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In this paper, we apply adaptive dynamic programming to the residential energy system control and management, with an emphasis on home battery use connected to power grids. The proposed scheme is built upon a self-learning architecture with only a single critic module instead of the action-critic dual module architecture. The novelty of the present scheme is its ability to improve the performance as it learns and gains more experience in real-time operations under uncertain changes of the environment. Simulation results demonstrate that the proposed scheme can achieve the minimum electricity cost for residential customers.