Due to the large torque density of magnetic gears (MGs), magnetic-geared permanent magnet machines (MGPMs) have become promising competitors in the family of direct-drive machines. The MGPM with sandwiched armature stator (MGPM-SAS) is a new deployment type of armature windings. Our investigation finds out that the MGPM-SAS has parallel power flow path in it. According to the power flow path, we simplify the model into coupling of a synchronous machine and a harmonic machine, develop the mathematical model of MGPM-SAS, and establish its simulation model based on traditional space vector pulse width modulation vector control (SVPWM-VC). The results verify that the mathematical model and controllability of MGPM-SAS are feasible.