Abstract
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.
Highlights
The increasing number of flexible loads in the power system, such as “smart” appliances and electric vehicles, will give customers the possibility to partially schedule their power consumption and have an active role in the management of the network
The study of flexible demand integration in the electricity market considers real-time pricing tariffs, as described, for example, in [30]: a price signal is broadcast to the devices which independently determine their power consumption and operate during the hours of the day with lower electricity prices
In the first case study we consider a population of flexible appliances for which the equilibrium condition (22) in Theorem 1 is satisfied for the given Di
Summary
The increasing number of flexible loads in the power system, such as “smart” appliances and electric vehicles, will give customers the possibility to partially schedule their power consumption and have an active role in the management of the network. Real-time pricing schemes are considered a promising solution to crucial issues emerging in power systems, such as increased variability and uncertainty from renewable generation and modified consumption patterns from electrification of transportation and heating These elements have been discussed and brought to the attention of regulators by a substantial number of papers and reports, such as [3,14,15]. After several experimental testbeds, real-time pricing is starting to be implemented in areas with large penetration of renewables and electric vehicles [4] and further diffusion is expected in the near future In this context, the presented analysis establishes whether real-time pricing can lead to stable market configurations or additional control actions are required to ensure safe and reliable system operation
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