Effects of Information and Time of Use Pricing on Irish Electricity Demand and Supply

In this dissertation I quantify residential behavior response to interventions designed to reduce electricity demand at different periods of the day. In the first chapter, I examine the effect of information provision coupled with bimonthly billing, monthly billing, and in-home displays, as well as a time-of-use (TOU) pricing scheme to measure consumption over each month of the Irish Consumer Behavior Trial. I find that time-of-use pricing with real time usage information reduces electricity usage up to 8.7 percent during peak times at the start of the trial but the effect decays over the first three months and after three months the in-home display group is indistinguishable from the monthly treatment group. Monthly and bi-monthly billing treatments are not found to be statistically different from another. These findings suggest that increasing billing reports to the monthly level may be more cost effective for electricity generators who wish to decrease expenses and consumption, rather than providing in-home displays. In the following chapter, I examine the response of residential households after exposure to time of use tariffs at different hours of the day. I find that these treatments reduce electricity consumption during peak hours by almost four percent, significantly lowering demand. Within the model, I find evidence of overall conservation in electricity used. In addition, weekday peak reductions appear to carry over to the weekend when peak pricing is not present, suggesting changes in consumer habit. The final chapter of my dissertation imposes a system wide time of use plan to analyze the potential reduction in carbon emissions from load shifting based on the Ireland and Northern Single Electricity Market. I find that CO2 emissions savings are highest during the winter months when load demand is highest and dirtier power plants are scheduled to meet peak demand. TOU pricing allows for shifting in usage from peak usage to off peak usage and this shift in load can be met with cleaner and cheaper generated electricity from imports, high efficiency gas units, and hydro units.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.