Nash Equilibrium in Strategic Bidding: A Binary Expansion Approach

Barroso, L.A.; Carneiro, R.D.; Granville, S.; Pereira, M.V.F.; Fampa, Marcia

doi:10.1109/tpwrs.2006.873127

Cited by 116 publications

(70 citation statements)

References 17 publications

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“…Following [6], a day ahead market consists of three phases: bidding, market clearing and pricing. The bidding phase is when the agents, relying on their own methodologies, decide their bids in form of price and quantity curves.…”

Section: Day-ahead Marketsmentioning

confidence: 99%

“…In short term, the small variability of inflows makes the problem similar to the thermal bidding problems. However, in medium term, the inflows may vary significantly as exposed in [19][20] [21], leading to more complex problems with fewer works, mainly for the price maker case [6].…”

Section: B Bidding Strategiesmentioning

confidence: 99%

“…For the multi agent case we have [32] where Stakelberg equilibria is achieved by a tailored algorithm, and [6] where the MILP model of [29] is expanded to accommodate the multi-agent case using Nash equilibrium, see appendix 2.…”

Section: Thermal Price Makermentioning

confidence: 99%

“…In such model, we have the following constraints in the sub-problem: (5) represents the hydro balance; (6) enforces that the energy produced by each hydro in all blocks must match the turbined water; (7) represents the load balance that enforces how much energy must be produced to meet the demand; (8)- (11) …”

Section: B Cost Based Operationmentioning

confidence: 99%

“…The first two main classes of problems arising from these changes are the investment [5] and the production problem [6] also known as operantion and dispatch problem. While the first is deeply connected to system expansion planning and is a long term problem, with a time scale of around 10 years, the second one is a shorter term problem, of scales varying from days to few years.…”

Section: Introductionmentioning

confidence: 99%

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Modelling Power Markets With Multi-Stage Stochastic Nash Equilibria

Garcia¹,

Chabar²

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ThanksTo all my family, specially my mother and father who stood by my side and gave me all the support one could ever dream with during this long way. Also to my brother João Pedro and my step-father Ricardo for the company.To PUC-Rio for providing an excellent environment.To my great friends that were present during all these long years.To my friends from PUC-Rio for the endless discussions, specially Gustavo Amaral, Mario Souto, Alexandre Moreira and Bruno Fanzeres.To my professors Carlos Tomei and Carlos Kubrusly for helping me to discover my interests and find my way in mathematics.To my advisor Alexandre Street who guided during most of my electrical engineering course and introduced me to optimization applied to power systems.To my good friends in UC Santa Barbara, specially my advisor over there João Pedro Hespanha.To all my friends at PSR, specially Julio Alberto Dias, Luiz Carlos da Costa Junior and Camila Metello who helped me day and night, also to Sergio Granville and Luiz Augusto Barroso for the many conversations and insights that made this work possible.To my co-advisor Mario Veiga for introducing me to the topic of this work and giving me all the support without which it would not have been possible. AbstractThe modelling of modern power markets requires the representation of the following main features: (i) a stochastic dynamic decision process, with uncertainties related to renewable production and fuel costs, among others; and (ii) a game-theoretic framework that represents the strategic behaviour of multiple agents, for example in daily price bids.These features can be in theory represented as a stochastic dynamic programming recursion, where we have a Nash equilibrium for multiple agents. However, the resulting problem is very challenging to solve. This work presents an iterative process to solve the above problem for realistic power systems. The proposed algorithm is consist of a fixed point algorithm, in which, each step is solved via stochastic dual dynamic programming method.The application of the proposed algorithm are illustrated in case studies with the real power systems. MODELAGEM DE MERCADOS DE ENERGIA COM EQUILIBRIO DE NASH STOCÁSTICO MULTI-ESTÁGIO ResumoA modelagem dos mercados de energia modernos exige a representação das seguintes características principais: (i) um processo de decisão dinâmico estocástico , com incertezas relacionadas aos os custos de produção e dos combustíveis renováveis, entre outros; e (ii) teoria dos jogos que representa o comportamento estratégico de múltiplos agentes , por exemplo, em propostas de preços diárias.Esses recursos podem ser , em teoria, representados como uma recursão de programação dinâmica estocástica, onde temos um equilíbrio de Nash para múltiplos agentes. No entanto, o problema resultante é muito difícil de resolver.Este trabalho apresenta um processo iterativo para resolver o problema acima para sistemas de energia realistas. O algoritmo proposto é composto de um algoritmo de ponto fixo, no qual, cada passo é resolvido através do mét...

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Section: Day-ahead Marketsmentioning

confidence: 99%

Section: B Bidding Strategiesmentioning

confidence: 99%

Section: Thermal Price Makermentioning

confidence: 99%

Section: B Cost Based Operationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling Power Markets With Multi-Stage Stochastic Nash Equilibria

Garcia¹,

Chabar²

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Strategic offers in day‐ahead market co‐optimizing energy and reserve under high penetration of wind power production: An MPEC approach

Tsimopoulos

Georgiadis

2019

AIChE Journal

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This work based on Stackelberg hypothesis, which considers a conventional power producer exercising their dominant position in an electricity pool with high penetration of wind power production. A bi‐level optimization model is used to describe the delivery of a single settled hourly auction process. The upper‐level problem illustrates the expected profit optimization of the strategic producer whereas the lower‐level problem represents the energy‐only market clearing process through a two‐stage stochastic program. The bi‐level problem is recast into mathematical programming with equilibrium constraints (MPEC), which is then reformulated into an MILP. These transformations occur using the Karush‐Kuhn‐Tucker optimality conditions and the strong duality theory. Energy dispatch and reserve deployment are co‐optimized under various scenarios of wind production uncertainty realization. The suggested model provides optimal strategic offers and local marginal prices under different levels of wind penetration and network line transmission capacities. © 2018 American Institute of Chemical Engineers AIChE J, 65: e16495 2019

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Stochastic model predictive control operation strategy of integrated energy system based on temperature‐flowrate scheduling model considering detailed thermal characteristics

Wei

Sun

et al. 2020

Int J Energy Res

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Summary A scheduling model is a prerequisite for an operation strategy of integrated energy system (IES). Existing scheduling models of IES, however, are typically based on heat‐transfer variables either completely or partially, which oversimplify detailed thermal characteristics. To this end, a novel scheduling model is proposed where all thermal processes are modeled by temperature and flowrate of working fluids. This improvement renders the capability to the scheduling model to incorporate different thermal processes. Furthermore, the nonlinear product terms of temperature and flowrate in the proposed model are linearized by the binary expansion method. Based on the linearized scheduling model, a stochastic model predictive control (SMPC) operation strategy is exploited to optimize the economic performance by energy forecast, scenario reduction, rolling optimization, and feedback correction. Afterwards, four operation modes considering different temperature changes of the devices, networks, and the environment are performed and compared. The results found that thermal characteristics will affect device operation results and the degree of influence varies. The network temperature changes have the broadest influence, followed by the device and the ambient temperature changes. Moreover, system operation costs are also affected by detailed thermal characteristics. The total cost, the gas cost, and the electricity cost under Mode 2 are almost the same to those of Mode 1. However, the first two costs are reduced by 3.4% and 5.3% under Mode 3, and are reduced by 2.7% and 4% under Mode 4, despite that the electricity cost increases by 0.2% under Mode 3 and remains almost the same under Mode 4. These indicate that reliability and economy of an IES are affected by thermal characteristics, and it is thus the necessity to consider detailed thermal characteristics in an operation. Moreover, the results demonstrate the capability of the generalized temperature‐flowrate based scheduling model and the effectiveness of the SMPC operation strategy.

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Nash Equilibrium in Strategic Bidding: A Binary Expansion Approach

Cited by 116 publications

References 17 publications

Modelling Power Markets With Multi-Stage Stochastic Nash Equilibria

Modelling Power Markets With Multi-Stage Stochastic Nash Equilibria

Strategic offers in day‐ahead market co‐optimizing energy and reserve under high penetration of wind power production: An MPEC approach

Stochastic model predictive control operation strategy of integrated energy system based on temperature‐flowrate scheduling model considering detailed thermal characteristics

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