Roland Malhamé was a pioneer in the development of physically based electrical load models.
In 1983, his doctoral thesis developed the first models of aggregated thermostatic loads, based on statistical mechanics. These models have since experienced a significant resurgence of interest, particularly given the growing pressure to integrate more renewable energy sources into electrical grids. Indeed, when solar or wind power is heavily utilized in a grid, it creates risks of instability because these energy sources are highly volatile. However, in a grid, it is essential to constantly maintain a balance between electricity generation and demand. While fossil fuel energy sources are controllable but increasingly undesirable, the same cannot be said for intermittent renewable sources. Therefore, energy storage becomes a crucial element in maintaining the generation/demand balance. The approach then becomes one of storing excess energy and using that storage when there is a surge in demand. Thermostatically controlled loads distributed across the grid (electric heating, electric water heaters, air conditioning), as well as the energy storage associated with electric vehicle batteries, are examples of electrical loads linked to forms of storage present in the grid.
One research objective is to identify such loads and create business models that encourage customers to allow an aggregator to coordinate their loads while maintaining comfort and security, thereby enabling greater integration of intermittent renewable energy sources. However, coordinating such a large number of heterogeneous loads, individually small but very numerous (sometimes in the millions), is a challenge requiring unconventional decentralized control methods. For over a decade, Roland Malhamé has been working with other researchers and students on the development and application of mean-field game theory. Indeed, prescriptive game theory (i.e., games where the cost function of agents is defined with a coordination objective) is a prime avenue for synthesizing decentralized control systems, since each agent can focus on a local optimization, but the cost functions are designed in such a way that a collection of local optimizations allows for the achievement of a collective objective. In this context, mean-field games open up very interesting perspectives because they allow us to exploit the existence of a large number of agents with negligible individual weight to obtain decentralized control laws that enable the achievement of collective objectives using very little communication. This is achieved in part thanks to the predictability arising from the law of large numbers. Our applications are primarily focused on energy and collective navigation problems, similar to those encountered by schools of fish. We are also exploring learning problems in this context.