Optimisation of electrical network configuration: Complexity and algorithms for ring topologies

Barth, Dominique; Mautor, Thierry; Moissac, Arnaud De; Watel, Dimitri; Weisser, Marc-Antoine

doi:10.1016/j.tcs.2021.01.023

Cited by 5 publications

(7 citation statements)

References 21 publications

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“…An extension of our approach will have to take into account the dynamic configuration of the network, meaning that the capacity of its components must be able to adapt to each set of prosumer demands. The proposed RL approach will then have to be coupled with a dynamic configuration algorithm of the smart grid topologies, inspired, for example, by [39].…”

Section: Discussionmentioning

confidence: 99%

Distributed Reinforcement Learning for the Management of a Smart Grid Interconnecting Independent Prosumers

Barth

Cohen-Boulakia²,

Ehounou

2022

Energies

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In the context of an eco-responsible production and distribution of electrical energy at the local scale of an urban territory, we consider a smart grid as a system interconnecting different prosumers, which all retain their decision-making autonomy and defend their own interests in a comprehensive system where the rules, accepted by all, encourage virtuous behavior. In this paper, we present and analyze a model and a management method for smart grids that is shared between different kinds of independent actors, who respect their own interests, and that encourages each actor to behavior that allows, as much as possible, an energy independence of the smart grid from external energy suppliers. We consider here a game theory model, in which each actor of the smart grid is a player, and we investigate distributed machine-learning algorithms to allow decision-making, thus, leading the game to converge to stable situations, in particular to a Nash equilibrium. We propose a Linear Reward Inaction algorithm that achieves Nash equilibria most of the time, both for a single time slot and across time, allowing the smart grid to maximize its energy independence from external energy suppliers.

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Section: Discussionmentioning

confidence: 99%

Distributed Reinforcement Learning for the Management of a Smart Grid Interconnecting Independent Prosumers

Barth

Cohen-Boulakia²,

Ehounou

2022

Energies

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“…Determining whether there is a feasible orientation for a given electrical network leads to the following decision problem, which is shown to be NPcomplete for general graphs [3], but polynomial for trees [4].…”

Section: Flow In the Oriented Tree And Feasible Orientationmentioning

confidence: 99%

“…This percentage is called the load of the node. In [3,4] we prove that this existence problem is NP-complete for general network topologies but polynomial for trees.…”

Section: Introductionmentioning

confidence: 98%

“…Reliability can be defined as the capacity of the electrical system to supply electricity in the quantity and with the quality demanded by consumers by using available sources reliably and fairly. Thus, to guarantee reliability, the objective here is to find the configuration satisfying the demands of the consumers [6,18,22] by saturating as little as possible the production capacity of (heterogeneous) sources and the flow capacity of links and switches [3,5].…”

Section: Introductionmentioning

confidence: 99%

“…We therefore introduce three metrics that can answer this problematic. As done, in [3], we introduce the load reserve, which is the difference between the maximum and the minimum loads of the sources. This load reserve should be minimized.…”

Section: Introductionmentioning

confidence: 99%

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Configuring an heterogeneous smartgrid network: complexity and approximations for tree topologies

Barth,

Mautor,

Watel

et al. 2023

J Glob Optim

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We address the problem of configuring a power distribution network with reliability and resilience objectives by satisfying the demands of the consumers and saturating each production source as little as possible. We consider power distribution networks containing source nodes producing electricity, nodes representing electricity consumers and switches between them. Configuring this network consists in deciding the orientation of the links between the nodes of the network. The electric flow is a direct consequence of the chosen configuration and can be computed in polynomial time. It is valid if it satisfies the demand of each consumer and capacity constraints on the network. In such a case, we study the problem of determining a feasible solution that balances the loads of the sources, that is their production rates. We use three metrics to measure the quality of a solution: minimizing the maximum load, maximizing the minimum load and minimizing the difference of the maximum and the minimum loads. This defines optimization problems called respectively min-M, max-m and min-R.In the case where the graph of the network is a tree, it is known that the problem of building a valid configuration is polynomial. We show the three optimization variants have distinct properties regarding the theoretical complexity and the approximability. Particularly, we show that min-M is polynomial, that max-m is NP-Hard but belongs to the class FPTAS and that min-R is NP-Hard, cannot be approximated to within any exponential relative ratio but, for any ε > 0, there exists an algorithm for which the value of the returned solution equals the value of an optimal solution shifted by at most ε.

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Overlapping Channel Allocation Method for Wireless Communication Network Based on Discrete Particle Swarm Optimization Algorithm

Qin,

Zhu,

Zhang

et al. 2024

Int J Comput Intell Syst

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Optimisation of electrical network configuration: Complexity and algorithms for ring topologies

Cited by 5 publications

References 21 publications

Distributed Reinforcement Learning for the Management of a Smart Grid Interconnecting Independent Prosumers

Distributed Reinforcement Learning for the Management of a Smart Grid Interconnecting Independent Prosumers

Configuring an heterogeneous smartgrid network: complexity and approximations for tree topologies

Overlapping Channel Allocation Method for Wireless Communication Network Based on Discrete Particle Swarm Optimization Algorithm

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