Superconducting cable for power applications must have high stability against power system failures. The Nb₃Sn superconductor is expected to be used for AC power machines from this point of view. It is very important to estimate the AC loss and stability margin under practical conditions. We have developed an Nb₃Sn 400-kVA class AC coil composed of a six-stranded cable with a stainless steel center strand. The Nb₃Sn cable was made by the React and Wind method. In fabricating the coil, we have given careful consideration to the stress of the reacted Nb₃Sn. From the analysis of the results, the major component of AC loss was the coupling loss. The temperature margin was as high as 4.19K at the cable just before quenching. The reduced critical current due to the temperature rise was found to be consistent with the quench current. The Nb₃Sn coil was proven to have a temperature margin large enough to be robust against power system failures.