Permanent magnet synchronous machine and a compressor using the same

PROBLEM TO BE SOLVED: To allow for enhancement of torque and efficiency, even if the use of reluctance torque is difficult.SOLUTION: A permanent magnet synchronous machine includes a stator 9 having a plurality of teeth 11 and stator coils 12, and a rotor 1 arranged for the stator via a gap in the radial direction and forming magnet housing holes 4, where a plurality of permanent magnets inserted into the magnet housing holes are arranged in the circumferential direction. In the permanent magnet synchronous machine, the interlinkage flux Ψp (Wb) of one phase of the stator coil by the permanent magnets, the direct axis inductance Ld (H) and horizontal axis reluctance Lq (H) when conducting a current effective value Irms (Arms) to the stator coil, and the current effective value Irms (Arms) satisfy a relation Irms<0.293×(√2×Ψp)/(Lq-Ld) and, at the same time, the stator interlinkage flux Ψ (Wb) and the Ψp satisfy a relation Ψ/Ψp<1.