Lyapunov stability analysis for M3C based fractional frequency transmission system utilizing generalized participation factors

The fractional frequency transmission systems occurs different oscillations due to the interactions between wind farm, submarine cable, and M3C components under the large signal disturbances. However, current Lyapunov based stability analysis for high-order systems typically employs methods such as T–S fuzzy theory to construct Lyapunov functions. Unlike the participation factors in small signal stability analysis, it leads to an inability to quantitatively analyze the impact of interactions between different frequency components in system with multi-frequency coupling characteristics. This paper firstly proposes the Lyapunov function for the fractional frequency PMSG offshore wind power transmission system (FOWS), which considers the dynamics of the mentioned components. Additionally, the stability regions are compared for unveiling the pattern of the components interaction, when analyzing the dynamic characteristics of different blocks from the generalized system matrix individually with the overall analysis results. Furthermore, the generalized participation factor is defined to quantitatively assess large signal interaction stability. Subsequently it is also analyzed how control and circuit parameters within individual components affect system stability, revealing instability mechanisms under various disturbance conditions. And the comprehensive stability enhancement strategies are proposed that consider interactions involving multiple frequencies and components. Finally, MATLAB model is established to ensure the effectiveness.