Abstract: In this research project a permanent magnet synchronous machine is simulated using the developed mathematical models. In the synchronous motor model we have simulated its operation under a variable load. Its apparent power is 6.2 kva and its maximum speed is 30000 tr mn 1, its power supply was 500 V. The synchronous motor has four poles and permanent magnets with Br =0.82T. The rotor mean radius is 39.5 mm with an active length of 50 mm.Two different methods have been used: In the first approach the unknown variables are vector potential nodal values and mesh currents. In the second approach only the potential vector is kept as an unknown variable and expressing the electrical values in function of the same vector.