Comprehensive Parameter Optimization of Composite Harmonic Injection for Capacitor Voltage Fluctuation Suppression of MMC

Modular multilevel converter (MMC) is widely employed in high-voltage direct current (HVDC) systems for the long-distance renewable energy transmission, where the larger submodule (SM) capacitors significantly increase its size, weight and cost. Conventional capacitor voltage fluctuation suppression methods, such as composite harmonic injection (CHI) strategies, can achieve lightweight MMC. However, these approaches often neglect the dynamic constraints between harmonic injection parameters and their coupled effect on modulation wave, which not only leads to suboptimal global solutions but also increases the risk of system overshoot. Therefore, this paper proposes a comprehensive CHI parameters optimization method to minimize capacitor voltage fluctuations, thereby allowing for a smaller SM capacitor. First, the analytical expression of SM average capacitor voltage is developed, incorporating the injected second-order harmonic circulating current and third-order harmonic voltage. On this basis, an objective function is defined to minimize the sum of the fundamental and second-order harmonic components of the average capacitor voltage, with the harmonic injection parameters and modulation index as optimization variables. Then, these parameters are optimized using a particle swarm optimization (PSO) algorithm, where their constraints are set to prevent modulation wave overshoot and additional power loss. Finally, the optimization method is validated through a ±500 kV, 1500 MW MMC-HVDC system under various power conditions in PSCAD/EMTDC (version 4.6.3). In addition, simulation results demonstrate that the proposed method can achieve a 13.33% greater reduction in SM capacitance value compared to conventional strategies.