Energy Management of a Building Cooling System With Thermal Storage: An Approximate Dynamic Programming Solution

Abstract

This paper concerns the design of an energy management system for a building cooling system that includes a chiller plant (with two or more chiller units), a thermal storage unit, and a cooling load. The latter is modeled in a probabilistic framework to account for the uncertainty in the building occupancy. The energy management task essentially consists in the minimization of the energy consumption of the cooling system, while preserving comfort in the building. This is achieved by a twofold strategy. The cooling power request is optimally distributed among the chillers and the thermal storage unit. At the same time, a slight modulation of the temperature set-point of the zone is allowed, trading energy saving for comfort. The problem can be decoupled into a static optimization problem (mainly addressing the chiller plant optimization) and a dynamic programming (DP) problem for a discrete time stochastic hybrid system (SHS) that takes care of the overall energy minimization. The DP problem is solved by abstracting the SHS to a (finite) controlled Markov chain, where costs associated with state transitions are computed by simulating the original model and determining the corresponding energy consumption. A numerical example shows the efficacy of the approach

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“…The proposed policy includes the value iteration function that decreases monotonically and converges to the Bellman's solution. Other applications of ADP are examined in [42,43,44,45] to achieve battery's efficiency and coordination. However, the above studies have proposed methods that are difficult to handle MG's scheduling, especially if high dimensional state spaces are involved.…”

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“…Model (27) subject to constraints (28) and (29) is equivalent to model (30) subject to constraints (28), (31) and (32). This latter model has the advantage of being linear so that it can be expressed in compact form along the look-ahead discretized time horizon [t i , t f ] as follows:…”

“…and Ξ D are suitably defined matrices. Note that those elements of vectors s C and s D that correspond to a zero charge and discharge command in vectors (31) and (32). Given that the charge and discharge commands are mutually exclusive, we have that s C ⊤ s D = 0.…”

“…apply to the energy exchange s, or bounds (31) and (32) apply to the charge and discharge inputs s C and s D . Table 3 summarizes the relevant quantities related to the storage model.…”

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