This study presents a new non-linear passivity-based controller for a wound-rotor synchronous machine, acting as a motor drive. The control objectives are stated in the dq-frame, and the port-controlled Hamiltonian model is also obtained. A power flow analysis allows to state the control goals in terms of ohmic losses reduction, and motivates the use of the field current for the reactive power compensation. From the Hamiltonian structure, the simultaneous interconnection and damping assignment technique is used to compute the control action, which results in a controller with a simpler architecture than the standard one for this class of machines, able to cope with both positive and negative external mechanical loads and having thus bidirectional power capabilities. The robustness of the control action is also taken into account in the design procedure. Finally, the computed controller is validated via numerical simulations.