## Anitescu discusses mathematics challenges of energy systems

July 16, 2014Mihai Anitescu gave an invited presentation on June 12–13, 2014, at the initial meeting to launch the National Research Council study of the next-generation electric grid.

The study, funded by DOE, is titled *Analytic Research Foundations for the Next Generation Electric Grid*.

Anitescu’s presentation was designed to familiarize the study participants with the mathematics challenges of energy systems. He began with a description of the existing and foreseen challenges posed by the large and increasing complexity of the power grid. These include the large number of components – such as number of transmission and distribution lines and the enormous range of time scales from microseconds in power electronics to a few decades in transmission planning. Moreover, researchers need to account for the uncertainty in ambient condition, and increasingly, renewable-driven supply, the competing goals of cost efficiency and increased reliability, and the fact that we want to extract even more value out of the power grid, by allowing bidirectional energy transfer, by including more logic in all devices down to appliance levels (“smart grid”), and by coupling new technologies to it such as plug-in hybrid vehicles.

“All these factors mean that we have a rich environment for mathematical research,” said Anitescu.

He emphasized that sophisticated modeling techniques – such as multiscale algorithms, that reduce the spatial, temporal, and functional complexity – are widely used in modeling, but systematic error analysis of these techniques is rare. In turn, this situation potentially creates risks that may be difficult to estimate currently. Contingency analysis – ensuring that energy dispatch is safe even when critical components fail – is another challenge because of its complexity, which is exponential in the already large number of components. And in the area of graph analysis, the deep connections between network topologies and physical properties are far from being completely elucidated. As a result, the power grid is a target-rich environment for mathematicians, who can significantly help in elucidating some of the mysteries of the current and future power grid, by carrying out new analysis of multiscale techniques, by identifying new mathematical patterns that can simplify the complexity of the description of power systems, and by developing mathematical areas in areas up to now unexplored.

According to Anitescu, the area of mathematical optimization is undoubtedly the “glue-all” topic for the power grid. Many if not most problems are “minimize cost, subject to physical constraint and reliability metric constraints, or margins,” he said.

But optimization faces new mathematical and numerical challenges in the area before leading to better answers. “An important trend is putting more physics – more details and more dynamic constraints – in the system when optimizing it,” said Anitescu. “And accounting for uncertainty further complicates the issue.” He noted that important stakeholders believe stochastic optimization should be a key paradigm in accommodating uncertainty but it requires a large number of good scenarios and hence will need development of smart algorithms.

Highlighting Anitescu’s presentation were numerous illustrations of applications being tackled successfully on today’s supercomputers. For example, a stochastic economic dispatch for Illinois with up to 2 billion variables and 10,000 scenarios was solved in under an hour on the IBM Blue Gene/P at Argonne National Laboratory. In another example, he presented the economic benefits of transmission topology control: in a one-hour simulation the base cost was $541,000; if similar savings were achieved throughout the year, the estimated savings would be $80 million for the PJM Interconnection.

Anitescu also cited numerous areas in which further study is essential. For example, the optimal power flow problem is solved by a semidefinite programming relaxation, but practical estimates of the order of relaxations are lacking. Partitioned integration and new linear algebra are needed in order to help solve moderate-sized problems rapidly. Also needed are better approaches to existing methods such as best path computation in rare event sampling. And getting fully expressed models and constraints, if possible, is essential for convincing stakeholders to adopt algorithms resulting from new research.

“The power grid presents enormous ongoing and upcoming opportunities and challenges for mathematical sciences. An integrated computer science/math/power grid environment is the proper approach to strike the proper depth/relevance mix that fits all participants,” Anitescu said.

Colleagues contributing to this work: Christopher Demarco (U Wisconsin), Victor Zavala (Argonne), Mahantesh Halappanavar (PNNL), Henry Huang (PNNL), Guang LIn (PNNL), Shaobu Wang (PNNL), Dan Molzahn (U Michigan), Kory Hedman (Arizona State), Shmuel Oren (U Cal, Berkeley), Shrirang Abhyankar (ANL), Cosmin Petra (ANL), Emil Constantinescu (ANL), Jonathan Weare (U Chicago)