The microgrid is a new concept of integrating the distributed energy resources (DER) within the grid. The management of the heterogeneous sources of energy presents a challenge, especially as most of the DER are unpredictable. Besides, implementing microgrids should be economically beneficial to the customer; this will raise the challenge of decreasing the costs while ensuring the energy balance. In this paper, we used a stochastic approach based on a model-free Markov decision process (MDP) to

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... derive the optimal strategy for the home energy management system. The approach aims to decrease the energy bill while taking into account the intermittency of the renewable energy resources (DER) and other constraints. While other proposals charge the battery from the utility energy, making the state of charge (SOC) of the battery a deterministic variable, our work adopts a scenario where the battery is charged from the excess of the generated energy, which makes the SOC a nondeterministic variable affected by the uncertain character of the renewable energy. Therefore, our model considers the randomness at two levels: renewable energy level and battery SOC level. We take into account the complexity of the solution, and we propose a simple strategy that can be implemented easily in microgrids.