Dealing with probabilistic constraints at EDF

Dealing with
probabilistic
constraints at EDF
Simon Fécamp (EDF R&D) |
[email protected]
09/17/2014
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SUMMARY
1.
EDF HYDRO POWER PLANTS
2.
FROM THE PRACTICAL PROBLEM TO THE THEORICAL FRAMEWORK OF RIVER MANAGEMENT
3.
STUDY ON A HEURISTIC APPROACH TO COPE WITH PROBABILISTIC CONSTRAINTS
4.
DISCUSSION / IMPROVEMENTS
Simon Fécamp | 09/17/2014 | 2
EDF Hydro power
plants
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EDF HYDRO POWER PLANTS
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EDF HYDRO POWER PLANTS
447 hydro power plants :
45 plants above 100 MW
Biggest hydro power plant in France : 1840 MW (Grand’Maison)
Biggest reservoir in metropolitan France : 1030 hm3 (Serre-Ponçon)
Total installed power : 19600 MW
Including 2400 MW of pump/turbine power
+ 1800 MW of pump only power
Total capacity : 45 TWh / year (out of ~ 500 TWh / year produced by EDF)
Distributed in 40 valleys
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Practical problem /
theoretical
framework
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PRACTICAL PROBLEM
2 main objectives in hydro power plants management
Electricity demand supply + flexibility in power generation
Optimization to reduce the costs of production and to secure the electricity supply
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PRACTICAL PROBLEM
Respecting numerous constraints related to environment and to uses of water
other than hydro power generation :
Safety in the valleys
Water supply for agriculture
Environment constraints : water turbidity, salinity, fishes
Tourism needs
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PRACTICAL PROBLEM
Decisions on hydro power plants are often guided by constraints
Not all constraints can be respected for any situation (water inflow scenarios)
We will aim at respecting them but not for all situation
⇒ Negotiated target probabilities of respect
Valley management has to ensure at least the target probability of respect will be
observed for each constraint.
Decisions on reservoirs have to reflect everything is done to anticipate constraints
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THEORETICAL FRAMEWORK
The global problem of demand meeting for all the power plants can’t be addressed
at once
decomposition
Global simulations to access scenarios of marginal costs of production and flexibility
Similar to a price decomposition
Problems addressed separately for each valley
Since no other coupling than demand meeting between valleys
For each valley, strategy obtained by a standard SDP :
Hydro power generation valued by marginal costs of production + flexibility
Calculating valley expected revenue depending on main reservoirs levels
• 1 or 2 main reservoirs per valley
dimension of SDP is 1 or 2.
Short range optimization for small reservoirs
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THEORETICAL FRAMEWORK
State variable : st
Expected valuation of the
valley depends mainly on st
Year-range
optimization
Scenarios of water inflows to
the different reservoirs
Scenarios of marginal costs
to value power and flexibility
generated by plants
Week-range
optimization
reservoirs
Volumes and outflows
bounded by constraints
turbines
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THEORETICAL FRAMEWORK
Problem :
•
•
•
•
Gt collected revenue from the valley at timestep t
st vector of state variables
wt vector of random variables describing water inflows and prices
VT ending evaluation of the valley
addressed by SDP :
But some transition problems are not feasible
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THEORETICAL FRAMEWORK
So we rather apply the following formula to relax constraints if needed :
Some constraints need to be anticipated
No penalty applied to the valley expected revenue in case of violated constraints
Instead, implementation of a “constrained management” :
• If a condition on a reservoir level isn’t fulfilled, controls in the river are based on a non-economic
criteria
• Otherwise, usual maximization of the valley expected revenue
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THEORETICAL FRAMEWORK
Constrained management with a condition of maximum level on a reservoir :
For instance to avoid water spillage on a dam
Reservoir
level
Constrained management
Above the condition on
maximum level, the
strategy consists in
lowering the reservoir
level as much as
possible.
Economic management
Timestep
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THEORETICAL FRAMEWORK
The matter is to build conditions of the constrained management that would
anticipate constraints
It is easily done when the constraint has to be anticipated for all scenarios
How about probabilistic constraints ?
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A HEURISTIC
APPROACH TO
COPE WITH
PROBABILISTIC
CONSTRAINTS
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HEURISTIC APPROACH
Presentation of a study ran last year about how to adapt constrained management
to probabilistic constraints problems
We will see how analyzing probabilities of respect will help us adjusting conditions
to anticipate probabilistic constraints.
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EVALUATION OF PROBABILITIES
We want to build conditions on the volume of a reservoir to observe at least a given
probability of respect
We should evaluate probabilities of respect depending on reservoir level
It can be done through the SDP by introducing a new function defined as follows :
Ft is 0 if kth constraint is violated at timestep t
Else it is Ft+1
The expectation of Ft for all st lead us to the probability of respect of the kth constraint
depending on the reservoir level
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EVALUATION OF PROBABILITIES
Example of probability of respect obtained with given conditions on a reservoir for
which we want to anticipate water spillage :
In this case, whatever the conditions we build no probability over 73 % can be expected
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EVALUATION OF PROBABILITY
Instance of anticipation of water spill on a reservoir
Insufficient conditions
Probability of respect not reaching at least target value.
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EVALUATION OF PROBABILITY
Conditions are too hard
Conditions are sufficient
But we employ constrained management in some areas where probability of respect is
over the target value ⇒ unnecessary loss of revenue
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EVALUATION OF PROBABILITY
This is what we want :
Conditions are sufficient
Constrained management only when probability is below target
Constrained management each time probability is below target
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BUILDING CONDITIONS
Probabilities can’t be used directly to create conditions at each timestep
We analyze a probability of respect without doing any constrained management
Blue curve corresponds to the target probability of respect
This curve provides too hard conditions
We will then try to iterate this
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ITERATING WORKS
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DISCUSSION /
IMPROVEMENTS
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DISCUSSION
The heuristic approach gives us a sequence of sufficient conditions on a reservoir
level to anticipate constraints with the expected probability of respect.
Built conditions are not necessary
Works well for us because :
• No penalty in water utility values to anticipate constraints or conditions
• Many constraints
The constrained management seems complex but it actually makes a relatively
easy calculus :
It converges fast (usually 4 iterations), needs no parameter at all
Easy comprehension of results
Thus ease negotiations in case of constraints that should be relaxed
Behavior we want in case of chance of not fulfilling the constraints probabilities of
respect
Tricky point : the conditions don’t anticipate each other, their role is only to
anticipate real constraints
Constrained management isn’t avoided ⇒ makes hard scenarios anticipate constraints.
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IMPROVEMENTS
Modeling of conditions on 2 reservoirs at the same time not made yet
Convexity needed in the curve describing same probability of respect depending on 2
levels of 2 reservoirs.
Convergence ?
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THANK YOU !
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