Transcript Hydro Optimization for Fun and Profit

Hydro Optimization
Tom Halliburton
Variety
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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
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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
Transmission
system
Small
headpond
Power house
Concrete or earth dam
Tailwater
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
MW
Peakers
Flexible plant
Base load plants
Zero cost resources
Must run
Hours
Long Term Planning
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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
Lake Level
$0/MWh
$5/MWh
$15/MWh
$30/MWh
$100/MWh
Time
SDDP - by Mario Pereira
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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
At each state point
Solve one LP for each
inflow outcome
t
State (storage)
t+1
Time
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
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
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Key output – water values from large lakes
Maintenance planning
Permitting studies
Plant upgrade studies
Day or Week Ahead
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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:
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Overflow spill weirs
Rate of change of flow constraints
Non convex unit characteristics
Unit prohibited zones
Spinning reserve
Unit Modeling
MW
Maximum
efficiency
Full load
Rough running ranges
Water Flow
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
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
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
Two unit loads
One 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)