Mean field optimization for aggregated systems with common noise

The decarbonization of electricity generation is leading to deep changes in the power system. One of these changes is the integration of a growing share of intermittent renewable energy production, making it more difficult to balance supply and demand in real time. However, the increasing number of controllable energy systems could counterbalance this loss of control over production. Examples of such energy systems are stationary or electric vehicle batteries, thermal storage systems such as hot water tanks, buildings with high thermal inertia, or multi-energy systems. However, using these systems to balance the power system requires, on the one hand, knowing how to optimally control individual systems, also known as agents, in the presence of uncertainties and, on the other hand, knowing how to optimally control the aggregation of these systems. However, optimizing the aggregate of agents is not equivalent to optimizing each agent individually. They interact with each other through electricity market prices, which are themselves partly determined by the aggregate behavior of the agents.
To solve this problem, an approach recently developed by Pfeiffer and al. consists in using a so-called mean-field relaxation, as developed by Lasry and Lions, and an adaptation of the Frank-Wolfe algorithm to solve the aggregation problem by solving independent sub-problems that can be processed in parallel. Each of these sub-problems is a Stochastic Optimal Control Problem (SOCP).
This thesis proposes, on the one hand, to generalize Pfeiffer’s work to aggregation problems with uncertainties common to all agents, such as the price of electricity, and, on the other hand, to achieve an efficient numerical coupling between the Frank-Wolfe algorithm and methods for solving PCOS by progressive hedging. These methods make it possible to use fast deterministic optimal control algorithms in a stochastic framework. This thesis is a first step for towards the development of an energy management system for an aggregate of energy systems.

Keywords: Mean field optimization, stochastic optimal control, Frank-Wolfe algorithm, energy management

• Academic supervisor    Dr. Laurent PFEIFFER, Laboratoire Signaux et Systèmes - Université Paris-Saclay 
• Doctoral School    ED 574 EDMH (ED Hadamard)
• IFPEN supervisor    Dr Paul MALISANI, ORCID : 0000-0002-7073-155X  
• PhD location    IFPEN, Rueil-Malmaison, France  
• Duration and start date    3 years, starting in the fourth quarter 2024 (Novembre 4)
• Employer    IFPEN
• Academic requirements    M.Sc. in  applied mathematics, optimization, probability, control theory    
• Language requirements    English level B2 (CEFR)     

To apply, please send your cover letter and CV to the IFPEN supervisor indicated below.