Event-triggered consensus of multiagent systems (MASs) has attracted tremendous attention from both theoretical and practical perspectives due to the fact that it enables all agents eventually to reach an agreement upon a common quantity of interest while significantly alleviating utilization of communication and computation resources. This paper aims to provide an overview of recent advances in event-triggered consensus of MASs. First, a basic framework of multiagent event-triggered operational mechanisms is established. Second, representative results and methodologies reported in the literature are reviewed and some in-depth analysis is made on several event-triggered schemes, including event-based sampling schemes, model-based event-triggered schemes, sampled-data-based event-triggered schemes, and self-triggered sampling schemes. Third, two examples are outlined to show applicability of event-triggered consensus in power sharing of microgrids and formation control of multirobot systems, respectively. Finally, some challenging issues on event-triggered consensus are proposed for future research.

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An Overview of Recent Advances in Event-Triggered Consensus of Multiagent Systems

Peer-to-Peer energy trading in a Microgrid

According to the feed-in tariff for encouraging local consumption of photovoltaic (PV) energy, the energy sharing among neighboring PV prosumers in the microgrid could be more economical than the independent operation of prosumers. For microgrids of peer-to-peer PV prosumers, an energy-sharing model with price-based demand response is proposed. First, a dynamical internal pricing model is formulated for the operation of energy-sharing zone, which is defined based on the supply and demand ratio (SDR) of shared PV energy. Moreover, considering the energy consumption flexibility of prosumers, an equivalent cost model is designed in terms of economic cost and users’ willingness. As the internal prices are coupled with SDR in the microgrid, the algorithm and implementation method for solving the model is designed on a distributed iterative way. Finally, through a practical case study, the effectiveness of the method is verified in terms of saving PV prosumers’ costs and improving the sharing of the PV energy.

Energy-Sharing Model With Price-Based Demand Response for Microgrids of Peer-to-Peer Prosumers

The advent of more proactive consumers, the so-called “prosumers”, with production and storage capabilities, is empowering the consumers and bringing new opportunities and challenges to the operation of power systems in a market environment. Recently, a novel proposal for the design and operation of electricity markets has emerged: these so-called peer-to-peer (P2P) electricity markets conceptually allow the prosumers to directly share their electrical energy and investment. Such P2P markets rely on a consumer-centric and bottom-up perspective by giving the opportunity to consumers to freely choose the way they buy their electric energy. A community can also be formed by prosumers who want to collaborate, or in terms of operational energy management. This paper contributes with an overview of these new P2P markets that starts with the motivation, challenges, market designs moving to the potential future developments in this field, providing recommendations while considering a test-case.

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Peer-to-peer and community-based markets: A comprehensive review

This paper provides an overview and makes a deep investigation on sampled-data-based event-triggered control and filtering for networked systems. Compared with some existing event-triggered and self-triggered schemes, a sampled-data-based event-triggered scheme can ensure a positive minimum inter-event time and make it possible to jointly design suitable feedback controllers and event-triggered threshold parameters. Thus, more attention has been paid to the sampled-data-based event-triggered scheme. A deep investigation is first made on the sampled-data-based event-triggered scheme. Then, recent results on sampled-data-based event-triggered state feedback control, dynamic output feedback control, $H_\infty$ filtering for networked systems are surveyed and analyzed. An overview on sampled-data-based event-triggered consensus for distributed multiagent systems is given. Finally, some challenging issues are addressed to direct the future research.

An Overview and Deep Investigation on Sampled-Data-Based Event-Triggered Control and Filtering for Networked Systems

To reduce information exchange requirements in smart grids, an event-triggered communication-based distributed optimization is proposed for economic dispatch. In this work, the $\theta$ -logarithmic barrier-based method is employed to reformulate the economic dispatch problem, and the consensus-based approach is considered for developing fully distributed technology-enabled algorithms. Specifically, a novel distributed algorithm utilizes the minimum connected dominating set (CDS), which efficiently allocates the task of balancing supply and demand for the entire power network at the beginning of economic dispatch. Further, an event-triggered communication-based method for the incremental cost of each generator is able to reach a consensus, coinciding with the global optimality of the objective function. In addition, a fast gradient-based distributed optimization method is also designed to accelerate the convergence rate of the event-triggered distributed optimization. Simulations based on the IEEE 57-bus test system demonstrate the effectiveness and good performance of proposed algorithms.

Distributed Event-Triggered Scheme for Economic Dispatch in Smart Grids

This paper proposes a control framework, called pulse-modulated intermittent control, which unifies impulsive control and sampled control. Specifically, the concept of pulse function is introduced to characterize the control/rest intervals and the amplitude of the control. By choosing some specified functions as the pulse function, the proposed control scheme can be reduced to sampled control or impulsive control. The proposed control framework is applied to consensus problems of multiagent systems. Using discretization approaches and stability theory, several necessary and sufficient conditions are established to ensure the consensus of the controlled system. The results show that consensus depends not only on the network topology, the sampling period and the control gains, but also the pulse function. Moreover, a lower bound of the asymptotic convergence factor is derived as well. For a given pulse function and an undirected graph, an optimal control gain is designed to achieve the fastest convergence. In addition, impulsive control and sampled control are revisited in the proposed control framework. Finally, some numerical examples are given to verify the effectiveness of theoretical results.

Pulse-Modulated Intermittent Control in Consensus of Multiagent Systems

This paper introduces a distributed algorithm for sparse load shifting in demand-side management with a focus on the scheduling problem of residential smart appliances. By the sparse load shifting strategy, customers’ discomfort is reduced. Although there are many game theoretic models for the demand-side management problem, the computational efficiency of finding Nash equilibrium that globally minimizes the total energy consumption cost and the peak-to-average ratio is still an outstanding issue. We develop a bidirectional framework for solving the demand-side management problem in a distributed way to substantially improve the search efficiency. A Newton method is employed to accelerate the centralized coordination of demand side management strategies that superlinearly converge to a better Nash equilibrium minimizing the peak-to-average ratio. Furthermore, dual fast gradient and convex relaxation are applied to tackle the sub-problem for customers’ best response, which is able to relieve customers’ discomfort from load shifting or interrupting. Detailed results from illustrative case studies are presented and discussed, which shows the costs of energy consumption and daily peak demand by our algorithm are reduced. Finally, some conclusions are drawn.

Efficient Computation for Sparse Load Shifting in Demand Side Management

The resource allocation problem is studied and reformulated by a distributed interior point method via a $\theta$ - logarithmic barrier. By the facilitation of the graph Laplacian, a fully distributed continuous-time multiagent system is developed for solving the problem. Specifically, to avoid high singularity of the $\theta$ - logarithmic barrier at boundary, an adaptive parameter switching strategy is introduced into this dynamical multiagent system. The convergence rate of the distributed algorithm is obtained. Moreover, a novel distributed primal–dual dynamical multiagent system is designed in a smart grid scenario to seek the saddle point of dynamical economic dispatch, which coincides with the optimal solution. The dual decomposition technique is applied to transform the optimization problem into easily solvable resource allocation subproblems with local inequality constraints. The good performance of the new dynamical systems is, respectively, verified by a numerical example and the IEEE six-bus test system-based simulations.

Chaojie Li

Papers

Energy-Sharing Model With Price-Based Demand Response for Microgrids of Peer-to-Peer Prosumers

Distributed Event-Triggered Scheme for Economic Dispatch in Smart Grids

Pulse-Modulated Intermittent Control in Consensus of Multiagent Systems

Efficient Computation for Sparse Load Shifting in Demand Side Management

Distributed Optimal Consensus Over Resource Allocation Network and Its Application to Dynamical Economic Dispatch