A Semi-Decentralized Scheme for Integration of Price-Responsive Appliances in the Electricity Market

Abstract

A novel semi-decentralized control strategy is proposed for the integration in the power system of large populations of flexible loads, such as electric vehicles and "smart" appliances. To characterize the interactions between the single agents and their effects on the grid, a game theory framework is adopted. The price responsive appliances are modelled as competing players, characterizing a stable and efficient solution as a Nash equilibrium (no device has unilateral interest in changing its scheduled power consumption when the final electricity price is considered). We extend previous results on distributed control of flexible demand, proposing a partial centralization of the power scheduling at critical time instants. In this way, it is possible to ensure convergence to a Nash equilibrium for a wider range of scenarios, considering higher penetration levels of flexible demand and a wider range of parameters for the devices. The effectiveness of the proposed scheme is theoretically proved and its performance is evaluated in simulations, considering a future UK grid with high penetration of flexible demand.

A Graphical Measure of Aggregate Flexibility for Energy-Constrained Distributed Resources

“…These include EVs [26], [27], home storage devices [28], [29] and diesel generators [30], [31]. It should be noted that a comparable policy to that which we propose, applied to a continuum of devices, is also relevant in price-determined settings [32] and enables the coordination of devices within areas of flat prices.…”

Minimizing Unserved Energy Using Heterogeneous Storage Units

“…It should be noted that the authors of [1] considered the task of directly assigning a piecewise constant input according to (8), but showed that this is suboptimal; (22) is in fact the correct way to convert (8) into discrete time. For the special case of a single store, the authors of [1] did propose a greedy policy that is equivalent to (22). Figure 1 describes a discrete time algorithm that implements the policy (22) as follows.…”

Minimizing Unserved Energy Using Heterogeneous Storage Units

“…This allows us to study properties of the system in a general sense, without considering price dynamics in detail. However, a comparable policy to that which we propose, applied to a continuum of devices, is also relevant in such settings [22] and enables the coordination of devices within areas of flat prices. [14] is concerned with trading off the use of a battery and a diesel generator to support renewable resources, and uses constraints to ensure no mismatch between supply and demand.…”

“…We then iterate over this list to find the interval [y i−1 , y i ] that containsẑ fulfilling (20) and, if necessary, linearly interpolate between its limits. Having found z, we then allocate u according to (22). (b) Method for findingẑ using the energy balance of (20).…”

“…= t 2 −t 1 and ẑ is allocated according to (20). The piecewise constant policy is then simply formed by implementing (22) from each time instant to the next. This policy satisfies the following results:…”