A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching

It is well-known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that the U.S. should "encourage, as appropriate, the deployment of advanced transmission technologies" including "optimized transmission line configurations". As such, many authors have studied the problem of determining an optimal set of transmission lines to switch off to minimize the cost of meeting a given power demand under the direct current (DC) model of power flow. This problem is known in the literature as the Direct-Current Optimal Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on heuristic algorithms for generating quality solutions or on the application of DC-OTS to crucial operational and strategic problems such as contingency correction, real-time dispatch, and transmission expansion. The mathematical theory of the DC-OTS problem is less well-developed. In this work, we formally establish that DC-OTS is NP-Hard, even if the power network is a series-parallel graph with at most one load/demand pair. Inspired by Kirchoff's Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new formulation to build a cycle-induced relaxation. We characterize the convex hull of the cycle-induced relaxation, and the characterization provides strong valid inequalities that can be used in a cutting-plane approach to solve the DC-OTS. We give details of a practical implementation, and we show promising computational results on standard benchmark instances

Low-temperature positron-lifetime studies of proton-irradiated silicon

The positron-lifetime technique has been used to identify defects created in high-purity single-crystal silicon by irradiation with 12-MeV protons at 15 K, and the evolution of the defects has been studied by subsequent annealings between 20 and 650 K. Two clear annealing steps were seen in the samples, the first starting at 100 K and the other at 400 K. The first is suggested to be a result of the migration of free, negatively charged monovacancies, and the second is connected to the annealing of some vacancy-impurity complexes, probably negatively charged vacancy-oxygen pairs. The specific trapping rate of positrons to both of these negatively charged monovacancy-type defects has been found to have a clear T-0.5 dependence. The positron lifetime in perfect Si is measured to be 217±1 ps, and the monovacancy lifetime is found to be 275±5 ps. Also the negatively charged vacancy-oxygen complexes were found, both experimentally and theoretically, to give rise to a positron lifetime of about 275 ps