On applying a minimization technique to the harmonic elimination PWM control: the bipolar waveform

The well-known harmonic elimination pulse-width modulation (HE-PWM) method for inverter control is revisited. The HE-PWM waveform presents many challenges. It has multiple solutions that not only need to be found as easily and as fast as possible, but must also be evaluated in order to identify the best technique when overall harmonic performance is concerned. Algorithms presented so far rely on starting values that are close to the exact solutions to ensure convergence. A new method based on resultant theory promises limited success since it can only work when a small number of harmonics is to be eliminated. In this paper, it is shown that a minimization technique in combination with a random search results in a relatively simple approach that finds all possible sets of solutions. It is confirmed that numerous independent sets of solutions exist and the ones that offer better harmonic performance are identified. Three cases are reported in detail, including when two, four and six nontriplen odd harmonics are to be eliminated.