Lecture 2 Reservoir Capacity Yield Analysis

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Lectuure 2Reservoir Capaccity Yield Analysis(h(howtto sizei a reserrvoiri andd measure ititsperforrmance)CVEN 5838 Aug 28, 2008

Reservoir Yield: Controolled Release from areservoiri ((or system off reservoirs).i )Often expressed as a ratio of % of mean annnual flow.flow EE.g.,g 70% yield means thereservoir can provide a regulated release ofo 70% of the mean annual flow.The Yield depends on the active storage capacitycof the reservoirReliability of Yield: probability that areservoir will be able to meet thedemand in any particular time interval(usually a year)Reliability Ns/NNs is number of intervals in whichdemand was met; N is the totalnumber of intervalsFirm Yield: can be met 100% of timeCVEN 5838 Aug 28, 2008

Estimating Active Storage CapacityMass Balance Equuation of ReservoirsSt-1 Qt – Rt – Lt StWhereSt-1 is storage at end of previouss time intervalSt is storage at end of current time intervalQt is inflows at current time inteervalRt is release at current time inteervalLt isi lloss ((evap/seepage)/) att currrentt timetiintervali tlReservoirs have a fixed storage caapacity, K, soSt K for each intervalCVEN 5838 Aug 28, 2008

Mass Diagram Anallysis (Rippl) MethodFind the maximum positive cumulative diffeerence between a sequence of preprespecifiedp((desired)) reservoir releases Rt annd known inflows Qt.Record of historical inflows is used, typically40Example: Nine periodperiod-ofof--record flows:35[1, 3, 3, 5, 8, 6, 7, 2, 1]2.3.Plot cumulativesAdd demand lineFind max deficitinflow volumme11.3025Rt 44201510501CVEN 5838 Aug 28, 200823InflowCumulative Inflow45time6789

Mass Diagram Anallysis (Rippl) MethodRepeat the hydrologic sequencee in case critical period is at endStart demand line at full reservoirCalculate ActiveStorage Ka as maxaccumulated storageover 2 successiveperiods of recordCVEN 5838 Aug 28, 2008Rt 44

Mass Diagram Anallysis (Rippl) MethodThe maximum capacity is determmined by the Critical PeriodCritical Drawdown Period:Longest period from fullreservoir condition toemptinessCritical Period:Longest period from fullcondition,ditiththroughhemptiness and to a fullcondition againgCVEN 5838 Aug 28, 2008

Problems with Masss Diagram Method¾Reservoir release needs to be constant (this is notaccurate for monthly intervaal as demands are oftenseasonal)¾Assumes that future hydroloogy is like the past¾Cannot compute storage size for a given reliability¾Evaporation and other losses that depend on level inreservoir cannot be factoredd into analysisCVEN 5838 Aug 28, 2008

Reservoir Planning by Simulation¾Simulation models are basedd on mass balance equationsand take into account all timee-varying processes as well aselevation--based processes ((losses)elevationSimulation based techniquess are called Behavior Analysis¾Why is it difficult to use simuulation for reservoir sizing?¾Another type of “simulation” is based on deficit instead ofstorage.storage This solves some of the simulation problemsproblems.¾Approach is called Sequent Peak AlgorithmCVEN 5838 Aug 28, 2008

Sequent Peeak AnalysisLet Kt be the maximum total storage reqquirements needed; Set K0 0Example: Nine periodperiod-ofof--record flows: [1,[ 3, 3, 5, 8, 6, 7, 2, 1]Apply the equationconsecutively for up to2x the total length ofthe record.The maximum of all Ktis the required storagecapacity for thespecified releases Rtand inflows QtCVEN 5838 Aug 28, 2008

Accounting for LossesEvaporation and Rainfall (net losses) depeend on Surface AreaSurface area depends on storage non linearly:But can be approximated linearly:CVEN 5838 Aug 28, 2008

Accountingg for losses¾Losses can alter the critical pperiod and change the storagecapacity¾NetN t evap ((equations)ti) can bbee includedi l d d iin storagetbbaseddsimulations directly¾LeleLl anddMMontaseritiddevelopel edd methodsth d ffor iincludingl di evapin SPA in an interative approoach(See McMahon et al., Sequeent Peak Algorithm paper onclass website)¾An alternative evapp modelcan be used directly with SPPACVEN 5838 Aug 28, 2008

ReliaabilityReliability (time(time--based) - Ns/NR iliResiliance– SpeedSd off recoveryVulnerabilityy – severityy of failure ((volumetric reliability)y)(Tradeoffs on these 3 lead to very tricky desiggn; several authors have developed indicesthat attempt to combine these (Loucks, 1997; Zongxue, 1998)Reliability and Vulnerability can be integrated into SPA:zzzDetermine number of failure perriods permitted (from reliability)Determine reduced maximum reeduced capacity permitted (fromvulnerability)See example in McMahonCVEN 5838 Aug 28, 2008

Classification of S-Y-P Procedures(Storage – Yieldd – Performance)CVEN 5838 Aug 28, 2008

Behavior Analysis – stoorage based simulation((detailed simulattions of pprocesses))Case 1: Estimate System PerformanceActive capacitypy of reservoir is known.Series of demands is given (could be stochastic).sStarting condition is known or assumed.Historical or synthetic inflows are usedd(could be many traces) (index seqquential or monte carlo)Case 2: Find size of reservoir under conssiderationSeries of demands is known (could bee stochastic)series of inflows is given (historical or ggenerated stochastic)Performance criterion is specifiedEstimate reservoir capacity; do simulations; adjust until get performancedesiredCase 3: Estimate Yield of an existing reseervoirSpecify performance criteria (reliabilityy, vulnerability, maybe resiliance)Use historic or stochastic hydrologyEstimate demand (yield) and iterate unntil meet performance criteriaNeed to know and model detailed operating proceduresCVEN 5838 Aug 28, 2008

Additional important topics¾ Optimizationtechniquesssimple ones can give ideentical results to SPAmore complex methods can include costfunctions¾ Multiple reservoir systemmssingle-reservoir techniques can be extended to multisinglemultireservoir systemsdetermine size at each sitespecify operating policies foor releases and demands(heuristic policies have been developed)typical objective is to keep reservoirs balancedCVEN 5838 Aug 28, 2008

rence between a sequence of prerence between a sequence of pre--d known inflows Q t. y 35 40 25 30 m e R 4 15 inflow volu 20 t 5 10 0 12 345 67 8 9 time Inflow Cumulative Inflow. . emptiness and to a full condition again CVEN 5838 Aug

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