Optimizing pulse patterns with bernoulli polynomials

A method for controlling an electrical converter, the electrical converter converting an input voltage (vin) into a multi-level output voltage (vout), the method comprising:

• determining an optimized pulse pattern (u(x));
• determining switching states from the optimized pulse pattern (u(x));
• and
• applying the switching states to semiconductor switches of the electrical converter, such that the multi-level output voltage (vout) is generated,
• wherein the optimized pulse pattern (u(x)) comprises a plurality of switching transitions (Δu), each switching transition (Δui) encoding a transition between two different levels of the multi-level output voltage (vout), at a switching angle (xi),
• wherein the optimized pulse pattern (u(x)) is determined by optimizing a cost function,
• wherein the cost function J(x)=ΔuTA(x)Δu is a cost matrix A(x), which is multiplied from both sides with a vector Δu composed of the plurality of switching transitions (Δui), and
• wherein each entry of the cost matrix A(x) depends on fourth order Bernoulli polynomials into which the switching angles (xj) are input.