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AC losses in the conduction-cooled low temperature superconducting (LTS) pulse coil with stored energy of 1 MJ are estimated. The 1 MJ coil is a superconducting pulse coil for 1 MW, 1 sec UPS-SMES. UPS-SMES is an uninterruptible power supply (UPS) with superconducting magnetic energy storage (SMES) for protection of production lines of an industrial plant or large-scale experimental devices such as a fusion device, from a momentary voltage drop and an instant power failure. The winding conductor for the 1 MJ coil is a NbTi/Cu Rutherford cable, which is extruded with aluminum. The 1 MJ coil was wound by a new twist winding method. A 1 MJ coil was fabricated and cooling and excitation tests were carried out. In this paper, two methods to estimate ac losses in conduction-cooled LTS coils are proposed. One method estimates ac losses in the coil under steady-state conditions. The other method estimates ac losses in the coil under transient-state conditions. For estimation of ac losses in the 1 MJ coil, measurement of temperature in the coil during tests and thermal analysis using the two-dimensional finite element method are compared. These procedures clarified that the 1 MJ coil has low losses.