Harmonic-Constrained Three-Level Optimized Pulse Patterns for Grid-Connected Converters With $LCL$ Filters

This paper presents the computation of three-level optimized pulse patterns (OPPs) for converters connected to the grid via <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$LCL$</tex-math></inline-formula> filters. To this aim, the conventional OPP optimization problem is reformulated to account for the transfer function from the switching signal harmonics to the grid current harmonics. In addition, by incorporating constraints on grid current harmonics into the proposed OPP optimization problem, compliance with harmonic grid standards is ensured. Moreover, the restrictions that are typically imposed on multilevel switching signals, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> quarter-wave symmetry and unipolar switch positions, are relaxed in the proposed problem. This relaxation enables a reduction in current harmonic distortions within certain modulation intervals compared to conventional OPPs that do not limit grid current harmonics. The presented numerical results and real-time tests demonstrate the superior harmonic performance of the proposed harmonic-constrained relaxed OPPs, outperforming not only conventional modulation methods, such as space vector modulation (SVM), but also selective harmonic elimination (SHE) and conventional OPPs. Finally, further investigations reveal that the proposed OPPs maintain compliance with harmonic grid standards, even under variations in system parameters or when the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$LCL$</tex-math></inline-formula> filter is downsized.