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This article describes the shape optimization of detective coils for initial rotor position estimation in the drive system of permanent magnet synchronous motors. The characteristics of magnetic circuits in rotating machinery are very complicated. The magnetic flux distribution in the air gap is nonsinusoidal due to the influence of slots, magnets, and magnetic saturation, etc. By utilizing the slot ripple influence and taking the effects of both magnetic saturation and permanent magnets into consideration, an optimization of the detective coil by means of a genetic algorithm combined with a hybrid finite element and boundary element method is reported. This produces a global optimal solution in a shorter time. © 1998 American Institute of Physics.