390723 On the Use of Multistage Stochastic Programming for the Design of Smart Grid Coordinated Building Thermal Energy Storage Systems
Energy consumption by Heating Ventilation and Air Conditioning (HVAC) systems is usually heaviest when electricity prices are at their highest. One approach to reducing energy costs is to employ Building Thermal Energy Storage (BTES) to time-shift power consumption away from periods of high energy cost to periods of low cost.
Due to the uncertainty of electricity prices, the problem of optimal equipment sizing must be formulated as a stochastic program. However, rather than being a fairly simple two-stage stochastic program, the dynamics imposed by the storage devices requires the formulation to be of the far more challenging multistage class.
In this work, we propose a novel approximate solution procedure for this class of multistage stochastic programming problems. The approach utilizes the computational efficiency of the recently developed method of Economic Linear Optimal Control (ELOC) and its extension Constrained ELOC. The proposed method occurs in two stages. The first is a global search over the here-and-now variables as well as the parameters of the ELOC policy. However, this first search assumes a statistical constraint enforcement mechanism (similar to chance constrained optimization). In the second step is a gradient based search over the here-and-now variables, but used the Constrained ELOC policy to enforce point-wise-in-time constraints. To address the possible occurrence of an infeasible solution from the Constrained ELOC policy a fairly simple barrier type approach is used to improve convergence properties.