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Hydro Optimization

Hydro Optimization . Tom Halliburton. Variety. Stochastic Deterministic Linear, Non-linear, dynamic programming Every system is different Wide variety of physical constraints Studied for many years - lots of legacy systems. Time Scales. Long term expansion planning

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Hydro Optimization

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  1. Hydro Optimization Tom Halliburton

  2. Variety • Stochastic • Deterministic • Linear, Non-linear, dynamic programming • Every system is different • Wide variety of physical constraints • Studied for many years - lots of legacy systems.

  3. Time Scales • Long term expansion planning • Long / medium term operational planning • Week / day ahead ahead planning • Market clearing • Short term operations planning • Real time economic dispatch • Real time unit loading

  4. LargeLake Transmission system Penstock Small headpond Power house Concrete or earth dam Tailwater

  5. Water Value • Value of an extra increment of water • If lake full, extra spilled  Value = 0 • If empty, extra replaces combustion turbine or avoids blackout  high value • Expected marginal value of water = E[marginal cost of thermal station displaced by generation from this water] • Dual value of flow balance equation in LP • Use water so that Marginal Value of water used this period = EMV of water in storage

  6. Merit Order Dispatch MW Peakers Flexible plant Base load plants Zero cost resources Must run Hours

  7. Long Term Planning • 10 to 30 year horizon, 1 to 4 week time step • Hydro, thermal, transmission system • Transmission important especially with hydro • Some aggregation of chains of stations • Model large reservoirs only • Stochastic load, inflows, thermal plant availability • Load duration curve load representation

  8. Long Term Planning • Simulation of a specified set of conditions • Optimization to get a reasonable hydro operating pattern • Thermal dispatch models (eg Henwood) use rule based dispatch. Hydro operating patterns specified by user • Stochastic inflows, energy limitation problematic • Use of mean flows risky

  9. Stochastic DP with Heuristic • 30 year hydro-thermal planning with HVDC constraint in New Zealand • Determine reservoir levels at which EMV = marginal cost of each thermal plant • 60 simulations of detailed operation using historical inflows • Major impact on electricity planning in NZ • Used for long term planning, medium term operations

  10. Reservoir Guidelines Lake Level $0/MWh $5/MWh $15/MWh $30/MWh $100/MWh Time

  11. SDDP - by Mario Pereira • Stochastic Dual Dynamic Programming’ • 1 to 10 year horizon, weekly / monthly time steps • Used in numerous countries • Stochastic DP with a sampling strategy to enable multi reservoir optimization • Hydro, thermal, with detailed transmission system, area interchange constraints • Solves an LP for each one period sub problem

  12. SDDP • Simulate forward with 50 inflow sequences, using a future cost function – gives upper bound on objective function • DP backward optimization considering only storage states that the simulation passed through - gives lower bound on objective • Each optimization iteration adds hyper planes to the future cost function, improving the approximation

  13. SDDP Subproblems At each state pointSolve one LP for each inflow outcome State (storage) t t+1 Time

  14. SDDP Future Cost Future Cost One hyper plane per state point Slope = average dual of water balance Height = average cost to go from that state Storage Level

  15. Medium Term Planning • 1 or 2 year horizon, weekly time steps • Load duration curve • Norwegian power pool model - successive approximations DP • Hydro Quebec “Gesteau” - stochastic dynamic program • Acres International, Charles Howard, PG&E … stochastic linear programming solved by CPLEX. • SDDP – Central America, Colombia,……

  16. Medium Term Planning • Stochastic DP or Stochastic LP – gaining due to increased LP solver power • Key output – water values from large lakes • Maintenance planning • Permitting studies • Plant upgrade studies

  17. Day or Week Ahead • 24 to 168 hour horizon • One hour, ½ hour time steps - chronological • Deterministic • Link to medium term model by water values • Maybe with bid curve generation strategy • LP, sometimes with successive linearizations, sometimes MIP • Detailed model of waterways, lakes, hydro units

  18. Day or Week Ahead • Send output to market operator or real time control center • Nasty features: • Overflow spill weirs • Rate of change of flow constraints • Non convex unit characteristics • Unit prohibited zones • Spinning reserve

  19. Unit Modeling MW Maximum efficiency Full load Rough running ranges Water Flow

  20. Market Clearing • 24 hour horizon, 1 or ½ hour steps • Bids and offers can be specific to each bus • Optimize accounting for transmission system losses and constraints for optimal clearing price at each bus. • CEGELEC ESCA (NZ, Australia) • Simple price / quantity stack Cal PX • Ignore coupling of time periods – problems for hydro operators

  21. Hydro Economic Dispatch • 30 to 120 minutes horizon, 10 minute steps • Used in control center with SCADA • Takes system status from SCADA (lake levels, flows, current set points) • Time step short, run frequently, 10 minutes • Given a load change, what should be done • Answer needed quickly • Feasibility essential, optimality desirable

  22. Hydro Economic Dispatch • Input water values, overall strategy from day ahead model • Models whole system of stations, canals, lakes, gates, spillways • Individual units, stop / start costs • Environmental constraints, operating rules • Issue new set points automatically, with operator review

  23. Optimal Unit Loading • Static optimization, solve on demand • Objective: Minimize water use for given station output how many units should be on-line what load on each unit • Run by operator or within a SCADA system • Simple, quick, clearly defined payoff • Every unit is a unique individual – even more so with age – cavitation repairs

  24. Optimal Unit Loading • Tailrace and headrace geometry, penstock losses, interaction between units. • Calibrate unit performance using ultrasonic flow measurement, accurate MW meters • Rough running zones • Non symmetrical station layout – different tailwater levels, penstock losses.

  25. Optimal Unit Loading Two unit loads Three unit loads One unit loads Desired station load

  26. Decision making • Year ahead to set water values • Week/day ahead using water values to generate market bids • Market clearing model to determine day ahead results • Day ahead model to plan implementation • Real time instructions issued to control center by grid operator

  27. Decision making • Economic Dispatch determines allocation of grid operator requests • Station receives set points • Unit loading algorithm adjusts unit set points • ED runs frequently • AGC adjusts some unit set points to correct frequency or Area Control Error (Ace)

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