Recently a few MJ superconducting magnetic energy storage ($mu$ SMES) devices become commerci-ally available as one of the energy storage devices for uniterruptible power supply (UPS) systems. For such a ($mu$ SMES) devics, a few kA class superconducting cables with high current density, high stability and excellent pulse characteristics are required. To acquire data for the superconduction cables related to design and fabrication of a 0.7 MJ $mu$ SMES device, we tested critical currents and quench characteristics for several winding tensions and various remping rates especially. It is shown from the results that winding tensions have much influence on quench currents of the $mu$ SMES devices.