TY - JOUR

T1 - Hierarchical Mean-Field Type Control of Price Dynamics for Electricity in Smart Grid

AU - Frihi, Zahrate El Oula

AU - Choutri, Salah Eddine

AU - Barreiro-Gomez, Julian

AU - Tembine, Hamidou

N1 - Funding Information:
We gratefully acknowledge support from Tamkeen under the NYU Abu Dhabi Research Institute grant CG002, and U.S. Air Force Office of Scientific Research under Grant No. FA9550-17-1-0259.
Publisher Copyright:
© 2021, The Editorial Office of JSSC & Springer-Verlag GmbH Germany.

PY - 2022/2

Y1 - 2022/2

N2 - This paper solves a mean-field type hierarchical optimal control problem in electricity market. The authors consider n − 1 prosumers and one producer. The ith prosumer, for 1 < i < n, is a leader of the (i − 1)th prosumer and is a follower of the (i + 1)th prosumer. The first player (agent) is the follower at the bottom whereas the nth is the leader at the top. The problem is described by a linear jump-diffusion system of conditional mean-field type, where the conditioning is with respect to common noise, and a quadratic cost functional involving, the square of the conditional expectation of the controls of the agents. The authors provide a semi-explicit solution of the corresponding mean-field-type hierarchical control problem with common noise. Finally, the authors illustrate the obtained result via a numerical example with two different scenarios.

AB - This paper solves a mean-field type hierarchical optimal control problem in electricity market. The authors consider n − 1 prosumers and one producer. The ith prosumer, for 1 < i < n, is a leader of the (i − 1)th prosumer and is a follower of the (i + 1)th prosumer. The first player (agent) is the follower at the bottom whereas the nth is the leader at the top. The problem is described by a linear jump-diffusion system of conditional mean-field type, where the conditioning is with respect to common noise, and a quadratic cost functional involving, the square of the conditional expectation of the controls of the agents. The authors provide a semi-explicit solution of the corresponding mean-field-type hierarchical control problem with common noise. Finally, the authors illustrate the obtained result via a numerical example with two different scenarios.

KW - Electricity price dynamics

KW - hierarchical control

KW - mean-field-type control

KW - smart grids

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U2 - 10.1007/s11424-021-0176-3

DO - 10.1007/s11424-021-0176-3

M3 - Article

AN - SCOPUS:85124443898

VL - 35

JO - Journal of Systems Science and Complexity

JF - Journal of Systems Science and Complexity

SN - 1009-6124

IS - 1

ER -