Identifying small groups of lines, whose removal would cause a severe blackout, is critical for the secure operation of the electric power grid. We show how power grid vulnerability analysis can be studied as a bilevel mixed integer nonlinear programming problem. Our analysis reveals a special structure in the formulation that can be exploited to avoid… (More)
I am pleased to deliver, on behalf of nearly 100 contributing computational scientists from leading universities, Department of Energy laboratories, and other federal agencies, the report Report of the First Multiscale Mathematics Workshop: First Steps toward a Roadmap. There is an urgent need for investment in the area of multiscale mathematics. This… (More)
The Dissertation of John Loffeld is approved, and it is acceptable in quality and form for publication on microfilm and electronically: 2013 iii Dedicated to my parents in gratitude for their endless love, support, and encouragement.