Publications

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This document is an online supplement for Sparse, Dense, and Compact Linearizations of the AC OPF. Here we present complete derivations of the formulations examined, details of the lazy constraint algorithm, and full computational results supporting Sparse, Dense, and Compact Linearizations of the AC OPF.

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This paper presents a multi-Time period two-stage stochastic mixed-integer linear optimization model which determines the optimal hardening investments to improve power system resilience to natural disaster threat scenarios. The input to the optimization model is a set of scenarios for specific natural disaster events, that is based on historical data. The objective of the optimization model is to minimize the expected weighted load shed from the initial impact and the restoration process over all scenarios. The optimization model considers the initial impact of the severe event by using electromechanical transient dynamic simulations. The initial impact weighted load shed is determined by the transient simulation, which allows for secondary transients from protection devices and cascading failures. The rest of the event, after the initial shock, is modeled in the optimization with a multi-Time period dc optimal power flow (DCOPF) which is initialized with the solution from the dynamic simulation. The first stage of the optimization model determines the optimal investments. The second stage, given the investments, determines the optimal unit commitment, generator dispatch, and transmission line switching during the multi-Time period restoration process to minimize the weighted load shed over all scenarios. Note, an investment will change the transient simulation result, and therefore change the initialization to the DCOPF restoration model. The investment optimization model encompasses both the initial impact (dynamic transient simulation results) and the restoration period (DCOPF) of the event, as components come back online. The model is tested on the IEEE RTS-96 system.

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Exploration of the fundamental chemical behavior of the AlCl{sub 3}/SO{sub 2}Cl{sub 2} catholyte system for the ARDEC Self-Destruct Fuze Reserve Battery Project under accelerated aging conditions was completed using a variety of analytical tools. Four different molecular species were identified in this solution, three of which are major. The relative concentrations of the molecular species formed were found to depend on aging time, initial concentrations, and storage temperature, with each variable affecting the kinetics and thermodynamics of this complex reaction system. We also evaluated the effect of water on the system, and determined that it does not play a role in dictating the observed molecular species present in solution. The first Al-containing species formed was identified as the dimer [Al({mu}-Cl)Cl{sub 2}]{sub 2}, and was found to be in equilibrium with the monomer, AlCl{sub 3}. The second species formed in the reaction scheme was identified by single crystal X-ray diffraction studies as [Cl{sub 2}Al({mu}-O{sub 2}SCl)]{sub 2} (I), a scrambled AlCl{sub 3}{center_dot}SO{sub 2} adduct. The SO{sub 2}(g) present, as well as CL{sub 2}(g), was formed through decomposition of SO{sub 2}CL{sub 2}. The SO{sub 2}(g) generated was readily consumed by AlCl{sub 3} to form the adduct 1 which was experimentally verified when 1 was also isolated from the reaction of SO{sub 2}(g) and AlCl {sub 3}. The third species found was tentatively identified as a compound having the general formula {l_brace}[Al(O)Cl{sub 2}][OSCl{sub 2}]{r_brace}{sub n}. This was based on {sup 27}Al NMR data that revealed a species with tetrahedrally coordinated Al metal centers with increased oxygen coordination and the fact that the precipitate, or gel, that forms over time was shown by Raman spectroscopic studies to possess a component that is consistent with SOCl{sub 2}. The precursor to the precipitate should have similar constituents, thus the assignment of {l_brace}[Al(O)Cl{sub 2}][OSCl{sub 2}]{r_brace}{sub n}. The precipitate was further identified by solid state {sup 27}Al MAS NMR data to possess predominantly octahedral A1 metal center which implies {l_brace}[Al(O)Cl{sub 2}][OSCl{sub 2}]{r_brace}{sub n} must undergo some internal rearrangements. A reaction sequence has been proposed to account for the various molecular species identified in this complex reaction mixture during the aging process. The metallurgical welds were of high quality. These results were all visually determined there was no mechanical testing performed. However, it is recommended that the end plate geometry and weld be changed. If the present weld strength, based on .003' - .005' penetration, is sufficient for unit performance, the end plate thickness can be reduced to .005' instead of the .020' thickness. This will enable the plug to be stamped so that it can form a cap rather than a plug and solve existing problems and increase the amount of catholyte which may be beneficial to battery performance.

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The effect of the density and in-plane distribution of interfacial interactions on crack initiation in an epoxy-silicon joint was studied in nominally pure shear loading. Well-defined combinations of strong (specific) and weak (nonspecific) interactions were created using self-assembling monolayers. The in-plane distribution of strong and weak interactions was varied by employing two deposition methods: depositing mixtures of molecules with different terminal groups resulting in a nominally random distribution, and depositing methyl-terminated molecules in domains defined lithographically with the remaining area interacting through strong acid-base interactions. The two distributions lead to very different fracture behavior. For the case of the methyl-terminated domains (50 {micro}m on a side) fabricated lithographically, the joint shear strength varies almost linearly with the area fraction of strongly interacting sites. From this we infer that cracks nucleate on or near the interface over nearly the entire range of bonded area fraction and do so at nearly the same value of local stress (load/bonded area). We postulate that the imposed heterogeneity in interfacial interactions results in heterogeneous stress and strain fields within the epoxy in close proximity to the interface. Simply, the bonded areas carry load while the methyl terminated domains carry negligible load. Stress is amplified adjacent to the well-bonded regions (and reduced adjacent to the poorly bonded regions), and this leads to crack initiation by plastic deformation and chain scission within the epoxy near the interface. For the case of mixed monolayers, the dependence is entirely different. At low areal density of strongly interacting sites, the joint shear strength is below the detection limit of our transducer for a significant range of mixed monolayer composition. With increasing density of strongly interacting sites, a sharp increase in joint shear strength occurs at a methyl terminated area fraction of roughly 0.90. We postulate that this coincides with the onset of yielding in the epoxy. For methyl-terminated area fractions less than 0.85, the joint shear strength becomes independent of the interfacial interactions. This indicates that fracture no longer initiates on the interface but away from the interface by a competing mechanism, likely plastic deformation and chain scission within the bulk epoxy. The data demonstrate that the in-plane distribution of interaction sites alone can affect the location of crack nucleation and the far-field stress required.

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