Stochastic Model Predictive Control for Building HVAC Systems: Complexity and Conservatism

This paper presents a stochastic model predictive control (SMPC) approach to building heating, ventilation, and air conditioning (HVAC) systems. The building HVAC system is modeled as a network of thermal zones controlled by a central air handling unit and local variable air volume boxes. In the first part of the paper, simplified nonlinear models are presented for thermal zones and HVAC system components. The uncertain load forecast in each thermal zone is modeled by finitely supported probability density functions (pdf). These pdfs are initialized by using historical data and updated as new data becomes available. In the second part of the paper, we present a SMPC design that minimizes expected energy cost and bounds the probability of thermal comfort violations. SMPC uses predictive knowledge of uncertain loads in each zone during the design stage. The complexity of a commercial building requires special handling of system nonlinearities and chance constraints in order to enable real- time implementation, minimize energy cost, and guarantee thermal comfort. The paper focuses on the trade-off between computational tractability and conservatism of the resulting SMPC scheme. The proposed SMPC scheme is compared with alternative SMPC designs, and the effectiveness of the proposed approach is demonstrated by simulation and experimental tests.