MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Civil and Environmental Engineering

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deparmen of Civil and Environmenal Engineering Waer Reource Syem Lecure 17 River Bain Planning Screening Model Nov River Bain Planning River bain planning i concerned wih conrucion and operaion of waer reource faciliie uch a: Reervoir Canal and aqueduc Irrigaion projec Hydroelecric plan Navigaion faciliie (e.g. lock) There are everal baic planning ak aociaed wih large river bain projec: Deerminaion of projec locaion and ize Scheduling and equencing of projec Real-ime operaion of projec ubjec o variable (uncerain) inpu Evaluaion of projec reliabiliy and reilience when inpu are variable (uncerain) Allocaion of projec co and benefi and aociaed financing iue Focu here on creening and imulaion apec of planning. Idenify configuraion operaing policie and likely benefi of he river bain plan Screening Analye Begin wih a map and chemaic diagram idenifying promiing ie for faciliie. Faciliie conidered: 1. Reervoir 2. Hydropower 3. Irrigaion area 4. Expor and irrigaion diverion 5. Impor and irrigaion reurn Organize he plan by: = ie (locaion of reervoir river diverion or low-head power faciliy) f = faciliy (reervoir power expor impor irrigaion) = ime (e.g. eaon or year) 1

2 Relaionhip beween ie and beween propoed faciliie a a given ie are repreened in a nework chemaic. Simple example (one ie): Original Propoed Plan Tribuary flow (meaured) River T + 1 Upream flow (meaured) F Impor I River Upream flow (meaured) F Inflow Q Evap es Reervoir orage S Sie locaion () Tribuary flow T+1 Releae D Hydropower P Expor E Land L Impor I+1 Downream flow (meaured) F + 1 Downream flow (meaured) F + 1 Primary deciion variable conidered (defined for each ie and/or ime in compaible uni) re land imp exp Faciliie ize/capaciie C C C C C [variou uni] Reervoir orage S [volume] Tribuary inflow T [volume/eaon] Reervoir inflow Q [volume/eaon] Reervoir releae D [volume/eaon] Impor and expor flow rae I E [volume/eaon] Irrigaed land L [area] Hydropower oupu P [energy] Some propoed faciliie may no be buil (i.e. opimum capaciie are 0). Screening Problem Formulaion For creening purpoe ue amorized objecive funcion All logic inpu and deciion variable repreen long-erm average logic condiion for each eaon during a ypical year All ime-dependen variable repea every year : Benefi are obained every eaon depend on ime-dependen ae (expor flow power energy culivaed land) Operaing co are incurred every eaon depend on faciliy capaciie Capial co are incurred only a iniial ime depend on faciliy capaciie 2

3 f f f Maximize B O d( r T ) K Projec deign f Benefi Operaing co Capial co T r(1 + r) d ( r T ) = Dicoun facor r = inere rae T = planning period (yr) T (1 + r) 1 Subjec o following conrain caegorie: 1. Capaciy 2. Flow (waer balance) 3. Irrigaion 4. Hydropower Example: Rio Colorado Bain Argenina Illurae creening model wih cae udy baed on plan developed for he Rio Colorado river bain in Argenina (ee figure below). Cae udy documened in Major D.C. and R.L. Lenon Applied Waer Reource Syem Planning Prenice Hall Bae plan deigned o maximize naional income 3 eaon define a ypical year ( = 1 2 3). Sie are locaed a each reervoir river expor or low-head (no reervoir) power faciliy a indicaed on propoed projec map (below). Seaonal Benefi: For Rio Colorado each benefi i aumed linearly proporional o an aociaed ae variable Sae are conrained by capaciie. f fmax Each capaciy C (a deciion variable) i conrained by maximum capaciy C (a pecified inpu). f Benefi ae and capaciy > 0 only if aociaed faciliy ineger variable y = 1 : exp expmax exp ~ E y Non-reervoir expor exp expmax re exp ~ E y Reervoir expor Expor : B = land land max exp ~ L y Non-reervoir irrigaed land land land max re ~ L y Reervoir irrigaed land re 0 = reervoir no buil ineger variable y = 1 = reervoir buil 3

4 Hydropower: B ~ P P max re y max y Reervoir power Low-head power Condiionaliy conrain: Reervoir-relaed expor power and irrigaion faciliie canno re be buil unle reervoir i buil ( y = 1). Capial co: For Rio Colorado variable co are aumed linearly proporional o capaciy re re re re Reervoir: K γ y + γ C re γ fixed re γ fixed = fixed = fixed capial co [$] re var = variable capial co [$/uni capaciy] ~ re C If y = 1 (o benefi > 0) fixed co are incurred. Capial co for expor and impor channel power and irrigaed land faciliie are defined in he ame way. Operaing Co: re re re O = γ K [$/eaon] re γ = fracion of capial co required for operaion/mainenance each eaon Capaciy Conrain Reervoir orage: re S re remax re C y [volume] Flow in channel from/o reervoir or river: exp E exp expmax re C y exp expmax exp or C y [volume/eaon] imp I imp impmax re C y imp impmax exp or C y [volume/eaon] Land irrigaed from reervoir or river diverion land L land landmax re C y land or C landmax exp y [area] Hydropower P ΔC [energy] max re C y Δ = 1 [eaon] or max C y Flow conrain Flow in each of he 3 eaon aumed o repea every year Q = F + I T + 1 = I + T + 1 [power] Reervoir inflow Tribuary Impor 4

5 S + 1 = S + Δ[ Q E D e ( S )] S 1 = S 4 F + 1 = D + I T + 1 All ae are non-negaive Evaporaion-orage funcion e ( S ) Irrigaion Conrain Differen amoun of land may be culivaed each eaon. Waer required o culivae land area L E τ Reervoir waer balance Cyclical orage Ouflow o nex ie i an inpu derived from opography. = L = irrigaion waer requiremen [deph/(eaon area)] Downream reurn flow: τ + 1 = ( 1 ρ ) E ρ = conumpive ue coefficien [unile] I Hydropower Conrain Energy produced depend on releae (reervoir) or ream flow (low head) and head: P ( H ( S ) Head-orage funcion = ε D H S ) = efficiency [unile] ε Reul of Rio Colorado Sudy Screening model produce following reul: i an inpu derived from opography. 1. Configuraion of plan (faciliie buil wih heir capaciie): re re exp exp imp imp land y C y C y C C y C 2. Seaonal value of ae: S e S ) Q ( D I E L P H ( S ) 3. Benefi and co for each faciliy and for overall plan: The bae run which maximize naional income produced following plan: Reervoir conruced: 3 of 3 reervoir in he upper (Mendoza) porion of bain 0 of 2 reervoir in cenral porion 1 of 3 reervoir (Cae de Piedra) in lower porion Irrigaion area conruced: 10 of 17 poible area buil in all 3 porion of he bain Hydropower plan conruced: 2 of 13 poible plan conruced in upper porion on diverion aqueduc 5

6 Inerbain ranfer (expor) conruced: 2 of 2 expor (upper porion) and 1 of 2 impor (cenral porion) Oher cae uing differen objecive puing prioriy on regional income irrigaion income ec give differen configuraion ee Major and Lenon (1979). The following figure were aken from Major David C and R.L. Lenon. Applied Waer Reource Syem Planning. Upper Saddle River NJ: Prenice Hall ISBN: Map of Rio Colorado Bain Aliude Profile Along Rio Colorado River Faciliie in Rio Colorado Lower Bain Schemaic of Propoed Rio Colorado Bain Plan Reervoir Co-Capaciy Curve Reervoir Volume-Deph Curve Reervoir Area-Deph Curve Figure removed due o copyrigh rericion. 6