Harmonic elimination for multilevel converters with unequal DC levels by using the polynomial homotopy continuation algorithm

As there are no general methods to choose the initial values for the selective harmonic elimination (SHE) problem of multilevel converters with unequal DC levels, it is difficult to solve the switching angles from SHE equations by using the commonly used numerical and intelligent methods. Although the algebraic methods have no requirement on choosing initial values and can find all the solutions, the computation burden is extremely huge as the degrees of the equations are too high and cannot be reduced by the elementary symmetric polynomials as the equations are no longer symmetric due to the unequal DC levels. Aiming at this problem, this paper proposes a polynomial homotopy continuation (PHC) algorithm based method to solve the SHE equations with unequal DC levels. This method has the same properties as the algebraic methods that has no requirement on choosing initial values and all the possible solutions can be found. By using this method, the switching angles for a staircase modulated 7-level cascaded-H bridge (CHB) converter with unequal DC sources are solved in the full range of modulation index. Experiments verify the correctness and effectiveness of this method.