Methodological Approach for the Study and Representation of Complex Behaviors on Electricity Markets

Main Article Content

Johnny Valencia-Calvo http://orcid.org/0000-0003-1821-2039
Carlos Jaime Franco-Cardona http://orcid.org/0000-0002-7750-857X
Gerard Olivar-Tost http://orcid.org/0000-0003-1862-4842
Isaac Dyner

Keywords

Complex behavior, system dynamics, Poincare maps, dynamical systems, energy markets, methodology, modeling and simulation

Abstract

In the this paper, we show a methodological summary to simulate and understand the complex behavior of energy market models. The goal of this work is to propose the business approach of system dynamics, with the dynamical systems and its mathematical point of view. Additionally we present two ways to perform sensitivity analysis on models based on system dynamics. The first one is numerical sensitivity analysis, and the second one is using Poincaré maps. Finally, we conclude that there is complementarity between the mathematical framework and the business applications for the market. This will allow us to achieve greater exploitation for our models.

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References

[1] S. M. Londoño Hernandez and A. Lozano, “Revisión de herramientas aplicadas al modelamiento de mercados de electricidad,” Ingeniería e Investigación, vol. 29, no. 3, pp. 67–73, 2009. 196

[2] J. Aracil, “On the qualitative properties in system dynamics models,” European Journal of Economic and Social Systems, vol. 13, no. 1, pp. 1–18, 1999. [Online]. Available: http://dx.doi.org/10.1051/ejess:1999100 196, 197, 199, 200, 207

[3] J. D. Sterman, Business Dynamics, S. Isenberg, Ed. Massachusetts: Jeffrey J. Shelstad, 2000. 196, 199, 201, 209, 215

[4] N. Ghaffarzadegan and G. P. Richardson, “How small system dynamics models can help the public policy process,” System Dynamics Review, vol. 27, no. 1, pp. 22–44, 2011. [Online]. Available: http://dx.doi.org/10.1002/sdr.442 196

[5] D. C. Lane, “IFORS’ Operational Research Hall of Fame Jay Wright Forrester,” Intl. Trans. in Op. Res., vol. 13, pp. 483–492, 2006. 197

[6] D. C. Lane and J. D. Sterman, “Profiles in Operations Research : Jay Wright Forrester,” Springer, 2011. 197

[7] Y. A. Kuznetsov, S. Rinaldi, and A. Gragnani, “One-Parameter Bifurcations in Planar Filippov Systems,” International Journal of Bifurcation and Chaos, vol. 13, no. 08, pp. 2157–2188, 2003. [Online]. Available: http://dx.doi.org/10.1142/S0218127403007874 197

[8] A. Ford, J. Wright, and F. Prize, “System Dynamics and the Electric Power Industry,” System Dynamics Review, vol. 13, no. 1, pp. 57–85, 1997. [Online]. Available: goo.gl/xoCpQF 197

[9] J. Aracil and F. Gordillo, Dinámica de Sistemas. Madrid: Alianza Universidad de Textos, 1997. 197, 201

[10] J. M. Redondo, “Modelado de Mercados de Electricidad,” Tesis doctoral, Universidad Nacional de Colombia, 2012. [Online]. Available: http://www.bdigital.unal.edu.co/10220/ 197, 200

[11] J. Valencia, G. Olivar, C. J. Franco, and I. Dyner, “Non-Smooth Dynamics in a Model of Energy Market,” International Journal of Bifurcation and Chaos, vol. in press, p. 20, 2015. 197, 198, 207, 217

[12] J. Valencia, C. J. Franco, and G. Olivar, “Análisis cualitativo de un mercado de electricidad nacional basado en dinámica de sistemas,” in Encuentro Colombiano de Dinámica de Sistemas 2013, no. X, 2013, p. 9. 197, 198, 207

[13] M. Di Bernardo, E. Fossas, G. Olivar, and F. Vasca, “Secondary Bifurcations and High Periodic Orbits in Voltage Controlled Buck Converter,” International Journal of Bifurcation and Chaos, vol. 7, no. 12, pp. 2755–2771, 1997. [Online]. Available: http://dx.doi.org/10.1142/S0218127497001862 198, 210

[14] J. Valencia and G. Osorio, “Nonlinear numerical analysis of a cam-follower impacting system,” in 2011 IEEE Second Latin American Symposium on Circuits and Systems (LASCAS). IEEE, Feb. 2011, pp. 1–4. [Online]. Available: http://dx.doi.org/10.1109/LASCAS.2011.5750317 198, 211

[15] A. M. Foley, B. P. O Gallachoir, J. Hur, R. Baldick, and E. J. McKeogh, “A strategic review of electricity systems models,” Energy, vol. 35, no. 12, pp. 4522–4530, 2010. [Online]. Available: http://dx.doi.org/10.1016/j.energy.2010.03.057 198, 208

[16] J. D. Sterman, “Deterministic chaos in an experimental economic system,” Massachusetts Institute of Technology, vol. 1, no. 1, p. 51, 1988. 200, 215

[17] J. Aracil, Publicaciones de Ingeniería de Sistemas: Dinámica de sistemas, 4th ed. Madrid: Isdefe, 1995. 200

[18] I. Dyner, “Energy modelling platforms for policy and strategy support,” The Journal of the Operational Research Society, vol. 51, no. 2, pp. 136–144, 2000. [Online]. Available: http://www.jstor.org/stable/254253 204

[19] M. Castañeda, I. Dyner, and C. J. Franco, “The effects of decarbonisation policies on the electricity sector,” ieee latin america transactions, vol. 13, no. 5, pp. 1407–1413, 2015. [Online]. Available: http://dx.doi.org/10.1109/TLA.2015.7111996 204

[20] J. C. B. D. Figueiredo, “Caos determinístico em um modelo simplificado de cadeia produtiva,” Produção, vol. 23, no. 2, pp. 257–268, 2012. [Online]. Available: http://dx.doi.org/10.1590/S0103-65132012005000050 215

[21] Z. Liu, H. Yang, and M. Lai, “Electricity price forecasting model based on chaos theory,” 2005 International Power Engineering Conference, pp. 1–449, 2005. [Online]. Available: http://dx.doi.org/10.1109/IPEC.2005.206950 215

[22] D. Guégan, “Chaos in economics and finance,” Annual Reviews in Control, vol. 33, no. 1, pp. 89–93, 2009. [Online]. Available: http://dx.doi.org/10.1016/j.arcontrol.2009.01.002 216