Model predictive control with reference tracking

1. An electrical system, comprising:

an electrical converter comprising a plurality of semiconductor switches, wherein the electrical converter is adapted for generating a two-level or multi-level output voltage from an input voltage by switching the plurality of semiconductor switches, and a controller;

wherein the controller executes a method for controlling the electrical converter comprising:

receiving a reference electrical quantity (i s *) and an actual electrical quantity (i s ), the reference electrical quantity being determined from measured currents, voltages, torques, and/or speeds;

determining a sequence of future electrical quantities of the electrical converter from the actual electrical quantity;

determining a maximal cost value based on the sequence of future electrical quantities;

iteratively determining an optimal switching sequence for the electrical converter, wherein a switching sequence includes a sequence of future switching states for the semiconductor switches of the electrical converter; and

selecting the first switching state of the optimal switching sequence as a next switching state (u) to be applied to the semiconductor switches of the electrical converter,

wherein the optimal switching sequence is iteratively determined by:

extending a switching sequence by appending a possible switching state to the switching sequence;

determining a cost value for the extended switching sequence with a cost function based on the sequence of future electrical quantities, the cost function being based on a norm of a matrix equation with a triangular matrix, which is multiplied with the extended switching sequence, and the cost function is based on a difference between an unconstrained solution and the triangular matrix multiplied with the extended switching sequence, the unconstrained solution being determined from the future electrical quantities before iteratively determining an optimal switching sequence; and

discarding the extended switching sequence, when the cost value is higher than the maximal cost value; and

an electrical load supplied by the electrical converter.

2. The method of claim 1 , wherein the triangular matrix is computed offline and depending only on the topology of the electrical converter.

3. The method of claim 1 , wherein the maximal cost value is determined with the cost function applied to a guessed switching sequence based on an optimal switching sequence determined at a previous time step.

4. The method of claim 1 , wherein, for extending a switching sequence, only switching states are appended that result in extended switching sequences in which a phase voltage is switched only by one step up or down.

5. The method of claim 1 , wherein: the iteration is executed at each time step; the sequence of future electrical quantities starts at an actual time step and is determined up to a horizon of time steps; and the sequence of future switching states starts at the actual time step and is determined up to the horizon of time steps.

6. The method of claim 1 , wherein the reference and/or actual electrical quantity includes at least one of reference and/or actual current, a reference and/or actual flux, a reference and/or an actual voltage, a reference and/or an actual torque, a reference and/or an actual power, and a reference and/or actual speed.

7. The method of claim 1 , wherein a future electrical quantity includes at least one of a future current, a future voltage, and a future flux of an electrical machine, a filter, transformer, load, grid and/or a cable connected to the electrical converter.