Floods can cause power outages with widespread impacts on socio-economic activities dependent on electricity for their functioning. Effective flood risk management requires comprehensive damage assessment, yet methodologies to estimate the entire range of expected damages are lacking. This paper presents a new modeling and simulation probabilistic framework for the assessment of damages to power grids exposed to floods. The framework combines modeling tools and approaches from engineering, economics and sociology, namely a flood inundation model to generate stochastic hazard scenarios, fragility curves to describe the stochastic failure process of components in the power grid conditioned to the hazard, a simulation-based model to analyze the power flow, and a socio-economic model to characterize the customers connected to the power grid. Consequently, the framework enables: (i) considering the stochastic magnitude and frequency of floods, (ii) evaluating the vulnerability of power grids components, (iii) estimating their spatio-temporal probabilities of failure, (iv) analyzing the cascading effects across power transmission and distribution networks, and (v) assessing the impact of power outages on the final customers and their likelihood. A synthetic case study is worked out by adapting the IEEE 14 power grid benchmark to the Italian context, proving how the framework allows the identification of the most critical components for the security of power supply during flooding. The outcomes from the implementation of the framework can support civil protection agencies and grid operators in the decision on pre- and post-disruption mitigation strategies, so to guarantee public safety, secure power supply and ensure financial well-being.