Pierre Carpentier, Jean-Philippe Chancelier, Michel De Lara
ENSTA and École des Ponts ParisTech
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Pierre Carpentier (ENSTA ParisTech), Jean-Philippe Chancelier and Michel De Lara (École des Ponts ParisTech) have been working together for more than ten years at the Optimization and Systems Group at Cermics, the applied mathematics research center of École des Ponts ParisTech. Their central theme of investigation is about numerical methods in stochastic optimization. Their main application is the management of energy systems under uncertainty, in collaboration with industrial partners.
The course presents stochastic control theory in discrete time, especially the dynamic programming approach, and extensions to more advanced topics, like risk constraints, stochastic viability and informational constraints in large-scale systems. Courses alternate with computer practical works. The main examples are taken from dam management under uncertainty. However, the practical issues, the general theory and the numerical methods presented can be applied to other uncertain sources of energy (wind, solar) and, more generally, to the management of smart power systems.
The CIRM School Stochastic Control for the Management of Renewable Energies (STOCORE) is hosted by the Centre International de Rencontres Mathématiques (CIRM) at Marseille (South of France) between 8-12 April 2013. The CIRM School STOCORE is in the realm and continuation of the Institut Henri Poincaré (IHP) trimester MABIES Mathematics of Bio-Economics (2013, January 7 - April 5), organized by Michel De Lara and Luc Doyen, itself a contribution to the Mathematics of Planet Earth - MPE2013 initiative.
Pierre Carpentier (UMA-ENSTA ParisTech)
Jean-Philippe Chancelier (CERMICS-École des Ponts ParisTech)
Michel De Lara (CERMICS-École des Ponts ParisTech)
The organizers work together at the Optimization and Systems Group at Cermics, the applied mathematics research center of École des Ponts ParisTech. Their central theme of investigation is about numerical methods in stochastic optimization. Since 2000, the Optimization and Systems Group has developed a deep scientific partnership with EDF R&D (Électricité de France Research & Development), forming PhD who have become executives of the OSIRIS department (Optimisation, simulation, risques et statistiques pour les marchés de l'énergie). The group has jointly elaborated methods adapted to the management of energies: coordination of production units under constraint of satisfaction of an uncertain demand, extension of the minimization of production costs on average to include financial and physical risks constraints. These works have been valorized both academically (publications) and within companies.
The new structure of power systems, with decentralized and highly variable production sources (renewable energies like wind or photovoltaic) and consumption sinks (accumulators, transport), challenges optimization methods for their management. Indeed, when solutions were looked after as open-loop control in a deterministic setting, they now become closed-loop, or policies, or random variables depending on how nonanticipativity constraints are handled.
We present stochastic control theory in discrete time, illustrated with examples from dam management under uncertainty. After having introduced the basic concepts and tools, especially the dynamic programming approach, we turn to more advanced topics, risk constraints, stochastic viability and informational constraints in large-scale systems. Indeed, environmental issues on the one hand, and safety questions (blackouts) on the other compel us to introduce certain types of constraints (in probability) and risk (risk measures) in the optimization framework. The so-called ``curse of dimensionality'' haunts the adaptive optimal control of systems displaying large size, dynamical aspects, and uncertainties. Many approaches have been developed for deterministic dynamical systems to tackle the large size issue. Their extension to stochastic systems raises difficult questions, especially on how to deal with decentralized information. We present decomposition-coordination approaches in the stochastic setting.
Courses alternate with computer practical works.
The School STOCHORE welcomed 41 full time participants, including the staff, plus 2 short term visitors from a SME. The staff was composed of the 3 organizers, plus PhD student Vincent Leclère, and the video technician Fabrice Tual. The 36 other participants were partly in academic research centers (25, mostly PhD or postdoc students) and partly in companies (EDF, GDF-Suez, ISA-XM, etc.). The School STOCHORE succeded in attracting an audience beyond France. The international participation was high: 16 among 36 came from abroad.
We thank the CIRM for offering 40 financial supports for food and lodging. Only 1 full time participant and the 2 short term visitors had to pay their food and lodging. Participants were particularly grateful to the CIRM for offering such financial and material conditions (food, accomodation, amphitheaters, nice surroundings).
The majority of participants worked in the energy field, and were looking for mathematical methods adapted to their problems. On the last day, the organizers sollicitated feedback from the participants to assess the School. Comments were positive. A few suggestions to marginally improve the courses have been proposed, but the general assessment was quite good. Concerning the computer sessions, more substantial changes have been put forward by the participants.
The expectations of the participants suggest that a new school on themes like ``dynamic energy storage management'', ``energy management with storage and adaptive tariffs'' would interest a substantial public.
The CIRM School STOCORE is aimed at a public of
The CIRM School STOCORE will take place between 8-12 April 2013 at the Centre International de Rencontres Mathématiques (CIRM) at Marseille (South of France).
There are no registration fees. Accommodation and meals are provided at CIRM, at zero cost for fourty registered participants (else, the cost is 450 euros).
Registration is open.
For registration, please send an email
We have limited funding for PhD and post-doctorate students, who should add a one-page motivation letter to their one-page CV.
Renewable energies (solar, wind, biomass, hydro-power, geothermal) display strong variability in availability and high spatial dispersion. Their penetration in the energy mix leads countries to reflect about options allowing to make their electrical system more flexible and to decrease the risks of blackouts. The evolutions in the fields of computing and telecoms make technological innovations, for instance smart grids, possible. Electrical networks are more and more instrumented (sensors, probes) and this allows to obtain new information on the consumers and on production availability. Progress in network communications should make these data available for (real time) computations giving new opportunities for control and optimization strategies.
The electrical system will be much more complex than today, with a multiplicity of actors, of flows and stocks, and a strong variability: scattered and higly variable production, decentralized storage (accumulators), adaptive management of the demand (``diffuse effacement''). From the energies management point of view, this will definitely require to work on dynamical systems consisting of numerous interconnected subsystems, and subjected to strong uncertainties. The challenge is to develop ways and methods of management to allow to save resources in the supply of the service, but also to guarantee a safe management (blackout). Environmental issues will also compel us to introduce specific types of constraint in the optimization framework.
Optimization is challenged by the complexity of the emerging electrical systems, displaying large size, dynamical aspects, and uncertainties. To tackle problems with those three characteristics, decentralized optimization methods, and especially decomposition-coordination approaches, may prove particularly adapted.
In economy, it is long established that, under proper conditions, a Pareto optimum can be decentralized by an appropriate price system under budget constraints. These prices are obtained by tatonnement (trial and error, market). In mathematics, the decomposition-coordination methods for the optimization of deterministic dynamical systems consist in decomposing the system into units managed individually; the coordination is made by various approaches, like prices or quantities transmitted to the decentralized units, and adaptively given by a higher level Uzawa algorithm .
Notice that, in power systems, the decomposition is natural, with consumption and generation decision centers identified (in other problems, decomposition is looked after, like in Benders or Dantzig-Wolfe algorithms used in Operations Research). In addition, a coordinator may also be quite natural like ERDF in the French systems dealing with different energy producers (companies such as EDF, GDF-Suez, etc.).
We can see the decomposition-coordination by prices as an adaptive dynamic pricing allowing to decentralize the global optimum of a central planner. In the presence of uncertainties, the difficulty comes from the fact that these prices become random variables, and that their calculation turns out to be numerically prohibitive. Recent techniques have been developed to tackle decomposition-coordination in the stochastic framework [5,1].
The central idea is that, at every node in the network, the satisfaction of the demand by a supply is replaced by a constraint of satisfaction on average, conditional on some proper information. This method has already been tested for a single coupling constraint, with convincing results. The stake is to extend such methods to multiple local constraints, for appropriate selections of information patterns (which may vary locally).
What is more, environmental issues on the one hand, and safety questions (blackouts) on the other will compel us to introduce certain types of constraints (in probability) and risk (risk measures) in the optimization framework. Here too, specific mathematical approaches (stochastic viability ) and algorithms have been recently developed and tested on small scale problems. Their extension to networks is under consideration.