Using linear programming models for minimizing harmonics values in cascaded multilevel inverters

Linear programming models are formulated and solved to determine the switching angles that optimally minimize the values of the undesired harmonics in cascaded multilevel inverters with staircase output voltage waveform. Three cases are discussed. Case 1 assumes fixed equal values of the input dc voltages. A mixed integer linear programming (MILP) model is applied. In case 2 this model is modified to be applied for controllable equal values of the input dc voltages. In case 3 controllable different values of the input dc voltages are assumed. In this case a linear programming model is formulated, that further minimize the values of the undesired harmonics. The proposed models for these cases are solved to minimize the values of the non-tripled odd harmonics from the 5th till the 31st for 5-level and 7-level cascaded multilevel inverters and the obtained percentage values of these harmonics relative to the main harmonic are less than 4.8% and 1.7% respectively in case 2, and less than 4.8% and 1% respectively in case 3. Other inverter levels are also investigated in cases 2 and 3.