Distributed Coordination of Price-Responsive Electric Loads: A Receding Horizon Approach

Abstract

This paper presents a novel receding horizon framework for the power scheduling of flexible electric loads performing heterogeneous periodic tasks. The loads are characterized as price-responsive agents and their interactions are modelled through an infinite-time horizon aggregative game. A distributed control strategy based on iterative better-response updates is proposed to coordinate the loads, proving its convergence and global optimality with Lyapunov stability tools. Robustness with respect to variations in the number and tasks of players is also ensured. Finally, the performance of the control scheme is evaluated in simulation, coordinating the daily battery charging of a large fleet of electric vehicles.

Probabilistic sensitivity of Nash equilibria in multi-agent games: a wait-and-judge approach

“…for any fixed β ∈ (0, 1). We can now state our main result: Theorem 6: Fix β ∈ (0, 1) and let ε(•) be defined as in (6). Under Assumptions 1, 2 and 4 the following holds:…”

“…We analyse the results of several randomly generated cases, differing in the parameters characterizing the EV constraints X i , selected from a uniform random distribution: specifically, P i ∈ [6,15] kW, and E i is chosen to be feasible in the specified time interval (∼0-35 kWh per 12 h interval). Regarding the uncertainty samples, the pairs {A m , b m } M m=1 are i.i.d.…”

“…The nominal electricity price, i.e., the diagonal entries {a t } T t=1 of the matrix A 0 , have been derived by rescaling a winter weekday demand profile in the UK [43], whereas b 0 = 0. The robust charging schedules have been obtained by implementing Algorithm 1 with γ inn = 10 −14 , γ out = 10 −5 and τ ∈ [4,6]; the setting considered in this example can be cast into a decentralized QP optimization, which has been efficiently solved on a dualcore 7th gen. Intel processor using Matlab.…”

“…NE problem formulations have become popular candidates for distributed and decentralized control architectures, as they naturally lend themselves to price-based implementations, easily fitting in the operational requirements of liberalized resource markets [4]. Applications in smart grid, transportation, and IT are envisioned among the possible beneficiaries [5], [6], [7], [8], [9]. In connection with public infrastructures, a large number of studies followed the seminal work of Wardrop [10], focusing on the relation between the achieved equilibria and the social welfare; among recent results, we mention [11], [12], [7], [13], [14].…”

An iterative algorithm for regret minimization in flexible demand scheduling problems

“…However, these elements are subject to relevant uncertainties, which might have a substantial impact on the efficiency and benefits of the proposed control schemes. One possible approach to tackle this issue is to adopt receding-horizon schemes 16,17 or real-time algorithms 7 that modify the charging profile of the EVs on the basis of updated system conditions, implicitly accounting for imperfect predictions. Other works have considered the application of competition online algorithms, 18 stochastic dynamic programming 19 or robust min-max optimization.…”