On Distributed Scheduling of Flexible Demand and Nash Equilibria in the Electricity Market

Abstract

This paper presents a novel game theory approach for large-scale deployment of price-responsive electrical appliances. In the proposed distributed control scheme, each appliance independently schedules its power consumption on the basis of a broadcast demand/price signal, aiming to complete its task at minimum cost. The conflicting interactions of the appliances, competing for power consumption at the cheapest hours of the day, are modelled through a differential game with a continuum of players, and efficient deployment of flexible demand is characterized as a Nash equilibrium. A novel approach is adopted to derive necessary and sufficient equilibrium conditions: intrinsic properties of the problem (price monotonicity, unidirectionality of power transfers) are exploited to perform an equilibrium study based on sublevel sets of the considered demand profiles. As a result, it is possible to determine for which penetration levels of flexible demand, types of appliances and inflexible demand profiles it is possible to achieve an equilibrium. Such stable configuration is achieved through the broadcast of a single demand/price signal and does not require iterated exchange of information between devices and coordinator. In addition, the global optimality of the equilibrium is proved, necessary conditions for Pareto optimality are derived, and a preliminary analysis of devices with partial time availability is carried out. The performance of the proposed control strategy is evaluated in simulation, considering realistic future scenarios of the UK power system with large penetration of flexible demand.

An iterative algorithm for regret minimization in flexible demand scheduling problems

“…To solve the minimax regret optimization problem more efficiently, we propose an iterative algorithm in which the power schedule u(⋅) converges to the optimal solution u * (⋅) in (10), and accordingly the regret R(u) converges to R(u * ). In order to do so, it is useful to derive a more explicit expression of the regret, as detailed below:…”

“…In order to fully achieve these potential benefits while limiting undesired consequences (e.g., network congestion, price volatility), it is crucial to develop efficient and robust control strategies for the charging of the EVs. A significant amount of research has investigated this topic after the seminal papers, 5,6 proposing decentralized and game-theory approaches, [7][8][9][10] adaptive strategies 11 or Lagrange relaxation methods 12 to achieve an efficient large-scale integration of the EVs in the power system. These analyses have been expanded to consider additional elements such as coupling constraints between the devices, 13 network topology 14 or the degradation costs of the EVs' batteries.…”