Hydro Optimization

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Hydro Optimization

• Tom Halliburton

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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.

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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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Large Lake
Transmission system
Penstock
Small headpond
Power house
Concrete or earth dam
Tailwater
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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 Emarginal
  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
MW
Peakers
Flexible plant
Base load plants
Zero cost resources
Must run
Hours
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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
0/MWh
5/MWh
15/MWh
30/MWh
100/MWh
Time
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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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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

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SDDP Subproblems
At each state pointSolve one LP for each inflow
outcome
State (storage)
t
t1
Time
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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, PGE
  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
MW
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)