatons (d) GA wth Ftness Approxmaton: Dstrbuton of number of generatons Fg 5 Results of expermentatons Table 4 Expermentaton results Genetc algorthm (GA) Success rate 79% Average number of generatons 44 Average ftness value 83 Average CPU tme per smulaton 27 h GA wth ftness approxmaton Success rate 98% Average number of generatons 44 Average ftness value 85 Average CPU tme per smulaton 36 h form: (y,y 2,y 3,y 4,y 5 ) = 5 w F (y ) (2) = Ths composton has been fnally chosen because we found out that for ths problem the ntersecton was too restrctve (only one objectve wth a low value s suffcent to severely affect the whole performance) and the unon was too lazy (only one objectve wth a hgh value s suffcent to have a hgh global performance) Thus, we have fnally appled the weghted sum operator, whch s a good trade-off between ntersecton and unon, whch gves a global performance proportonal to the optmalty degree of each sngle objectve To obtan the weght for each fuzzy set n the prevous composton we worked wth the desgner of ths knd of turbo gas, n order to acheve a good combnaton of weghts that can represent the theoretcal drectons that they try to reach when workng on the start-up of ths knd of process Wth ths functon we try to work n cooperaton wth human behavour, learnng from the experence, nstead of replacng the human factor 4 Optmzaton wth evolutonary computaton In ths secton we descrbe the optmzaton of the cost functon defned n the prevous secton by the means of an evolutonary algorthm Evolutonary computaton methods have been used successfully n many optmzaton problems The ablty to perform a parallel search explorng n the soluton space and explotng the best solutons found s crtcal for the most complex problems In our case the soluton s genotype represents a start-up sequence encodng the varables descrbed n Table We mplemented a real-coded genetc algorthm wth a number vector s genotype representng normalzed process nput varables We choose a real-values encodng because of the contnuous search space and n ths way we avoded the dscretzaton due to bnary codng The normalzaton of the nput varables, between and, s to make mutaton operators parameters heterogeneous gven that nputs varables dffer strongly n magntude (see Table ) A Gaussan mutaton operator s mplemented addng a random value followng a normal dstrbuton to the genotype s genes, e: g m = g + N(,) (3) where g s the th gene and s the standard devaton of the gaussan dstrbuton We used a unform crossover wth a bnary tournament selecton and then as ftness functon we use the fuzzy functon shown n Eq (2) (see Fg 3 for a dagram of the ftness model), whch s wthn the range [, ] Two termnaton crtera have been set for ths algorthm: maxmum number of generatons and a target ftness value Algorthm s parameters selected after a set of expermentatons are shown n Table 3

5 44 I Bertn et al / Appled Soft Computng (2) 4 46 Fg 6 Plot of relatons between objectves Table 5 Comparson between soluton provded by plants manager and best solutons of both approaches Y Y2 Y3 Y4 Y5 Experts 2,7 43, GA (values) 4,8 99, GA wth FA (values) 6,569 5, GA (mprovement) 35% 25% 25% 7% % GA wth FA (mprovement) 25% 6% 6% 3% 2%

6 I Bertn et al / Appled Soft Computng (2) Approxmatng the ftness functon for computaton load reducton Algorthm Calculate Approxmate Ftness f(x) Requre: pont x, archve R :dstance(x,r x )< DISTANCE THRESHOLD then 2: j nearest (x,r x ) Get the ndex of the nearest pont from x nsde the archve f (x) R f j 3: f (x) R f j 4:else 5:dstance(x,R x )< RANDOM THRESHOLD then 6:N neghbourhood(x) Get the ponts whch dstance from x s below the threshold 7: f (x) +dstance(x,r x ) Rf N 8:else 9: f(x) random(,) : end f :end f Evolutonary algorthms appled to computatonal expensve problems, lke the one consdered n ths paper, could be tme consumng due to ther stochastc nature To tackle ths ssue we mplemented an approxmaton method (pseudo-code s shown n algorthm 5) for the ftness wth the purpose of reducng the number of ftness functon calls All the ponts evaluated are stored nto an archve R contanng the pont s n-dmensonal coordnates and ther ftness value n the last column, wth the followng form: x x n f x 2 x 2n f 2 R = [R x R f ] = (4) x k x kn f k When the ftness value of a new pont s requested, a search wthn the archve s performed to fnd a smlar pont, consderng two ponts smlar f ther eucldean dstance s below a certan threshold (DISTANCE THRESHOLD), n ths case we assume for the requested pont the same ftness value of the smlar one already nsde the archve Dfferently, f there s not a smlar pont, the method computes the ftness values n two ways: randomly, f the nearest pont nsde archve dstance s above a threshold (RAN- DOM THRESHOLD), otherwse nterpolatng the ftness value of the nearest ponts (see Fg 4) The nterpolated ftness of the requested pont s obtaned from a weghted sum of the nearest ponts ftness values consderng weghts nversely proportonal to the eucldean dstance of the ponts (see lne 7 n algorthm 5) At the end of each generaton the best ndvdual of the populaton s evaluated wth the real ftness functon and added to the archve The archve represents the nformaton we have collected on the ftness model and the proposed method tres to approxmate new ponts ftness wth an nterpolaton unless the pont s too dstant In such case, randomness represents the lacks of nformaton about that part of the ftness space and a random value enhances the possblty of explore unknown areas wth the probablty related to the ftness of the best ndvdual In fact, especally at the begnnng of the evoluton, a random value has an hgher probablty to have a better ftness value than the best soluton already nto the populaton 6 Results We performed 4 of the algorthm usng the GA nterfaced wth the software smulator used to compute the ftness functon value In Fg 5 s shown the dstrbuton of the best solutons ftness values at the end of the expermentatons and n Fg 5 the same for the number of generatons The average number of generatons s 44, e the number of functon calls s 828 because at each generaton a number of ftness evaluatons equal to the populaton sze s performed The same number of s performed wth the ftness approxmaton method, n Fg 5(c) and (d) are shown respectvely the dstrbuton of the best solutons ftness values and the same for the number of generatons at the algorthm s stop In Table 4 there s a comparson of the performance of both the approaches, wth and wthout ftness approxmaton For DISTANCE THRESHOLD and RANDOM THRESHOLD we used respectvely a value of and, chosen after a set of prelmnary tests In the ftness approxmaton scheme we perform a sngle ftness functon evaluaton for each generaton (the best solutons at the end of the generaton), n ths way an average run needs only 44 ftness functon calls nstead of the 828 needed wthout ftness approxmaton We compared the optmal solutons found by both approaches wth the soluton provded by the experts, n Table 5 we show the value of the fve output varables (see Table ) for each soluton and mprovement of such soluton calculated as: Y Y e d = range max range mn wth Y e s the th output varable of the soluton provded by experts, range max and range mn the operatve ranges of the th varable (see Table ) The sgn of the devaton s put postve f the devaton s consdered an mprovement, negatve vce versa 7 Conclusons When n an optmzaton problem the objectves are conflctng and subject to operatonal constrants, lke n ndustral applcatons, black-box approaches lke evolutonary algorthms mght gve good performances due to ther stochastc nature, assumng that an effectve problem s representaton could be found Multobjectve optmzaton problems can be coped wth two dfferent methodologes: Pareto-based optmzaton and sngle-objectve reducton wth expert knowledge modellng In the frst case, consderng all the objectves wth the same prorty, a Pareto front contanng all the non-domnated solutons s obtaned, n our case the applcaton of ths mult-objectve approach was not consdered successful due the complexty of the problem and other factors (see Ref [4] for further detals) Fuzzy logc-based approach permts to model the experts knowledge, reducng the problem to a sngle-objectve one whch can be tackled wth classcal evolutonary algorthms A major drawback for stochastc algorthms such EAs can be the hgh number of ftness evaluatons needed n order to explore the soluton space and fnd the optmal solutons In applcatons where ftness functon s partcularly tme-consumng, lke the one n ths paper, we can try to nterpolate the ftness value of the new ponts from the solutons already evaluated assumng a statc envronment where the ftness value of a solutons does not change durng the tme Despte the nterpolaton we mplemented s not complex t provdes better performances n the applcaton of a genetc algorthm, leadng to a reducton of the overall number of ftness functon evaluatons avodng the evaluatons of smlar or dentcal solutons In our tests we obtaned a strong reducton of the number of ftness evaluatons and a consequent decrease of the tme needed for the optmzaton of the start-up phase from 27 h to 36 for smulatons However, both the approaches lead to a startup sequence whch s better than the already used one accordng to the plants operator and the results whch show (see Table 5) (5)

7 46 I Bertn et al / Appled Soft Computng (2) 4 46 an mprovement n three objectves and a worsenng (n energy producton) References [] F Alobad, R Postler, J Ströhle, B Epple, H-G Km, Modelng and nvestgaton start-up procedures of a combned cycle power plant, Appled Energy 85 (2) (28) [2] F Tetsuya, An optmum start up algorthm for combned cycle, Transactons of the Japan Socety of Mechancal Engneers 67 (66) (2) [3] F Casella, F Pretolan, Fast start-up of a combned-cycle power plant: a smulaton study wth modelca, n: Proceedngs 5th Internatonal Modelca Conference, 26, pp 3 [4] H-J Zmmermann, Fuzzy set theory-and ts applcatons, 3rd edton, Kluwer Academc Publshers, Norwell, MA, USA, 996 [5] S Ogaj, L Marna, S Sampath, R Sngh, S Prober, Gas-turbne fault dagnostcs: a fuzzy-logc approach, Appled Energy 82 () (25) 8 89, do:6/japenergy2474 [6] RP Fasel, V Palade, RJ Patton, J Quevedo, S Daley, Fault dagnoss of an ndustral gas turbne usng neuro-fuzzy methods, n: Preprnts of the 5 th IFAC World Congress, 22 [7] K Goebel, AM Agogno, Fuzzy sensor fuson for gas turbne power plants, SPIE 379 (999) 52 6, do:7/23437, aporg/lnk/?psi/379/52/ [8] A Boulos, K Burnham, A fuzzy logc approach to accommodate thermal stress and mprove the start-up phase n combned cycle power plants, Proceedngs of the Insttuton of Mechancal Engneers, Part B: Journal of Engneerng Manufacture 26 (22) [9] H Matsumoto, Y Ohsawa, S Takahas, T Akyama, H Hanaoka, O Ishguro, Startup optmzaton of a combned cycle power plant based on cooperatve fuzzy reasonng and a neural network, IEEE Transactons on Energy Converson 2 () (997) 5 59, do:9/ [] Y Jn, A comprehensve survey of ftness approxmaton n evolutonary computaton, Soft Computng 9 () (25) 3 2 [] C Koch, F Czesla, G Tsatsarons, Optmzaton of combned cycle power plants usng evolutonary algorthms, Chemcal Engneerng and Processng: Process Intensfcaton 46 () (27) 5 59, do:6/jcep26625 (Specal Issue on Process Optmzaton and Control n Chemcal Engneerng and Processng) [2] R Dobrowolsk, A Wtkowsk, R Lethner, Smulaton and optmzaton of power plant cycles, n: Proceedngs of the 5th Internatonal Conference on Effcency, Costs, Optmzaton, Smulaton and Envronmental Impact of Energy Systems, 22, pp [3] ET Bonatak, K Gannakoglou, Prelmnary desgn of optmal combned cycle power plants through evolutonary algorthms, Evolutonary and Determnstc Methods for Desgn Optmzaton and Control wth Applcatons to Industral and Socetal Problems, EUROGEN (25) 25 [4] I Bertn, MD Felce, F Morett, S Pzzut, Start-up optmsaton of a combned cycle power plant wth multobjectve evolutonary algorthms, n: Applcatons of Evolutonary Computaton, vol 625/2 of Lecture Notes n Computer Scence, Sprnger, Berln/Hedelberg, 2, pp 5 6