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Simulating System Performance

Simulating System Performance. Water Resources Planning and Management Daene C. McKinney. Reservoir Management. Important task for water managers around the world. Models used to simulate or optimize reservoir performance

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Simulating System Performance

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  1. Simulating System Performance Water Resources Planning and Management Daene C. McKinney

  2. Reservoir Management • Important task for water managers around the world. • Models used to • simulate or optimize reservoir performance • design reservoirs or associated facilities (spillways, etc.).

  3. Operating Rules • Allocate releases among purposes, reservoirs, and time intervals • In operation (as opposed to design), certain system components are fixed: • Active and dead storage volume • Power plant and stream channel capacities • Reservoir head-capacity functions • Levee heights and flood plain areas • Monthly target outputs for irrigation, energy, water supply, etc • Others are variable: Allocation of • stored water among reservoirs • stored and released water among purposes • stored and released water among time intervals

  4. St Rt Qt X1t X2t K Dt Rt Release available water & deficits occur Release demand spill excess Release demand & demand met Dt Demand Sufficient water to meet demands Reservoir fills and demand met Dt Dt+K St+ Qt Standard Operating Policy • Reservoir operating policy - release as function of storage volume and inflow Rt = Rt(St,Qt)

  5. D hedging K Hedging Rule • Reduce releases in times of drought (hedging) to save water for future releases in case of an extended period of low inflows.

  6. Start t = 0 St = S0 St X1t R Qt X2t t = t + 1 X3t K File Read Qt Compute Rt, Xit, i=1,…n Data Storage St+1 = St +Qt -Rt No Yes Stop System Simulation Operating Policy Allocation Policy • Create network representation of system • Need inflows for each period for each node • For each period: • Perform mass balance calculations for each node • Determine releases from reservoirs • Allocate water to users Done?

  7. St R Qt X1t X2t K Example • Using unregulated river for irrigation • Proposed Reservoir • Capacity: K = 40 million m3 (active) • Demand: D = 30  40  45 million m3 • Winter instream flow: 5 mil. m3 min. • 45 year historic flow record available • Evaluate system performance for a 20 year period • Simulate • Two seasons/year, winter (1) summer(2) • Continuity constraints • Operating policy Flow statistics

  8. R2,t Release available water Dt Release demand Dt K Dt+K S2,t+ Q2,t Release demand + excess Summer Operating Policy Storage at beginning of summer

  9. Performance Evaluation • How well will the system perform? • Define performancecriteria • Indices related to the ability to meet targets and the seriousness of missing targets • Simulate the system to evaluate the criteria • Interpret results • Should design or policies be modified?

  10. Performance Criteria - Reliability • Reliability – Frequency with which demand was satisfied • Define a deficit as: • Then reliability is: • where n is the total number of simulation periods

  11. Performance Criteria - Resilience • Resilience = probability that once the system is in a period of deficit, the next period is not a deficit. • How quickly does system recover from failure?

  12. Performance Criteria - Vulnerability • Vulnerability = average magnitude of deficits • How bad are the consequences of failure?

  13. h(y) g(x) y x Simulate the System Reservoir operating policy Allocation policy Policies Hydrologic time series Model output System Input Output Model

  14. Uncertainty • Deterministic process • Inputs assumed known. • Ignore variability • Assume inputs are well represented by average values. • Over estimates benefits and underestimates losses • Stochastic process • Explicitly account for variability and uncertainty • Inputs are stochastic processes • Historic record is one realization of process.

  15. FY(y) FX(x) h(y) h(y) g(x) g(x) Simulate each Input sequence X y y x x Simulate the System Reservoir operating policy Allocation policy Distribution of inputs Policies Generate multiple input sequences Compute statistics of outputs System Get multiple output sequences Model

  16. The Simulation • Simulate reservoir operation • Perform 23 equally likely simulations • Each simulation is 20 years long • Each simulation uses a different sequence of inflows (realization)

  17. Example – Realization 1

  18. Results Average failure frequency = 0.165 Average reliability = 1- 0.165 = 0.835 = 83.5% Actual failure frequency  [0, 0.40] Actual Reliability  [100%, 60%]

  19. Predictability: High – solid line Med – dashed line Low – dotted line Understanding: High – green arrow Med – blue arrow Low - red arrow Importance: High – thick line Med – medium line Low – thin line Physical EnvironmentFeedback Sub Model to FAV Local Physical Environment (tides, freshwater flow) + Riparian Vegetation Heavy metals Salinity Nutrients DO - Surface, Subsurface Light + - - - Wind, Flow Velocity Temp - + + + + Substrate Org Matter FAV Establishment and Growth FAV Patch + Dispersal + + Small Substrate Grain Size + + - Subsurface Light Lars Anderson, UC Davis Stuart Siegel, WWR Mark Stacey, UCB

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