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Hydro Optimization - PowerPoint PPT Presentation

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

Tom Halliburton

• Stochastic

• Deterministic

• Linear, Non-linear, dynamic programming

• Every system is different

• Wide variety of physical constraints

• Studied for many years - lots of legacy systems.

• Long term expansion planning

• Long / medium term operational planning

• Market clearing

• Short term operations planning

• Real time economic dispatch

LargeLake

Transmission system

Penstock

Power house

Concrete or earth dam

Tailwater

• 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

MW

Peakers

Flexible plant

Zero cost resources

Must run

Hours

• 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

• 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

• 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

Lake Level

\$0/MWh

\$5/MWh

\$15/MWh

\$30/MWh

\$100/MWh

Time

• 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

• 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

At each state pointSolve one LP for each inflow outcome

State (storage)

t

t+1

Time

Future Cost

One hyper plane per state point

Slope = average dual of water balance

Height = average cost to go from that state

Storage Level

• 1 or 2 year horizon, weekly time steps

• 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,……

• Stochastic DP or Stochastic LP – gaining due to increased LP solver power

• Key output – water values from large lakes

• Maintenance planning

• Permitting studies

• 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

• 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

MW

Maximum efficiency

Rough running ranges

Water Flow

• 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

• 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

• Feasibility essential, optimality desirable

• 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

• 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

• 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.

• 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

• Economic Dispatch determines allocation of grid operator requests