Structural design of distributed energy networks by a hierarchical combination of variable- and constraint-based decomposition methods

A near-optimal solution method of a large-scale design problem of a distributed energy network, consisting of multiple energy-supply systems under power and heat interchanges, is developed by hierarchically combining variable- and constraint-based decompositions. The design problem is formulated using mixed-integer linear programming, and its scale increases with the number of connected energy-supply systems and daily patterns of energy demand. By focusing on the hierarchical relationship between design and operation variables, the original problem is decomposed into an upper-level design problem and lower-level coordinated operation problems based on the Benders decomposition. By focusing on power- and heat-interchange constraints, the coordinated operation problem is further decomposed into a master problem concerning power and heat interchanges and subproblems for energy supply in each energy-supply system based on the Dantzig-Wolfe decomposition. A near-optimal solution is calculated through a two-level iterative calculation, consisting of delayed constraint generation between the design problem and the coordinated operation problems and delayed column generation between the master problem and the subproblems in each coordinated operation problem. The near-optimal solution method is applied to the structural design problem of distributed energy networks incorporating 5–100 cogeneration systems, in which suboptimal solutions cannot be found in the conventional solution method.