Taiwan's power system is isolated and not supported by other interconnected systems. Consequently, the system frequency immediately reflects changes in the system loads. Pumped storage units are crucial for controlling power frequency. These units provide main or auxiliary capacities, reducing the allocation of frequency-regulating reserve (FRR) and further reducing generation costs in system operations. Taiwan's Longmen Nuclear Power Plant is set to be converted for commercial operations, which will significantly alter the spinning reserves in the power system. Thus, this study proposes a safe and economic pumped storage unit dispatch strategy. This strategy is used to determine the optimal FRR capacity and 1-min recovery frequency in a generator failure occurrence at the Longmen Power Plant. In addition, this study considered transmission capacity constraints and conducted power flow analysis of the power systems in Northern, Central, and Southern Taiwan. The results indicated that, in the event of a failure at Longmen Power Plant, the proposed strategy can not only recover the system frequency to an acceptable range to prevent underfrequency load-shedding, but can also mitigate transmission line overloading.