Abstract
In the following chapter, we present a model for the supply and demand of electricity in a domestic market based on system dynamics. Additionally, the model shows piecewise smooth differential equations arising from the diagram of flows and levels, using dynamical systems theory for the study of stability of the equilibrium points that have such a system. We also present simulations, nonlinear numerical analysis, and qualitative analysis to the system of differential equations obtained, which is characterized by dynamics not smooth, due to the way decisions are made in that market. Using the software package Vensim and event-based scheme implementation in Matlab are verified as different saturation phenomena, oscillations, fixed points, among others, and the relationship between leverage points and stability of equilibrium points. Finally, we conclude the effects of climate seasonality in the market. Furthermore, we show that the system becomes periodically forced due to the external variable.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alzate, R., Bernardo, M., Giordano, G., Rea, G., Santini, S.: Experimental and numerical investigation of coexistence novel bifurcations and chaos in a cam-follower systems. SIAM J. Appl. Dyn. Syst. 8(2), 592–623 (2009)
Angulo, F., Olivar, G., Osorio, G., Escobar, C., Ferreira, J., Redondo, J.: Bifurcation in non-smooth systems. Nonlinear Sci. Numer. Simul. 16, 1783–1786 (2011)
Aracil, J.: On the qualitative properties in system dynamics models. Eur. J. Econ. Soc. Syst. 13(1), 1–18 (1999)
Aracil, J., Toro, M.: Métodos Cualitativos en dinámica de sistemas. Secretariado de publicaciones de la Universidad de Sevilla. Editorial Kronos s.a. Sevilla. España. (1993)
Bernardo, M., Budd, C., Champneys, A.R., Kowalczyk, P.: Piecewise-smooth dynamical systems: Theory and applications, vol. 163. Springer, London (2008)
Bernardo, M., Nordmarkc, A., Olivard, G.. Discontinuity-induced bifurcations of equilibria in piecewise-smooth and impacting dynamical systems. Physica D. 237(1), 119–136 (2008)
Budd, F., Piiroinen, P.: Corner bifurcations in non-smoothly forced impact oscillators. Physica D Nonlinear Phenom. 220, 127–145 (2006)
Colombo, A., Bernardo, M., Hogan, S.J., Jeffrey, M.R.: Bifurcations of piecewise smooth flows: Perspectives, methodologies and open problems. Physica D. 271, 32–47 (2011)
Ford, A., Wright, J., Prize, F.. System dynamics and the electric power industry. 13(1), 57–85 (1997)
Forrester, J.W.: IFORS’ Operational Research Hall of Fame Jay Wright Forrester. Int. Trans. Oper. Res. 13, 483–492 (2006)
Forrester, J.W.: System dynamics. 23(2), 359–370 (2007)
Ghaffarzadegan, N., Lyneisb, J., Richardsona, J.: How small system dynamics models can help the public policy process. Syst. Dyn. Rev. 27, 22–44 (2011)
Koster, M.: Vibrations of cam mechanisms. Phillips technical library series. Macmillan, London (1974)
Kustetsov, Y.: Elements of applied bifurcation theory. Applied Mathematic Sciences, vol. 112, 3rd edn. Springer, New York (2010)
Lane, D.C., Sterman, J.D., Forrester, J.W.: Profiles in Operations Research: Jay Wright Forrester. Springer (2011)
Londoño, S., Lozano, C.: Revisión de herramientas aplicadas al modelamiento de mercados de electricidad. Rev. Ing. Investig. 3, 67–73 (2009)
Norton, R.: Cam Design and Manufacturing Handbook. Industrial Press Inc., New York (2002)
Quintero, M., Isaza, F.: Dependencia hidrológica y regulatoria en la formación de precio de la energía en un ssistema hidrodominado: Caso sistema eléctrico colombiano. Rev. Ing. Univ. Medellín 12(22), 85–96 (2013) (ISSN 1692-3324)
Redondo, J.: Modelo de oferta y demanda de un mercado nacional de electricidad. Encuentro Colombiano de Dinámica de Sistemas Eudii. En Su Vigésimo Tercera Versión. Problematicos Complejas (2012)
Sterman, J.D.: Business Dynamics: Systems Thinking and Modeling for a Complex World. McGraw Hill, Boston (2000)
Valencia, J., Osorio, G.: Nonlinear numerical analysis of camfollower impacting systems. In: LASCAS2011 - Latin American Symposium on Circuits and Systems (2011)
Acknowledgment
The authors thank the National University of Colombia and Colciencias for the economic support in this research.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Valencia, J., Olivar, G., Franco, C., Dyner, I. (2015). Qualitative Analysis of Climate Seasonality Effects in a Model of National Electricity Market. In: Tost, G., Vasilieva, O. (eds) Analysis, Modelling, Optimization, and Numerical Techniques. Springer Proceedings in Mathematics & Statistics, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-12583-1_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-12583-1_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12582-4
Online ISBN: 978-3-319-12583-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)