Analysis of Ripple/Harmonic Coupling Characteristics of M³C Under Grid-Side Asymmetric Faults

The secure operation of the fractional frequency transmission system faces significant challenges during grid-side asymmetric faults. This vulnerability stems from two critical technical barriers: the frequency disparity between interconnected grids obscures post-fault interaction mechanisms, complicating system response analysis and the inherent complexity of modular multi- level matrix converter introduces substantial analytical difficulties in fault characteristic identification. This paper proposes a 2D phasor analytical framework that systematically decouples the interactive relationships within M³C. Through an iterative analytical approach, the investigation reveals the dynamic cross-coupling mechanisms between ripples and harmonics under asymmetric faults, particularly addressing the nonlinear interactions between bridge-arm current and submodule capacitor voltage. The proposed method realises the modelling of multi-component under-grid-side asymmetric faults, precisely delineates the internal coupling modes and further reveals the fault transmission mechanism in the form of a generalised model introduced by fault participation factors. The effectiveness of the proposed method and the accuracy of the analysis are validated through case studies involving three fault scenarios in MATLAB/Simulink.