In future distribution grids, prosumers (i.e., energy consumers with storage and/or production capabilities) will trade energy with each other and with the main grid. To ensure an efficient and safe operation of energy trading, in this paper, we formulate a peer-to-peer energy market of prosumers as a generalized aggregative game, in which a network operator is responsible to enforce the operational constraints of the system. We design a distributed market-clearing mechanism with convergence guarantee to an economically-efficient, strategically-stable, and operationally-safe configuration (i.e., a variational generalized Nash equilibrium). Numerical studies on the IEEE 37-bus testcase show the scalability of the proposed approach and suggest that active participation in the market is beneficial for both prosumers and the network operator.

In this paper, we propose a distributed model predictive control (MPC) scheme for economic dispatch of energy systems with a large number of active components. The scheme uses a distributed optimization algorithm that works over random communication networks and asynchronous updates, implying the resiliency of the proposed scheme with respect to communication problems, such as link failures, data packet drops, and delays. The distributed optimization algorithm is based on the augmented Lagrangian approach, where the dual of the considered convex economic dispatch problem is solved. Furthermore, in order to improve the convergence speed of the algorithm, we adapt Nesterov's accelerated gradient method and apply the warm start method to initialize the variables. We show through numerical simulations of a well-known case study the performance of the proposed scheme.

A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient, equilibrium. In this paper, we solve this open problem by leveraging results from fixed-point selection theory and in turn derive distributed algorithms for the computation of an optimal GNE in monotone games. We then extend the technical results to the time-varying setting and propose an algorithm that tracks the sequence of optimal equilibria up to an asymptotic error, whose bound depends on the local computational capabilities of the agents.

We formulate for the first time the economic dispatch problem among prosumers in an integrated electrical and gas distribution system (IEGDS) as a game equilibrium problem. Specifically, by approximating the nonlinear gas-flow equations either with a mixed-integer second-order cone (MISOC) or a piecewise affine (PWA) model and by assuming that electricity and gas prices depend linearly on the total consumption, we obtain a potential mixed-integer game. To compute an approximate generalized Nash equilibrium (GNE), we propose an iterative two-stage method that exploits a problem convexification and the gas-flow models. We quantify the quality of the computed solution and perform a numerical study to evaluate the performance of our method.