A matrix converter system having a current control mode operation comprising: a matrix converter having a switching matrix coupled between a low voltage side and a high voltage side, wherein the matrix converter is coupled at its low voltage side to a generator for receiving an input power including an input current and transforming the input power into an output power at its high voltage side, wherein a load is coupled to the high voltage side; a load observer configured to estimate a load current that flows to the load from the high voltage side of the matrix converter as a function of a switching state of the switching matrix, an output voltage output at the high voltage side of the matrix converter, and the input current; and a model predictive controller, MPC, configured to select the switching state of the switching matrix to meet one or more control objectives defined by minimization of a multi-objective function that tracks the output voltage and the input current using the estimated load current; wherein the load observer is further configured to determine the output current as a function of a transpose of the switching function and the input current, and to determine an estimated output voltage as the integration of a difference between the output current and the estimated load current; and preferably wherein determining the estimated load current by the load observer further includes applying a correction factor to a difference between the estimated output voltage and the output voltage; and wherein the matrix converter system further includes a reactive current generator that is configured to generate a reactive current reference as a function of the estimated output voltage and back electromotive frequency, EMF, of the controllable generator, wherein the reactive current reference is used to determine an input current reference that is provided to the MPC and used to avoid saturation of the matrix converter. a matrix converter having a switching matrix coupled between a low voltage side and a high voltage side, wherein the matrix converter is coupled at its low voltage side to a generator for receiving an input power including an input current and transforming the input power into an output power at its high voltage side, wherein a load is coupled to the high voltage side; a load observer configured to estimate a load current that flows to the load from the high voltage side of the matrix converter as a function of a switching state of the switching matrix, an output voltage output at the high voltage side of the matrix converter, and the input current; and a model predictive controller, MPC, configured to select the switching state of the switching matrix to meet one or more control objectives defined by minimization of a multi-objective function that tracks the output voltage and the input current using the estimated load current; wherein the load observer is further configured to determine the output current as a function of a transpose of the switching function and the input current, and to determine an estimated output voltage as the integration of a difference between the output current and the estimated load current; and preferably wherein determining the estimated load current by the load observer further includes applying a correction factor to a difference between the estimated output voltage and the output voltage; and wherein the matrix converter system further includes a reactive current generator that is configured to generate a reactive current reference as a function of the estimated output voltage and back electromotive frequency, EMF, of the controllable generator, wherein the reactive current reference is used to determine an input current reference that is provided to the MPC and used to avoid saturation of the matrix converter.