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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 l.jpg

Hydro Optimization

Tom Halliburton

Variety l.jpg

  • Stochastic

  • Deterministic

  • Linear, Non-linear, dynamic programming

  • Every system is different

  • Wide variety of physical constraints

  • Studied for many years - lots of legacy systems.

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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

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Transmission system


Small headpond

Power house

Concrete or earth dam


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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

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Merit Order Dispatch



Flexible plant

Base load plants

Zero cost resources

Must run


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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

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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

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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

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Reservoir Guidelines

Lake Level







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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

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  • 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

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SDDP Subproblems

At each state pointSolve one LP for each inflow outcome

State (storage)




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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

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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,……

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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

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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

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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

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Unit Modeling


Maximum efficiency

Full load

Rough running ranges

Water Flow

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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

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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

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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

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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

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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.

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Optimal Unit Loading

Two unit loads

Three unit loads

One unit loads

Desired station load

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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

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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)