Multireservoir Simulation Using Multipurpose Constraints and Object-Oriented Software Design

Transcription

1 Mulreservor Smulaon Usng Mulpurpose Consrans and Objec-Orened Sofware Desgn Marcelo A. Ccogna, Darrell G. Fonane, Ieda G. Hdalgo and João E. Lopes 3 Anhanguera Educaconal S.A., Alameda Mara Terea,.000, Valnhos, São Paulo, Brasl; PH 55 (9) 35-75; emal: marceloccogna@gmal.com. Dep. of Cvl Engneerng, Colorado Sae Unversy, F. Collns, CO 8053; emal: {darrell.fonane, eda.hdalgo}@colosae.edu. 3 Duke Energy Inernaonal Geração Paranapanema, Av. Das Nações Undas,.90, São Paulo, SP, Brasl; emal: jelopes@dglne.com.br ABSTRACT The hydroelecrc shor erm plannng s que challengng n order o respec all he operaonal resrcons concerned wh hydropower generaon. A dealed smulaon model combnng mulpurpose consrans and objec-orened sofware desgn s presened for shor erm decson suppor. The objec-orened desgn perms a mahemacal srucure ha separaes he decson asks from he regular hydroelecrc compuaon. The man operaonal polcy allows users o evaluae a hydro generaon schedule usng nflow forecasng. In oher words, he smulaor can accep hydro generaon as daa npu and conver o waer flow varables (urbnes dscharge and spllage), usng he nflow forecas and he nal reservor s sorage. The waer balance equaon, hydro generaon and effcency calculaon modules are synchroned wh mulreservor operaon. As an mporan resul, hs smulaor can auomacally correc he npu daa of he operaonal polcy, savng subsanally me n he decson-makng process. A es problem on 94-reservor subsysem whn he Bralan Inegraed Hydropower Generaon Sysem was smulaed usng an hourly me-sep over a one-week horon wh good performance, demonsrang he smulaon model s capables for solvng a large scale hydropower operaon problem. SIMULATIO MODEL In reservor managemen pracces, a smulaon model can be used as a valuable plannng ool o evaluae he mpac of changes o he sysem's confguraon or operaonal objecves. The desred generaon or release schedulng can be checked usng nflow forecasng n order o sasfy he enre se of operaonal consrans. A he real me operaon sage, a smulaon ool can be used o quckly check operaonal alernaves due o emergency evens or plannng and real-me ncongruence. In pos-operaon sudes, a smulaor can be appled as a daa consoldaon ool n exhausve nspecon of recorded rajecores feasbly (Hdalgo e al., 009). Insered n a compuer-aded scenaro, Yeh (985) ces smulaon as a modelng echnque ha s used o approxmae he behavor of a sysem on he compuer, represenng all he characersc of he sysem by a mahemacal descrpon. Wurbs (993) provded exensve ls of smulaon compuer models for reservor sysem analyss. Usng he classfcaon presened by Wurbs, hs model can be classfed as a convenonal smulaon model n he sense ha no formal opmaon or mahemacal programmng algorhms are used. However,

2 wll be shown ha he daa srucure for he jon operaon of hydro plans can be represened as a nework flow model and hs desgn can represen a dealed hydroelecrc mahemacal model. The smulaon of mulpurpose reservor operaon s also presened. Fonane (997) provded a relevan reservor operaons plannng model hrough fuy dynamc programmng o deal wh mprecse objecves. Ths model gudes he mulpurpose mplemenaon of he presen smulaon model. The mahemacal model and sofware desgn are presened wh emphass on a praccal applcaon so ha fuure researchers are able o reproduce hese resuls. The auhors beleve ha any knd of opmaon model for reservor operaon has lmaons (Labade, 004). Also, s hard o fnd comparson sudes among dfferen models and her resuls. In hs sense, dfferen operaonal polces can be checked n a dealed smulaon model, wh a parcular objec-orened desgn, o address performance analyses and o evaluae dsance beween model resuls and real problem aspecs. A es sudy on 94-reservor sub-sysem of Bralan hydro plans s presened as demonsraon of smulaon model s capables and compuaonal performance. The user nerface s descrbed o presen useful sofware resources for mulreservor operaon analyss. The concludng secon dscusses desgn and mplemenaon experence and plans for fuure developmen. Reservor Model The reservor operaon has lms and consrans assocaed wh he mum and mnmum waer levels, as descrbed n Fgure. For reservors wh hydroelecrc powerhouses, he mnmum level akes no accoun he mnmum head ha perms generaon. The c level represens he dam cres elevaon. m c mn r Fgure. Reservor operaonal waer levels. Above he mum operaonal level, here s an absolue mum waer level relaed o dam secury. The smulaon model presened here has a parcular compuaon module ha auomacally deals wh reservor consrans under emergency suaons, as wll be descrbed no he sofware desgn secon. Hydroelecrc Model The smulaon model has a dealed represenaon of he hydro plans, focused on a complee se of operaon consrans and nonlnear equaons. Fgure llusraes an arrangemen of he man operaonal varables. Ths paper uses he

3 SI uns sandard o presen he daa for he Bralan hydro plans, alhough he modelng resources can use oher sandards for general applcaon. x r q u Fgure. Hydro plan s man varables arrangemen. Hydroelecrc power avalably s drecly relaed o he poenal energy creaed by a dam,.e. depends on he dfference beween upsream and downsream waer levels. Therefore he gross head s drecly calculaed as: h g = ( x) ( u) () where: h g s he gross head (m). x s he waer sorage n he reservor (0 6 m³ or hm³). u s he oal waer release (ouflow), ha s, he sum of he dscharge q and he spllage s (m³/s). (x) s he forebay elevaon (m) as a funcon of he waer sorage x. r (u) s he alrace elevaon (m) as a funcon of he waer release u. The forebay and alrace equaons could be expressed as any funcon of reservor sorage and oal ouflow, respecvely. In he case of Bralan hydroelecrc plans, hose funcons are commonly represened by polynomals. There are also losses from he poenal energy due o frcon of flow hrough raceways, racks and gaeways (Mead, 908). These losses can be esmaed as a quadrac funcon of urbne dscharges, as expressed n Equaon (). Therefore, he pensock head losses are measured n lengh uns. where: h pl s he pensock head losses (m). c s a hydraulc loss parameer (s /m 5 ). q s he oal urbne waer dscharge (m³/s). r h pl = c.q () Afer he head and losses descrpon, he kernel of hydro plan operaon s he hydropower producon funcon. Ths model deals he hydro producon as shown n Equaon (3).

4 where: p= k. η. η.( h h ) q (3) T G g pl. p s he nsananeous power obaned n he converson process of he hydraulc poenal energy o elecrc energy (MW). k s he gravy consan, mulpled by he waer specfc wegh and dvded by 0 6. Ths consan manages he power oupu n MW. Is value s (MW/(m³/s)/m). Ths consan can also embed un ransformaon facors. η T s he effcency parameer of he urbne n he converson process of he poenal energy o mechancal energy. η G s he effcency parameer of he generaor n he converson process of he mechancal energy o elecrcal energy. The urbne effcency can be expressed as funcon of head and hydro power. Some machnery projecs have head and dscharge as basc npu daa for effcency compuaon. Ths smulaon model acceps any combnaon from gross or ne head and power or dscharge. Due o s shape, hs funcon s also known as he effcency s hll curve and an example could be noed n Fgure 3a. Also, effcency conour lnes are commonly par of he urbnes nformaon (Fgure 3b). The urbne and generaor manufacer has operaonal lms expressed as funcons of gross or ne waer head. The mum hydro power lm depends on head n wo sages (Fgure 3b): a) for head smaller han h ef, he power s drec proporonal o he head, snce s lmed by hydraulc avalable energy; b) when head s bgger han h ef, he power ransferred o he urbnegeneraor s shaf can damage he equpmen, so valves or wcke gaes gearng are necessary o keep he oupu power consan and beneah he elecrcal damage lm. The h ef head s called effecve head. A mnmum hydro power lm can be mposed and expressed as a funcon of waer head as well (Fgure 3b). (a) Turbne Operaon Characerscs (b) ef p p = g( h) Effcency Power (MW) Head (m) mn h ef h h Fgure 3. Example of he urbne effcency funcon - hll curve - and mum and mnmum power producons funcons. The mum spll capacy s can be expressed as a funcon of reservor waer level. Dependng on he exsence of gaes, wo spllway operaons are possble: conrolled and unconrolled. Fgures 4a and 4b show examples of hese funcons. The erm s prj s relaed o he capacy projeced for he spllway. The forebay sc s he waer level on he spllway cres.

5 (a) prj s s = Maxmum Spllage Funcons f ( ) (b) prj s 0 mn sc 0 mn sc Fgure 4. Unconrolled and conrolled mum spll funcons. As can be seen, he smulaon model has a dealed represenaon of he reservor and hydro power operaon. The nex secon descrbes he mulreservor model and he adoped mplemenaon srucure and desgn. Mulreservor Smulaon Ths secon presens a nework flow formulaon for he mulreservor smulaon problem as a emporally expanded arborescence (a sysem wh a reelke srucure, Rosenhal, 98). Fgure 5 shows he hydro elemens represened by he smulaon model. The model assumes ha he exogenous nflows y o he reservor sysem are deermnsc or provded by nflow forecasng models. Reservors could be smple waer sorage reservors such as node number 3, or could have powerhouses and hydro plans. Specal rver flow conrol saons can be smulaed as well (node 7). Dversons srucures, such as channels and unnels, are able o be smulaed, as llusraed by he lnked-reservor 3 and 4 example. The praccal 94-reservor sudy presen laer s a bgger replcaon of he hydro elemens example shown n Fgure 5. Also, hs sudy smulaes wo real dverson srucures from he Bralan hydroelecrc sysem: he Perera Barreo s channel ha lnks he Ilha Solera and Três Irmãos reservors locaed n he Paraná Rver basn and a dverson unnel lnkng he reservors Jordão and Segredo n he Iguaçu Rver basn. These waer dversons are governed by he hydraulc rules for he nerconnecng channels and unnels. y y 4 y 5 y 4 5 y 6 y 3 3 d 34 y Reservor Powerhouse Conrol saon Waer Body Fgure 5. Hydro elemens avalable for mulreservor smulaon.

6 Rosenhal s represenaon, a deermnsc nework flow opmaon model, requres ha no reservor has more han one oher reservor drecly downsream from. Ths consran s vald for he 94-reservor Bralan hydropower sysem. However, he dverson varable was creaed o overcome hs resrcon, snce a smulaon model should accommodae srucural expansons. The second mposon was relaed o he roung effec beween adjacen reservors. Ths resrcon was overcome wh adapaons n he expanded arborescence srucure, as shown n Fgure 6. Pas sae Four-nerval smulaon Pos-horon balance workflow W. Body Fgure 6. Three-reservor and four-nerval hydro sysem as a emporally expanded arborescence wh roung effec represenaon. In he roung effec represenaon llusraed n Fgure 6, sold arrows represen releases and broken-lne arrows represen sorages ranspored beween me nervals. These sorage arcs form he emporally expanded nework srucure from he arborescence. Noe ha wo addonal arc-node ses are necessary o complee he srucure: he lef represens he recen pas releases before he frs smulaon me nerval; and he rgh are he pos-horon arcs and nodes, whou release arcs, ha are necessary o complee and manan mass balance. The reservor mass balance equaon (4) s very dealed n erms of mulpurpose consrans. where: x = + + ( q, + s, + ev, + mu, + d ). fuc (4), x, y, f ( uk, r ), k Ω, are plan and me ndexes, respecvely. There are reservors and T nervals. The sorage varables x are ndexed as me nsans (nal - and fnal ). The flow varables are averages durng he me nerval. y s he reservor nflow (m³/s). Ω s he drec upsream reservors ndex se. Wh he r me lag, he sum of upsream releases represens he roung effec compuaon. s s he spllage flow (m³/s). ev s he reservor evaporaon calculaed as a waer flow (m³/s). I akes no accoun he reservor area a he average volume (x + x - )/, leadng o an erave calculus.

7 mu represens he reservor mulple-uses expressed as waer flows (m³/s). As example, rrgaon and waer supply assocaed wh one reservor could be smulaed wh hs varable. d represens he waer dversons from reservor, also expressed as waer flow (m³/s). The dverson can be reach anoher reservor, rver or an exernal hydro elemen no presen no he sudy confguraon. f uc s he un converson facor beween flow and sorage varables. As a powerful modelng resource, he un converson facor f uc embeds no he smulaon model he ably o use any me nerval. Ths model can compue sudes wh monhly, daly, hourly, half hour or even any combnaon ha composes a mxed nerval horon. Consderng Bralan general uns hm³ for sorage and m³/s for sreamflows, hs facor became: f uc = (5) 6 0 The mulreservor model ncludes he operaonal consrans relaed o sorage, mnmum and mum releases, mum dscharge as a funcon of gross head and mum spll as a funcon of reservor sorage level. p x u mn x x (6) mn,,, u u (7) mn,,, ( h) p p ( h) (8), q q ( ) (9),, h s s ( ) (0), I s mporan o noe ha consrans (6) o (0) use nerval ndexng o represen he mulpurpose consrans, as presened n followng secon. Mulpurpose Consrans Typcally, reservor mulple purposes nclude a combnaon of purposes lke hydroelecrc power generaon, waer supply for rrgaon, domesc and ndusral use, waer qualy mprovemen, flood conrol, wldlfe and envronmen manenance, navgaon and recreaon (Yeh and Becker, 98). The hydroelecrc purpose was descrbed n prevous subsecons. Through mulple-use mu and waer dverson d varables from Equaon (4) s possble o smulae waer supply and rrgaon purposes. A seasonal mnmum waer level or sorage may be mposed o guaranee waer supply mpoundng, navgaon and recreaon purposes as well. The release consrans from Equaon (7) perm smulang fsh-wldlfe manenance and navgaon operaonal lms. Flood conrol s generally acheved by mananng reserve sorage n each of he many reservors as an ancpaon conrol procedure for hgh-flow perods. Ths can be acheved wh emporary upper bound sorage lms ha are smaller han he reservor mum, as expressed n Equaon (6). SOFTWARE DESIG Ths secon descrbes he use of objec-orened modelng as a powerful approach for desgnng a mulreservor smulaor. Slobodan e al. (997) presen

8 objec-orened desgn as a successful modelng ool o he Egypan waer resources plannng. The naural objec-orened paron beween polcy commmen and daa perms he consrucon of wha-f search scenaros n an easer way o faclae he decson-makng process. Anoher neresng objecorened experence s dealed presened by Belkhouche (999) and can be used as a gude o objec-orened desgn of daabase and sofware resources o waer qualy sysems. Also, Horsmann (997) provdes an nformave nroducon o objec-orened sofware developmen. The presen smulaon model was mplemened usng objec-orened sofware desgn. As expeced, he sofware was bul usng classes o represen all mulreservor smulaon aspecs. There are classes o represen he hydro plan s man componens and he nework flow elemens. Also, here are exra classes o suppor he sofware organaon, such as horon descrpon and daabase connecors and daa provders. The whole class dagram s que lenghy, however, some mporan deals from he objec-orened desgn are shown o gude furher researchers. Daa Srucures The key sep for a compuaonal mplemenaon of he smulaon model s o nerpre he mass balance equaon (4) as a nework flow node (Rosenhal, 98). The node flow equlbrum has equvalence wh he mass balance usng arcs o represen operaonal consrans, as presened n Fgure 7. The r me delay represens he roung effec of upsream releases. y, k Ω f ) ( u k, r x,-, x, ev, mu, q, s, Fgure 7. Mass balance equaon equvalence wh a nework node. The nodes for he enre nework can be smply sored as a b-dmensonal marx M xt represenng he operaon varables from he reservor durng he me nerval. Oher daa srucures usng a node s lnked lss can be used as well, bu a recangular marx provdes good performance and reasonable se sorage. The arcs are bul as lnks beween nodes and sored as nodal properes. Objec-Orened Desgn The smulaon model uses an objec-orened resource called polymorphsm o creae a mahemacal srucure ha spls he decson asks from he hydroelecrc compung asks n dfferen sofware componens. As a drec resul, he smulaon model acceps dfferen operaonal polces, keepng apar he hydro compuaonal kernel composed of he operaonal resrcons, waer balance equaon, power generaon and effcency funcons. A smulaon algorhm flowchar s shown n Fgure 8 n order o llusrae he polymorphc composon of he operaonal polcy and he hydro compuaonal kernel. Noe ha he hydro kernel has a specal resource o correc decsons ha can lead he reservor o an nfeasble sae.

9 Sar Daa Seup gven y, x, = 0 Decson Makng (q, s ex-ane ) Oper. Polcy Hydro Kernel Waer Balance for each ( (ex ex-pos ) Feasble Sae No Decson Correcons Yes = + Yes T No End Fgure 8. Smulaon algorhm wh objec-orened polymorphsm appled o paron of operaonal polcy and he hydro compuaonal kernel. The polymorphsm concep has many defnons bu o hs smulaon model means ha he same operaon may behave dfferenly for dfferen classes (Horsmann, 997). In oher words, he polymorphsm wll be used o promoe a paron beween he operaon polcy and he hydroelecrc and reservor compuaons. Ths objec-orened concep perms he resulan smulaon sofware o have an expandable and adapable collecon of operaon polces. Operaonal Polces The operaon polcy objec s responsble o deermne he reservor s oal waer release. If he reservor has a powerhouse, he amoun of he urbnes dscharge s also necessary. Mahemacally, he operaonal polcy can be expressed as a funcon f p of he avalable polcy varables from Equaon (4): [ q, s * * * ] = f ( x, x, y, f ( u ), ev, mu, d ) (),, p,,, k, r,,, k Ω where he * denoes varables ha are no drecly avalable for polcy analyses and may be esmaed. For example, he fnal sorage a nerval and evaporaon can be esmaed as a funcon of he release deermned by he operaonal polcy. Any exernal operaonal polcy ha has as s resul he release and spllage varables can be smulaed wh hs model. From hs polymorphc srucure, a parcular operaonal polcy was mplemened o ransform hydro generaon dspach, composed of generaon goals and urbnes un commmen, no he dscharge and spllage decson varables. The generaon-release ransformaon s based on an erave and dealed procedure over he hydro producon equaon (3), where he power s gven and he release and spllage are calculaed recursvely. Ths polcy ams o check generaon schedulng usng an nflow forecas, gven he nal reservor sorage sae and keepng he hydroelecrc kernel nac. As one can see, hs polymorphc desgn can accomplsh oher ypes of polces, ncludng he decson resuls from opmaon models (Wurbs, 993).

10 CASE STUDY Ths secon brefly demonsraes a es on a 94-reservor Bralan hydro subsysem ha demonsraes he smulaor s capables and performance. The generaon sysem has 75,944 MW as nsalled capacy and a one-week horon generaon schedulng was checked n erms of sasfyng he hydroelecrc consrans. Smulaon Sudy Man Characerscs Reservors 94 Basn/Rvers 8/33 Dranage area Insalled capacy,6,43 km² 75,944 MW Dverson srucures Conrol saons Horon 7 days Inervals 68 hours Fgure 9. The 94-reservor map from Bralan Inegraed Hydropower Generaon Sysem and s man characerscs. The es checks, for each reservor, an hourly one-week horon generaon schedulng usng a daly nflow forecas provded by an exernal hydrologc model. All he varables rajecores (see secon abou mulreservor model) are avalable n sngular abs as chars or n ables. Fgure 0 shows he sofware and user nerface for a sudy s daa npu and resul analyses. The lef frame s a sudy navgaor resource ha shows sudes n a ree vew organaon. The daa and resuls access are provded by a abs swch. Fgure 0. Smulaon sofware and s user nerface. The es was run n compuer wh a 3.0 GH Penum IV processor and GB of RAM. The 94-reservor and 68-hour horon sudy akes.4 seconds on average o be smulaed. As one can noe, hs s good compuaonal performance for a smulaon model wh he operaonal polcy ha convers generaon goals no release and spllage rajecores wh auo consran feasbly checkng. CO CLUSIO Ths paper presens a mulreservor smulaon sysem wh dealed hydroelecrc modelng and mulpurpose consrans. The sofware s based on nework flow srucure o represen mulreservor jon operaon. Two smple, bu

11 powerful, model resources were presened o perm general smulaon applcaon: a un converson facor for he hydropower producon funcon and a mul and mxed me nerval facor for he mass balance equaon. Due o he objec-orened desgn, he operaonal polces and hydro compuaonal kernel were dvded no dfferen sofware componens. Wh hs desgn s possble o check dfferen and exernal operaonal polces n a dealed smulaon model. Also s suable o address performance analyses and evaluang he dsance beween compuer-aded model resuls and real problem performance. A es sudy on 94-reservor subsysem of Bralan hydro plans wh a one-week horon generaon schedulng was made usng nflow forecasng wh a focus on meeng he operaonal consrans. The smulaon model performed very well n erms of reservor operaon accuracy and requred compuaonal me. REFERE CES Belkhouche, B., Demchouk, I., and Senberg, L. J. (999). Desgn of objecorened waer qualy sofware sysem. J. Waer Resour. Plan. Manage., ASCE, 5(5), Fonane, D. G., Gaes, T. K., and Moncada E. (997). Plannng reservor operaons wh mprecse objecves. J. Waer Resour. Plan. Manage., ASCE, 3(3) Hdalgo, I. G., Fonane, D. G., Soares Flho, S., and Ccogna, M. A. (009). A smulaor of he hydroelecrc plans operaon as a ool for analyng daa. Acceped for he 009 World Congress on Compuer Scence and Informaon Engneerng (CSIE), Los Angeles/Anahem, Calforna, USA. Horsmann C. S. (997). Praccal Objec-Orened Developmen n C++ and Java. John Wley & Sons. Labade J. W. (004). Opmal operaon of mulreservor sysems: sae-of-hear revew. J. Waer Resour. Plan. Manage., ASCE, 30(), 93-. Mead, D. W. (908). Chaper II - Hydraulcs. Waer Power Engneerng: The heory, nvesgaon and developmen of waer powers, Frs Edon, McGraw-Hll, New York, Rosenhal, R. (98). A nonlnear nework flow algorhm for maon of benefs n a hydroelecrc power sysem. Operaon Research. 9(4), Sgvaldason, O. T. (976). A smulaon model for operang a mulpurpose mulreservor sysem. Waer Resources Research, (), Slobodan, P. S., Hussam, F., and Amn, E.-S. (997). The use of objec-orened modelng for waer resources plannng n Egyp. Waer Resources Managemen, Kluwer Academc Publshers,, Yeh, W. W-G., and Becker L. (98). Mulobjecve analyss of mulreservor operaons. Waer Resources Research, 8(5), Yeh, W. W-G. (985). Reservor managemen and operaons models: A sae-ofhe-ar revew. Waer Resources Research, (), Wurbs, R.A. (993). Reservor-sysem smulaon and opmaon models. J. Waer Resour. Plan. Manage., ASCE, 9(4),