Abstract: With the increase of the proportion of renewable energy generation in the local power grid and the reduction of the frequency regulation capacity, low-frequency impedance changes of the system and the weakening of the frequency maintenance characteristic lead to the potential low-frequency instability of the local power grid. The current weak grid assumption and the analysis method of fixed fundamental frequency do not correspond to the frequency regulation characteristics of the power grid,resulting in limitation on analysis of the instability mechanism for the low-frequency oscillation coupled with the frequency fluctuation. Aiming at the local power grid with diesel synchronous generator sets and grid-connected inverters, a framework of power generation model dominated by renewable energy is constructed with voltage, current, fundamental frequency disturbance,which covers the external characteristics of impedances and disturbance characteristics of the fundamental frequency. Based on the established coupling relationship between power grid strength, penetration rate, and grid-side equivalent impedance, the lowfrequency impedance changes at the source grid side and the induced low-frequency instability inducements are analyzed after the strong grid is weakened. The return ratio matrix containing the fundamental frequency disturbance term is constructed, the potential impact of the frequency characteristic term on the low-frequency instability of the system is analyzed, and the system stability with different penetration rates is predicted. Finally, combined with the results of the hardware-in-the-loop experiment,compared with the traditional fixed fundamental frequency analysis method under the critical instability condition, the proposed model can accurately predict the low-frequency instability problem of the local power grid with low-frequency regulation capacity dominated by a high proportion of renewable energy. The correctness of the above theoretical analysis is verified.