Formulación del problema de flujos de potencia considerando dependencia de temperatura en líneas de transmisión

Abstract

In this thesis, a fully coupled temperature-dependent power flow (FC-TDPF) algorithm is developed, aimed at improving the estimation of losses in electric power systems. Unlike the conventional power flow approach, which assumes a constant electric resistance value in transmission lines, the proposed model considers a resistance’s variation as a function of conductor temperature, which depends on the electric current, Joule effect losses, and climatic conditions. The methodology integrates a thermal model coupled to the electrical model in a unified framework of analysis. The resulting integrated model is solved using the Newton-Raphson method by incorporating additional partial derivatives into the Jacobian matrix to capture the system’s sensitivity to thermal variations. Furthermore, real physical effects influencing temperature, such as convection, thermal radiation, and solar heat gain, are included in accordance with IEEE Std 738™-2012. The algorithm was implemented in MATLAB® and it was validated using the IEEE 30- bus system, the New England 39-bus system, IEEE 57-bus system and a large-scale real-world case of the Polish 2736-bus system. Results show increases in line’s resistance and variations in active power losses, confirming the relevance of thermal analysis, especially in heavily loaded lines or under extreme climatic conditions. This research provides useful tools for the planning and operation of modern power networks, including comparative tables, graphs of loss differences, and identification of critical lines with significant thermal impact.

In this thesis, a fully coupled temperature-dependent power flow (FC-TDPF) algorithm is developed, aimed at improving the estimation of losses in electric power systems. Unlike the conventional power flow approach, which assumes a constant electric resistance value in transmission lines, the proposed model considers a resistance’s variation as a function of conductor temperature, which depends on the electric current, Joule effect losses, and climatic conditions. The methodology integrates a thermal model coupled to the electrical model in a unified framework of analysis. The resulting integrated model is solved using the Newton-Raphson method by incorporating additional partial derivatives into the Jacobian matrix to capture the system’s sensitivity to thermal variations. Furthermore, real physical effects influencing temperature, such as convection, thermal radiation, and solar heat gain, are included in accordance with IEEE Std 738™-2012. The algorithm was implemented in MATLAB® and it was validated using the IEEE 30- bus system, the New England 39-bus system, IEEE 57-bus system and a large-scale real-world case of the Polish 2736-bus system. Results show increases in line’s resistance and variations in active power losses, confirming the relevance of thermal analysis, especially in heavily loaded lines or under extreme climatic conditions. This research provides useful tools for the planning and operation of modern power networks, including comparative tables, graphs of loss differences, and identification of critical lines with significant thermal impact.