Rising levels of CO2, a finite supply of fossil fuels, national vulnerability to disruptions in energy supplies due to weather, geologic events and terrorists, and the critical importance of an aging electric power grid have made the robust supply of energy a major national priority. Recent events reinforce this situation. A sudden freeze on Feb 2, 2011 produced rolling blackouts in Texas. The 2008 blackout brought the Northeast to its knees. And the recent earthquake off the coast of Japan demonstrated the impact of unanticipated events on even the most sophisticated, well prepared countries.

It is essential that we make the correct decisions about investments to meet our energy requirements over the long term. In addition, we need to learn how to make the most of the resources we have, using the existing infrastructure to ensure a robust, cost-effective supply of energy to meet the demands of a growing economy that strikes a balance between costs and environmental constraints. Over the past 20 years, dramatic savings have been achieved in transportation and logistics using algorithmic advances in linear, nonlinear and integer programming. In the 1980s, we could solve problems with dozens of integer variables; today, we have algorithms that can solve complex problems with tens of thousands of integer variables.

We do not have general purpose algorithms for solving problems that combine optimization and uncertainty. Even simple forms of uncertainty can make small deterministic optimization problems into problems that are beyond the power of our largest computers. Yet we have to address the many forms of uncertainty that can arise in the planning of our energy systems. For example, we have good models of the uncertainty of wind, yet we do not have even the basic mathematics to deal with the heavy-tailed behavior of electricity spot prices. Yet, these problems pale in comparison to what we face to model the events that led up to the nuclear plant failures in Japan, or the Northeast blackout in 2008.

Uncertainty is one of the most intractable challenges we face in the design of new algorithms, but it is not the only challenge. We would like to model the effect of residential consumption behaviors on the grid. We do not have the tools to model the dynamics of 50 million households on the PJM power grid. We have to plan investments over decades while also dealing with dynamics that evolve on the scale of hours, minutes and seconds. We have to capture the twin towers of complex physical systems that evolve in the presence of different forms of uncertainty. All of these questions introduce issues that cannot be solved with current modeling and algorithmic technologies.

A series of themes cut across this Special Focus. These themes combine methodological challenges such as the need to deal with different time and spatial scales, metrics for risk and reliability, and the challenges of managing large datasets and sharing models for algorithmic testing:

• Multiscale Temporal Models. Electricity generation, transmission, consumption and storage occurs on time frames ranging from fractions of a second to months, in the presence of uncertainties that include brief voltage fluctuations, hourly load and wind variations, daily demand cycles, and seasonal rainfall patterns. The presence of storage, generator ramp rates, and the transportation of physical resources (such as coal and natural gas) has the effect of linking time periods. One can easily see the need for models with tens or hundreds of thousands of time periods.

• Multiscale Spatial Models. Models that capture energy generation, consumption and storage at the level of individual residences and businesses will help us understand how different elements of the grid respond to weather patterns (such as localized cloud cover), demand patterns, the ability to store energy and the ability of the grid to handle the increased load created both by the need to charge electric vehicles, and the need to transmit electricity in both directions. These models will be massive and will require advances in modeling and algorithmic technologies. Risk and reliability measures Risk pervades the design of energy systems. We need to incorporate risk measures so that we meet desired economic and policy objectives. Each problem class introduces unique risk issues that reflect both the nature of different sources of uncertainty and the economic consequences of different types of events.

• Data Representation and Model Sharing. The design of flexible models and efficient algorithms involves the task of making data available for other researchers, and devising ways to share models that makes it possible to perform comparisons of models and algorithms.

• Stochastic Optimization Wind, solar, and electricity prices and loads are all variable and stochastic, but the nature of the uncertainty is different for each. Forward electricity contracts provide mechanisms for reducing price volatility that does not exist with wind and loads. Wind and solar have uncertainties, but with sharply contrasting characteristics in terms of our ability to forecast them. Long-term energy investments have to recognize uncertainty in both technology (breakthroughs in batteries) and policies (such as a carbon tax). Stochastic optimization arises in almost every problem domain in energy systems. Stochastic optimization is an umbrella term that encompasses communities that go under names such as stochastic search, simulation optimization, stochastic programming, approximate dynamic programming, reinforcement learning, and optimal control. Most academic are familiar with subsets of these methods, usually in the context of specific problem classes. However, solving specific problems requires being familiar with a broad range of tools to increase the likelihood that the right tool is being used for a particular problem. The research community needs a better understanding of the unique capabilities of different algorithmic strategies, which requires avoiding the traditional phenomenon where a group of researchers develops expertise in a particular class of algorithms.

We will advance our knowledge in these areas through a series of activities that help to bring together the different communities in energy and mathematics with the goal of identifying the needs that we face, showcasing promising research, highlighting areas that need additional research and then taking steps to enable this research. Workshops in this Special Focus will highlight specific problem domains in the design and control of energy systems and identify modeling and algorithmic challenges that must be addressed in order to solve important operational and policy problems. Research activities expected to come out of the workshops includes the development and testing of algorithms to solve a wide range of stochastic optimization problems arising in energy operations and planning, algorithms for multiscale models, and the development of repositories for data and models to support algorithmic research. Advancing the state of the art in models and algorithms requires the ability to share data and, in some cases, models that can serve as benchmarks. We plan to identify a series of grand challenges that can serve as benchmarks to advance algorithms for major problem classes. We will also produce tutorials to help the community with the challenge of modeling complex problems, and in particular stochastic optimization problems.

Opportunities to Participate:

• Workshops: A variety of workshops and mini-workshops are being planned

• Working Groups: Interdisciplinary ``working groups'' will explore special focus research topics.

• Tutorial: A tutorial will provide background knowledge to those who wish to participate in the special focus or just get an introduction to some of the fundamental issues in the field.

• Seminar Series: There will be a mix of research talks and practitioner presentations.

• Visitor Programs: Applications for research and graduate student visits to the center are invited. Some funds may be available for travel and local support.

• Graduate Student Support: Funds will be set aside for graduate students interested in attending workshops. Students interested in visiting DIMACS during the special focus are encouraged to apply to the special focus organizers.

• Publications: We anticipate that a variety of publications, including AMS-DIMACS volumes, technical reports, abstracts and notes on the WWW, and DIMACS modules will result from the special focus.

Index of Special Focus on Energy and Algorithms

DIMACS Homepage