In this paper, a distributed price-responsive energy management algorithm is proposed for a smart residential energy system (RES) equipped with multiple energy storage devices. First, the future system states are predicted via an iterative learning approach based on the lifted domain representation. Then, RES management is formulated as an optimization problem by taking into account the time-varying electricity rate, battery properties, and system operational constraints. Finally, we adopt the Alternating Direction Method of Multipliers (ADMM) and compute the optimal charging/discharging actions of local batteries in a distributed manner to establish a flexible, scalable, and computation-efficient power network. Numerical simulation is provided to illustrate the performance of our proposed algorithm.