We consider a large population of decision makers that choose their evolutionary strategies based on simple pairwise imitation rules. We describe such a dynamic process by the replicator dynamics. Differently from the available literature, where the payoffs signals are assumed to be updated continuously, we consider a more realistic scenario where they are updated occasionally. Our main technical contribution is to devise two event-triggered communication schemes with asymptotic convergence guarantees to a Nash equilibrium. Finally, we show how our proposed approach is applicable as an efficient distributed demand response mechanism.

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Model Predictive Control (MPC) has recently gained increasing interest in the adaptive management of water resources systems due to its capability of incorporating disturbance forecasts into real-time optimal control problems. Yet, related literature is scattered with heterogeneous applications, case-specific problem settings, and results that are hardly generalized and transferable across systems. Here, we systematically review 149 peer-reviewed journal articles published over the last 25 years on MPC applied to water reservoirs, open channels, and urban water networks to identify common trends and open challenges in research and practice. The three water systems we consider are inter-connected, multi-purpose and multi-scale dynamical systems affected by multiple hydro-climatic uncertainties and evolving socioeconomic factors. Our review first identifies four main challenges currently limiting most MPC applications in the water domain: (i) lack of systematic benchmarking of MPC with respect to other control methods; (ii) lack of assessment of the impact of uncertainties on the model-based control; (iii) limited analysis of the impact of diverse forecast types, resolutions, and prediction horizons; (iv) under-consideration of the multi-objective nature of most water resources systems. We then argue that future MPC applications in water resources systems should focus on addressing these four challenges as key priorities for future developments.

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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.

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A non-centralized model predictive control (MPC) scheme for solving an economic dispatch problem of electrical networks is proposed in this paper. The scheme consists of two parts. The first part is an event-triggered repartitioning method that splits the network into a fixed number of non-overlapping sub-systems (microgrids). The objective of the repartitioning procedure is to obtain self-sufficient microgrids, i.e., those that can meet their local loads using their own generation units. However, since the algorithm does not guarantee that all the resulting microgrids are self-sufficient, the microgrids that are not self-sufficient must then form a coalition with some of their neighboring microgrids. This process becomes the second part of the scheme. By performing the coalition formation, we can decompose the economic dispatch problem of the network into coalition-based sub-problems such that each subproblem is feasible. Furthermore, we also show that the solution obtained by solving the coalition-based sub-problems is a feasible but sub-optimal solution to the centralized problem. Additionally, some numerical simulations are also carried out to show the effectiveness of the proposed method.

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A multi-agent optimization problem motivated by the management of energy systems is discussed. The associated cost function is separable and convex although not necessarily strongly convex and there exist edge-based coupling equality constraints. In this regard, we propose a distributed algorithm based on solving the dual of the augmented problem. Furthermore, we consider that the communication network might be time-varying and the algorithm might be carried out asynchronously. The time-varying nature and the asynchronicity are modeled as random processes. Then, we show the convergence and the convergence rate of the proposed algorithm under the aforementioned conditions.

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We consider the economic dispatch problem for a day-ahead, peer-to-peer (P2P) electricity market of prosumers (i.e., energy consumers who can also produce electricity) in a distribution network. In our model, each prosumer has the capability of producing power through its dispatchable or non-dispatchable generation units and/or has a storage energy unit. Furthermore, we consider a hybrid main grid & P2P market in which each prosumer can trade power both with the main grid and with (some of) the other prosumers. First, we cast the economic dispatch problem as a noncooperative game with coupling constraints. Then, we design a fully-scalable algorithm to steer the system to a generalized Nash equilibrium (GNE). Finally, we show through numerical studies that the proposed methodology has the potential to ensure safe and efficient operation of the power grid.

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Owing to wake effects, the power production of each turbine in a wind farm is highly coupled to the operating conditions of the other turbines. Wind farm control strategies must take into account these couplings and produce individual power commands for each turbine. In this case, centralized control approaches might be prone to failures due to the high computational burden and communication dependency. To overcome this problem, this paper proposes a non-centralized scheme based on splitting the wind farm into almost uncoupled sets of turbines by solving a mixed-integer partitioning problem. In each set of turbines, a model predictive control strategy seeks to optimize the distribution of the power set-points among turbines such that the impact of the power losses due to the wake effect is reduced. Then, a supervisory controller coordinates the generation of each group to satisfy the power demanded by the grid operator. The effectiveness of the proposed control scheme in terms of reduction of computational costs and power regulation is confirmed by simulations for a wind farm of 42 turbines.@en

We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically time-varying communication networks. We consider the standard assumptions of Nesterov's method and show that the sequence of the expected dual values converge toward the optimal value with the rate of \mathcal{O}(1/{k^2}). Furthermore, we provide a simulation study of solving an optimal power flow problem with a well-known benchmark case.

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High penetration of distributed generation will be characteristic to future distribution networks. The dynamic, intermittent, uncertain and deregulated nature of distributed generation raises the need for online, distributed economic dispatch techniques. In this paper, we demonstrate the application of such approaches using population dynamics. We propose a congestion management algorithm and demonstrate the notable properties and requirements of the proposed approach. @en

A novel partitioning approach for linear switching large-scale systems is presented. We assume that the modes of the switching system are unknown a priori but can be detected. We propose an online partitioning scheme that can partition the system when the mode switches, thus adapting the partition to the mode. Moreover, after the system has been partitioned, we apply a decentralized state-feedback control scheme to stabilize the system. We also apply a dwell time stability scheme to prove that the closed-loop system remains stable even after both the mode and partition changes. The proposed approach is illustrated by means of an automatic generation control problem related to frequency deviation regulation in a large-scale power network.

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Nowadays, large wind farms are expected to guarantee stability of the electrical grid contributing with ancillary services, such as frequency support. To this end, wind farm controllers must set the power generation of each turbine to compensate generation and demand imbalances. With the aim of optimizing primary frequency support, this paper proposes a partitioning approach to split large wind farms into several disjoint subsets of turbines according to the wake propagations through the wind farm. The partitioning problem is solved as a mixed-integer multi-objective optimization problem stated to maximize the strength of the coupling among the turbines due to the wake effect. Thus, no additional information sharing related to the wake propagations needs to be considered between the subsets. Different control tasks are assigned to the local controller of each subset, such that the total power generated meets the power demanded by the grid while the power reserve for enhancing primary frequency support is maximized. Finally, as an application of the proposed model, a decentralized wind farm control strategy is designed and compared with a centralized approach.@en

This paper considers detectability of deviation of sensors from their nominal behavior for a class of linear time-invariant discrete-time systems in the presence of bounded additive uncertainties. Detectable sensor faults using interval observers are analyzed considering two distinct approaches: invariant-sets and classical fault-sensitivity method. It can be inferred from this analysis that both approaches derive distinct formulations for minimum detectable fault magnitude, though qualitatively similar. The core difference lies in the method of construction of the invariant set offline in the former method and the reachable approximation of the convergence set using forward iterative techniques in the latter. This paper also contributes in giving a formulation for minimum fault magnitudes with invariant sets using an observer-based approach. Finally, an illustrative example is used to compare both approaches.@en