4/25/2016
University of California, Davis Department of Land, Air and Water Resources
Introduction to Simulation Models
ESM-121 Water Science and Management
Samuel Sandoval Solis, PhD Assistant Professor
Presentation 4 of 10
Hoover Dam Shasta Dam Oroville Dam 158 m 159 m 230 m 35.2 Km3 5.6 Km3 4.4 Km3 4.2 bill. KWh 1.8 bill. KWh 2.2 bill. KWh $49M - 1936 $36M - 1945
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• Masonry - Arch Dams • Gravity Dams • Embankment dams • Rock-fill and earth-fill dams • Spillways
St Q R t K t
Q t K
St
Rt
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Allocate reservoir release Rt to 3 users and provide instream flow Qt
Operating Policy Allocation Policy
• Simulation models: Predict response to given design • Optimization models: Identify optimal design or operation
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• Address “What if …” questions • What will likely happen • Include larger hyd, econ, Operating Policy and env. data • i.e. “evaluate change given a design or policy”
Allocation Policy
• Used for design: - “Maximize the Net Benefits …” or - “Minimize the shortages” • Look for the best (ideal) operation • Perfect foresight
Optimization model T 3 Objective Maximize Bi (xit ) Benefits: Bi(xit ) t1 i1 x x x R t 1, 2, Decision Variables: xit 1t 2t 3t t
Constraints St1 St It Rt t 1, 2,
St K t 1, 2,
Optimization model
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Reservoir operating policy Allocation policy
Rt 8
Release available x1 i 6 water x2 x3 4 Dt Release Release demand Allocation, Allocation, X demand + excess 2
0 Dt K Dt+K St+ Qt 0 2 4 6 8 10 12 14 16 Release, R Policies
g(x) Hydrologic h(y) Model time series output x y
Input System Output
Model
Deterministic process Stochastic process Inputs assumed known. Explicitly account for variability Ignore variability and uncertainty Assume inputs are well Inputs are stochastic processes represented by average values. Historic record is one realization Over estimates benefits and of process. underestimates losses
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Reservoir operating policy Allocation policy
Rt 8
Release available x1 i 6 water x2 x3 4 Dt Release Release demand Allocation, Allocation, X demand + excess 2
0 Dt K Dt+K St+ Qt 0 2 4 6 8 10 12 14 16 Release, R Distribution of inputs
FX(x) FY(y) Policies X Generate multiple input sequences Compute h(y) statistics of g(x) outputs y Simulate each System h(y) g(x) x Input sequence Get multiple output sequences y x Model
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