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A novel axial-axial flux compound-structure permanent-magnet synchronous machine (CS-PMSM), which is a hybrid electric vehicle (HEV) power train concept, is integrated by two axial flux disk machines. As the two machines share a common rotor [a magnet rotor with permanent magnets (PMs) on both sides], there may be magnetic coupling between them. Three-dimensional (3D) finite-element method (FEM) calculation shows that the two machines have little magnetic coupling if they have the same pole number and consistent magnetization direction of the two layers of PMs on the common rotor. The performance of the CS-PMSM is evaluated on criteria such as power, power per unit volume and mass, torque, and torque ripple. The power and torque equations of this type of machine are deduced and verified with 3D FEM. After the optimization of diameter ratio and pole number, the power and power per unit active volume and mass are high. The torque ripple is much reduced due to the optimization of the pole arc embrace and magnet skewing angle.