Extreme events represented by typhoons occur frequently and pose a severe threat to the frequency security of receiving-end power grids, while the fast regulation capability of energy storage is of great significance for maintaining frequency security. To this end, a stochastic optimization method is proposed that considers the entire process of regulating the frequency response of energy storage support under extreme events. First, a probabilistic failure model of DC interconnection lines under typhoon scenarios is established. Second, the frequency response characteristics of the entire process based on energy storage regulation after faults are analyzed, and analytical expressions for power-energy reserve capacity are derived. A criterion is then proposed to quantify the effects of frequency deviation while reflecting the frequency regulation contributions of synchronous generators and energy storage, as well as system resilience. Subsequently, a security-constrained stochastic optimization model is constructed. In the first stage, the system cost is minimized, and in the second stage, a probabilistic model of the DC interconnection lines under typhoon scenarios is embedded to ensure grid frequency security. Finally, the effectiveness of the proposed model is verified on an improved asynchronously interconnected power grid and a regional receiving-end power grid. The results show that the proposed model can effectively enhance system resilience under extreme events and improve post-fault frequency dynamic performance.