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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.

Abstract-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.

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This paper proposes a novel tariff scheme and a new optimization framework in order to address the recovery of fixed investment costs in transmission network planning, particularly against rising demand elasticity. At the moment, ex-post network tariffs are utilized in addition to congestion revenues to fully recover network costs, which often leads to over/under fixed cost recovery, thus increasing the investment risk. Furthermore, in the case of agents with elastic market curves, ex-post tariffs can cause several inefficiencies, such as mistrustful bidding to exploit ex-post schemes, imperfect information in applied costs and cleared quantities, and negative surplus for marginal generators and consumers. These problems are exacerbated by the increasing price-elasticity of demand, caused for example by the diffusion of demand response technologies. To address these issues, we design a dynamic ex-ante tariff scheme that explicitly accounts for the effect of tariffs in the longterm network planning problem and in the underlying market clearing process. Using linearization techniques and a novel reformulation of the congestion rent, the long-term network planning problem is reformulated as a single mixed-integer linear problem which returns the combined optimal values of network expansion and associated tariffs, while accounting for price-elastic agents and lumpy investments. The advantages of the proposed approach in terms of cost recovery, market equilibrium and increased social welfare are discussed qualitatively and are validated in numerical case studies. y b τ d t,m,i,k it replaces the product b τ m,i d t,k y b τ g t,m,i,p it replaces the product b τ m,i g t,p