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Compact and lightweight direct-drive generators in large rating are desired for offshore wind farm applications. A key goal for such generators is that they be manufactured and tested in a factory and shipped to the site as fully assembled units. A possible approach to achieving this goal is to construct both rotor and stator windings with high-temperature superconducting (HTS) materials. The magnesium diboride (MgB2) superconductor wire currently becoming available with properties suitable for application in large rotating machines appears to be the most cost-effective option for such machines. This paper presents a design concept for a 10-MW 10-r/min generator using MgB2 wire for both rotor and stator coils. The concept design includes ambient-temperature magnetic iron on both the rotor and the stator. The field winding on the rotor employs race-track-shaped excitation coils operating at 20 K. The armature winding on the stator also uses race track coils operating at 20 K. All coils employ round cables build with commercially available MgB2 wire. Coils are cooled with available off-the-shelf cryocoolers. The concept the 10-MW generator is expected to be less than 5 m in diameter, less than 2 m in axial length, weigh around 52 000 kg, and cost about $3.2 million (including the cost of power electronics).