Multi-Timescale Decision and Optimization for HVAC Control Systems with Consistency Goals

Many optimization problems for heating, ventilation, and air conditioning (HVAC) control systems usually refer to multiple timescales. This paper studies a two-timescale decision problem for indoor temperature regulation by HVAC with the objective to improve user's comfort under limited energy consumption. A slow timescale is divided into several fast timescales, so the two timescales have inherent association. Using states of fast timescale to represent the state of its slow timescale properly is challenging, thereby the weighted mean type is proposed in this paper. We find that the realizability and consistency in two-timescale cannot be guaranteed in existing empirical models, which are the bases for physical application. Therefore, this paper proposes a method that building the fast timescale model first and then inducing the slow timescale model from the fast timescale model. In addition, such a problem in the high-order system is more complex, whose solution is also discussed in this paper. The results of case studies show that the induced model can guarantee the consistency and realizability and meet the user desired temperature for comfort. Note to Practitioners - This paper was motivated by the multi-timescale problem that making a decision of controlling the indoor temperature for the user's comfort with energy constraint. Existing approaches to build a two-timescale model by experience would cause the inconsistent deviation. If the HVAC works in a closed environment system like a space station, besides crew comfort, the temperature for experiments in the space station should be accurate. Therefore, the deviation from the actual temperature and the desired temperature will cause adverse effects. In this paper, we mathematically derive the thermal state transfer equations and analyze some problems. Then, this paper suggests a new approach to build the two-timescale model for various conditions, in which the models of two timescales are consistent with each other. Preliminary experiments suggest that this approach is feasible and effective. In future research, we will jointly make optimization and decision of multiple appliances in home energy management (HEM) system.