The permanent magnet synchronous machine is a rotating electrical machine with a classic 3-phase stator like that of an induction machine, but rotor is different and has surface-mounted permanent magnet. The performance of permanent magnet synchronous machine has improved rapidly by the progress in electromagnetic material technology. Now permanent magnet synchronous machine is widely used because it has many advantages such as robustness against the enviroment, high efficiency, light weight and small size. Because of advantages above, especially those featuring high efficiency, permanent magnet synchronous machine is frequently used in industry and is a key equipment in renewable energy applications. In this paper mathematical model of permanent magnet synchronous machine is shown, methods for parameter measurements and the concept of vector control are described. At the end a simulation model of permanent magnet synchronous machine made in Matlab/Simulink program is given.