The battery energy storage system (BESS) has been envisaged as an effective solution for renewable energy accommodation in power systems. However, the residual capacity and maximum power of large-scale BESS are highly affected by thermally-induced incidents such as battery degradation and Thermal Runaway (TR) propagation. In the prior-art studies, the impacts of thermally-induced incidents on the BESS service performance have not been well modeled, resulting in relatively over-optimistic reliability estimation of power systems. In this paper, the reliability of large-scale grid-connected BESSs as well as its impacts on the overall reliability of power systems are investigated considering the battery degradation and TR propagation. To quantify the time-varying performance of the BESS, a multi-state model is constructed. The proposed model describes the aging process of batteries inside the BESS, incorporating the combined effects of sequential TR and the performance degradation of the surrounding batteries due to heat absorption. Based on the Monte Carlo method, scenarios that reflect the uncertainties of the intermittent wind generation and fluctuating loads are simulated. An optimal scheduling model is deployed, and a solution algorithm is proposed to calculate the scheduling results of the BESS in the real-time performance range subject to its thermal conditions. Case studies are conducted to validate the effectiveness of the proposed model and technique.