After asynchronous interconnection, the Yunnan Power Grid has experienced a long-term Ultra-Low Frequency Oscillation (ULFO) which can be significantly suppressed through the optimization of PID parameters of the Turbine Governor (TG). However, the variation of TG parameters leads to some hidden problems in the power grid, such as the coupling between the TG and the Generator Excitation Regulator (GER) and Low Frequency Oscillation (LFO) caused by damping reduction. These problems seriously threaten the safe and stable operation of the Yunnan Power Grid. This paper develops a comprehensive suppression strategy of LFO and ULFO to handle the coupling problem between TG and GER in the Yunnan Power Grid under asynchronous interconnection. In detail, an efficient Multi-Verse Optimization (MVO) algorithm is employed to rapidly obtain optimal PID parameters of the TG and the GER. Lastly, simulation experiments are implemented based on optimal PID parameters obtained under manual tuning, and a Genetic Algorithm (GA) and the MVO algorithm. These validate the effectiveness and advantages of the proposed strategy. This work is supported by the National Natural Science Foundation of China (No. 61963020).