The electric grid is an indispensable critical infrastructure that people rely on every day. The Department of Energy (DOE) envisions that by 2030, the grid will have evolved into an intelligent energy system, a smart grid. By “smart,” DOE anticipates that the grid will have the characteristics of (1) customer participation, (2) integration of all generation and storage options, (3) new markets and operations, (4) power quality for the 21st century, (5) asset optimization and operational efficiency, (6) self-healing from disturbances, and (7) resiliency against attacks and disasters.1 The next-generation electric grid must be more flexible and resilient than today’s. For example, the mix of generating sources will be more heterogeneous and will vary with time (e.g., contributions from solar and wind power will fluctuate), which in turn will require adjustments such as finer-scale scheduling and pricing. The availability of real-time data from automated distribution networks, smart metering systems, and phasor data hold out the promise of more precise tailoring of services and of control, but only to the extent that large-scale data can be analyzed nimbly.
Today, operating limits are set by off-line (i.e., non-real-time) analysis. Operators make control decisions, especially rapid ones after an untoward event, based on incomplete data. By contrast, the next-generation grid is envisioned to offer something closer to optimized utilization of assets, optimized pricing and scheduling (analogous to, say, time-varying pricing and decision making in Internet commerce), and improved reliability and product quality. In order to design, monitor, analyze, and control such a system, advanced mathematical capabilities must be developed to ensure optimal operation and robustness; the envisioned capabilities will not come about simply from advances in information technology. Within just one of the regional interconnects, a model may have to represent the behavior of hundreds of thousands of components and their complex interaction affecting the performance of the entire grid. While models of this size can be solved now, models where the number of components is many times larger cannot be solved with current technology. As the generating capacity becomes more heterogeneous due to the variety of renewable sources, the number of possible states of the overall system will increase. While the vision is to treat it as a single interdependent, integrated system, the complete system is multiscale (in both space and time) and multiphysics, is highly nonlinear, and has both discrete and continuous behaviors, putting an integrated view beyond current capabilities. In addition, the desire to better monitor and control the condition of the grid leads to large-scale flows of data that must in some cases be analyzed in real time. Creating decision-support
1 U.S. Department of Energy, Smart Grid Research & Development Multi-Year Program Plan (MYPP) 2010-2014—September 2012 Update, September 2012, http://energy.gov/oe/downloads/smart-grid-rd-multi-year-program-plan-2010-2014-September-2012-update.
systems that can identify emerging problems and calculate corrective actions quickly is a nontrivial challenge. Decision-support tools for non-real-time tasks—such as pricing, load forecasting, design, and system optimization—also require new mathematical capabilities.
Mathematical modeling and control of the electric grid has been an active area of research for decades. However, in 1996 a major outage that affected 11 Western states and 2 Canadian provinces—coupled with emerging concerns that computers would malfunction after December 31, 1999—increased awareness of a lack of complete understanding of the overall system and its frailties. For several decades the Electric Power Research Institute funded a program of research to develop tools for recognizing early signs of instability and means to counter them. That research was largely of a mathematical nature.
More recently, DOE has been supporting research to develop the analytical and computational tools that will be necessary for the next-generation grid. Many frontier areas of the mathematical sciences are represented in that body of research. For example, the 2011 DOE conference Computational Needs for the Next Generation Electric Grid identified seven computational challenges associated with the operation and planning of the electric power system:
- Cloud computing,
- Hierarchical models,
- Analysis and planning for contingencies,
- Modeling of infrastructure interdependencies,
- Modeling and controlling multi-time-scale and multidimensional power systems,
- Optimization under uncertainty, and
- Unit commitment and economic dispatch.2
Other than the first of these, all require or could benefit from new tools from the mathematical sciences. In short, the future grid will rely on integrating advanced computation and massive data to create a better understanding that supports decision making. That future grid cannot be achieved simply by using the same mathematics on more powerful computers. Instead, the future will require new classes of models and algorithms, and those models must be amenable to coupling into an integrated system.
To complement this research specifically focused on tools for the next-generation grid, a range of potentially applicable research exists. Examples include research into the general topics of uncertainty quantification, simulation and analysis of complex adaptive systems, simulation and analysis of multi-time-scale systems, and methods for characterizing and controlling resilience and reliability. This research is taking place in a range of science and engineering disciplines. More generally, complex adaptive systems have been studied for several decades, and a good deal of “mathematical machinery” has been developed.
While many of the necessary tools are inherently mathematical, the best progress in these complex areas is achieved through multidisciplinary efforts, involving a community with diverse strengths and perspectives. In order to develop the next generation of tools required for the challenges of the smart grid, DOE commissioned the National Research Council (NRC)3 to engage in a study with the following charge:
- What are the critical areas of mathematical and computational research that must be addressed for the next-generation electric transmission and distribution (grid) system? Identify future needs. In what ways, if any, do current research efforts in these areas (including non-U.S. efforts) need to be adjusted or augmented?
- Because this research frontier is best approached by a community that is truly multidisciplinary—including not only a cutting-edge knowledge of mathematics, statistics, and computation, but also a deep understanding of the emerging electric grid and of the questions that need answering to realize its potential—How
2 U.S. Department of Energy, Computational Needs for the Next Generation Electrical Grid. Proceedings April 19-20, 2011 (J.H. Eto and R.J. Thomas, eds.), LBNL-5105E, 2012, http://energy.gov/oe/downloads/proceedings-computational-needs-next-generation-electric-grid-workshop-april-19-20-2011.
3 Effective July 1, 2015, the institution is called the National Academies of Sciences, Engineering, and Medicine. References in this report to the National Research Council are used in a historical context identifying programs prior to July 1.
can DOE help to effectively build this community? What mix of backgrounds is needed and how can the community be developed? How can DOE extend its reach beyond its existing ties?
To address this charge, the NRC assembled a committee of 15 members who collectively have academic, industrial, and national laboratory experience in both power systems and the relevant mathematical areas. In addition to meeting five times over the course of the study, a subset of the committee planned and ran a workshop on February 11-12, 2015, at the Arnold and Mabel Beckman Center of the National Academies in Irvine, California, to gain outside perspectives. The agenda of that workshop is appended to this report, and a published summary of that workshop is available at http:///www.nap.edu/21808.
The grid itself and the conditions under which it operates are changing, and the end state is uncertain. For example, new resources, especially intermittent renewable energy such as wind and solar, are likely to become more important, and these place new demands on controlling the grid to maintain reliability. At the same time, the increasing affordability of storage technology may ease controllability. Many technical improvements could be made to the grid, such as those noted below, but this report does not aim to cover them all nor does it presume one possible future grid scenario over another. The next-generation grid will require the efforts of many other scientific disciplines, including economics, social science, market planning, and risk analysis, to name a few, and some of these have significant mathematical content. After discussions with the study’s sponsor, the committee interpreted its charge to focus on those mathematical research directions with broad impact, and which must be advanced in order to enable the next-generation grid, rather than to discuss the full range of possible improvements to the grid or mathematics that may play a secondary role in the next-generation grid’s planning or management.
The committee also recognizes that acceptance of the conclusions and recommendations in this report by key industry segments—utilities, grid and market operators, market participants, software and system vendors, and the research community—is essential if productive research and development is to be conducted and successful results adopted. Some of the recommendations—for alternating current (ac) optimal power flow (ACOPF), for stochastic scheduling, and for integration of different time-scale models—need buy-in from key user segments to garner support for the research and development (R&D) efforts. Others, such as development and use of open data sets for testing, need buy-in to change in the way things are done. However, suggestions for obtaining this necessary buy-in were beyond the committee’s charge.
This report contains the recommendations of the committee for new research and policies to improve the mathematical foundations for the next-generation grid.
- New technologies for measurement and control of the grid are becoming available. Wide area measurement systems provide a much clearer picture of what is happening on the grid, which can be vital during disruptions, whether from equipment failure, weather conditions, or terrorist attack. Such systems send a huge amount of data to control centers, but the data are of limited use unless they can be analyzed and the results presented in a way suitable for timely decision making.
- Improved models of grid operation can also increase the efficiency of the grid, taking into account all the resources available and their characteristics; however, a systematic framework for modeling, defining performance objectives, ensuring control performance, and providing multidimensional optimization will be needed. If the grid is to operate in a stable way over many different kinds of disturbances or operating conditions, it will be necessary to introduce criteria for deploying more sensing and control in order to provide a more adaptive control strategy. These criteria include expense and extended time for replacement.
- Other mathematical and computational challenges arise from the integration of more alternative energy sources (e.g., wind and photovoltaics) into the system. Nonlinear alternating current ACOPF can be used to help reduce the risk of voltage collapse and enable lines to be used within the broader limits, and flexible ac transmission systems and storage technology can be used for eliminating stability-related line limits.
- Transmission and distribution are often planned and operated as separate systems, and there is little feedback between these separate systems beyond the transmission system operator’s knowing the amount of power to be delivered and the distribution system operator’s knowing what voltage to expect. As different
types of distributed energy resources, including generation, storage, and responsive demand, are embedded within the distribution network, different dynamic interactions between the transmission and distribution infrastructure may occur. One example is the synchronous and voltage stability issues of distributed generation that change the dynamic nature of the overall power system. It will be important in the future to establish more complete models that include the dynamic interactions between the transmission and distribution systems, including demand-responsive loads.
- In addition, there need to be better planning models for designing the sustainable deployment and utilization of distributed energy resources. Estimating future demand for grid electricity and the means to provide it entail uncertainty. New distributed-generation technologies move generation closer to where the electricity is consumed. Climate change will introduce several uncertainties affecting the grid. In addition to higher temperatures requiring increased air conditioning loads during peak hours, shifting rainfall patterns may affect the generation of hydroelectricity and the availability of cooling water for generating plants. The frequency of intense weather events may increase. Policies to reduce emissions of carbon dioxide, the main greenhouse gas, will affect generating sources. Better tools to provide more accurate forecasting are needed.
- Modeling and mitigation of high-impact, low-frequency events (including coordinated physical or cyberattack; pandemics; high-altitude electromagnetic pulses; and large-scale geomagnetic disturbances) is especially difficult because few very serious cases have been experienced. Outages from such events could affect tens of millions of people for months. Fundamental research in mathematics and computer science could yield dividends for predicting the consequences of such events and limiting their damage.
Ten years ago, few people could have predicted the current energy environment in the United States—from the concern for global warming, to the accelerated use of solar and wind power, to the country’s near energy independence. Each of these developments, and others, will profoundly shape the future electric grid, and with it the analytic challenges and associated mathematical advances needed to cope with those developments. For that reason, the committee’s recommendations do not focus on overcoming the inadequacies of specific algorithms or techniques. Rather, its recommendations are designed to help direct future research as the grid evolves and to give the nation’s R&D infrastructure the tools it needs to effectively develop, test, and use this research. The committee’s recommendations are in four areas: data availability, modeling capabilities, improved algorithms, and the organizational structure needed to integrate improvements in these areas and to make them accessible to a large community of researchers.
The recommendations and their discussion that follow are grouped so that those concerning the same subject are discussed together. For that reason, some are listed out of sequence.
Current algorithms do not scale well to the anticipated growth in the number of nodes in a large marketing area. One algorithm that does so is of particular importance: the mathematical programming formulation of the ACOPF problem. The problem is discussed in Chapter 2 and formulated mathematically in Chapter 7.
Recommendation 1: The Department of Energy should develop and test a full ac optimal power flow (ACOPF) model with an optimization algorithm using all nodes in the market area, taking advantage of supercomputers and parallel processing and respecting all thermal and voltage constraints. (Chapter 2)
The committee believes that available data are not sufficiently used by either the power industry or other potential researchers. It found that data used by the community of power engineers to develop and test algorithms are not available to the larger community because specialized software is needed to access them. To make the data available to a larger research community, the committee makes the following two recommendations:
Recommendation 2: The Federal Energy Regulatory Commission (FERC) should require that all text file formats used for the exchange of FERC715 power flow cases be fully publicly available. (Chapter 3)
Recommendation 3: The Federal Energy Regulatory Commission should require that descriptions of all models used in system-wide transient stability studies be fully public, including descriptions of any associated text file formats. (Chapter 3)
Most of the data being generated by the electric power industry are viewed as proprietary, both because they would reveal information about company operations and because they might reveal information useful to terrorists. For this reason, synthetic data that are sufficient to mirror real operations are required for future research.
Recommendation 4: Given the critical infrastructure nature of the electric grid and the critical need for developing advanced mathematical and computational tools and techniques that rely on realistic data for testing and validating those tools and techniques, the power research community, with government and industry support, should vigorously address ways to create, validate, and adopt synthetic data and make them freely available to the broader research community. (Chapter 6)
Recommendation 9: The Department of Energy should sponsor additional efforts to create synthetic data libraries to facilitate studies of, and tool building for, the reliability and control of the future electric grid. (Chapter 8)
The committee believes that, for reasons that are not completely clear, the power industry is not making sufficient use of the data available to it—perhaps because it does not fully recognize the value of such data for both prediction and control. The power industry hires very few data scientists.
Recommendation 7: The Department of Energy should support research on data-driven approaches applied to the operations, planning, and maintenance of power systems. This would include better machine-learning models for reliability, comprehensible classification and regression, low-dimensional projections, visualization tools, clustering, and data assimilation. A partial goal of this research would be to quantify the value of the associated data. (Chapter 6)
The two mathematical areas that the committee believes will yield greatly improved capabilities are dynamical systems and mathematical programming, particularly nonlinear and nonconvex programming.
Recommendation 6: The Department of Energy should support research to extend dynamical systems theory and associated numerical methods to encompass classes of systems that include electric grids. In addition to simulation of realistic grid models, one goal of this research should be to identify problems that exemplify in their simplest forms the mathematical issues encountered in simulating nonlinear, discontinuous, and stochastic time-dependent dynamics of the power system. The problems should be implemented in computer models and archived in a freely available database, accompanied by thorough documentation written for both mathematicians and engineers. Large grid-sized problems that exemplify the difficulty in scaling the methods should be presented as well. (Chapter 4)
Recommendation 8: Order-of-magnitude improvements in nonlinear, nonconvex optimization algorithms are needed to enable their use in wholesale electricity market analysis and design for solving the ac optimal power flow problem. Such algorithms are essential to determine voltage magnitudes. Therefore the Department of Energy should provide enhanced support for fundamental research on nonlinear, nonconvex optimization algorithms. (Chapter 6)
There is a similarity between the electric grid and the climate system—both are sufficiently complex as to defy precise analysis. For that reason, the use of various kinds of machine learning, along with improved control and optimization algorithms, is important.
Recommendation 5: Integration of theory and computational methods from machine learning, dynamical systems, and control theory should be a high-priority research area. The Department of Energy should support such research, encouraging the use of real and synthetic phasor measurement unit data to facilitate applications to the power grid. Establishment of test-beds for physical experiments would provide valuable additional sources of data. (Chapter 6)
The committee believes that the electric generation research community would benefit from the availability of new open-source software.
Recommendation 10: The Department of Energy and National Science Foundation should sponsor the development of new open-source software for the next-generation electric grid research community. (Chapter 8)
Finally, the committee has found a need for coordination among a community broader than the national research laboratories.
Recommendation 11: In view of the importance of its efforts to coordinate power grid research at the national laboratories, the Department of Energy should broaden this coordination to include academic and industry researchers. (Chapter 8)
Recommendation 12: The Department of Energy should establish a National Electric Power Systems Research Center to address fundamental research challenges associated with analysis for the future electric system. The center would act as an interface between the power industry, government, and universities in developing new computational and mathematical solutions for data and modeling issues and in sharing valuable data. (Chapter 8)