The unprecedented growth of solar generation adoption indicates that solar can become a major source of modern and clean energy in just a few decades for our power grids. Despite solar's growing criticality for generation, few studies have proposed models to capture solar generation infrastructure's behavior during natural disasters. Here, we present an integrative methodology to quantify solar generation during hurricanes. The methodology is based on a stochastic model that combines a tropical cyclone hazard model, solar irradiance quantification, solar panel vulnerability, and a model for irradiance decay during hurricane conditions. The irradiance decay model is newly developed through mixed-effect regression on a dataset that merges historical Global Horizontal Irradiance and Atlantic hurricane activity. The proposed stochastic model can be integrated into large grid resilience's models for a wide range of detailed applications that require forecasting power system capacity during storms, such as contingency planning for extreme events. We use the stochastic model to analyze 21 states in the Eastern U.S. for various storms to showcase the methodology's broad applicability. Our results show that for events with return periods of up to 33 years, the loss in generation stems from cloud conditions during hurricanes. However, less frequent events can cause solar panel failure, especially in southern regions of the U.S., triggering complete loss of solar generation. Given that solar generation is expected to grow significantly, these results advocate for higher standards in the structural design of solar panels as well as the deployment of storage for disaster resilience.