Mathematical formulation of pulse amplitude modulation selective harmonic elimination in multilevel three phase inverters

In this paper multilevel cascaded H-bridges (CHB) three phase inverters with 2n dc sources, n=1,2,3,... are considered and a mathematical formulation providing both 2n switching angles and dc voltage source to eliminate n+1 harmonics and their respective multiple from their output voltage waveform, is proposed. The computed angles don't depend on modulation index and the source voltages linearly vary with it. The proposed procedure finds the solution through an analytical formula that avoids to solve transcendental systems and presents very low computational cost. A lot of low order harmonics are eliminated, returning a very low total harmonic distortion (THD). Particularly for 9-level configuration, the first not mitigated harmonic is the 17th and the percentage THD is 5.59%.