A trilevel model for best response in energy demand-side management

Aussel, Didier; Brotcorne, Luce; Lepaul, Sébastien; Niederhäusern, Léonard von

doi:10.1016/j.ejor.2019.03.005

Cited by 54 publications

(51 citation statements)

References 17 publications

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“…A trilevel electricity market model comprising of four actors, electricity suppliers for selling electricity, local agents that purchase, sell and utilize electricity, aggregators for buying and selling electricity, and end users for consuming electricity, is proposed in [80].…”

Section: Game Approachesmentioning

confidence: 99%

Recent Challenges and Methodologies in Smart Grid Demand Side Management: State-of-the-Art Literature Review

Nasir¹,

Bukhari

Raza³

et al. 2021

Mathematical Problems in Engineering

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The concept of smart grid was introduced a decade ago. Demand side management (DSM) is one of the crucial aspects of smart grid that provides users with the opportunity to optimize their load usage pattern to fill the gap between energy supply and demand and reduce the peak to average ratio (PAR), thus resulting in energy and economic efficiency ultimately. The application of DSM programs is lucrative for both utility and consumers. Utilities can implement DSM programs to improve the system power quality, power reliability, system efficiency, and energy efficiency, while consumers can experience energy savings, reduction in peak demand, and improvement of system load profile, and they can also maximize usage of renewable energy resources (RERs). In this paper, some of the strategies of DSM including peak shaving and load scheduling are highlighted. Furthermore, the implementation of numerous optimization techniques on DSM is reviewed.

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Section: Game Approachesmentioning

confidence: 99%

Recent Challenges and Methodologies in Smart Grid Demand Side Management: State-of-the-Art Literature Review

Nasir¹,

Bukhari

Raza³

et al. 2021

Mathematical Problems in Engineering

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“…Although single-follower normal-form Stackelberg games can be solved in polynomial time [8,22,39], the problem becomes NP-hard when multiple followers are present, even when the equilibrium is assumed to be either optimistic or pessimistic [6,11]. Existing approaches [3,6] primarily leverage the leaderfollower structure in a bilevel optimization formulation [10], which can be solved by reformulating the followers' best response into non-convex stationary and complementarity constraints in the leader's optimization problem [43]. Various optimization techniques, including branch-and-bound [11] and mixed-integer programs [6], are then adopted to solve these reformulated problems.…”

Section: Related Workmentioning

confidence: 99%

“…Stackelberg games are commonly adopted in many real-world applications, including security [15,19], wildlife conservation [14], and commercial decisions made by firms [3,34,46]. Moreover, many realistic settings involve a single leader with multiple self-interested followers such as wildlife conservation efforts with a central coordinator and a team of defenders [15,16]; resource management in energy [3] with suppliers, aggregators, and end users; or security problems with a central insurer and a set of vulnerable agents [21,34]. Solving Stackelberg games with multiple followers is challenging in general [5,11].…”

Section: Introductionmentioning

confidence: 99%

Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games

Wang¹,

Xu²,

Perrault³

et al. 2021

Preprint

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A growing body of work in game theory extends the traditional Stackelberg game to settings with one leader and multiple followers who play a Nash equilibrium. Standard approaches for computing equilibria in these games reformulate the followers' best response as constraints in the leader's optimization problem. These reformulation approaches can sometimes be effective, but often get trapped in low-quality solutions when followers' objectives are non-linear or non-quadratic. Moreover, these approaches assume a unique equilibrium or a specific equilibrium concept, e.g., optimistic or pessimistic, which is a limiting assumption in many situations. To overcome these limitations, we propose a stochastic gradient descentbased approach, where the leader's strategy is updated by differentiating through the followers' best responses. We frame the leader's optimization as a learning problem against followers' equilibrium, which allows us to decouple the followers' equilibrium constraints from the leader's problem. This approach also addresses cases with multiple equilibria and arbitrary equilibrium selection procedures by back-propagating through a sampled Nash equilibrium. To this end, this paper introduces a novel concept called equilibrium flow to formally characterize the set of equilibrium selection processes where the gradient with respect to a sampled equilibrium is an unbiased estimate of the true gradient. We evaluate our approach experimentally against existing baselines in three Stackelberg problems with multiple followers and find that in each case, our approach is able to achieve higher utility for the leader.Preprint. Under review.

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“…The author concludes that this approach outperforms methods based on the problem reformulation using the KKT conditions, regarding both solution quality and computational efficiency on practically relevant problem sizes. Aussel et al (2020) proposed a trilevel multi-leader multi-follower model for load shifting induced by ToU pricing. The energy supplier defines time-differentiated prices to which the consumers adapt by shifting their loads, either directly through local agents or indirectly through aggregators.…”

Section: Designing Tou Tariffs-retailer-consumer Interactionmentioning

confidence: 99%

Bilevel optimization to deal with demand response in power grids: models, methods and challenges

Antunes

Alves

Ecer

2020

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This paper presents a review of selected models, methods, and challenges associated with the use of bilevel optimization in problems that involve consumers' demand response arising in the power sector. The main formulations and concepts of bilevel optimization are presented. The importance of demand response as a "dispatchable" resource in the evolution of power networks to smart grids is emphasized. The hierarchical nature of the interaction between decision-makers controlling different sets of variables in several problems involving demand response is highlighted, which establishes bilevel optimization as an adequate approach to decision support. The main concepts and solution approaches to those problems are underlined, in the context of the theoretical, methodological, and computational issues associated with bilevel optimization.

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A trilevel model for best response in energy demand-side management

Cited by 54 publications

References 17 publications

Recent Challenges and Methodologies in Smart Grid Demand Side Management: State-of-the-Art Literature Review

Recent Challenges and Methodologies in Smart Grid Demand Side Management: State-of-the-Art Literature Review

Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games

Bilevel optimization to deal with demand response in power grids: models, methods and challenges

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