Distributed Control of Micro-Storage Devices With Mean Field Games

Paola, Antonio De; Angeli, David; Štrbac, Goran

doi:10.1109/tsg.2015.2405338

Cited by 24 publications

(25 citation statements)

References 11 publications

(12 reference statements)

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“…To simplify the equilibrium analysis and the design of the broadcast signal, the appliances population is described as a continuum, assuming that the impact of the single device on total demand and electricity price is negligible and only the global behaviour of the devices population needs to be considered in such sense. Similar approaches have been previously applied in power systems contexts, studying large-scale market interactions [16], frequency control provision by thermostatic loads [2], coordination of electric vehicles [7] and energy arbitrage with micro-storage devices [9]. The main novelty of the present work is that the dynamic behaviour of the appliances is implicitly modelled by exploiting intrinsic properties of the problem (monotonicity of electricity price and unidirectionality of power exchanges).…”

Section: Introductionmentioning

confidence: 91%

On Distributed Scheduling of Flexible Demand and Nash Equilibria in the Electricity Market

2017

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This paper presents a novel game theory approach for large-scale deployment of price-responsive electrical appliances. In the proposed distributed control scheme, each appliance independently schedules its power consumption on the basis of a broadcast demand/price signal, aiming to complete its task at minimum cost. The conflicting interactions of the appliances, competing for power consumption at the cheapest hours of the day, are modelled through a differential game with a continuum of players, and efficient deployment of flexible demand is characterized as a Nash equilibrium. A novel approach is adopted to derive necessary and sufficient equilibrium conditions: intrinsic properties of the problem (price monotonicity, unidirectionality of power transfers) are exploited to perform an equilibrium study based on sublevel sets of the considered demand profiles. As a result, it is possible to determine for which penetration levels of flexible demand, types of appliances and inflexible demand profiles it is possible to achieve an equilibrium. Such stable configuration is achieved through the broadcast of a single demand/price signal and does not require iterated exchange of information between devices and coordinator. In addition, the global optimality of the equilibrium is proved, necessary conditions for Pareto optimality are derived, and a preliminary analysis of devices with partial time availability is carried out. The performance of the proposed control strategy is evaluated in simulation, considering realistic future scenarios of the UK power system with large penetration of flexible demand.

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Section: Introductionmentioning

confidence: 91%

On Distributed Scheduling of Flexible Demand and Nash Equilibria in the Electricity Market

2017

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“…Mean field games have been previously applied in power system contexts, considering for example electric vehicles [20], storage [21] or TCLs [22]. However, to the best of our knowledge, this is the first paper that implements some fundamental elements in a mean field game framework:…”

Section: B Contributionsmentioning

confidence: 99%

“…where the angular brackets denote floor and ceiling functions. The numerical integration of the transport equation 15can then be performed as in [21,Section IV], initializing m i at 0 and iterating the following over j and k:…”

Section: A Integration Schemesmentioning

confidence: 99%

A Mean Field Game Approach for Distributed Control of Thermostatic Loads Acting in Simultaneous Energy-Frequency Response Markets

Paola

Trovato

Angeli

et al. 2019

IEEE Trans. Smart Grid

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“…To achieve this, the set of merchant companies is approximated as a continuum [29]. Similar approaches have been previously considered in other economic [30], [31] and smart grid [32], [33] applications. The proposed approximation makes the impact of each infinitesimal player's decisions on system quantities negligible, allowing us to derive mathematical conditions for the existence of the merchant planning solution, characterized as a Nash equilibrium.…”

Section: Contributionsmentioning

confidence: 99%

Investigating the Social Efficiency of Merchant Transmission Planning Through a Non-cooperative Game-Theoretic Framework

Paola

Papadaskalopoulos

Angeli

et al. 2018

IEEE Trans. Power Syst.

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Abstract-Merchant transmission planning is considered as a further step towards the full liberalization of the electricity industry. However, previous modeling approaches do not comprehensively explore its social efficiency as they cannot effectively deal with a large number of merchant companies. This paper addresses this fundamental challenge by adopting a novel non-cooperative game-theoretic approach. Specifically, the number of merchant companies is assumed sufficiently large to be approximated as a continuum. This allows the derivation of mathematical conditions for the existence of a Nash Equilibrium solution of the merchant planning game. By analytically and numerically comparing this solution against the one obtained through the traditional centralized planning approach, the paper demonstrates that merchant planning can maximize social welfare only when the following conditions are satisfied: a) fixed investment costs are neglected and b) the network is radial and does not include any loops. Given that these conditions do not generally hold in reality, these findings suggest that even a fully competitive merchant transmission planning framework, involving the participation of a very large number of competing merchant companies, is not generally capable of maximizing social welfare.Index Terms-Game theory, merchant transmission investors, Nash equilibrium, transmission planning. NOMENCLATUREA. Indices t ∈ T Index and set of time periods m ∈ M Index and set of network branches n ∈ N Index and set of network nodes l ∈ L Index and set of network loops i ∈ I Index and set of merchant transmission companies B. Parameters w tWeighting factor of period t T Power generation at node n and period t (MW) D n,t Power demand at node n and period t (MW) f m,t Power flow on branch m at period t (MW) P n,t Net power outflow from node n at period t (MW) λ n,t Locational marginal price at node n and period t (£/MWh) D. Functions T m (·) Transmission investment cost for branch m (£/h) C n,t (·) Cost of generation at node n and period t (£/h) B n,t (·) Benefit of demand at node n and period t (£/h) J(i, ·) Profit of company i (£/h)

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Distributed Control of Micro-Storage Devices With Mean Field Games

Cited by 24 publications

References 11 publications

On Distributed Scheduling of Flexible Demand and Nash Equilibria in the Electricity Market

On Distributed Scheduling of Flexible Demand and Nash Equilibria in the Electricity Market

A Mean Field Game Approach for Distributed Control of Thermostatic Loads Acting in Simultaneous Energy-Frequency Response Markets

Investigating the Social Efficiency of Merchant Transmission Planning Through a Non-cooperative Game-Theoretic Framework

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