Threshold-Crossing Limits and Model-Fidelity Assessment of Supervised NLM Error Shaping for MMC Circulating-Current Control

Finite-level nearest-level modulation (NLM) couples modular multilevel converter (MMC) internal dynamics to a discontinuous arm-voltage execution error. Building on an established proportional reduced-order quasi-resonant (P-ROQR) circulating-current regulator and a Fourier-based NLM error-correction concept, this study investigates the interaction between harmonic pre-distortion and circulating-current control under discrete NLM execution. A unified energy/error model and an exact threshold-crossing representation show that sub-level pre-distortion can affect the converter only when an integer insertion command changes. However, threshold opportunity alone does not guarantee closed-loop improvement. A causal cycle-wise quantization-error shaping (QES) layer is therefore combined with a threshold-aware efficacy supervisor that rejects candidate shaping actions when they do not alter the discrete actuator or are predicted to increase the circulating-current response. During large operating-point changes, the QES path is temporarily blocked and is reactivated after coefficient reacquisition and smooth recovery. The fixed QES implementation is first examined in mean-arm and individual-submodule models, where its performance is shown to depend strongly on numerical and model fidelity. In the individual-submodule model, fixed QES reduces the selected high-order component but increases the total circulating-current rms and peak. In the ten-submodule-per-arm model, supervised QES reduces circulating-current rms relative to both fixed QES and the P-ROQR baseline, although its steady-state current peak and switching-transition count remain above the baseline values. During the tested power step, transient blocking keeps the peak circulating-current deviation close to the P-ROQR result while reducing the additional excursion introduced by fixed QES. These results support the use of local prediction to screen candidate shaping actions within the investigated simulation conditions; performance in larger MMC systems and hardware implementations remains to be established.