This study proposes a dq-axis modelling of a Permanent Magnet Synchronous Motor (PMSM) with copper-loss and core-loss taken into account. The proposed models can be applied to PMSM control and drive with loss minimization in simultaneous consideration. The study presents simulation results of direct drive of a PMSM under no-load and loaded conditions using the proposed models with MATLAB codes. Comparisons of the results are made among those obtained from using PSIM and SIMULINK software packages. The comparison results indicate very good agreement.