DS0207 - Approches de la transition énergétique par les sciences humaines et sociales

Control and simulAtion of Electrical Systems, interAction and RobustnesS – CAESARS

A better understanding of tomorrow's electrical system

Control and simulAtion of Electrical Systems, interAction and RobustnesS

Better control and simulation of electrical systems for energy transition

The aim of this ANR project is to make decisive progress in the design of theoretical and numerical decision-support tools for the electrical sector. We have focused on four applications. <br />- Storage: Anticipating and accompanying the development of storage systems at the local and/or global level to quantify the services that can be rendered, optimizing the dimensioning and location of storage means according to the targeted uses.<br />- Decarbonation of the product mix: To shed light on the evolution of the electrical system in the context of decarbonation, taking into account the emission market and the constraints of pollutant emissions and the development of renewable energies.<br />- Pricing and investment in a competitive environment: Quantify and optimize the investments and dismantling required by technology, taking into account the global electricity system including the competitive environment.<br />- Risk Management: Optimize risk management decisions: inventory management, physical and financial hedging, impact of extreme events affecting the resilience of the system.

This ANR project brought together teams with strong and complementary expertise to design new efficient numerical methods for random and stochastic models appearing in electrical systems, in the framework of ecological transition, taking into account model uncertainty phenomena, robustness and large scale issues. The teams' expertise covers issues in analysis, control, stochastic modelling, numerical and statistical methods, and modelling of electrical systems. Our research program has been declined according to the following tasks, which are transversal to the 4 major applications mentioned above :
- Efficient algorithms based on stochastic control equations;?
- Stochastic and mean-field games;
- Analysis of rare events in optimal decision making and risk management;
- Sensitivity analysis, uncertainty quantification, model and parameter uncertainty.

On the scientific level, the teams have made significant progress in the following areas
- simplified but relevant modeling of electrical systems despite their complexity;
- the numerical resolution of new non-linear equations appearing.
Overall, the project has strengthened the links between the stochastic analysis community and the community of Intelligent Energy Management, and has produced numerical solutions on simplified case studies, for a better popularization to a non-specialist public. A CIFRE PhD thesis and two ANR projects followed.

Our work has been able to address all energy application topics (Storage, Decarbonation of production mix, Pricing and investment in competitive environment, Risk management) with major advances in control tools (notably McKean-medium field) on both theoretical and numerical aspects. The coupling of these tools with energy management applications has been fruitful to develop use cases with palpable and interpretable results. This encourages us to continue these collaborations and enrich the models and methodologies.

The number of publications (directly related to the ANR and in which the ANR is acknowledged) is 44 articles in international peer-reviewed journals (37 published/accepted, 7 submitted) and 2 book chapters (published). A quarter of these publications are between several ANR project partners, and the numerous exchanges within the ANR have stimulated overall production. A STochastic OPTimization (StOpt) library has been developed and put in open source on gitlab.

Our aim is to develop together with our industrial partner EDF numerical and theoretical tools which are essential for decision making in a random environment related with the ecological transition. For this we propose to develop simplified mathematical models together with numerical methods, in order to give an answer to major applications, as for example :
+ The problems of storage related with the development of renewable energies ;
+ The development of decision tools in a context of ecological transition and decarbonisation ;
+ The need of dynamic investment models in a competitive environment with different energy producers ;
+ The risk management in extreme situations and with many risk factors.
In our approach our expertise in developing efficient numerical methods in stochastic control, in stochastic and mean-field games as well as for models with uncertainty, combined with the practical expertise of EDF will be crucial, to produce understandable results which can then be used as a guide for efficient public and utilities decisions.

Backward stochastic differential equations (BSDE) are a powerful tool of control, known and also already tested by EDF R&D. Related with the problems explained above, our objective consists in the study of efficient algorithms for BSDE in high dimension as required by applications, and to enlarge the class of control problems which can be considered with. The dynamic modelling of investment in a competitive environment is related with the study of stochastic games, and in the case of a large number of agents, with mean-field games. We will focus on investment games in which the agents have different objectives. A major problem for the games will be to develop a suitable notion of equilibrium, while for the mean-field games our objective is to include in the model a control of the local risk.
Accounting for extreme situations in the Decision-Making tools constitutes another original aspect of the project. Our aim is also to develop methodologies to assess and measure extremes risks, identify and anticipate critical situations, by using the technics of rare events. We integrate extreme risks in the resolution of stochastic control problems.

Moreover, as industrial and societal issues concern several decades, the stochastic model and the optimisation criteria are imperfectly identified, the uncertainty of the risk modelling is large. We tackle these issues by following two ways: first, using a « worst case » approach, using the theory of decision robustness. Second, with the quantification of uncertainty and sensitivity analysis.

The research objectives of the project are not only of great interest for EDF but also for any company having to take decisions for a long time horizon, with a large number of variables or with model uncertainty, which is the case for sectors related with energy.

Our research programme is split into the following milestones, which are transversal to the major applications aforementioned:
Task 1. BSDE-based efficient algorithms for optimal stochastic control ;
Task 2. Stochastic and mean-field games ;
Task 3. Rare event analysis in optimal decision and risk management ;
Task 4. Sensitivity analysis,

The research results obtained in the frame of the project will be disseminated by publication in international journals with referee system, by a summer school and a conference, but also by the development of a public bank of benchmark problems and by making available the open-source codes of the developed programs.

Project coordination

Gobet Emmanuel (Centre de Mathématiques Appliquées)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

Université du Maine Laboratoire Manceau de Mathématiques
EDF Electricité de France - R&D
Ecole Polytechnique Centre de Mathématiques Appliquées

Help of the ANR 271,120 euros
Beginning and duration of the scientific project: December 2015 - 36 Months

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