Stage-Wise Calculation of Short-Circuit Fault Currents in M3C-Based Offshore Wind Power Flexible Low-Frequency Transmission Systems

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The modular multilevel matrix converter (M3C)based flexible low-frequency transmission system for offshore wind power integration faces challenges in fault current analysis due to the nonlinear control loops of the converter itself. Post-fault currents exhibit distinct characteristics under varying time scales, which are difficult to analytically resolve, thereby complicating the design and parameter setting of control protection devices in low-frequency systems. To address these issues, this paper combines protection operation sequences with converter control strategies to define four post-fault stages: M3C capacitor response, M3C control response, AC feed-in transient, and steady-state. Analytical solutions for fault currents in the first two stages relevant to circuit breaker operation are derived. Specifically, an equivalent circuit model for inter-arm current loops during the M3C capacitor response stage is established, enabling analytical derivation of fault current expressions. For the M3C control response stage, an equivalent voltage source model incorporating the converter's voltage-frequency (VF) control characteristics is developed, and fault current solutions are obtained through integration with fault boundary conditions. Finally, a simulation platform implemented in PSCAD/EMTDC validates the accuracy of the proposed methodology.

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