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This paper describes an analytical technique for prediction of open circuit eddy-current loss in armature windings and permanent magnets (PM) of series double excitation synchronous machines. First, a 2-D exact analytical solution of open circuit magnetic field distribution in idealized geometry of series double excitation synchronous machine is established. It involves solving Maxwell's equations in stator slots, air gap, PM region, and rotor slots. Then, magnetic vector potential solutions in the stator slots and PM regions are respectively used for prediction of resistance limited eddy currents in armature windings and permanent magnets. This analytical model is then used to estimate eddy-current loss in armature windings and permanent magnets. The validity of the developed model, which is also applicable to conventional designs of permanent-magnet machine, is verified by time-stepped transient finite-element analysis (FEA). The developed model is then used to quantify the effectiveness of segmenting the magnets and armature windings in reducing the eddy-current loss.