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In this paper, we present a prediction-based dynamic programming (DP) control approach, a nonlinear model predictive control (NMPC) approach, and a linear optimal control (LOC) approach to analyze the minimization of the total energy use of a hybrid ground-coupled heat pump (hp) system (incorporating a ground-coupled hp, a gas boiler, a passive cooler, and an active chiller) under operational constraints. A large-scale emulator model (based on finite-volume method and the equivalent-diameter approach) is used for the borehole system and for the assessment of different control algorithms. A nonlinear autoregressive exogenous model is identified from the inputoutput data generated by the emulator model to be used in a DP-based controller. Since DP is a global optimal control method, it was used as a reference for performance assessment. Next, a state-space reduced-order control-oriented model with a larger sampling time is obtained from the emulator model using the so-called proper orthogonal decomposition model reduction technique. This model is used in an NMPC algorithm to see how much NMPC is suboptimal with respect to the DP in terms of annual energy use minimization. Finally, a series of LOCs based on constant hp coefficients of performance is tested to see how much the system performance deteriorates. The control algorithms are used for the satisfaction of heating-cooling demands of three types of buildings: 1) heating dominated; 2) cooling dominated; and 3) thermally balanced. The effects of constraining thermal buildup/depletion of ground, variable electricity prices, and marginal violation of thermal comfort on the performance of the different controllers applied are also separately analyzed.

In this paper, a convexification approach is presented for a class of non-convex optimal/model predictive control problems more specifically applied to building HVAC control problems. The original non-convex problems are convexified using a convex envelope approach. The approach is tested on two case studies: a benchmark building HVAC system control problem from the literature and control of a hybrid ground-coupled heat pump (HybGCHP) system. For the first application, convexified model predictive control was used and results were compared with fuzzy and adaptive control results. For the HybGCHP system, convexified optimal control was applied and the results were compared with dynamic programming based optimal control. In the first case superior performance was observed over the corresponding fuzzy and adaptive control results from the literature. For the HybGCHP system the associated convexified optimal control gave almost global optimal results in terms of responses and cost criteria. The suggested method is especially useful for optimal building HVAC control/design problems which include non-convex bilinear or fractional terms. Since a polynomial expression can be recursively expressed as a system of bilinear equations, the proposed method, in principle, can be applied to all systems where polynomial non-convexities exist.

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