Mean-Field Control and Neural Optimization for Renewable Energy Systems with Storage Constraints

The accelerating deployment of renewable energy has profoundly transformed modern power systems. Solar and wind are among the cheapest electricity sources, yet their production is intermittent and nondispatchable. As a result, maintaining supply-demand balance increasingly depends on energy storage systems capable of shifting energy over time and providing fast ancillary services. The historical evolution of storage, from pumped hydropower to lithium-ion batteries, has shaped today’s technological landscape and motivated optimisation methods that account for uncertainty, system-level interactions, and operational constraints. From a mathematical viewpoint, these challenges naturally call for stochastic control models in which both the dynamics and the objective depend not only on individual trajectories but also on their distribution across a large population. This leads to mean-field (McKean–Vlasov) formulations, where drift, diffusion, and cost depend on the law of the state. In applications such as storage fleets or aggregated prosumers in a smart grid, performance criteria are often distributional (e.g., limits on overload probability), and are thus expressed as law constraints. This thesis develops a constrained mean-field control framework combined with exact penalisation and neural optimisation. Controlled McKean–Vlasov dynamics are approximated through particle simulations, while feedback controls are parameterised by neural networks and trained via a forward–backward Monte Carlo scheme. Numerical experiments, including a stylised smart-grid model, show that the resulting policies can coordinate large populations, smooth aggregate demand, and enforce distributional reliability constraints under uncertainty.