The paper focuses on the problem of rotor position estimation for the nonsalient permanent magnet synchronous motor (PMSM) that is used as a generator in a windmill system. The paper presents the design and analysis of a Full Order EMF observer that is based on the PMSM model in the stationary reference frame. The inputs in the observer are the motor voltages and currents (which are measured) and the motor speed. The convergence of the observer is first analyzed assuming that the speed signal is available - it is shown how to design the feedback gains such that the observer is asymptotically stable. Second, the observer is analyzed under the assumption that the speed signal used is different from the real speed. This corresponds to the situation when a speed estimate would be used (instead of the real speed) in an attempt to obtain a sensorless observer. The PMSM is treated as a linear, time-varying system and the observer presented is analyzed using Lyapunov's stability theory. It is shown that, under correct speed, the observer converges. Under improper speed signal, the estimates have errors and the design gains do not influence these errors and cannot eliminate them. However, since the errors are relatively small, the method could be used in a sensorless drive if the estimated rotor position is corrected with a correction block. The theoretical findings are validated by simulations.