This paper presents an analytical approach of eddy-current loss in a high temperature superconducting magnetic energy storage coil based on finite-element algorithm and numerical circuit analyses. A solenoidal coil with step-shaped cross-sectional shape is introduced to reduce the total eddy-current loss of the whole coil by diminishing the eddycurrent losses located at two coil ends. Two coil-current-dependent formulas are derived to estimate the eddy-current loss, e.g., 294 J for a 1.2 H/880 A Bi-2223 solenoidal coil in a 1000 V/500 kW constant-power energy discharge process and then the uncontrolled energy discharge process.Index Terms-Controlled energy discharge, eddy-current loss, magnetic field, superconducting coil, superconducting magnetic energy storage (SMES).
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