This paper investigates the optimal coordination of multiple interacting heating, ventilation, and air conditioning (HVAC) appliances in buildings such as air conditioners and refrigerators, in time-varying electricity pricing environments. Each load is modeled as a first-order differential equation with a binary (ON–OFF) switching control function. An energy cost minimization problem is then formulated with weighted penalties on the temperature deviation from the desired setpoint and the control input fluctuation. Using the dynamic programming (DP) method, the cost-optimal trajectories are computed, which indicate precooling of the loads in anticipation of higher electricity prices. Moreover, the loads are desynchronized in the presence of local renewable generation to maximize the on-site consumption of the local energy. The presented results provide useful insights for the development of predictive control policies for optimal energy management in buildings.

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