Electric demand response and bounded rationality: mean-field control for large populations of heterogeneous bounded-rational agents

The increased penetration of renewable energy sources into existing power systems induces challenges in supply–demand balancing. Demand-side flexibility is seen as an option to accommodate variability and limited predictability from generation. Heat pumps at residential level, if well coordinated, can be one those sources. complexity involved high though, since their coordinated operation combines control, population effects the fact agents may actually not behave rational decision-makers. We describe here a control framework that accounts for aspects altogether. Decentralized model predictive large populations heterogeneous employed. As cost minimized affected by behaviour whole through electricity price, decentralized re-thought mean-field game. Existence uniqueness Nash equilibrium are discussed while Picard–Banach algorithm used solution approach. It extended case bounded-rational agents. impact on system dynamics modelling bounded illustrated numerical simulations. This article part theme issue ‘The mathematics systems’.