Smart grids are fostering a paradigm shift in the realm of power distribution systems. Whereas traditionally different components of the power distribution system have been provided and analyzed by different teams through different lenses, smart grids require a unified and holistic approach that takes into consideration the interplay of communication reliability, energy backup, distribution automation topology, energy storage, and intelligent features such as automated fault detection, isolation, and restoration (FDIR) and demand response. In this paper, we present an analytical model and metrics for the survivability assessment of the distribution power grid network. The proposed metrics extend the system average interruption duration index, accounting for the fact that after a failure, the energy demand and supply will vary over time during a multi-step recovery process. The analytical model used to compute the proposed metrics is built on top of three design principles: state space factorization, state aggregation, and initial state conditioning. Using these principles, we reduce a Markov chain model with large state space cardinality to a set of much simpler models that are amenable to analytical treatment and efficient numerical solution. In case demand response is not integrated with FDIR, we provide closed form solutions to the metrics of interest, such as the mean time to repair a given set of sections. Under specific independence assumptions, we show how the proposed methodology can be adapted to account for multiple failures. We have evaluated the presented model using data from a real power distribution grid, and we have found that survivability of distribution power grids can be improved by the integration of the demand response feature with automated FDIR approaches. Our empirical results indicate the importance of quantifying survivability to support investment decisions at different parts of the power grid distribution network. Copyright © 2014 John Wiley & Sons, Ltd.