Convergence and optimality of a new iterative price-based scheme for distributed coordination of flexible loads in the electricity market

Abstract

Abstract-This paper proposes a novel distributed control strategy for large-scale deployment of flexible demand. The devices are modelled as competing players that respond to iterative broadcasts of price signals, scheduling their power consumption to operate at minimum cost. By describing their power update at each price broadcast through a multi-valued discrete-time dynamical system and by applying Lyapunov techniques, it is shown that the proposed control strategy always converges to a stable final configuration, characterized as a Wardrop (or aggregative) equilibrium. It is also proved that such equilibrium is socially efficient and optimizes some global performance index of the system (e.g. minimizes total generation costs). These results are achieved under very general assumptions on the electricity price and for any penetration level of flexible demand. Practical implementation of the proposed scheme is discussed and tested in simulation on a future scenario of the UK-grid with large numbers of flexible loads.

On the Efficiency of Nash Equilibria in Aggregative Charging Games

“…In other words our impossibility result holds also for the case of homogeneous populations. This is not in contrast with the result in [2] or [10], because therein the setsX were assumed to be simplexes with upper bounds constraints. Here we claim that there exists a convex setX (not a simplex with upper bounds) such that PoA M does not converge to 1.…”

“…The homogeneity assumption is relaxed in [9], where the authors provide similar efficiency results of those in [2], but limited to linear price functions and in a probabilistic sense. Non linear price functions are considered in [10], but the efficiency results pertain to the notion of Wardrop equilibrium and charging constraints are limited to upper bounds. We observe that all the previous works assume that the price at time t depends only on the consumption at the same time instant.…”

“…The result in [2] can be equivalently stated as the fact that for homogeneous populations with simplex constraints, the PoA converges to 1 as the population size grows. Our main contributions are: 1) We show that the PoA for charging games with linear price function (that might however depend on all charging instants) and generic convex constraints always converges to 1, complementing [2], [8]- [10]; 2) For charging games with generic convex constraints and nonnegative price function that depends only on the instantaneous demand, we show that the PoA converges to 1 if the price function is a positive pure monomial (i.e., αz k for some α, k > 0). On the contrary, if the price function does not have this form, it is possible to construct a sequence of games whose PoA does not converge to 1.…”

Incentive mechanisms to prevent efficiency loss of non-profit utilities

“…In particular, the average cost pricing scheme guarantees that the utility collects the estimated total cost. Game theory has been widely used in demand response studies to analyze interactions of selfish agents with conflicting interests [10,11,12,13,14,15]. In this case, the conflict arises because customers may compete for a limited resource.…”

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

“…Within this context, alternative approaches and multiple extensions have been proposed, either for the load scheduling problem or for the underlying aggregative game formulation. Recent works account for battery degradation of EVs [8], propose control schemes with increased decentralization [9] or reduced iterations [10], analyse the existence and optimality of the game equilibria [11], [12], [13] or consider coupling constraints between agents [14].…”