Price-Based Schemes for Distributed Coordination of Flexible Demand in the Electricity Market

Abstract

Abstract-This paper proposes novel distributed control schemes for large-scale deployment of flexible demand. The problem of efficiently coordinating price-responsive appliances operating in the electricity market is tackled within a gametheoretical framework. Adopting the concept of Nash equilibrium and Lyapunov-based techniques, a new iterative control algorithm is designed in order to always converge to a satisfactory solution for the individual customers, which aim at minimizing their energy costs. From the system perspective, it is shown that global quantities such as total generation costs are reduced at each algorithm iteration. These results are achieved for any penetration level of flexible demand and for all types of interruptible electrical appliances. The proposed control scheme can be applied in practice through a one-shot implementation that, at the price of a negligible degradation of the equilibrium performance, ensures faster convergence to a stable solution. Simulation results are also presented, testing the novel schemes in realistic future scenarios of the Great Britain power system with high penetration of flexible demand.

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

“…Alternative one-shot schemes have already been derived, allowing the system operator to internally perform most of the calculations and coordinate the flexible appliances by broadcasting a single price signal (different in general for each load). These techniques, discussed in detail in [13], ensure significantly reduced execution times Fig. 1.…”

“…This paper proposes a novel design methodology for distributed coordination of flexible demand. On the basis of the initial analysis and preliminary results presented in [13], the iterative power scheduling update by the flexible appliances is modelled as the evolution of a discretetime dynamical system, described by a multi-valued correspondence. This allows a rigorous theoretical analysis that, through the application of established stability tools (e.g.…”

A Mean Field Game Approach for Distributed Control of Thermostatic Loads Acting in Simultaneous Energy-Frequency Response Markets

“…The seminal papers [16], [17] have proposed iterative updates of broadcast price/control signals to achieve a desirable coordination of the flexible loads, characterized as a game equilibrium. These approaches have been recently expanded in multiple directions, considering for example increased decentralization [18] or reduced iterations [19].…”

“…• The price signals used for the coordination of the appliances are derived from a unit commitment (UC) model, rather than designed ad hoc or obtained through simplified closed-form expressions [16]- [19]. As a result, the considered prices accurately reflect the cost of electricity and the value of response, accounting for different generation technologies and detailed FR requirements.…”

“…An upwind method [27] is applied in (19): the partial derivative V T is approximated with forward differences when u = 0 and f(T j , u) > 0 and with backward differences when u = P ON and f(T j , u) < 0. This reduces the integration error and avoids issues at the temperature bounds of the discretized grid.…”