  We discuss how multi-grid computing schemes can be used to design
hierarchical coordination architectures for energy systems. These hierarchical
architectures can be used to manage multiple temporal and spatial scales and
mitigate fundamental limitations of centralized and decentralized
architectures. We present the basic elements of a multi-grid scheme, which
includes a smoothing operator (a high-resolution decentralized coordination
layer that targets phenomena at high frequencies) and a coarsening operator (a
low-resolution centralized coordination layer that targets phenomena at low
frequencies). For smoothing, we extend existing convergence results for
Gauss-Seidel schemes by applying them to systems that cover unstructured
domains. This allows us to target problems with multiple timescales and
arbitrary networks. The proposed coordination schemes can be used to guide
transactions in decentralized electricity markets. We present a storage control
example and a power flow diffusion example to illustrate the developments.
