Related papers: Multi-Grid Schemes for Multi-Scale Coordination of…

Demand response represents a significant but largely untapped resource that can greatly enhance the flexibility and reliability of power systems. This paper proposes a hierarchical control framework to facilitate the integrated coordination…

The convergence of multigrid methods degrades significantly if a small number of low quality cells are present in a finite element mesh, and this can be a barrier to the efficient and robust application of multigrid on complicated geometric…

One critical value microgrids bring to power systems is resilience, the capability of being able to island from the main grid under certain conditions and connect back when necessary. Once islanded, a microgrid must be synchronized to the…

We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…

The flexible, efficient, and reliable operation of grid-interactive efficient buildings (GEBs) is increasingly impacted by the growing penetration of distributed energy resources (DERs). Besides, the optimization and control of DERs,…

The convergence rate of a multigrid method depends on the properties of the smoother and the so-called grid transfer operator. In this paper we define and analyze new grid transfer operators with a generic cutting size which are applicable…

We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…

In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…

Data centers (DCs) can help decarbonize the power grid by helping absorb renewable power (e.g., wind and solar) due to their ability to shift power loads across space and time. However, to harness such load-shifting flexibility, it is…

This paper presents a time decomposition strategy to reduce the computational complexity of power system multi-interval operation problems. We focus on the economic dispatch problem. The considered scheduling horizon is decomposed into…

We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…

Hierarchical optimization architectures are used in power systems to manage disturbances and phenomena that arise at multiple spatial and temporal scales. We present a graph modeling abstraction for representing such architectures and an…

We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…

This paper points out some key drawbacks of today's modeling and control underlying hierarchical electric power system operations and planning as the hidden roadblocks on the way to decarbonization. We suggest that these can be overcome by…

We study the convergence of multigrid schemes for the Helmholtz equation, focusing in particular on the choice of the coarse scale operators. Let G_c denote the number of points per wavelength at the coarse level. If the coarse scale…

Leveraging electrochemical and thermal energy storage systems has been proposed as a strategy to reduce peak power in data centers. Thermal energy storage systems, such as chilled water tanks, have gained increasing attention in data…

Modern energy systems in vehicles and built infrastructure are governed by high-dimensional dynamics spanning multiple physical domains (e.g., electrical, thermal, mechanical) and timescales. This tutorial paper presents a graph-based…

Grid technologies aim at enabling a coordinated resource-sharing and problem-solving capabilities over local and wide area networks and span locations, organizations, machine architectures and software boundaries. The heterogeneity of…

We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence…