Reservoir Yield R&D Unit

Transcription

1 Reservoir Yield R&D Unit Water Supply Workshop June 2011 Beth Faber PhD, PE Hydrologic Engineering Center USACE

2 Water Supply / Firm Yield R&D Unit Survey the methods in use to compute firm yield for water supply contracts Evaluate methods Investigate consistent method that is flexible enough to apply in all or most cases, and build tools to implement Report on Yield Analysis Methods is posted at: ftp://ftp.hec.usace.army.mil/public/watersupply/

3 Outline Yield Concepts and Methods Simple Yield Computation Methods Iterative Simulation Data, Simulation Details Computation time interval Gains and Losses, Variable Demand Water Supply Contracts, Water Accounting Complexities in water accounting Reliability Multi-reservoir systems Reservoirs in Parallel, Reservoirs in Series, Coordination Including higher-priority uses, lower priority uses

4 Re-distribution of Water in Time We build reservoirs to accumulate and release water to improve the distribution in time... Within-year Reservoir Storage Reservoir stores wet season water for use in the dry season Over-year Reservoir Storage Reservoir stores wet year water for use in dry years or extended drought Evaluation of demand and local hydrology will determine if within- or over-year is needed, and the required volume

5 Reservoir Storage Inflow Demand Year 1 Year 2 Year 3 Year 4 Year 5

6 Storage / Yield of a Reservoir Firm Yield = amount of flow that can be provided on a regular basis (yield average flow) Firm yield, critical yield, safe, reliable, minimum The most basic evaluation is the at-site Storage / Yield relationship. actual firm yield Firm Yield actual reservoir storage volume Average Flow Reservoir Storage Volume

7 Storage / Yield Relationship In a study, there are 2 ways to ask the question: Planning: For a given demand, what storage volume is needed at that location? Reassessment: For a given reservoir or storage pool, what is the firm yield? repeat, to generate storage/yield relationship Supply Contract what volume needed in existing reservoir s Conservation Pool to supply requested yield? (...share of inflow, share of space)

8 Storage / Yield Relationship There are various methods for determining the relationship between reservoir storage and firm yield Simple Methods Rippl Mass Diagram Sequent Peak Algorithm Iterative Reservoir Simulation simulation of reservoir operation over a period of record can capture more complex operations, priorities, demand patterns and physical losses trial-and-error search to determine firm yield for defined storage capacity

9 Input Data Needed... The supply data used can be either the historical record, or a critical dry period within the record a synthetic data series or drought event either full inflow, or inflow belonging to user The demand requirements can be either 100% of actual or forecasted demand Partial demand, or demand met with some frequency or reliability

10 Example Inflow Series = 4,857 cfs 1 KAF/mo = 16.5 cfs = 10.7 mgd

11 Rippl Mass Curve Approach

12 Rippl Mass Curve Approach

13 Sequent Peak Algorithm

14 Sequent Peak Algorithm 4068 KAF

15 Simple Iterative Simulation

16 Resulting Storage/Yield Curve Storage Volume (KAF)

17 Complete Storage/Yield Curve Storage Volume (KAF)

18 Storage/Yield Curve as rate/volume Storage Volume (KAF)

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20 Outline Yield Concepts and Methods Simple Yield Computation Methods Iterative Simulation Data, Simulation Details Computation time interval Gains and Losses, Variable Demand Water Supply Contracts, Water Accounting Complexities in water accounting Reliability Multi-reservoir systems Reservoirs in Parallel, Reservoirs in Series, Coordination Including higher-priority uses, lower priority uses

21 Computation Time-interval Previous example was a monthly computation Averaging flows over longer durations tends to smooth the highs and lows Storage reservoirs also smooth the highs and lows H We ll try an example

22 Another Example average flow This is a daily computation The storage/yield curve has many different critical periods Firm Yield is the flow rate that can be satisfied over time by storing water for later use more storage = more yield up to avg flow Storage = 220 KAF Storage = 504 KAF Yield = 1000 cfs (60 kaf/mo) Yield = 1500 cfs (90 kaf/mo) KAF/ mo KAF/ mo

23 daily flow critical period for 1500 cfs average flow, longer durations

24 511 KAF 1500 cfs 511 KAF 504 KAF -1.4% 1500 cfs 511 KAF 496 KAF -3% 1500 cfs

25 511 KAF 461 KAF -10% 1500 cfs 511 KAF 412 KAF -20% 1500 cfs 511 KAF 308 KAF -40% 1500 cfs

26 Storage/Yield Curve for various intervals

27 Inclusion of Losses and Gains

28 Variable Demand Demand Pattern Jan Mar May Jul Sep Nov Jan

29 Outline Yield Concepts and Methods Simple Yield Computation Methods Iterative Simulation Data, Simulation Details Computation time interval Gains and Losses, Variable Demand Water Supply Contracts, Water Accounting Complexities in water accounting Reliability Multi-reservoir systems Reservoirs in Parallel, Reservoirs in Series, Coordination Including higher-priority uses, lower priority uses

30 Water Supply Contracts The more common question asked in the Corps is: In this reservoir, what storage volume is required to yield 200 cfs? A reservoir exists, and has a Conservation pool. How much volume does a user require (as a contract account), to store water for their own use? Difference between this question and the simple firm yield from storage is the user s share of inflow Riparian rights? %-of-pool Prior Appropriation? How do other operational priorities affect that yield? Is there a high priority season flood pool? 1031 cfs 685 cfs % 19% 15%

31 Maximize Firm Yield with Water Accounting Water Account: a floating or vertical pool within the Conservation Pool of the reservoir Account is specified to meet some purpose such as water supply Withdrawals for specified purpose are subtracted from water account balance That purpose s share of inflow is added to account balance For firm yield computation, either minimize required account capacity to meet demand, or maximize demand for a given account capacity But, there can be many complexities in accounting

32 Tracking a water account - Simple case Firm yield = 685 cfs = 50% of 1371 cfs

33 Tracking a water account variable demand Firm yield = 668 cfs 25

34 Tracking a water account variable guide curve Firm yield = 760 cfs 1

35 Tracking a water account variable guide curve Firm yield = 622 cfs 9

36 Tracking a water account - Simple case Firm yield = 685 cfs = 50% of 1371 cfs

37 Tracking a water account surplus inflow Firm yield = 720 cfs 5

38 surplus inflow, seasonal Guide Curve, seasonal demand critical period is in 1991 Firm yield = 721 cfs GC

39 surplus inflow, seasonal Guide Curve, seasonal demand draft WS account critical period is in 1991 Note: 635 cfs if constant demand, up from 622 cfs w/o surplus Firm yield = 592 cfs

40 surplus inflow, seasonal Guide Curve, seasonal demand constant %-of-inflow compromise: %-of-inflow stays 50% Firm yield = 689 cfs GC

41 free withdrawal during flood draft Firm yield = 721 cfs didn t affect the critical draft

42 Tracking Water Account In a real example, simulating reservoir and water account, there were many issues to discuss. Seasonal Flood Pool, WS, Recreation, Hydropower Issues to resolve about assumptions of the study were: DATA Inflows (adjust to natural ) Historical use Guide Curve Is water account constant capacity, or constant %-pool? W WS Do we model flexibility in GC when computing firm yield? Return flow What actual, what credit? Priority of Use Flood Protection Water Supply Recreation Hydropower Physical (evap, rainfall, leakage)

43 Question on accounting for evaporation When doing water accounting, how is evaporation charged? Is a user charged in proportion to their capacity %-ofpool? often there is large area inactive pool, all users responsible BUT, subtracting evap might make an account go negative Is a user charged in proportion to their current %-ofpool? account cannot go negative BUT, other users responsible for more of inactive pool evaporation when one user drafts their account low

44 Outline Yield Concepts and Methods Simple Yield Computation Methods Iterative Simulation Data, Simulation Details Computation time interval Gains and Losses, Variable Demand Water Supply Contracts, Water Accounting Complexities in water accounting Reliability Multi-reservoir systems Reservoirs in Parallel, Reservoirs in Series, Coordination Including higher-priority uses, lower priority uses

45 Reliability Reliability = probability system will not fail The period-of-record provides a limited description of potential dry periods (critical periods). We can compute firm yield based on the worst drought of record, but there s still a chance a more severe drought will occur. Depending on the worst of the record provides inconsistent reliability depends on length of record and random occurrence of dry periods

46 Alternatives to Critical Period Options to increase or evaluate reliability: build in a factor of safety buffer volume of x% compute firm-yield/reliability using stochastic time-series evaluate drought of specified return period evaluate many (stochastic) examples of N-year record Generate a longer synthetic (stochastic) time-series. Aggregate to annual volumes, compute mean, variance, skew, and serial-correlation Use auto-regressive lag-1 AR(1) stochastic streamflow model to generate longer record of possible annual volumes Disaggregate to monthly/daily Perform yield analysis requiring various reliability levels

47 Initial 41-year record of annual volumes (first example) Use AR(1) to generate longer record More examples of drought events compute μ, σ, γ, ρ serial correlation = ρ = 0.24 Generated 100-year record of annual volumes Q(t) = μ + (Q(t-1)-μ)*ρ + random error(σ,γ)

48 1000 years

49 Reservoir Storage trace for 1000 years, volume needed for 100 kaf/month Release = 100 KAF/mo 1 failure in 1000 years, reliability = 99.9% Required Volume = 1,434 KAF Disaggregated annual to monthly, then firm yield simulation Reliability is 99.9% (1 failure in 1,000 years) for no failures in 1,000 years, increases to 1,768 KAF

50 Reservoir Storage trace for 1000 years, volume needed for 100 kaf/month Release = 100 KAF/mo 10 failures in 1000 years, reliability = 99% Required Volume = 783 KAF 10 failures in 1000 years Reliability is 99% (1 in 100) 2 years

51 Storage Requirement vs Reliability 669 KAF

52 Release = 200 KAF/mo 1 failures in 1000 years, reliability = 99.9% Required Volume = 6,894 KAF

53 storage/yield relationship based on period of record at site storage/yield relationships based on stochastic streamflow record and reliability

54 500 examples of 41-year record Demand = 100 KAF/mo Initial storage requirement = 669 KAF histogram or PDF CDF Demand = 200 KAF/mo Initial storage requirement = 4,068 KAF histogram or PDF CDF

55 Outline Yield Concepts and Methods Simple Yield Computation Methods Iterative Simulation Data, Simulation Details Computation time interval Gains and Losses, Variable Demand Water Supply Contracts, Water Accounting Complexities in water accounting Reliability Multi-reservoir systems Reservoirs in Parallel, Reservoirs in Series, Coordination Including higher-priority uses, lower priority uses

56 Multi-Reservoir Systems Reservoirs in Parallel The easier question is what is the yield of the entire system, at the bottom? A tougher question is what is yield of each reservoir? Reservoirs in Series

57 Multi-Reservoir Systems When evaluating the yield of multiple reservoirs, the important factors are: the relative location of the reservoirs reservoirs in series, reservoirs in parallel, the ownership and coordination of the reservoir operation jointly-operated, coordination independently-operated location of use bottom of system, or each reservoir other uses, higher or lower priority

58 Multi-Reservoir Systems One reservoir = one yield analysis Reservoir systems often require several yield analyses (i.e., several applications of iterative simulation) Usually start by computing maximum firm yield for headwaters reservoirs Series: Then must make some assumptions about how much the headwaters reservoirs actually divert, and how much they pass Parallel: Must make some assumptions about how the reservoirs meet common obligations (maybe power or downstream)

59 Separately-owned Parallel System Reservoirs are separatelyowned, with independent operation. Need per-reservoir yield. EASY Finding yield of each reservoir requires only one step: 1. Iteratively simulate each reservoir, increasing diversion until one that exactly empties that reservoir is found. Reservoirs in Parallel capacity = 250 KAF avg annual inflow = 1170 KAF can store 21% capacity = 1100 KAF avg annual inflow = 1480 KAF can store 75%

60 Jointly-owned Parallel System Reservoirs have coordinated operation. Need firm yield of downstream site. Reservoirs in Parallel EASY Finding firm yield of the system requires only one step: 1. Using a reservoir model that captures the joint operation (e.g. using storage balance scheme) iterate until find maximum diversion that exactly empties both reservoirs.

61 Parallel System East Reservoir Separate Joint Max firm yield at East = 1479 cfs 1.3 cfs/kaf 0.9 KAF/yr/KAF West Reservoir Max total firm yield = 2152 cfs Max joint firm yield (downstream) = 2424 cfs Separate Joint Max firm yield at West = 673 cfs 3.3 cfs/avgkaf 2.4 KAF/yr/KAF

62 Jointly-Operated Series System Reservoirs are jointly-owned, with coordinated operation. Finding yield of each reservoir requires several steps: 1. Find firm yield of upstream reservoir (max upstream) 2. Assume no diversion at upstream reservoir, and find firm yield of downstream reservoir (max dwnstrm) 3. Vary upstream diversion from 0 to max upstream, compute downstream firm yield for each, find highest total Reservoirs in Series max 0 vary 0 to max capacity = 250 KAF avg annual inflow = 1170 KAF can store 21% max capacity = 1100 KAF avg annual inflow = 1480 KAF can store 75% result

63 Jointly-Operated Series System Upper Reservoir Max Upper Max Total Max firm yield at Upper = 1479 cfs Lower Reservoir Max Upper Max Total Max firm yield at Lower = 2424 cfs

64 Jointly-Operated Series System Upper Res Diversion Lower Res Diversion Total Diversion (cfs) (cfs) (cfs)

65 Separately-operated Series System Reservoirs are separately-owned, no coordinated operation. 1. Find firm yield of upstream reservoir (max upstream) 2. Assume upstream reservoir diverts maximum, find firm yield of downstream reservoir (min dwnstrm) 3. Assume upstream reservoir not present, find firm yield of downstream reservoir (max dwnstrm) 4. Vary upstream diversion from 0 to max upstream, compute downstream firm yield for each, find highest total Reservoirs in Series max 0 vary 0 to max min max result

66 Separately-operated Series System Upper Reservoir Max firm yield at Upper = 1479 cfs Max Upper Max Lower Lower Reservoir Max total firm yield = 2152 cfs Max Upper Max Lower Max firm yield at Lower = 673 cfs Max joint firm yield (downstream) = 2152 cfs Max firm yield at Lower = 1052 cfs

67 Separately-operated Series System Upper Res Diversion Lower Res Diversion Total Diversion (cfs) (cfs) (cfs)

68 Jointly-operated Parallel System Coordinated operation, have a common higher priority responsibility. (500 cfs dwnstrm) 1. Evaluate each reservoir alone, NO dwnstrm requirement, to find maximum firm yield (673, 1479) 2. At each reservoir, divert max yield (let s other reservoir meet downstream requirement). Adjust reservoir balance so both empty. 3. Trade-off analysis. Set diversion at one reservoir, maximize firm yield at the other, find max total Reservoirs in Parallel capacity = 250 KAF avg annual inflow = 1170 KAF can store 21% 500 cfs capacity = 1100 KAF avg annual inflow = 1480 KAF can store 75%

69 Jointly-operated Parallel System Coordinated operation, have a common higher priority responsibility. (500 cfs dwnstrm) 1. Evaluate each reservoir alone, NO dwnstrm requirement, to find maximum firm yield (673, 1479) 2. At each reservoir, divert max yield (let s other reservoir meet downstream requirement). Adjust reservoir balance so both empty. 3. Trade-off analysis. Set diversion at one reservoir, maximize firm yield at the other, find max total Reservoirs in Parallel Total = 1652 cfs capacity = 250 KAF avg annual inflow = 1170 KAF can store 21% 173 cfs 500 cfs set 1479 cfs capacity = 1100 KAF avg annual inflow = 1480 KAF can store 75%

70 Jointly-operated Parallel System Coordinated operation, have a common higher priority responsibility. (500 cfs dwnstrm) 1. Evaluate each reservoir alone, NO dwnstrm requirement, to find maximum firm yield (673, 1479) 2. At each reservoir, divert max yield (let s other reservoir meet downstream requirement). Adjust reservoir balance so both empty. 3. Trade-off analysis. Set diversion at one reservoir, maximize firm yield at the other, find max total Reservoirs in Parallel Total = 1744 cfs capacity = 250 KAF avg annual inflow = 1170 KAF can store 21% set 673 cfs 500 cfs 1071 cfs capacity = 1100 KAF avg annual inflow = 1480 KAF can store 75%

71 Jointly-operated Parallel System East Res Diversion West Res Diversion Total Diversion storage balance (cfs) (cfs) (cfs) % % % % %

72 Jointly-operated Parallel System East Reservoir from East shared firm yield at East = 1071 cfs firm yield at East = 1443 cfs West Reservoir Max total firm yield = 1744 cfs Max total firm yield = 1743 cfs from East shared Max firm yield at West = 673 cfs Firm yield at West = 300 cfs

73 Series System Reservoirs have a common higher priority responsibility. (500 cfs downstream) If jointly-operated reservoirs, total firm yield decreases by 500 cfs If independent (separately-operated) reservoirs, must explicitly define the obligation of each reservoir, and lower reservoir must pass the release from upper reservoir. Reservoirs in Series yield yield 500 cfs

74 Higher Priority vs Lower Priority Uses Higher priority uses in the reservoir with Water Supply will limit the firm yield available to WS Lower priority uses will not limit WS firm yield, but will instead be limited by WS compute either decreased overall satisfaction of lower priority use, OR decreased firm yield of lower priority use Higher priority uses are introduced into analysis to define WS firm yield Lower priority uses are evaluated for impacts after the WS firm yield is defined.

75 What about additional Lower Priority use? Using HEC-ResSim Adding a higher-priority use, and performing iterative simulation, finds the firm yield for WS ensuring the higher priority use is always satisfied. higher use fails, so yield rule fails, and iterate again w/lower diversion Adding a lower-priority use is more challenging. Prioritized operating rules act in the present, and so lowerpriority rule takes water if it s available now. This does not preserve water for the future use of water supply. Saving volume for the future requires water accounting.

76 What about additional Lower Priority use? Saving volume for the future requires water accounting. Simulate lower-priority use such that the use is satisfied when unspecified volume is available, and use is curtailed if there is no volume that does not belong to water account simplified approach that only does accounting for water supply OR, can specify water accounts for all uses, and use is curtailed when it s own water account is empty.

77 Accounting in Reservoir Systems The methods just described for firm yield of reservoir systems evaluate the entire conservation pool of each reservoir Instead, water accounts can exist in each reservoir In a coordinated system, water accounts can span reservoirs that are above the point of use either reservoir in series, or in parallel, as long as above Use is subtracted from account balance, share of inflow of each reservoir is added to account balance ResSim scripts have been written for multi-reservoir accounts

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79 Simple Iterative Simulation

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81 Rippl Mass Curve Approach