Flexible Design of Urban Water Distribution Networks

Transcription

1 4225 Flexble Desgn of Urban Water Dstrbuton Networks Danguang Huang 1, Kalanthy Varavamoorthy 1, Seneshaw Tsegaye 1 1 School of Cvl Engneerng, College of Engneerng and Physcal Scences, Unversty of Brmngham Abstract Wth ncreasng global change pressures (urbanzaton, clmate change etc. coupled wth exstng un-sustanablty factors and rsks nherent to conventonal urban water management, ctes of the future wll experence dffcultes n effcent decson makng on the nfrastructure development. Proectons of future global change pressures are plagued wth uncertantes whch cause dffcultes when developng urban water nfrastructures that are nsenstve to these global change uncertantes. In ths paper a methodology s presented that generates optmal urban water networks that are adaptable and sustanable under future global change pressures. These flexble systems are characterzed by ther ablty to cope wth uncertantes and have the capablty to adapt to new, dfferent, or changng requrements. The flexble desgn tool presented n ths paper conssts of two maor components. The frst component s a methodology for developng scenaro trees that reflect uncertantes assocated wth future demand for water. These scenaro trees represent the uncertanty envelope assocated wth demand proectons over tme. The second component s an optmzaton model that consders the phased desgn of the water network, takng nto account the lkelness of dfferent demand scenaros over tme (as expressed by the scenaro trees. The GA based optmzaton model dentfes the optmal staged development of the network that gves the optmal expected value of the network both n terms of costs and benefts. The flexble desgn tool s then appled to the desgn of an example network wth a desgn horzon of 30 year. The soluton s presented as a phased desgn n 5 year stages and s compared wth a desgn undertaken n the tradtonal way. Ths comparson clearly hghlghts the benefts and the effcacy of applyng flexble desgn approaches for water systems operatng under future uncertantes. Key words: uncertantes, flexble desgn, scenaro tree, optmzaton 1 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

2 Introducton Tradtonal practce dctates that the capacty of a water dstrbuton desgn s determned by proected desgn parameters (for example, water demand and deteroraton of water supply networks. Ths method tres to mnmze captal and operatonal costs whlst satsfyng these pre-defned requrements (such as water quantty and suffcent servce pressure. Optmzaton models have been developed to search for ths optmal/nearoptmal soluton (Dandy et al. 1996; Savc and Walters 1997; Wu and Smpson As the standard approach s based on the proected future changes, t does not nherently offer flexblty to adapt to the uncertanty that the system may face and also t does not subsequently analyze the consequences caused by such unpredctable crcumstances. In consequence, ths approach fals to delver satsfactory value f there are large estmaton errors on the desgn parameters. For nstance, f the desgned capacty s excess than the actual requred capacty, t wll cause unnecessary addtonal nvestment cost and there wll be a possblty of some real tme operaton problems. Water dstrbuton systems (WDS conssts of many functonal components, whch as a whole provde a satsfactory servce and would exst for a very long tme. Wth the characterstcs of complexty and long lfe cycle, desgn and operaton of WDS are potentally subected to uncertanty wthn ts long lfespan (Lansey et al. 1989; Kapelan et al and as a result WDS n many ctes suffer wth the consequences of these future changes and uncertanty. Both techncal and non-techncal (e.g. poltcal crcumstances factors determne the future changes and uncertanty. Furthermore due to the nter dependency of these factors, t s dffcult to make an approprate estmaton of these uncertan parameters. Prevous research has shown that the pont forecasts almost never equate to the actual real term condtons (Babade, de Neufvlle et al Decson makng on WDS desgn s often complcated by the dffculty n forecastng desgn parameters. Ths therefore calls for us to reconsder the way we desgn systems and develop new nnovatve methods that can counter the uncertanty. De Neufvlle (2004 mentoned three basc ways to manage uncertanty. There are uncertanty control, passve protecton and actve protecton. One example for uncertanty control n WDS s to develop more sophstcated forecastng model for desgn parameters, whch tres to mnmze estmaton errors by analyzng and buldng up the relatonshps between uncertanty and dfferent factors. The passve protecton methods, lke relable desgn n WDS (Babayan et al. 2005; Jayaram and Srnvasan 2008; Gustols et al. 2009, make system nsenstve to wde range of future operatonal condtons. Though the uncertanty control and passve protecton methods protect system performance from uncertanty to some degree, there are stll some dffcultes when applyng n WDS. Frst the relatonshps between uncertanty and factors n WDS are complex and not easy to be captured. Also, uncertanty s not always a negatve to be mtgated, but can also be a postve that may be exploted (de Neufvlle Therefore, actve protecton methodologes such as flexble desgn are advsable, whch can gve desgners the ablty to use the value of upsde opportunty n addton to mtgaton of down sde rsk. Flexble 2 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

3 4227 desgn methodology delvers a system wth the capablty of respondng to future changes n a more cost-effect way, thus decson-makers wth n bult flexblty tools can reduce rsks but may also beneft from upsde opportuntes, whch as a whole wll make the system delver more value n an uncertan world. Recent research has demonstrated the applcaton capablty of flexblty n system desgn. Zhao and Tseng (2003 showed a successful applcaton of flexblty n a car park desgn. The flexblty (enhanced foundaton and columns was embedded at the begnnng of a car park constructon, whch provded optons for future expanson. The uncertan car park demand was modeled by Monte Carlo smulaton and the flexblty value was calculated by comparson on the expected proft between a baselne desgn and flexble desgn. Zhao et al. (2004 presented a multstage stochastc model for decson makng n hghway development, operaton, expanson, and rehabltaton. The model used real optons as flexblty sources n both development and operaton phases of a hghway and Monte Carlo smulaton to account for the evoluton of uncertantes. Ths approach acheves decsonmakng optmalty by maxmzng the expected proft. The applcatons are also n communcatons satellte constellatons (De Weck et al. 2004, space systems (Nlchan and Hastngs 2007, mnng operatons (Cardn et al. 2008, offshore ol platforms (Ln 2008, transportaton network desgn (Ukkusur and Patl 2009, here ust name a few. These frutful applcatons n other felds demonstrate that flexblty has value for uncertan future crcumstances and should be mplemented n system desgn. However, ts use n WDS desgn s stll n ts nfancy and there s a gap n the lterature, whch requres further nvestgaton. Ths paper tres to develop a methodology that gves an opportunty to decson makers to desgn flexble water dstrbuton system. Unlke robust desgn whch characterzes a system ablty to be nsenstve towards changng envronments, flexble desgn deals wth uncertanty proactvely and gves system mangers the rght but not oblgaton to do mplement actons to respond to future changes. Wth embedded flexbltes, the system can adapt to changes more pragmatcally and effcently. The proposed flexble desgn methodology nvolves uncertanty modellng and flexblty based optmzaton by Genetc Algorthms (GA. The uncertantes are modeled by scenaro tree method. And then the flexblty based optmzaton tres to fnd the optmal combnatons of dentfed flexblty sources for the assumed possble future crcumstances. The system generated provdes effcent use of resources n the current clmate, whlst also allowng for future potental changes wthn ts lfe cycle. The man contrbutons of ths work are 1 modelng of uncertantes explctly on mult-stage; 2 dentfcaton of dfferent flexblty sources for assumed uncertantes; 3 development of a flexblty-base optmzaton usng GA. 2 Proposed Method The proposed flexble desgn methodology recognzes the uncertantes and bulds flexbltes n water dstrbuton system wth ablty to respond to future changes n tmely and cost effectve manner. Ths method conssts of two maor components. The frst component s a methodology for modelng of uncertanty usng scenaro tree. The second 3 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

4 4228 component s flexblty based optmzaton model that consders the phased desgn of the water network and the lkelness of dfferent scenaros wthn the lfe cycle. Ths GA based optmzaton model dentfes the optmal staged development of the network that gves the optmal expected value of the network both n terms of costs and benefts. The proposed approach allows the WDS to be optmally responsve to the future scenaros. The framework of proposed method s presented (see Fgure 1. Problem study and system defnton Flexblty source dentfcaton Possble future descrpton uncertan modellng Lfe cycle system solutons wth flexblty sources Valuaton of lfe cycle system solutons wth flexblty sources under possble futures 2.1 Uncertanty n WDS and modelng Most valuable lfe cycle system solutons Fgure 1. Flexblty analyss framework There exst many uncertantes durng the lfe-cycle of a system. De Weck et al. (2007 categorze the uncertantes nto endogenous ones and exogenous ones. Further suggestons were gven that the uncertantes durng the system desgn and operaton should be descrbed by separate models and then to be brought together to use an ntegrated uncertan model. Ths paper ust focuses on uncertan water demand, as water demand s one of the parameters to determne the requred capacty of the water dstrbuton system and s dffcult to make estmaton (Obradovc and Lonsdale Ths uncertan parameter nfluences the value of flexblty n WDS sgnfcantly, so the uncertanty on water demand should be expressed usng proper methods when desgnng flexble WDS. Snce the maor emphass of ths paper s gven on developng the methodology that can be used n desgnng flexble water dstrbuton system, the smplest forecast model (per capta requrements method s chosen for the demand predcton (more forecast method see Baumann et al The forecast method used depends only on the populaton: ( + r n Qt+ n = b Pt 1 (1 Where: Q t + n s the average daly aggregate water use, P s the resdental populaton n servce area at year t, b s the per capta water use, n s the forecast perod, and r s the annual populaton growth rate durng each forecast perod. 4 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

5 4229 In the employed scenaro tree method, dfferent water demand scenaros wth specfc happenng probablty are generated based on dfferent annual populaton growth rates. One example scenaro tree wth two forecast perod s provded (see Fgure 2. Startng from current state (known as root node, there are two possble future states for the next stage related to dfferent water uses due to dfferent populaton growth rates. Q 2 0 ( r 1 ( r2 Q 1 0 ( r 1 ( r2 Q 0 0 ( r 1 ( r2 Q 1 1 ( r 1 ( r2 Q 0 1 ( r 1 ( r2 Q 1 1 ( r 2 ( r1 ( r1 ( r2 Q 0 2 ( r 1 ( r2 Fgure 2. Two-perod scenaro tree In ths example, Q 0 0 s ntal water demand, r 1 and r 2 are two dfferent annual populaton growth rates. The superscrpt on r expresses the number of perods that water demand ncreases wth r. For a general problem wth one forecast perod of n years, the future state n each stage would be: Q ( 1+ n r ( + n r Q 0 0 ( r ( r ( r ( r 1 1 = ( Where: s the number of perods that water demand ncreases wth r 1 and s the number of perods that water demand ncreases wth r Flexblty-based Optmzaton Model Flexblty Sources There are two types of flexblty: flexblty n a system and flexblty on a system (Wang and de Neufvlle Flexblty n a system reles more on techncal components wthn the system whle flexblty on a system uses operatonal and manageral strateges. Both flexblty n and on the system allow more delvered value. Many flexblty sources for WDS could be consdered to deal wth the uncertan water demand. In ths work three general flexblty sources are dentfed and dscussed n more detal: staged deployment strategy, scenaro plannng strategy and capacty expanson flexblty. The frst flexblty source s staged deployment strategy that allows developng the system progressvely. The uncertan parameters on dfferent stages are analyzed, then decson on system development can be made to adapt to uncertanty n the best possble manner. Snce uncertan parameters are observed through tme, the rsks from the uncertanty are reduced. Furthermore, an economc opportunty s represented because ths strategy tres to mnmze 5 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

6 4230 the lfe cycle cost by pushng the expendtures towards future tmes as much as possble whch can be dscounted. The second flexblty source s scenaro plannng strategy that allows settng up dfferent system development packages to dfferent water demand scenaros. The scenaro plannng consders the value of nformaton and captures the nature of decson for engneerng system that t s a dynamc process yet not a statc one, so leads to a desgn choce that s more suted to dfferent future scenaros, whch clearly mproves the overall value of the system. The thrd flexblty source s capacty expanson flexblty that consders the possblty of system expanson. When demand grows temporally and spatally, the addtonal system capacty should be ready, whch normally requres large expendtures f the capacty expanson flexblty s not ncluded n the ntal system. Therefore t s necessary to buld capacty expanson flexblty n the system to servce more demand n a more costeffectve way, whch enables system to expand to meet future requrement wth relatve ease, thus potentally mproves the lfe cycle value of the systems Measure of flexblty An mportant part of flexble desgn s defnng measurable value delvery by the system. In general, the servce of a water dstrbuton system s hard to be measured only by monetary value. In ths paper, the uncertanty level was predefned by the scenaro tree method. Furthermore, we assumed that the beneft from system modfcaton for the next stage predefned uncertanty level s always larger than the expendtures. Then the flexblty value can be shown usng an ndrect ndcator: lfe cycle cost. The lfe cycle cost ncludes the cost from the ntal system and all other costs from swtchng system for the next stage. As a result, the flexblty value maxmzaton could be realzed by mnmzng the system lfe cycle cost Mathematcal model for flexblty The overall optmzaton obectve for flexble WDS s to mnmze the expected lfe cycle cost on varous desgn varables x whle at the same tme meetng the specfcaton of provdng enough water wth suffcent pressure under the pre-defned uncertan level. Consder system lfe cycle of T and tme wndow of t. The water demand state n stage s expressed by a vector, Q ( and [ 0,1, K T / t]. Full verson for Q s [ q, 1 q,2, q, N node N state, K ]. The uncertan water demand would be modeled by scenaro tree method. One scenaro, s, represents one possble water demand evoluton process: 0 1 T / t [ Qs, Qs, K Qs ]. The scenaro tree, S, ncludes all (or at least the most nterestng possble futures. Here we defne decson makng scenaro to nclude the nputs for the * * * optmzaton model on all stages for one specfc scenaro s: [ Q Q K Q ]. Then the mathematcal formulaton for ths flexblty-based optmzaton s: 0, s, 1, s, T / t, s 6 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

7 4231 ( x T P s f s mn x X ( = + R t s (3 s S 1 1 * s.t. Q Q q (4 In Out = f E p =, s h 0 (5 mn H H (6 Where: R s dscount rate, Ps s the probablty of scenaro f s the cost functon. Eq (4 and Eq (5 are contnuty constrant on each node and energy constrant for each loop, whch wll be solved by Epanet (Rossman Model Applcaton on Hypothetcal Network s, and ( The flexble desgn methodology was appled to one hypothetcal network (see Fgure 3. Water demand was consdered as uncertan parameter and then the result from flexble desgn was compared wth two rgd desgns. The problem of flexble desgn was formulated as a mult-stage decson model and smply assumed that only the envelope of the uncertan parameters s known n the frst stage. The proposed method s to help the decson maker fnd the best system development strategy, whch has the mnmum expected lfe cycle cost. Fgure 3. Network layout for the case study The network topology s pre-determned. Ths network needs to be phase desgned for 30 years whch s dvded nto three desgn perods. The network conssts of 7 nodes n the frst perod, 10 nodes n the second perod and 13 nodes n the thrd perod. The only supply source s a reservor wth the fxed hydraulc grade lne (HGL elevaton of 60 m. The mnmum pressure requrement on each demand node s 30 m at nstantaneous peak flow, whch s 1.8 tme average day flow. The fre flow condton s not consdered n the applcaton. There would be 18 ppes n the network fnally, the lengths of whch are all 2000 m and the Hazen-Wllams coeffcent C values of whch are 130 (constant n all 7 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

8 4232 stages. 10 commercal ppes are avalable n the market, the costs of whch are shown n Table 1. Costs are gven n $/ft. Cost for new ppes are gven n the column labeled new. Costs for replacng ppe n developed area are gven n the column labeled urban. Table 1. Costs for Ppe Layng (Walsk et al Ppe Dameter (n New ($/ft Urban ($/ft Uncertan average water demand s modeled n 6 perods wth tme wndow of 5 years. The ntal demand on each node s assumed as 15 L/s, whch wll ncrease by an annual growth rate ether of 2% or 4% wth a same probablty of 50%. The decson makng scenaro s generated from the full scenaro tree (see Fgure 4. Q 6 0 ( r 1 ( r2 Q 4 0 ( r 1 ( r2 Q 5 1 ( r 1 ( r2 Q 4 2 ( r 1 ( r2 Q 5 1 ( r 1 ( r2 Q 2 0 ( r1 ( r2 Q 3 1 ( r 1 ( r2 Q 4 2 ( r 1 ( r2 Q 3 3 ( r 1 ( r2 Q 4 2 ( r 1 ( r2 Q 2 2 ( r 1 ( r2 Q 3 3 ( r 1 ( r2 Q 2 4 ( r 1 ( r2 Fgure 4. Decson makng scenaro for the case study The system wll be developed on three dfferent methods. The Rgd desgn 1 s developed based on the assumpton that the hgh demand scenaro always happens n the system lfecycle. The Rgd desgn 2 s generated to have optmal performance under the most lkely scenaro. The obectves of these two approaches are to fnd the least-cost soluton under the specfc scenaro (see Table 3 for more detal. 8 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

9 4233 The flexble desgn would be generated from the flexble desgn methodology n ths paper. Wth the decson makng scenaros, dentfed flexblty sources and specfc cost related to dfferent development plan, more detal mathematcal formulaton for Eq (3 can be: Mnmze PP t Ps s S t= 1 = 1 3 S t t, ( D s L D D t ( + R t s 1 Unt Where: the dscount rate s set as 5%. The decson varables S s the replacement status of the ppe n year t ( S =1 f ppe replaced n year t, t replacement status of all the ppes s known and set as 1, and t (7 t S =0 else, for the frst stage the t D s represents the dameter of ppe n year t, whch s dscrete, takng any values from a predefned vector[ D, D L D 1 2 max ]. Addtonal constrants for ths non-return and dependent decson process are: Ds = Ds = L = D 1 2 s, =1, 2 PP 27 1 ( Ds = D x s = L = D + x+ s, x=0, 9, 18 and =1, 2 PP 1 2 x+ 9 2 ( Ds = D x s = D + x+ s, x=0, 3, 6, 9, 12, 15, 18, 21, 24 and =1, 2 PP 1 2 x+ 3 3 (10 Ths flexblty-based optmzaton s coded n C and solved by GA. GA provdes an effectve means to solve very large, path dependent, and non-convex problems (Holland 1975 and s proved to be effcent n water dstrbuton system optmzaton (Dandy et al. 1996; Savc and Walters 1997; Wu and Smpson 2001; Varavamoorthy and Al 2005; Kadu et al Table 2 compares the results of the optmal rgd and the best flexble desgns. Table 3 gves detals about the optmal rgd 1, 2 and the best flexble desgn. It demonstrates that flexble desgns provde a range of advantages over rgd desgns. The flexblty value here s defned as the performance mprovement and expected lfe-cycle cost reducton between the rgd desgns and flexble desgn. In ths case, the best flexble desgn: Search an ntal system platform whch can evolve to dfferent future states (the ntal system confguraton s developed based on a lttle modfcaton requrement for the future scenaros. The model also check the decson that compare whether t s cheaper to lay bg ppe n the platform confguraton than to lay small ntally and then replacng later. For example, the model output shows that layng small ppe (6 nch frst than replacng wth a bg one (10 nch for the ppe s cheaper than layng bg ppe (10 nch ntally. 9 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

10 4234 Improve the expected value of the proect (Reduces the expected lfe-cycle cost about 9.1%, compared wth the optmal rgd 1 Improve the ablty of system to avod expected rsk (The optmal rgd 2 has expected 1.39% supply defcency and maxmum 12.17% supply defcency Table 2. Summary of performance metrcs of optmal rgd 1, 2 and flexble desgns Value Metrc Rgd 1 (Hgh Demand Rgd 2 (Most Lkely Demand Flexble (Uncertan Demand E (Defcency None 1.39% None E (PV(Cost 3.49 (mllon $ 3.26 (mllon $ 3.33 (mllon $ Start Node Table 3. Lsts of the optmal Rgd 1, 2 and the best flexble desgn End Node Optmal Rgd 1 Optmal Rgd 2 Best Flexble Desgn Source ( Note: 6 (10 20 means replacng the ppe wth dameter 6 nch usng the ppe wth dameter 10 nch on year Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

11 Conclusons Ths paper demonstrates an approach of desgnng flexble water dstrbuton system. The method ntegrates uncertan modelng and flexblty based optmzaton model for developng a system whch has the ablty to cope wth uncertantes and have the capablty to adapt to new, dfferent, or changng requrements. In ths paper, a scenaro tree was used to model uncertan water. Then dfferent possble flexblty sources were dscussed. Flexblty sources consdered for uncertan future water demand are staged deployment strategy, scenaro plannng strategy and capacty expanson flexblty. Fnally, the uncertan model and dentfed flexblty were ntegrated nto an optmzaton model (GAbased to determne the soluton wth mnmum expected lfe cycle cost. In partcular, the method was appled n a hypothetcal water dstrbuton network, and the comparson between flexble and non flexble system of these networks has been done. The rgd desgns wthout consderng flexblty lead to hgher lfecycle cost and poor performance when condtons n the future change. However, the flexble desgn usng the developed methodology shows sgnfcant expected lfecycle cost savng and expected performance mprovng. Furthermore, the applcaton n the paper shows hgher computatonal effcency. Thus t s proved that the developed method s effcent n desgnng and managng flexble water dstrbuton system. Reference Babade, A., de Neufvlle, et al. (2009. Integrated method for desgnng valuable flexblty n ol development proects. SPE Proects, Facltes & Constructon 4(2: Babayan, A., Z. Kapelan, et al. (2005. Least-cost desgn of water dstrbuton networks under demand uncertanty. Journal of Water Resources Plannng and Management 131: 375. Baumann, D. D., J. Boland, et al. (1997. Urban water demand management and plannng, McGraw-Hll Professonal. Cardn, M. A., R. de Neufvlle, et al. (2008. A process to mprove expected value of mnng operatons. Mnng Technology: IMM Transactons secton A 117(2: Dandy, G. C., A. R. Smpson, et al. (1996. An mproved genetc algorthm for ppe network optmzaton. Water Resources Research 32(2: De Neufvlle, R. (2004. Uncertanty management for engneerng systems plannng and desgn. Engneerng Systems Symposum, MIT, Cambrdge, MA. De Weck, O., R. De Neufvlle, et al. (2004. Staged deployment of communcatons satellte constellatons n low earth orbt. Journal of Aerospace Computng, Informaton, and Communcaton 1(3: De Weck, O., C. Eckert, et al. (2007. A classfcaton of uncertanty for early product and system desgn. Massachusetts Insttute of Technology, Engneerng Systems Dvson, Cambrdge, MA. 11 Downloaded 01 Oct 2010 to Redstrbuton subect to ASCE lcense or copyrght. Vsthttp://

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