A Decomposition Approach for the Large Scale Synthesis/Design Optimization of Highly Coupled, Highly Dynamic Energy Systems

A general methodology for the decomposed optimization of highly coupled, highly dynamic energy systems is presented. The approach is based on the physical division of the system into units (sub-systems, components or disciplines) subject to functions describing the energy, cost and other couplings between them. Two versions of the approach are proposed. The first approach is called the Local-Global Optimization (LGO) Approach. LGO requires unit optimizations to be carried out with respect to purely local decision variables for various combinations of the functions that connect the units. The results are used to create an Optimum Response Surface (ORS) for the entire problem. The ORS is then searched by a system-level optimizer to find the values of the coupling functions that lead to an optimum system-level solution. The second approach proposed is an iterative version of LGO (ILGO). In this case, the ORS is closely approximated using a linear Taylor series expansion. The partial derivatives resulting from such an approximation are seen to correspond to the shadow prices (or marginal costs) typically used in the thermoeconomic literature. ILGO effectively and significantly reduces the number of unit optimizations required. The properties used to describe the coupling functions play a critical role in the convergence of ILGO to a global system-level optimum. A discussion of this and its implication for the choice of First or Second-Law based quantities for the optimization of systems is given.