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A design approach is presented for achieving optimal flux-weakening operation in surface permanent-magnet (SPM) synchronous machines by properly designing the machine's stator windings using concentrated, fractional-slot stator windings. This technique makes it possible to significantly increase the machine inductance in order to achieve the critical condition for providing wide speed ranges of constant-power operation. The conditions for optimal flux weakening can be achieved while simultaneously delivering sinusoidal line-to-line back-electromotive-force waveforms and low cogging torque. A closed-form analytical model is described that can be used to design SPM machines to achieve optimal flux-weakening conditions. This technique is applied to design a 6-kW SPM machine that achieves constant-power operation over a wide speed range. Performance characteristics of this machine are compared using both closed-form and finite-element analysis.