Offline Selective Harmonic Elimination With (2N+1) Output Voltage Levels in Modular Multilevel Converter Using a Differential Harmony Search Algorithm

(<inline-formula> <tex-math notation="LaTeX">$2N +1$ </tex-math></inline-formula>) selective harmonic elimination pulse-width modulation (SHE-PWM) is an effective switching strategy of the modular multilevel converter in medium-voltage cases. In these cases, the number of sub-modules (SMs) is not high. Compared to the traditional (<inline-formula> <tex-math notation="LaTeX">$N +1$ </tex-math></inline-formula>) SHE-PWM, (<inline-formula> <tex-math notation="LaTeX">$2N +1$ </tex-math></inline-formula>) SHE-PWM has <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> more voltage levels, thus it can yield much better harmonic performance. However, the task of selective harmonic elimination also becomes much more complicated since there are more switching angles to be determined. This paper proposes a differential harmony search algorithm (DHS) with a novel harmony improvisation procedure for solving this problem. The Bayesian optimization method is applied to find the optimal parameter configuration for DHS. The performance of DHS is compared with 6 other metaheuristic algorithms including differential evolution (DE), harmony search (HS), genetic algorithm (GA), particle swarm optimization (PSO), teaching and learning-based optimization (TLBO), and ant colony optimization (ACO). The comparison is conducted on a set of 100 (<inline-formula> <tex-math notation="LaTeX">$2N +1$ </tex-math></inline-formula>) SHE-PWM instances by varying the modulation index from 0.01 to 1.0 with a step of 0.01. The numerical results show that the proposed DHS outperforms other compared methods in terms of objective function values, algorithm robustness, the magnitude of fundamental harmonic, and the calculated total harmonic distortion values. The switching angles obtained by DHS are further validated by both Matlab/Simulink simulation and hardware experiment.