Mixed-mode Building, Stochastic MPC, Occupants’ Behavior
Between 4% to 20% of energy used for HVAC, lighting and refrigeration in a building is wasted due to issues associated with systems operations. It is estimated that proper building energy load control and operation can result in up to 40% utility cost savings. Current heuristic rules based on decision trees are difficult to define, manage and optimize as buildings become more complex. Advanced control strategies with weather forecast and cooling load anticipation, known as model predictive control (MPC), offer an attractive alternative for buildings with slow dynamics. However, MPC is mostly practiced through deterministic approaches. Deterministic MPC implicitly assumes that a dynamic model is able to perfectly predict the future behavior of the building over the desired control window, or prediction horizon. However, this assumption is clearly not rational because there will be both modeling errors and disturbances acting on the system over this period. One of these disturbances is associated with building occupant behaviors which interfere with deterministic assumptions. In this study, a probabilistic model of occupants’ behavior on window blind closing event is used to represent the disturbance coming from interactions of building residents with window blinds. This model is a multiple logistic regression analysis, based on a field study in an office building at the University of California, Berkeley (Inkarojrit, 2005). It considers the incident solar radiation on window surface and occupants’ self-reported brightness sensitivity as variable parameters to predict the closing event of blinds with 86.3% of accuracy. The probability of closing event is compared with a random number from the uniform distribution on the interval [0,1] at each time step and if it is greater than the random number, some indicator function will be equal to 1 (closing action) and vice versa. In order to implement the stochastic MPC, Monte Carlo simulation needs to be conducted due to the randomness of occupants’ behavior in closing the blinds. A test-building with mixed-mode cooling and high solar gains is considered as a test-bed. In our methodology, a detailed dynamic building model is developed and it is then used to identify the parameters of a 4th order linear time-variant state-space model. In the MPC formulation, the window opening schedule is optimized for the upcoming prediction horizon and the cost function is the minimization of energy usage subject to thermal comfort constraints during this horizon. Optimal control sequences based on the proposed stochastic MPC framework will be compared with deterministic MPC approaches to investigate possible advantages of considering uncertainties of occupant actions in model predictive controllers of buildings. References: Inkarojrit V., 2005. Balancing Comfort: Occupants’ Control of Window Blinds in Private Offices. PhD thesis, School of Architecture, University of California Berkeley.