Nonlinear model reduction and model predictive control of residential buildings with energy recovery

• Propose physically meaningful aggregate models based on building design parameters.
• Use singular perturbation theory to analyze building multiple time scale behavior.
• Derive nonstiff reduced-order models for use in model-based controllers.
• Synthesize economic and tracking MPC based on reduced-order models.
• Present simulation results using model of a test building.

Residential and commercial buildings account for a significant portion of the electricity consumed in the United States. Their operation is subject to fluctuations in weather and occupancy which, in turn, are reflected in large variations in the load that buildings impose on the grid during the day and at night time. In view of mitigating such fluctuations (and their broader impact on energy generation), understanding the dynamic behavior of buildings and a focus on energy management (rather than simply temperature control), is essential. In this paper, we begin by analyzing building dynamics and use singular perturbation arguments to provide a theoretical justification for the empirically acknowledged multiple time scale dynamic response of buildings. We also derive reduced-order models for the dynamics in each time scale for a prototype residential building. Our analysis accounts for the potential use of heat recovery ventilators (HRVs), and we show that the presence of energy recovery leads to the emergence of a dynamic behavior with three time scales, including an overall, system-wide component which involves both the building and the HVAC system. We use our dynamic results to formulate a set of synthesis guidelines for control systems addressing either temperature regulation or geared towards minimizing operating cost. A detailed simulation case study demonstrates the application of the derived reduced-order models in the design of a nonlinear predictive model-based optimal energy management strategy for a model of a single-zone test building situated on the University of Texas campus. The proposed controller exhibits excellent performance, can easily be executed in real-time and has the capability to shift peak loads as part of a demand flattening strategy.