Harmonic-Constrained Optimal Modulation for Converters Connected to a Distorted Grid

Compliance with harmonic grid standards becomes particularly challenging under non-ideal operating conditions, e.g., when other converters—bedsides the one of interest—inject harmonic distortions, referred to as disturbances, at the point of common coupling (PCC). This paper proposes optimized pulse patterns (OPPs) for grid-connected converters with an$LCL$filter that ensure PCC current and voltage harmonics meet the relevant harmonic grid standards, even in the presence of such disturbances. This is achieved by formulating the OPP problem as a robust optimization problem that explicitly accounts for external harmonic distortions and incorporates explicit current and voltage harmonic constraints. The proposed framework can be applied under different levels of disturbance information: (i) full knowledge of harmonic amplitudes and phases, (ii) uncertain but bounded characteristics, and (iii) complete lack of knowledge during the OPP computation. Numerical results and experimental tests demonstrate that the proposed OPPs achieve significantly better compliance with harmonic grid standards compared with advanced modulation strategies such as selective harmonic elimination (SHE) and conventional OPPs.