Equivalence of Multi-Time Scale Optimization for Home Energy Management Considering User Discomfort Preference
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 (EV), 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.
Decentralized optimization reduces the computational complexity, but it is hard to get the optimal solution. Reference schedule HEMs based on centralized optimization. Reference  builds models of thermal dynamic and battery of EV. It schedules the energy by a stochastic control method considering the electricity cost, the charging target of EV, and the user discomfort of temperature. Reference  studies a HEM system with HVACs, EVs and DGs. It builds Markov models for the wind turbines and photovoltaic panels, regards the HVACs as hard loads, and schedules the EVs through dynamic programming. Reference  uses an auto regressive moving average model of wind speed to forecast the output power of wind turbine, and solves the problem by genetic algorithm. Reference  builds models for photovoltaic panel and hard load, solves the problem by adaptive control method, and adjusts the charging power of batteries in real time to eliminate the disturbance of uncertainty. Reference  predicts the dynamic price in the future by a statistical method and schedules the EVs by thresholds of price. Reference , - describe the problem of HEM optimization in single-time scale. The dimension of solution is high because of the great amount of controllable loads and time slots in the period of optimization. The “combinatorial explosion” problem is encountered . Furthermore, with uncertainties, the solution may become invalid in practice . The HEM systems must refresh their predictions and re-optimize online. It’s hard to get the solution with high dimensions within a limited time.
The main contributions of this paper are summarized as follows: We propose a STS thermal model. The single-time scale thermal model should be transformed into a STS one while the problem of HEM optimization is transformed from single-time scale into multi-time scale. Both the changing outdoor temperature and input power of HVAC influence the equivalence of thermal model’s transformation. The proposed STS thermal model, which considers the changing outdoor temperature and input power of HVAC, eliminates the influence of outdoor temperature and reduces the one of input power of HVAC. We show and prove the equivalent conditions of problem’s transformation considering total electricity cost and user discomfort of temperature. The objective function that considers total electricity cost and user discomfort of temperature should satisfy the conditions to keep the equivalence of problem’s transformation. We propose an optimization algorithm for the problem of FTS HEM optimization. The optimal solution must satisfy the equivalent conditions. We utilize the conditions to construct the proposed algorithm that gives the solution directly according to the conditions. Unlike heuristic algorithm, the algorithm has no iteration; it can give an approximate optimal solution speedily.
We propose a STS thermal model and analyze the performance of the model in this paper. As the model considers the changing outdoor temperature and input power of HVAC, it is more suitable for the problem’s transformation from single-time scale to multi-time scale. We show the conditions that must be obeyed while transforming the problem into multi-time scale, and test the conditions in simulation. We propose an algorithm without iteration for the problem of FTS HEM optimization. The solution of proposed algorithm that is very close to the optimal one is obtained in a short time in simulation. In the paper, the coefficients of thermal model (3) and the battery’s efficiency of EV are constants, and the optimization only considers the total electricity cost and user discomfort of temperature. As future study, it is suggested to look into the problem of transformation while the coefficients are variables, and while the optimization has more considerations (such as the stabilization of total power consumption of home, user discomfort of ventilation).
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