This paper proposes a novel distributed solution for the operation of large populations of thermostatically controlled loads (TCLs) providing frequency support. A game-theory framework is adopted, modelling the TCLs as price-responsive rational agents that schedule their energy consumption and allocate frequency response provision in order to minimize their operational costs. The novelty of this work lies in the use of mean field games to abstract the complex interactions of large numbers of TCLs with the grid and in the introduction of an innovative market structure, envisioning distinct price signals for electricity and response. Differently from previous approaches, such prices are not designed ad hoc but are derived instead from an underlying system scheduling model.

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.

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.

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.

Power hardware-in-the-loop (PHIL) simulation leverages the advanced real-time emulation based technique to carry out in-depth investigations on novel real-world power components. Power amplifiers, sensors, and signal conversion units based power interfaces (PI) incorporate physical hardware systems and real-time simulation platforms into PHIL setups. However, the employment of any interfacing technique inevitably introduces disturbances such as sensor noise, switching harmonics, or quantization noise to PHIL systems. To facilitate quantitatively analyzing and assessing the impact of external disturbances on PHIL simulation systems, a framework for sensitivity analysis of PHIL setups has been developed in this paper. Detailed modelling principles related to the sensitivity analysis of PHIL systems and the inherent relationship between sensitivity transfer functions and stability criteria are elaborated along with theoretical and experimental validation. Based on this concept, accuracy assessment methods are employed in this framework to quantify generic sensitivity criteria. Moreover, physical passive load and converter-based PHIL setups are applied and experimental results are presented to characterize and demonstrate the applicability of the proposed framework.