Probability-Based Modeling and Analysis for PS-PWM in an MMC Distributed Control System With Sub-Module Asynchrony

Modular multilevel converters for high-voltage dc transmission applications normally adopt a distributed control system, where a large number of local controllers are employed, to manage considerable sub-modules (SMs) in the system. The manufacturing tolerance of crystal oscillators for local controllers introduces controller clock discrepancy and eventually leads to the asynchrony of triangular carriers implemented in individual SM for phase-shifted pulsewidth modulation scheme. Considering the tolerance of oscillators having a normal distribution, the deviation of the triangular carrier frequency is modeled based on the probability theory in this letter. The switching function model taking such asynchrony into account is proposed allowing quantitative analysis and evaluation of the switching harmonic contents. Good agreements of the harmonic contents have been achieved between the theoretical calculation and experimental results. The calculated switching harmonics can be used to determine the synchronization interval according to the system requirements.