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

Johnny Valencia-Calvo, Carlos Jaime Franco-Cardona, Gerard Olivar-Tost, Isaac Dyner


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.


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


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

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: 196, 197, 199, 200, 207

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

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: 196

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

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

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: 197

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: 197

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

J. M. Redondo, “Modelado de Mercados de Electricidad,” Tesis doctoral, Universidad Nacional de Colombia, 2012. [Online]. Available: 197, 200

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

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

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: 198, 210

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: 198, 211

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: 198, 208

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

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

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: 204

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: 204

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: 215

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: 215

D. Guégan, “Chaos in economics and finance,” Annual Reviews in Control, vol. 33, no. 1, pp. 89–93, 2009. [Online]. Available: 216



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Ingeniería y Ciencia 
ISSN: 1794-9165 
EISSN: 2256-4314