On the problem of controlling shiftable prosumer devices with price signals

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

2017

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.

Section: Introductionmentioning

confidence: 99%

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

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

2017

“…If one introduces the integralᾱ I (q) = q 0ᾱ (τ) dτ of the proportional constraintᾱ(q), it is possible to provide a closed-form expression for the solution of (12).…”

Section: A Optimal Scheduling Of the Individual Devicementioning

confidence: 99%

“…The introduction of a discontinuous price function is suggested in [11] to disincentivize the allocation of flexible demand after a certain threshold and limit the final energy price variation that the appliances can introduce. A stochastic technique is proposed in [12], broadcasting a randomized price to each appliance in order to avoid synchronicity of the power scheduling. With the same purpose, [13] suggests to introduce randomness on the controllers of the individual devices, considering at the same time an intermediate entity (aggregator) between the energy market and the individual customer.…”

Section: Introductionmentioning

confidence: 99%

Integration of Price-Responsive Appliances in the Energy Market Through Flexible Demand Saturation

IEEE Trans. Control Netw. Syst.

2018

Abstract-This paper proposes a novel decentralized technique for efficient integration of flexible demand in the electricity market. The analysis focuses on price-responsive appliances that schedule their power consumption on the basis of a demand/price signal received by a central entity. Previous work has shown that, when the devices population is sufficiently large to be described as a continuum, it is possible to provide necessary and sufficient conditions for the existence of a Nash equilibrium (no device has unilateral interest in changing its scheduling when considering the resulting profile of aggregate demand). These results are now extended in order to achieve an equilibrium also when the mentioned conditions are violated. To this purpose, a time-varying proportional constraint (equal for all devices) is introduced on the power rate of the price-responsive appliances so as to limit the variation of flexible demand that they can introduce at critical time instants. The proposed design technique not only guarantees existence of a Nash equilibrium but it also minimizes the global operation time of the appliances population. Simulation results are provided and it is shown that, under the considered assumptions, each individual appliance completes its task in minimum time.

“…Since centralized schemes [5] may not always be scalable to large systems with many independent agents, several distributed techniques have been proposed. These include adaptive strategies [6], Lagrange relaxation [7], stochastic pricing [8], [9] and the introduction of aggregators as mediating entities in the system [10]. Distributed optimization using the Alternating Direction Method of Multipliers (ADMM) has also received increasing attention [11], [12].…”

Section: Introductionmentioning

confidence: 99%

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

2017

IEEE Trans. Smart Grid

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.