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

• Long / medium term operational planning

• Week / day ahead ahead planning

• Market clearing

• Short term operations planning

• Real time economic dispatch

• Real time unit loading

Large Lake

Small headpond Power house

Concrete or earth dam

TailwaterPenstock

Transmission system

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

Merit Order Dispatch

Hours

MW

Must run

Zero cost resources

Base load plants

Flexible plant

Peakers

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

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

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

Reservoir Guidelines

Time

Lake Level $0/MWh

$15/MWh

$30/MWh

$5/MWh

$100/MWh

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

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

SDDP Subproblems

Time

State (storage)

t t+1

At each state pointSolve one LP for each inflow outcome

SDDP Future Cost

Storage Level

Future Cost One hyper plane per state point

Slope = average dual of water balanceHeight = average cost to go from that state

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,……

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

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

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

Unit Modeling

Water Flow

MWMaximum efficiency

Full load

Rough running ranges

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

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

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

Optimal Unit Loading

• Static optimization, solve on demand• Objective: Minimize water use for given station

outputhow many units should be on-linewhat 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

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.

Optimal Unit Loading

One unit loadsTwo unit loads Three unit loads

Desired station load

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

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)