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Interior permanent magnet (IPM) synchronous machines are vulnerable to generating unacceptably large stator iron losses during flux-weakening operation at elevated speeds. The purpose of this paper is to present a new analytical design approach to reduce the stator iron losses in IPM machines with multiple flux barriers during flux-weakening operation. The proposed technique achieves this objective by: (1) designing the rotor to minimize the total harmonic distortion (THD) of the spatial distribution of the rotor scalar magnetic potential (mmf); and (2) coupling the rotor with an appropriate stator configuration to suppress undesirable higher-order harmonics in the stator as much as possible. An analytical design method is presented to synthesize the "minimum-THD" rotor with multiple flux barriers. Finite element analysis is used to demonstrate that the application of this design technique can lead to a substantial reduction of the stator iron losses during flux-weakening operation.