Dual-Terminal Third-Order Super-Twisting Sliding Mode Control of M3C for Low-Frequency Transmission

Conventional controllers and standard super-twisting sliding mode controllers (STSMCs) are commonly applied to Modular Multilevel Matrix Converters (M3Cs) in flexible low-frequency power transmission. However, under conditions of multi-variable strong coupling and time-varying disturbances, they often exhibit limited suppression capabilities against complex, high-order internal cross-coupling dynamics, leading to residual fluctuations. To address these drawbacks, this paper proposes a nonlinear control strategy based on a third-order super-twisting sliding mode controller (TOSMC). Dual outer control loops are constructed under dual d-q rotating reference frames for capacitor voltage regulation at the power-frequency side and power control at the low-frequency side, respectively. A feedforward of the reference command based on cross-port power conservation is introduced to maintain fundamental power flow and the instantaneous macroscopic energy balance of the system. Meanwhile, a multi-integral robust compensation structure is adopted to realize real-time estimation and compensation of internal parameter perturbations and complex higher-order lumped disturbances, utilizing a continuous boundary layer function to eliminate inherent chattering. Simulation results demonstrate that in transient scenarios with step active power variation, compared with the STSMC, both methods exhibit robust and nearly identical macroscopic active power tracking with zero overshoot. However, the proposed TOSMC reduces the transient fluctuation amplitude of the average sub-module capacitor voltage by approximately 15%. Without sacrificing macroscopic dynamic response speed, the proposed control strategy ensures a smoother internal energy balancing process and superior high-order anti-disturbance performance, providing a feasible engineering solution for the reliable operation of M3Cs under complicated operating conditions.