Strengthening QC relaxations of optimal power flow problems by exploiting various coordinate changes

Motivated by the potential for improvements in electric power system economics, this dissertation studies the AC optimal power flow (AC OPF) problem. An AC OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering limits. The difficulty of an AC OPF problem is strongly connected to its feasible space\u27s characteristics. This dissertation first investigates causes of nonconvexities in AC OPF problems. Understanding typical causes of nonconvexities is helpful for improving AC OPF solution methodologies. This dissertation next focuses on solution methods for AC OPF problems that are based on convex relaxations. The quadratic convex (QC) relaxation is one promising approach that constructs convex envelopes around the trigonometric and product terms in the polar representation of the power flow equations. This dissertation proposes several improvements to strengthen QC relaxations of OPF problems. The first group of improvements provides tighter envelopes for the trigonometric functions and product terms in the power flow equations. Methods for obtaining tighter envelopes includes implementing Meyer and Floudas envelopes that yield the convex hull of trilinear monomials. Furthermore, by leveraging a representation of line admittances in polar form, this dissertation proposes tighter envelopes for the trigonometric terms. Another proposed improvement exploits the ability to rotate the base power used in the per unit normalization in order to facilitate the application of tighter trigonometric envelopes. The second group of improvements propose additional constraints based on new variables that represent voltage magnitude differences between connected buses. Using \u27bound tightening\u27 techniques, the bounds on the voltage magnitude difference variables can be significantly tighter than the bounds on the voltage magnitudes themselves, so constraints based on voltage magnitude differences can improve the QC relaxation --Abstract, page iv

Assessments of linear power flow and transmission loss approximations in coordinated capacity expansion problems

With rising shares of renewables and the need to properly assess trade-offs between transmission, storage and sectoral integration as balancing options, building a bridge between energy system models and detailed power flow studies becomes increasingly important, but is computationally challenging. Here, we compare approximations for two nonlinear phenomena, power flow and transmission losses, in linear capacity expansion problems that co-optimise investments in generation, storage and transmission infrastructure. We evaluate different flow representations discussing differences in investment decisions, nodal prices, the deviation of optimised flows and losses from simulated AC power flows, and the computational performance. By using the open European power system model PyPSA-Eur, we obtain detailed and reproducible results aiming at facilitating the selection of a suitable power flow model. Given the differences in complexity, the optimal choice depends on the application, the user’s available computational resources, and the level of spatial detail considered. Although the commonly used transport model can already identify key features of a cost-efficient system while being quick to solve, severe deficiencies under high loading conditions arise due to the lack of a physical grid representation. Moreover, disregarding transmission losses overestimates optimal grid expansion by 20%. Adding a convex relaxation of quadratic losses with three tangents to the linearised power flow and accounting for changing line impedances as the network is reinforced suffices to represent power flows and losses adequately in design studies. We show that the obtained investment and dispatch decisions are then sufficiently physical to be used in more detailed nonlinear simulations of AC power flow evaluating their technical feasibility

STRUCTURE-PROPERTY RELATIONSHIPS IN TWO-COMPONENT LIQUIDS

This thesis tackles several two-component liquids where we currently have a poor understanding of their fundamental structures and influence on properties. A novel approach was taken to investigate hydrophobic interactions.1 Rather than studying the aqueous liquid, for which only very low hydrophobe concentrations are possible, the metastable glassy state formed by thermally annealing a H2O/C60 fullerene vapour deposit was examined. These ‘trapped solutions’ of fullerene in an amorphous solid water (ASW) matrix were prepared in newly built apparatus (Chapter 3) using deposition rates of about 5 H2O monolayers per second to give a total mass > 1 g without crystalline ice contamination. H2O desorption rate analysis indicated that the limits of ASW growth are associated with the influence of deposition rate on porosity and consequent decreases in deposit to cooling plate heat transfer with increasing deposit thickness. Characterisations by FT-IR, Raman, optical absorbance and photoluminescence spectroscopies, as well as by X-ray and neutron diffraction showed unexpected continual structural relaxation until their crystallisation to ice I at 150–160 K (Chapter 4).2 Contrary to Frank and Evans’s description of ‘iceberg’ hydration structures,3 for C60 in ASW there is a weakening of the average hydrogen bonding interaction and increases in dynamics of the first hydration layer. The present work tentatively supports theories of hydrophobic hydration forces involving a disconnection of water in the hydration shell from the extended hydrogen bonding network (Chapter 5).4-5 The intermolecular interactions in the chloroform–acetone (negative) and benzene–methanol (positive) azeotropes were investigated by Raman spectroscopy and neutron diffraction. Structural models of pure liquid chloroform and the chloroform-acetone azeotrope were prepared by Empirical Potential Structural Refinement6 of experimental data and described using radial distribution functions, spatial density functions, orientation correlation functions and Kirkwood correlation factors. These analyses revealed that ‘super dipole’ Cl3H - Cl3H - Cl3H self-associations in pure liquid chloroform (29 % molecules) may contribute to its good solvent quality and anaesthetic properties (Chapter 6),7 and that C2H6O - HCCl3 hydrogen bonding interactions are present in the chloroform-acetone azeotrope (Chapter 7). Through comparisons of radial distribution functions between ‘like’ and ‘unlike’ species in the azeotropes it is revealed that the azeotropic vapour pressure condition is not only characterised by the non-ideality of intermolecular interaction but also by significant deviations in mixing character from that of a regular mixture; the benzene-methanol azeotrope exhibit microscopic statistical demixing and the chloroform-acetone azeotrope exhibits transient complexation