An Improved Problem Formulation for THD Minimization of Multilevel Inverters

Multilevel inverters (MLIs) generate a staircase sine wave. Switching angles at which the staircase output steps up/down determine modulation index (MI) and total harmonic distortion (THD). Hence, the optimal switching angles are of great interest that ensures a specific MI while minimizing THD. Several methods in the literature use weighted bi-objective optimization where two parts of the objective function consider MI and THD. This approach is affected by heuristically assigned weights to the parts of the objective function. The issue can be circumvented by imposing a predefined limit on MI error. However, the MI error is still nonzero that leads to sub-optimal results. In this work, the problem of finding the optimal switching angles is formulated as minimization of THD subjected to the constraint of ensuring a specific value of MI. A symmetric staircase sine wave having \(2k+1\) levels is described by k switching angles. Hence, the previous works consider the objective function in k dimensional space. However, this work considers THD minimization with \(k-1\) switching angles while the kth switching angle is calculated for the true value of desired MI. The proposed approach is applied to 7–15-level MLIs resulting in 5.2%, 3.94%, 2.28%, 1.92% and 1.47% THD, respectively. Compared to the results reported in the literature, the proposed approach results in a lower THD and ensures compliance of IEEE-519 standard at several instances where the other approaches fail. The computational results are validated through simulations and hardware implementation. Realization of true MI, reduction in the search space dimensions and minimization of THD below the previously reported results are major contributions of this work.