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Superconducting devices operating within a power system are expected to go through transient overload conditions during which the superconducting coil has to carry currents above the rated values. Designing the coil to remain superconducting through any possible fault scenario can be cost prohibitive, necessitating operation beyond the critical current for short periods. In order to set operating limits and design adequate protection systems for superconducting devices connected to a power system, the region of safe operation of these devices has to be described with general capability curves. Existing standards that define limits for these over-current situations are based on copper winding experience that do not apply to devices with superconducting components because of the highly nonlinear interaction between magnetic fields, operating temperature, and current density in the superconductor, and the rapidly varying material properties at cryogenic temperatures. In this paper, the behavior of superconducting coils during over-currents is discussed and a simplified capability curve is described to help standardize device capabilities. These curves are necessary to aid power system designers in appropriately designing the system and associated protection systems.