## Addressing the mathematical challenges of electrical energy systems

February 18, 2013The U.S. Department of Energy’s (DOE) Argonne National Laboratory has been awarded a grant from the DOE Office of Science to tackle the long-term mathematical challenges arising in complex electrical energy systems.

Researchers in Argonne’s Mathematics and Computer Science Division will receive a total of $17.5 million for the five-year project to lead the new Multifaceted Mathematics for Complex Energy Systems Project (M2ACS, pronounced "max"). They will collaborate with mathematicians from Pacific Northwest National Laboratory, Sandia National Laboratories, University of Wisconsin and University of Chicago.

The production, distribution, storage, and use of electrical energy are undergoing significant changes. Demand and production patterns are being altered radically by the advent of "smart grids," renewable generation, hybrid electric vehicles, and storage technologies. The mathematical descriptions of such systems raise numerous challenges, ranging from multiple spatial and temporal variables to uncertainty in future operating conditions.

"To address these challenges, we will develop, analyze, and integrate predictive models of system behavior, new optimization-based sampling approaches, and new analysis methods and scalable algorithms that can exploit the rich mathematical structure," said Mihai Anitescu, Argonne computational mathematician and director of M2ACS. "Our aim is to create the mathematical underpinnings of the future engineering analysis tools that will ensure the efficiency and resiliency of critical energy systems planning and operations."

A centerpiece of the project is an integrative research process that explores and exploits the multiple mathematical features -- "facets" -- of some of the nation’s critical complex energy systems from the direction of multiple mathematical disciplines. Such mathematical facets include the mixture of discrete and continuous variables, dynamical behavior of the system, and the probabilistic nature of some of the forcing and ambient conditions. This research process will allow complex applications to be tackled from multiple disciplinary directions with the latest mathematical ideas and scalable algorithms needed to exploit exascale computing.

"We will use this integrative research process to rapidly prototype the new mathematics techniques," said Anitescu. "These will be iteratively tested and refined on a well-defined set of electrical energy systems problems, including integrated grid and infrastructure planning and real-time system model calibration and prediction."

The M2ACS team members then will apply the results to DOE mission-critical problems: next-generation architectures for electricity generation, storage, and distribution; predictive control of cascading blackouts; and real-time contingency analysis. Particularly challenging are planning problems, which have horizons of decades while needing to respond to transient phenomena that occur in seconds.

The researchers also plan to organize tutorials and minisymposia, in alternating years targeting power-grid engineers and mathematicians. These efforts will be complemented by a summer program in which visitors can work with project members to test their ideas on the electrical energy problems.

"We are confident that we can succeed in this ambitious research agenda because we bring together the critical expertise needed—in optimization, dynamical systems, uncertainty quantification, random processes, data analysis, discrete mathematics, and linear algebra," said Anitescu.