TY - JOUR

T1 - Electric demand response and bounded rationality: mean-field control for large populations of heterogeneous bounded-rational agents

AU - Marín Radoszynski, Andrea

AU - Pinson, Pierre

PY - 2021

Y1 - 2021

N2 - 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 renewable energy generation. Heat pumps at residential level, if well coordinated, can be one of those flexibility sources. The complexity involved is high though, since their coordinated operation combines control, population effects and the fact agents may actually not behave as rational decision-makers. We describe here a coordinated control framework that accounts for those aspects altogether. Decentralized model predictive control for large populations of heterogeneous agents is employed. As the cost to be minimized is affected by the population behaviour as a whole through the electricity price, the decentralized control is re-thought as a mean-field game. Existence and uniqueness of a Nash equilibrium are discussed while the Picard-Banach algorithm is used as a solution approach. It is extended to the case of bounded-rational agents. The impact on system dynamics of modelling agents as bounded rational is illustrated through numerical simulations. This article is part of the theme issue 'The mathematics of energy systems'.

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

U2 - 10.1098/rsta.2019.0429

DO - 10.1098/rsta.2019.0429

M3 - Journal article

C2 - 34092108

SN - 1364-503X

VL - 379

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2202

M1 - 20190429

ER -