Stability Analysis and Enhancement of Grid-Following Offshore Wind Farms Integrated via Flexible Low-Frequency AC Transmission Considering Multi-Control-Loop Bandwidth Interaction

A flexible low-frequency AC transmission system (LFTS) can extend the AC export range of offshore wind farms, but interactions among converter control loops may restrict its stable operating region. This paper develops a unified small-signal model comprising a grid-following wind farm, low-frequency cable, modular multilevel matrix converter (M3C), and receiving grid. A matrix-valued generalized Nyquist return ratio, together with modal participation and parameter-sensitivity analyses, indicates that the approximately 30 Hz dominant mode is strongly associated with the coupled control and network dynamics involving the phase-locked loop, wind-farm outer loops, M3C low-frequency voltage control, and transmission network. Based on bandwidth separation, a coordination strategy is proposed to move the critical control dynamics away from the interaction region. Comparisons between the state-space model and MATLAB/Simulink R2023b time-domain simulations show local agreement at the tested operating points. Power-step, weak-grid, bandwidth-sweep, and parameter-variation tests show that the proposed strategy, implemented solely through controller-parameter coordination without requiring additional hardware, suppresses oscillations, improves small-signal stability, and indicates a higher representative tested power-transfer boundary than PLL retuning at SCR = 1.50; 16 and 25 MW per turbine are the respective instability test points.