Antonio De Paola

Distributed Control of Micro-Storage Devices With Mean Field Games

This paper proposes a fully distributed control strategy for the management of micro-storage devices that perform energy arbitrage. For large storage populations, the problem can be approximated as a differential game with infinite players (mean field game). Through the resolution of coupled partial differential equations (PDEs), it is possible to determine, as a fixed point, the optimal feedback strategy for each player and the resulting price of energy if that strategy is applied. Once this price is calculated, it can be communicated to the devices, which are able to independently determine their optimal charge profile. Simulation results are provided, calculating the fixed point through numerical integration of the PDEs. The original model is then extended in order to consider additional elements, such as multiple population of devices and demand uncertainty.

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

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.

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

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 game-theoretical 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.

Analysis of Nash equilibria in energy markets with large populations of price-responsive flexible appliances

This paper deals with flexible electrical devices that, on the basis of a broadcast price signal, schedule their individual power consumption in order to minimize their energy cost. If 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 in the energy market. This is done by comparing two functions which characterize, respectively, the valley capacity of the inflexible demand and the global properties of the appliances population. The equilibrium conditions, which do not require any iterative procedure to be applied, are finally tested in simulations.

Scheduling of Wind Farms for Optimal Frequency Response and Energy Recovery

This paper deals with control of variable speed wind turbines, which provide frequency support through temporary overproduction. In particular, it determines the optimal profile of power extraction among multiple generators in order to minimize the total loss of efficiency, while allowing for a prescribed increase in generation. Starting with the simplifying assumption of unconstrained generated/supplied power for the single turbine, the scheduling is characterized as the solution of an optimal control problem. On the basis of this result, a heuristic control strategy is proposed for the case of turbines with limited power output, investigating under which conditions this choice achieves optimality. Using a similar approach, the problem of energy recovery is also considered, calculating the optimal power profiles that bring back the turbines to their working point of maximum efficiency after having provided frequency response.

A framework for receding-horizon control in infinite-horizon aggregative games

Abstract A novel modelling framework is proposed for the analysis of aggregative games on an infinite-time horizon, assuming that players are subject to heterogeneous periodic constraints. A new aggregative equilibrium notion is presented and the strategic behaviour of the agents is analysed under a receding horizon paradigm. The evolution of the strategies predicted and implemented by the players over time is modelled through a discrete-time multi-valued dynamical system. By considering Lyapunov stability notions and applying limit and invariance results for set-valued correspondences, necessary conditions are derived for convergence of a receding horizon map to a periodic equilibrium of the aggregative game. This result is achieved for any (feasible) initial condition, thus ensuring implicit adaptivity of the proposed control framework to real-time variations in the number and parameters of players. Design and implementation of the proposed control strategy are discussed and an example of distributed control for data routing is presented, evaluating its performance in simulation.

Decentralized coordination of large populations of flexible electrical appliances through demand saturation

This paper presents a novel decentralized control strategy for integration of price-responsive loads in the electricity market. Previous work has shown that, by approximating the devices population 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 by introducing a time varying proportional constraint on the maximum power consumption of the appliances. This allows to saturate the flexible demand and obtain a Nash equilibrium for a much wider range of scenarios. The performance of the proposed control technique, which also minimizes the task time of all appliances, is tested in simulation.

Distributed frequency control by means of responsive wind generation

This paper approaches frequency control in power networks by operating on the generation side and using wind turbines that can dynamically adapt the generated power in response to frequency fluctuations. The proposed solution is fully distributed without any additional communication infrastructure. Moreover, in order to avoid instability due to synchronization of individual turbines, the designed controllers are stochastic.