(119c) On the Use of Multistage Stochastic Programming for the Design of Smart Grid Coordinated Systems

Due to the uncertainty of electricity prices, the problem of optimal equipment sizing for smart grid coordinated process 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. The proposed method will be illustrated using the example of an IGCC plant that has be made dispatch capable through the installation of gas storage units.