A Nested Decomposition Method for the AC Optimal Power Flow of Hierarchical Electrical Power Grids

The interconnected electrical power grids are operated by multilevel control centers with hierarchical architecture. Since large-scale renewables are integrated in different voltage levels, the traditional isolated operation of interconnected power grids is uneconomical and meets operational risk due to lack of coordination. Therefore, the coordination between control centers in different levels and areas are indispensable. However, existing distributed approaches may either encounter numerical problems or converge slowly when the nonlinear AC optimal power flow (ACOPF) models are applied. Moreover, the total iteration number presents an exponential increase with the levels of hierarchical grids. In order to improve computational efficiency, this paper proposes a nested decomposition method for the coordinated operation of multilevel ACOPF problem, which has superlinear convergence and can achieve the optimal solution (KKT point). 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 to nonlinear continuous optimizations with high efficiency. The paper also provides a rigorous proof for its convergence under the condition that the lower level optimization problems are convex with continuously differentiable objectives and constraints. Numerical tests are conducted with three trilevel power grid of different scales, which verify that the computational efficiency and scalability of the proposed algorithm are superior to those of existing methods.