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6 Mathematical Research Priorities Arising From the Electric Grid
Pages 93-110

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From page 93...
... But finding such a solution requires either fundamental advances in general algorithms for nonlinear, nonconvex optimization problems or insights that rely on the network structure of the power grid. The electricity markets pose challenges that go beyond improvements in optimization algorithms.
From page 94...
... This lack of easily available high-quality, realistic power grid data has become a thorny issue in a number of research communities that seek to address mathematical problems arising in power engineering, advance the state of the art in computation and simulation, and test new market designs that may result in better economic efficiencies. Some researchers with good access to power utilities enjoy the ability to test ideas on real data, but even here they are usually unable to publish full results from such tests in the open literature.
From page 95...
... In those latter cases the use of synthetic data -- that is, data that are not derived from real measurements but rather are synthesized from real measurements -- could be an option provided the data sets are sufficiently rich enough to support new findings that would have been discovered by using real data while masking certain information such as private information (health, census, and the like) , sensitive economic information, or specific parameters and topologies associated with a critical infrastructure.
From page 96...
... 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. Random Topology Networks This subsection describes a specific problem as an example of the type of mathematical research required to generate synthetic data.
From page 97...
... Finite-time Lyapunov exponents quantify this geometry, which results in a cloud of initial conditions flowing to become almost a multidimensional ribbon. In the language of machine learning, the flow map F advances trajectories by a time t as an approximation of a low-rank map.
From page 98...
... In particular, using data collected about the inputs and corresponding performance levels for various control parameter settings, a machine learning method should be able to create a function that predicts what the performance level is for a new control parameter setting. The expert system does not need to know anything about the dynamical system in order to make these predictions, it simply uses past data from the simulations.
From page 99...
... 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.
From page 100...
... Each area is responsible for coor dinating its resources so that its level frequency is regulated within acceptable limits and deviations from the scheduled net power exchange with the neighboring control areas are regulated accordingly. A closer look into this scheme reveals that it is intended to regulate frequency in response to relatively slow dis turbances, under the assumption that primary control of power plants has done its job in stabilizing the transients.
From page 101...
... In commercial transient stability packages this relatively common situation is often handled by splitting the integration time step. Increasing reliance on electronic control components makes this issue of hybrid simulation even more common.
From page 102...
... Progress in dynamical systems theory has repeatedly begun with the distillation of mathematical questions and conjectures that isolate critical issues in their simplest manifestations from the more complicated contexts in which they arose. An important example for the power grid that illustrates this strategy draws on the classification of bifurcations of vector fields.
From page 103...
... Creating Hybrid Data/Human Expert Systems for Operations When a serious problem occurs on the power grid, operators might be overloaded with alarms, and it is not always clear what the highest priority action items should be. For example, a major disturbance could generate thousands of alarms (Kezunoic and Guan, 2009)
From page 104...
... This may require an algorithm for image segmentation or image clustering. Machine Learning for Long-Term Planning Some of the key problems in the future power grid are behavioral: Will customers adopt certain energy-efficient behaviors if they are given rebates?
From page 105...
... The SDP relaxation just given is not the only convex relaxation for ACOPF and may not necessarily be the tightest (or, especially, the fastest: large SDPs can be challenging)
From page 106...
... Recommendation 8: Orders-of-magnitude improvement 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 (ACOPF) problem.
From page 107...
... In more accessible applications of robust optimization it is possible to pose the min-max problem as a single "compact" (polynomial-size) convex optimization problem.
From page 108...
... Coupled infrastructure simulations will benefit from the synthetic data libraries called for in Recommendation 9, and from the software called
From page 109...
... 2010. The topological and electrical structure of power grids.
From page 110...
... 2014b. Convex relaxation of optimal power flow, Part II: Exactness.


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