If the United States is to sustain its economic prosperity, quality of life, and global competitiveness, it must continue to have an abundance of secure, reliable, and affordable energy resources. There have been many improvements in the technology and capability of the electric grid over the past several decades. Many of these advances to the grid depend on complex mathematical algorithms and techniques, and as the complexity of the grid has increased, the analytical demands have also increased. The workshop summarized in this report was developed as part of an ongoing study of the Committee on Analytical Research Foundations for the Next-Generation Electric Grid. Mathematical Sciences Research Challenges for the Next-Generation Electric Grid summarizes the presentations and discussions from this workshop. This report identifies critical areas of mathematical and computational research that must be addressed for the next-generation electric transmission and distribution system and to identify future needs and ways that current research efforts in these areas could be adjusted or augmented.

Electricity is the lifeblood of modern society, and for the vast majority of people that electricity is obtained from large, interconnected power grids. However, the grid that was developed in the 20th century, and the incremental improvements made since then, including its underlying analytic foundations, is no longer adequate to completely meet the needs of the 21st century. The next-generation electric grid must be more flexible and resilient. While fossil fuels will have their place for decades to come, the grid of the future will need to accommodate a wider mix of more intermittent generating sources such as wind and distributed solar photovoltaics. Achieving this grid of the future will require effort on several fronts. There is a need for continued shorter-term engineering research and development, building on the existing analytic foundations for the grid. But there is also a need for more fundamental research to expand these analytic foundations. Analytic Research Foundations for the Next-Generation Electric Grid provide guidance on the longer-term critical areas for research in mathematical and computational sciences that is needed for the next-generation grid. It offers recommendations that are designed to help direct future research as the grid evolves and to give the nation's research and development infrastructure the tools it needs to effectively develop, test, and use this research.

Electricity is the lifeblood of modern society, and for the vast majority of people that electricity is obtained from large, interconnected power grids. However, the grid that was developed in the 20th century, and the incremental improvements made since then, including its underlying analytic foundations, is no longer adequate to completely meet the needs of the 21st century. The next-generation electric grid must be more flexible and resilient. While fossil fuels will have their place for decades to come, the grid of the future will need to accommodate a wider mix of more intermittent generating sources such as wind and distributed solar photovoltaics. Achieving this grid of the future will require effort on several fronts. There is a need for continued shorter-term engineering research and development, building on the existing analytic foundations for the grid. But there is also a need for more fundamental research to expand these analytic foundations. Analytic Research Foundations for the Next-Generation Electric Grid provide guidance on the longer-term critical areas for research in mathematical and computational sciences that is needed for the next-generation grid. It offers recommendations that are designed to help direct future research as the grid evolves and to give the nation's research and development infrastructure the tools it needs to effectively develop, test, and use this research.

This book links the challenges to which the electricity network is exposed with the range of new technology, methodologies and market mechanisms known under the name "smart grid." The main challenges will be described by the way in which they impact the electricity network: the introduction of renewable electricity production, energy efficiency, the introduction and further opening of the electricity market, increasing demands for reliability and voltage quality, and the growing need for more transport capacity in the grid. Three fundamentally different types of solutions are distinguished in this book: solutions only involving the electricity network (like HVDC and active distribution networks), solutions including the network users but under the control of the network operator (like requirements on production units and curtailment), and fully market-driven solutions (like demand response). An overview is given of the various solutions to the challenges that are possible with new technology; this includes some that are actively discussed elsewhere and others that are somewhat forgotten. Linking the different solutions with the needs of the electricity network, in the light of the various challenges, is a recurring theme in this book. Table of Contents: Introduction / The Challenges / Solutions in the Grid / Participation of Network Users / Market Incentives / Discussion / Conclusions

Americans' safety, productivity, comfort, and convenience depend on the reliable supply of electric power. The electric power system is a complex "cyber-physical" system composed of a network of millions of components spread out across the continent. These components are owned, operated, and regulated by thousands of different entities. Power system operators work hard to assure safe and reliable service, but large outages occasionally happen. Given the nature of the system, there is simply no way that outages can be completely avoided, no matter how much time and money is devoted to such an effort. The system's reliability and resilience can be improved but never made perfect. Thus, system owners, operators, and regulators must prioritize their investments based on potential benefits. Enhancing the Resilience of the Nation's Electricity System focuses on identifying, developing, and implementing strategies to increase the power system's resilience in the face of events that can cause large-area, long-duration outages: blackouts that extend over multiple service areas and last several days or longer. Resilience is not just about lessening the likelihood that these outages will occur. It is also about limiting the scope and impact of outages when they do occur, restoring power rapidly afterwards, and learning from these experiences to better deal with events in the future.

This book provides an overview of state-of-the-art research on “Systems and Optimization Aspects of Smart Grid Challenges.” The authors have compiled and integrated different aspects of applied systems optimization research to smart grids, and also describe some of its critical challenges and requirements. The promise of a smarter electricity grid could significantly change how consumers use and pay for their electrical power, and could fundamentally reshape the current Industry. Gaining increasing interest and acceptance, Smart Grid technologies combine power generation and delivery systems with advanced communication systems to help save energy, reduce energy costs and improve reliability. Taken together, these technologies support new approaches for load balancing and power distribution, allowing optimal runtime power routing and cost management. Such unprecedented capabilities, however, also present a set of new problems and challenges at the technical and regulatory levels that must be addressed by Industry and the Research Community.

Cutting edge computational mathematics are ubiquitous in renewable energy research. Problems in resilient and reliable electric grid operations, infrastructure planning, wind farm yaw control, and more demand sophisticated and scalable computational tools that enable the transition of renewable energy technologies from proof of concept to deployment into our energy system. The mission of the Computational Science Center at NREL is to lead the lab's efforts to solve energy challenges using high-performance computing (HPC), computational science, applied mathematics, scientific data management, visualization, and informatics. In this poster, we provide a short overview of three areas of computational mathematics research at NREL: wind power scenario generation for stochastic grid operations and infrastructure planning, improved rational function approximations for electromagnetic transients codes, and wind farm yaw control using a combination of the Alternating Direction Method of Multipliers (ADMM) and reinforcement learning (RL). Increasing penetrations of renewable energy into power grids motivate the investigation of new approaches to characterizing uncertainty for five-minute economic dispatch problems. Similarly, as the penetration of distributed energy resources on power grids increases, it becomes important to revisit our methods of modelling transient phenomena, i.e. electromagnetic transients programs. Finally, the combination of ADMM and RL for wind farm yaw control presented here can potentially increase the efficiency of the deployed distributed controllers by orders of magnitude.