Reduction of the manufacturing costs is one of the major concerns in the automotive industries. Removing the current sensors on the electric powertrain is a way to achieve this. In this paper, the current sensors of a stator of a wound rotor synchronous machine have been removed. In order to keep the control of the electric powertrain, the solution proposed here is to estimate the missing currents. To do so, a nonlinear observer based on the convergence of a Lyapunov candidate function has been developed for this application and compared to an extended Kalman filter. Since the parameters of the system may vary according to the operating point and the wear of the system, the robustness of the observers are tested with and without model errors and then validated on an experimental bench with a successful current sensorless control.