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Date of Award
Doctor of Philosophy (PhD)
The energy challenges of the 21st century require dramatic increases in the efficiency of the electrical grid. Towards this end, smart grid technologies provide a robust methodology to increase efficiency of electrical consumption in many ways. The successful design and implementation of a smart grid system draws on many different disciplines within science,
mathematics, and engineering. In this dissertation, we primarily focus on the application of graph-theoretic models to different aspects of smart grid.
This work is divided up into three sections. The first two sections focus on demand response programs in an electric grid. A demand response program, simply put, is a system in which the electric company sets a dynamic price throughout the day, then users modify their usage to save money. This method, if implemented correctly, can result in a more efficient
distribution of the load throughout the day. The first section focuses on prediction the adoption rate of these technologies. We develop a novel framework that incorporates elements of graph theory, innovation diffusion, and psychology to predict what individuals will opt into a demand response program. This framework is tested through a series of simulations to establish that it produces expected results in test cases and then to analyze the potential results in other cases. The results show the final number of demand response adopters after the network has reached an equilibrium.
We observe that factors that we would expect to have an impact, like the price of nondemand-response electricity and the conscientiousness of the population, have the expected positive impact upon the final number of adopters. Interestingly, we additionally observe the unexpected result that the level of adoption of one’s neighbors does not play an important role in the final equilibrium.
The second section concerns how to influence these decisions. A novel methodology is presented which leverages on the information diffusion capabilities of a smart grid to make users influential. This methodology is essentially an inversion of the classical node influence concept. We test the algorithm under simulations in a real demand response program, with the goal being to make the load curve more level throughout the day. Our results show that this method can significantly reduce the amount of variance in electricity usage throughout the day. Furthermore, generalizations of our method show that the performance of the method is heavily dependent upon the marginal changes to the users’ actions as a function of the parameters of interest. Other test cases show that the method is effective even if the temporary edges it creates are given a low weight. Additionally, we give an initial characterization of the relative effectiveness of multiple agents influencing the network in opposite directions, finding, again, that the marginal affect of changes on the parameters of interest to the output play an important role.
The third section concerns the design of traditional AC power transmission grids. In this section, we detail a methodology for testing the robustness of power grids based on graph theory and financial risk. Graph theory is used to model the power grid, and set-valued risk measures are used to analyze the effects of altering characteristics of the grid. We conduct numerical simulations to show the effectiveness of this model at determining requisite line capacity. These simulations are based on dividing the lines of a power grid into two categories - high importance and low importance lines, as measured by a modified centrality metric.
Our results are divided into two categories: evaluations of the risk when all lines have an equal chance of failing and evaluations of the risk when heavily loaded lines have a greater chance of failing. In the case where failure probability is dependent upon load, we observe sets of acceptable capacities that have multiple critical points, points where a decrease in
the capacity of one set of lines requires a substantial increase in the capacity of the other set of lines. This contrasts with the traditional approaches to risk analysis, which identify only a single critical point along a single dimension. In the case of load-independent failures, however, we observe a single critical point, suggesting that in these cases our methodology offers less of an improvement on the existing methodology.
R. M. Arthur, Michael Strube, Zachary Feinstein, Matthew Lew
Available for download on Saturday, August 15, 2116