Heating development analysis in long HTS objects with cooling

The numerical experiment to model heating development in long HTS object has been performed by use of the specially developed computer code. Cooling by liquid nitrogen was taken into account and parameters close to the real ones for HTS tapes were used in calculations. It was shown that depending on parameters' combination, particularly on current density, stable and unstable regimes can happen. At unstable regime the fast temperature runaway is combined with the strong heat localization. The safety current density levels were determined for two model tapes. The results are important for HTS power cables that should withstand large overload currents during some time in case of faults in a grid.