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July  2015, 11(3): 985-998. doi: 10.3934/jimo.2015.11.985

Electricity day-ahead markets: Computation of Nash equilibria

Margarida Carvalho 1, , João Pedro Pedroso 1, and  João Saraiva 2,

1. 

Faculdade de Ciências, Universidade do Porto and INESC TEC, Rua do Campo Alegre, 4169-007 Porto, Portugal, Portugal
2. 

Faculdade de Engenharia, Universidade do Porto and INESC TEC, Rua Dr. Roberto Frias, 4200 - 465 Porto, Portugal

Received  May 2012 Revised  June 2014 Published  October 2014

In a restructured electricity sector, day-ahead markets can be modeled as a game where some players - the producers - submit their proposals. To analyze the companies' behavior we have used the concept of Nash equilibrium as a solution in these multi-agent interaction problems. In this paper, we present new and crucial adaptations of two well-known mechanisms, the adjustment process and the relaxation algorithm, in order to achieve the goal of computing Nash equilibria. The advantages of these approaches are highlighted and compared with those available in the literature.
Keywords: Electricity market, Nash equilibria, adjustment process, combinatorial optimization, auctions/bidding., relaxation algorithm.
Mathematics Subject Classification: Primary: 91A80; Secondary: 90C27, 65K05, 90C5.
Citation: Margarida Carvalho, João Pedro Pedroso, João Saraiva. Electricity day-ahead markets: Computation of Nash equilibria. Journal of Industrial & Management Optimization, 2015, 11 (3) : 985-998. doi: 10.3934/jimo.2015.11.985
References:
[1]

P. Bajpai and S. N. Singh, Fuzzy adaptive particle swarm optimization for bidding strategy in uniform price spot market,, Power Systems, 22 (2007), 2152.  doi: 10.1109/TPWRS.2007.907445.  Google Scholar

[2]

A. G. Bakirtzis, N. P. Ziogos, A. C. Tellidou and G. A. Bakirtzis, Electricity producer offering strategies in day-ahead energy market with step-wise offers,, Power Systems, 22 (2007), 1804.  doi: 10.1109/TPWRS.2007.907536.  Google Scholar

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T. Barforoushi, M. P. Moghaddam, M. H. Javidi and M. K. Sheikh-El-Eslami, Evaluation of regulatory impacts on dynamic behavior of investments in electricity markets: A new hybrid dp/game framework,, Power Systems, 25 (2010), 1978.  doi: 10.1109/TPWRS.2010.2049034.  Google Scholar

[4]

L. A. Barroso, R. D. Carneiro, S. Granville, M. V. Pereira and M. H. C. Fampa, Nash equilibrium in strategic bidding: A binary expansion approach,, Power Systems, 21 (2006), 629.  doi: 10.1109/TPWRS.2006.873127.  Google Scholar

[5]

M. Carvalho, J. P. Pedroso and J. Saraiva, Nash equilibria in electricity markets,, In The Proceedings of the VII ALIO/EURO Workshop on Applied Combinatorial Optimization, (2011), 153.   Google Scholar

[6]

A. Conejo and F. Prieto, Mathematical programming and electricity markets,, TOP, 9 (2001), 1.  doi: 10.1007/BF02579062.  Google Scholar

[7]

J. Contreras, M. Klusch and J. B. Krawczyk, Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets,, Power Systems, 19 (2004), 195.  doi: 10.1109/TPWRS.2003.820692.  Google Scholar

[8]

F. Facchinei and C. Kanzow, Generalized Nash equilibrium problems,, 4OR: A Quarterly Journal of Operations Research, 5 (2007), 173.  doi: 10.1007/s10288-007-0054-4.  Google Scholar

[9]

D. Fudenberg and J. Tirole, Game Theory,, MIT Press, (1996).   Google Scholar

[10]

B. A. Gomes, Simulador dos operadores de mercado e sistema num mercado de energia eléctrica considerando restriçøes intertemporais,, Master's thesis, (2005).   Google Scholar

[11]

E. Hasan and F. D. Galiana, Fast computation of pure strategy Nash equilibria in electricity markets cleared by merit order,, Power Systems, 25 (2010), 722.  doi: 10.1109/TPWRS.2009.2037153.  Google Scholar

[12]

B. F. Hobbs, C. B. Metzler and J. -S. Pang, Strategic gaming analysis for electric power systems: An MPEC approach,, Power Systems, 15 (2000), 638.  doi: 10.1109/59.867153.  Google Scholar

[13]

J. Krawczyk and J. Zuccollo, Nira-3: An improved Matlab package for finding Nash equilibria in infinite games,, Computational Economics, 5 (2006).   Google Scholar

[14]

K. Lee and R. Baldick, Tuning of discretization in bimatrix game approach to power system market analysis,, Power Engineering Review, 22 (2002).  doi: 10.1109/MPER.2002.4311811.  Google Scholar

[15]

M. V. Pereira, S. Granville, M. H. C. Fampa, R. Dix and L. A. Barroso, Strategic bidding under uncertainty: A binary expansion approach,, Power Systems, 20 (2005), 180.  doi: 10.1109/TPWRS.2004.840397.  Google Scholar

[16]

D. Pozo and J. Contreras, Finding multiple Nash equilibria in pool-based markets: A stochastic EPEC approach,, Power Systems, 26 (2011), 1744.  doi: 10.1109/TPWRS.2010.2098425.  Google Scholar

[17]

D. Pozo, J. Contreras, Á. Caballero and A. de Andrés, Long-term Nash equilibria in electricity markets,, Electric Power Systems Research, 81 (2011), 329.  doi: 10.1016/j.epsr.2010.09.008.  Google Scholar

[18]

J. Saraiva, J. P. da Silva and M. P. de Leão, Mercados de Electricidade - Regulaçcão de Tarifação de Uso das Redes,, FEUPedições, (2002).   Google Scholar

[19]

Y. S. Son and R. Baldick, Hybrid coevolutionary programming for Nash equilibrium search in games with local optima,, Evolutionary Computation, 8 (2004), 305.  doi: 10.1109/TEVC.2004.832862.  Google Scholar

[20]

A. Vaz and L. Vicente, A particle swarm pattern search method for bound constrained global optimization,, Journal of Global Optimization, 39 (2007), 197.  doi: 10.1007/s10898-007-9133-5.  Google Scholar

show all references

References:
[1]

P. Bajpai and S. N. Singh, Fuzzy adaptive particle swarm optimization for bidding strategy in uniform price spot market,, Power Systems, 22 (2007), 2152.  doi: 10.1109/TPWRS.2007.907445.  Google Scholar

[2]

A. G. Bakirtzis, N. P. Ziogos, A. C. Tellidou and G. A. Bakirtzis, Electricity producer offering strategies in day-ahead energy market with step-wise offers,, Power Systems, 22 (2007), 1804.  doi: 10.1109/TPWRS.2007.907536.  Google Scholar

[3]

T. Barforoushi, M. P. Moghaddam, M. H. Javidi and M. K. Sheikh-El-Eslami, Evaluation of regulatory impacts on dynamic behavior of investments in electricity markets: A new hybrid dp/game framework,, Power Systems, 25 (2010), 1978.  doi: 10.1109/TPWRS.2010.2049034.  Google Scholar

[4]

L. A. Barroso, R. D. Carneiro, S. Granville, M. V. Pereira and M. H. C. Fampa, Nash equilibrium in strategic bidding: A binary expansion approach,, Power Systems, 21 (2006), 629.  doi: 10.1109/TPWRS.2006.873127.  Google Scholar

[5]

M. Carvalho, J. P. Pedroso and J. Saraiva, Nash equilibria in electricity markets,, In The Proceedings of the VII ALIO/EURO Workshop on Applied Combinatorial Optimization, (2011), 153.   Google Scholar

[6]

A. Conejo and F. Prieto, Mathematical programming and electricity markets,, TOP, 9 (2001), 1.  doi: 10.1007/BF02579062.  Google Scholar

[7]

J. Contreras, M. Klusch and J. B. Krawczyk, Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets,, Power Systems, 19 (2004), 195.  doi: 10.1109/TPWRS.2003.820692.  Google Scholar

[8]

F. Facchinei and C. Kanzow, Generalized Nash equilibrium problems,, 4OR: A Quarterly Journal of Operations Research, 5 (2007), 173.  doi: 10.1007/s10288-007-0054-4.  Google Scholar

[9]

D. Fudenberg and J. Tirole, Game Theory,, MIT Press, (1996).   Google Scholar

[10]

B. A. Gomes, Simulador dos operadores de mercado e sistema num mercado de energia eléctrica considerando restriçøes intertemporais,, Master's thesis, (2005).   Google Scholar

[11]

E. Hasan and F. D. Galiana, Fast computation of pure strategy Nash equilibria in electricity markets cleared by merit order,, Power Systems, 25 (2010), 722.  doi: 10.1109/TPWRS.2009.2037153.  Google Scholar

[12]

B. F. Hobbs, C. B. Metzler and J. -S. Pang, Strategic gaming analysis for electric power systems: An MPEC approach,, Power Systems, 15 (2000), 638.  doi: 10.1109/59.867153.  Google Scholar

[13]

J. Krawczyk and J. Zuccollo, Nira-3: An improved Matlab package for finding Nash equilibria in infinite games,, Computational Economics, 5 (2006).   Google Scholar

[14]

K. Lee and R. Baldick, Tuning of discretization in bimatrix game approach to power system market analysis,, Power Engineering Review, 22 (2002).  doi: 10.1109/MPER.2002.4311811.  Google Scholar

[15]

M. V. Pereira, S. Granville, M. H. C. Fampa, R. Dix and L. A. Barroso, Strategic bidding under uncertainty: A binary expansion approach,, Power Systems, 20 (2005), 180.  doi: 10.1109/TPWRS.2004.840397.  Google Scholar

[16]

D. Pozo and J. Contreras, Finding multiple Nash equilibria in pool-based markets: A stochastic EPEC approach,, Power Systems, 26 (2011), 1744.  doi: 10.1109/TPWRS.2010.2098425.  Google Scholar

[17]

D. Pozo, J. Contreras, Á. Caballero and A. de Andrés, Long-term Nash equilibria in electricity markets,, Electric Power Systems Research, 81 (2011), 329.  doi: 10.1016/j.epsr.2010.09.008.  Google Scholar

[18]

J. Saraiva, J. P. da Silva and M. P. de Leão, Mercados de Electricidade - Regulaçcão de Tarifação de Uso das Redes,, FEUPedições, (2002).   Google Scholar

[19]

Y. S. Son and R. Baldick, Hybrid coevolutionary programming for Nash equilibrium search in games with local optima,, Evolutionary Computation, 8 (2004), 305.  doi: 10.1109/TEVC.2004.832862.  Google Scholar

[20]

A. Vaz and L. Vicente, A particle swarm pattern search method for bound constrained global optimization,, Journal of Global Optimization, 39 (2007), 197.  doi: 10.1007/s10898-007-9133-5.  Google Scholar

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