Considering both self-heating of the normal zones propagating in coils wound with large-capacity superconductors and power consumption by external resistors, we have analyzed the temperature-rises in the coils and deduced new analytical formulas by introducing effective decay time constants and by considering energy-balancing in the system. Calculations by using this formula and computer simulations were conducted for small-scaled SMES coils wound with 20kA superconducting cable conductor and comparison was made between these results. It was found that our formula gave a temperature-rise higher by about twenty percents than the computer simulation result, while Wilson's formula gave a temperature-rise much higher than ours and of too safety side. It has been demonstrated that the formula is physically more reasonable and practical than Wilson's. However, the formula is more limited than computer simulations in taking-in of rigorous temperature-dependence of various properties and in dealing with complicated propagations of normal zones, so computer simulations are desirable for us to get more real temperature-rises to be expected in the coils.
