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Non-Smooth Dynamics in Energy Market Models: A Complex Approximation from System Dynamics and Dynamical Systems Approach

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Author
Valencia-Calvo J.
Olivar-Tost G.
Morcillo-Bastidas J.D.
Franco-Cardona C.J.
Dyner I.
TY - GEN T1 - Non-Smooth Dynamics in Energy Market Models: A Complex Approximation from System Dynamics and Dynamical Systems Approach AU - Valencia-Calvo J. AU - Olivar-Tost G. AU - Morcillo-Bastidas J.D. AU - Franco-Cardona C.J. AU - Dyner I. UR - http://hdl.handle.net/11407/5985 PB - Institute of Electrical and Electronics Engineers Inc. AB - This paper reports a general model that describes the supply and demand of electricity in a national market based on the system dynamics (SD) approach. From the resulting SD model, it derives piecewise smooth (non-smooth) differential equations from the nonlinear functions and feedback cycles of the corresponding stock-flow structure. Subsequently, the stability of the equilibrium points and non-smooth dynamics of the SD model are investigated using the dynamical systems theory. Filippov systems are found in the proposed SD model and non-smooth vector fields associated with generators investment decisions are accumulated. Under this combining methodology, the non-smooth dynamics of energy markets that are governed by the supply and demand laws are uncovered mathematically and deeply described. In fact, we extend our investigation results to any energy market model attached to various investment decisions, confirming the generalizability of our research. © 2013 IEEE. ER - @misc{11407_5985, author = {Valencia-Calvo J. and Olivar-Tost G. and Morcillo-Bastidas J.D. and Franco-Cardona C.J. and Dyner I.}, title = {Non-Smooth Dynamics in Energy Market Models: A Complex Approximation from System Dynamics and Dynamical Systems Approach}, year = {}, abstract = {This paper reports a general model that describes the supply and demand of electricity in a national market based on the system dynamics (SD) approach. From the resulting SD model, it derives piecewise smooth (non-smooth) differential equations from the nonlinear functions and feedback cycles of the corresponding stock-flow structure. Subsequently, the stability of the equilibrium points and non-smooth dynamics of the SD model are investigated using the dynamical systems theory. Filippov systems are found in the proposed SD model and non-smooth vector fields associated with generators investment decisions are accumulated. Under this combining methodology, the non-smooth dynamics of energy markets that are governed by the supply and demand laws are uncovered mathematically and deeply described. In fact, we extend our investigation results to any energy market model attached to various investment decisions, confirming the generalizability of our research. © 2013 IEEE.}, url = {http://hdl.handle.net/11407/5985} }RT Generic T1 Non-Smooth Dynamics in Energy Market Models: A Complex Approximation from System Dynamics and Dynamical Systems Approach A1 Valencia-Calvo J. A1 Olivar-Tost G. A1 Morcillo-Bastidas J.D. A1 Franco-Cardona C.J. A1 Dyner I. LK http://hdl.handle.net/11407/5985 PB Institute of Electrical and Electronics Engineers Inc. AB This paper reports a general model that describes the supply and demand of electricity in a national market based on the system dynamics (SD) approach. From the resulting SD model, it derives piecewise smooth (non-smooth) differential equations from the nonlinear functions and feedback cycles of the corresponding stock-flow structure. Subsequently, the stability of the equilibrium points and non-smooth dynamics of the SD model are investigated using the dynamical systems theory. Filippov systems are found in the proposed SD model and non-smooth vector fields associated with generators investment decisions are accumulated. Under this combining methodology, the non-smooth dynamics of energy markets that are governed by the supply and demand laws are uncovered mathematically and deeply described. In fact, we extend our investigation results to any energy market model attached to various investment decisions, confirming the generalizability of our research. © 2013 IEEE. OL Spanish (121)
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Abstract
This paper reports a general model that describes the supply and demand of electricity in a national market based on the system dynamics (SD) approach. From the resulting SD model, it derives piecewise smooth (non-smooth) differential equations from the nonlinear functions and feedback cycles of the corresponding stock-flow structure. Subsequently, the stability of the equilibrium points and non-smooth dynamics of the SD model are investigated using the dynamical systems theory. Filippov systems are found in the proposed SD model and non-smooth vector fields associated with generators investment decisions are accumulated. Under this combining methodology, the non-smooth dynamics of energy markets that are governed by the supply and demand laws are uncovered mathematically and deeply described. In fact, we extend our investigation results to any energy market model attached to various investment decisions, confirming the generalizability of our research. © 2013 IEEE.
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http://hdl.handle.net/11407/5985
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