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The problem of home energy management (HEM) optimization can be transformed from single-time scale into multi-time scale to decrease the computational complexity; however, the equivalence of transformation should be guaranteed. In this paper, we investigate the equivalence of multi-time scale HEM optimization, which includes electric vehicles, thermal appliances, and uncontrollable devices. The total electricity cost and user discomfort of temperature are considered. We propose a thermal model in multi-time scale to reduce the error of transformation. We show and prove the equivalent conditions of transformation. Based on the conditions, we present an improved optimization algorithm for the problem of multi-time scale HEM optimization. Numerical results show that the proposed model is more suitable for the transformation, the conditions are obeyed, and the proposed algorithm achieves better performance while solving the problem.
Liu et al. (Tue,) studied this question.