  With numerous distributed energy resources (DERs) integrated into the
distribution networks (DNs), the coordinated economic dispatch (C-ED) is
essential for the integrated transmission and distribution grids. For large
scale power grids, the centralized C-ED meets high computational burden and
information privacy issues. To tackle these issues, this paper proposes a
spatio-temporal decomposition algorithm to solve the C-ED in a distributed and
parallel manner. In the temporal dimension, the multi-period economic dispatch
(ED) of transmission grid (TG) is decomposed to several subproblems by
introducing auxiliary variables and overlapping time intervals to deal with the
temporal coupling constraints. Besides, an accelerated alternative direction
method of multipliers (A-ADMM) based temporal decomposition algorithm with the
warm-start strategy, is developed to solve the ED subproblems of TG in
parallel. In the spatial dimension, a multi-parametric programming projection
based spatial decomposition algorithm is developed to coordinate the ED
problems of TG and DNs in a distributed manner. To further improve the
convergence performance of the spatial decomposition algorithm, the aggregate
equivalence approach is used for determining the feasible range of boundary
variables of TG and DNs. Moreover, we prove that the proposed spatio-temporal
decomposition method can obtain the optimal solution for bilevel convex
optimization problems with continuously differentiable objectives and
constraints. Numerical tests are conducted on three systems with different
scales, demonstrating the high computational efficiency and scalability of the
proposed spatio-temporal decomposition method.
