A Hierarchical Approach Based on the Frank–Wolfe Algorithm and Dantzig–Wolfe Decomposition for Solving Large Economic Dispatch Problems in Smart Grids

A microgrid is an integrated energy system consisting of distributed energy resources and multiple electrical loads operating as a single, autonomous grid either in parallel to or “islanded” from the existing utility power grid, often referred to as a microgrid. The operations of a microgrid are different from those of traditional microgrids. In this paper, we present a decomposition method to solve the economic dispatch problem for a cluster of microgrids. The economic dispatch problem aims at determining both the power generation and demand levels of each microgrid under boundary and power flow constraints in order to minimize a non-linear convex economic cost, which is expressed as the combination of generation costs and demand utilities. Directly solving large economic dispatch problems is difficult because of the non-linearity of the objective function, memory limitations and privacy issues. We therefore propose a decomposition method based on a combination of the Frank–Wolfe algorithm to tackle the non-linearity and the Dantzig–Wolfe decomposition to solve the later two issues. Networks of microgrids both randomly generated and from real cases are used as test cases. The experimental results shows that the computation time increases slowly with the increasing complexity of the microgrid.