Most of the electrical power systems of large industrial plants, i.e. oil, gas, and petrochemical industries usually incorporate local generation as a measure to ensure continuity in the electrical supply to the critical processes of the plant. In some cases the amount of local generation may be enough to feed the complete demand of the industrial facility and in others, its amount may be just enough to keep running the critical processes during a major event. In this paper the analysis of the dynamical performance of two industrial facilities interconnected with the transmission network. The power system of each facility has local generation enough to supply the complete demand of the facility and uses the interconnection with the transmission network either to sell the generation excess to the utility or as a backup during emergency conditions due to a shortage of local generation. Results indicate that the frequency stability problem is an important issue in the dynamics of the industrial power systems following the lost of the industrial-utility tie.