A Nested Decomposition Method and Its Application for Coordinated Operation of Hierarchical Electrical Power Grids

Multilevel, multiarea, and hierarchically interconnected electrical power grids confront substantial challenges with the increasing integration of many volatile energy resources. The traditional isolated operation of interconnected power grids is uneconomical due to a lack of coordination; it may result in severe accidents that affect operational safety. However, the centralized operation of interconnected power grids is impractical, considering the operational independence and information privacy of each power grid. This paper proposes a nested decomposition method for the coordinated operation of hierarchical electrical power grids, which can achieve global optimization by iterating among upper- and lower-level power grids with exchange of boundary information alone. During each iteration, a projection function, which embodies the optimal objective value of a lower-level power grid projected onto its boundary variable space, is computed with second-order exactness. Thus, the proposed method can be applied widely to nonlinear continuous optimizations and can converge much more rapidly than existing decomposition methods. We conducted numerical tests of coordinated operation examples with a trilevel power grid that demonstrate the validity and performance of the proposed method.