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The paper addresses rare issue in cable ampacity calculations, namely the presence of discontinuities along the routes. One which occurs in almost all cable installations is the presence of joints. In a standard cable rating analysis, the joints are ignored, mostly because of difficulties in building analytical models that represent the heat transfer phenomena within them. However, they can be a limiting part of the cable rating and, therefore, there is a need to model them correctly. This paper introduces an analytical algorithm for cable rating calculations in the presence of discontinuities with an emphasis on cable joints. New developments are illustrated by several numerical examples. [ABSTRACT FROM AUTHOR]

Energy markets are crucial for integrating Distributed Energy Resources (DER) into modern power grids. However, this integration presents challenges due to the inherent variability and decentralized nature of DERs, as well as poorly adapted regulatory environments. This paper proposes a medium-term decision-making approach based on a comprehensive suite of computational tools for integrating DERs into Colombian energy markets. The proposed framework consists of modular tools that are aligned with the operation of a Commercial Virtual Power Plant (CVPP). The tools aim to optimize participation in bilateral contracts and short-term energy markets. They use forecasting, uncertainty management, and decision-making modules to create an optimal portfolio of DER assets. The suite's effectiveness and applicability are demonstrated and analyzed through its implementation with heterogeneous DER assets across various operational scenarios. [ABSTRACT FROM AUTHOR]