The Ld of a negative-salient permanent magnet synchronous motor (NSPMSM) is greater than Lq. When a NSPMSM is operating at or below the rated speed, the id is flux-intensifying current, which can improve the flux density of permanent magnets (PM). First, a NSPMSM is proposed and compared with a positive-salient permanent magnet synchronous motor (PSPMSM). The d-axis and q-axis equivalent magnet circuits of the NSPMSM are then established. According to the limitation of the equivalent magnet circuit, the PM dimensions formula and optimization of the finite element method (FEM), PM dimensions are determined, and the constant power speed ranges of the two motors are calculated. Second, the influence of the saliency ratio on the internal power factor angle and the average flux density of PM at different internal power factor angles are calculated. Third, the flux density of PM in two motors are calculated when the windings are short-circuited. Finally, the bypass function of the NSPMSM magnetic bridges during the flux-weakening state is analyzed. The results show that the flux-weakening magneto motive force (MMF) of the NSPMSM is smaller at high speed, the short-circuit current (SCC) is smaller when the windings are short-circuited, and the magnetic bridges protect the PM in the flux-weakening state, so the flux density of PM is larger.