The operation of the Large Hadron Collider calls for a thorough analysis of the thermo-electric behavior of the 13 kA superconducting bus-bars connecting its dipole and quadrupole main magnets. This presentation reports a synthesis of the work performed jointly by researchers and students at CERN and at the University of Bologna as a contribution to the understanding of the LHC incident occurred on September 19th 2008. This work is complementary to the analyses carried out at CERN by the MPE group. The aim of the work is to analyze the stability of the interconnections as far as the quality of manufacturing, operating conditions and protection system parameters are concerned. A first part of the work is devoted to the development of a numerical model suitable for the analysis of the faulty interconnections. The main type of defect analyzed is the lack of solder among the superconducting cable and the copper stabilizer components at the interface between bus bar and splice. The evaluation of the critical defect length limiting the maximum safe current for powering the magnets without risk of thermal runaway is provided, as a function of the RRR of cable and stabilizer, decay time constant of the LHC circuit, spatial distribution of the defect and cooling conditions. A second part of the work is related to the modeling of the heat transfer mechanism between the main superconducting bus bar and the surrounding helium bath. This study is aimed to analyze a set of experimental measurements on the heat transfer coefficient of the main bending dipole bus bars performed at CERN. The final part of the work consists in a preliminary analysis of the heat transfer mechanisms involved in the stability experiments of defective interconnections performed in the FRESCA facility.