Analysis of Nash equilibria in energy markets with large populations of price-responsive flexible appliances

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

doi:10.1109/cdc.2015.7403095

Cited by 5 publications

(18 citation statements)

References 10 publications

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“…The population of flexible appliances is characterized by a function f which is given by the sum of two truncated gaussian centered at 3h and 7h, while the total energy required for task completion of all devices amounts to 55GW h. In the present case, condition (9) for existence of an unconstrained Nash equilibrium, as established in [7], is not fulfilled. This can be seen in Fig.…”

Section: Simulation Resultsmentioning

confidence: 91%

“…The characterization of the flexible loads and the description of their interactions with the power system follows the modelling choices presented in [7]. For the purposes of this work, we consider interruptible appliances that can continuously modulate their power consumption and have complete time availability.…”

Section: Modelling Framework For Flexible Appliances and Energy Mmentioning

confidence: 99%

“…Important results in this respect have been provided in [7,, showing that a Nash equilibrium can be obtained (by broadcasting D = D i ) if and only if:…”

Section: B Nash Equilibria With Price-based Strategymentioning

confidence: 99%

“…Many different approaches have been proposed in such sense, including centralized techniques [3] and distributed mechanisms that use stochastic optimization [4], adaptive strategies [5] or Lagrange relaxation [6]. This paper follows the results presented in [7] where, approximating the flexible appliances population as a continuum and adopting a game theory framework, necessary and sufficient conditions are provided for convergence (in one step) to a Nash equilibrium. This means that all price-responsive appliances, having scheduled their power consumption according to a broadcast demand/price signal, have no incentive in changing their strategy when the resulting aggregate demand is considered.…”

Section: Introductionmentioning

confidence: 99%

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Decentralized coordination of large populations of flexible electrical appliances through demand saturation

Paola

Angeli

Štrbac

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-This paper presents a novel decentralized control strategy for integration of price-responsive loads in the electricity market. Previous work has shown that, by approximating the devices population as a continuum, it is possible to provide necessary and sufficient conditions for the existence of a Nash equilibrium (no device has unilateral interest in changing its scheduling when considering the resulting profile of aggregate demand). These results are now extended by introducing a time varying proportional constraint on the maximum power consumption of the appliances. This allows to saturate the flexible demand and obtain a Nash equilibrium for a much wider range of scenarios. The performance of the proposed control technique, which also minimizes the task time of all appliances, is tested in simulation.

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Section: Simulation Resultsmentioning

confidence: 91%

Section: Modelling Framework For Flexible Appliances and Energy Mmentioning

confidence: 99%

“…Important results in this respect have been provided in [7,, showing that a Nash equilibrium can be obtained (by broadcasting D = D i ) if and only if:…”

Section: B Nash Equilibria With Price-based Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Decentralized coordination of large populations of flexible electrical appliances through demand saturation

Paola

Angeli

Štrbac

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

Self Cite

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show abstract

“…As a starting point, we consider the theoretical analysis presented in De Paola et al (2015), where a suitable final solution has been characterized as a Nash equilibrium. Necessary and sufficient equilibrium conditions have been provided, determining the possibility of successfully coordinating, in a decentralized manner, large populations of price-responsive appliances.…”

Section: Introductionmentioning

confidence: 99%

A Semi-Decentralized Scheme for Integration of Price-Responsive Appliances in the Electricity Market

2017

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A novel semi-decentralized control strategy is proposed for the integration in the power system of large populations of flexible loads, such as electric vehicles and "smart" appliances. To characterize the interactions between the single agents and their effects on the grid, a game theory framework is adopted. The price responsive appliances are modelled as competing players, characterizing a stable and efficient solution as a Nash equilibrium (no device has unilateral interest in changing its scheduled power consumption when the final electricity price is considered). We extend previous results on distributed control of flexible demand, proposing a partial centralization of the power scheduling at critical time instants. In this way, it is possible to ensure convergence to a Nash equilibrium for a wider range of scenarios, considering higher penetration levels of flexible demand and a wider range of parameters for the devices. The effectiveness of the proposed scheme is theoretically proved and its performance is evaluated in simulations, considering a future UK grid with high penetration of flexible demand.

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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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Analysis of Nash equilibria in energy markets with large populations of price-responsive flexible appliances

Cited by 5 publications

References 10 publications

Decentralized coordination of large populations of flexible electrical appliances through demand saturation

Decentralized coordination of large populations of flexible electrical appliances through demand saturation

A Semi-Decentralized Scheme for Integration of Price-Responsive Appliances in the Electricity Market

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

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