Analysis of the power grid: structure and secure operations
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Power Grids form one of the vital backbone-networks of our society providing electricity for daily socio-economic activities. Given its importance, there is a greater need to understand the structure and control of the power grid for fair power market computations and efficient delivery of electricity. This work studies two problems associated with different aspects of today's power grid network and combines techniques from network science, control theory and optimization to analyze them. The first problem relates to understanding the common structural features observed in several power grids across the world and developing a trackable modeling framework that incorporates these features. Such a framework can lead to insights on structural vulnerability of the grid and help design realistic test cases to study effects of structural and operational reinforcements as the grid evolves with time. We develop a generative model based on spatial point process theory that provably produces the distinct exponential degree distribution observed in several power grids. Further, critical graph parameters like diameter, eigen-spread, betweenness centralities and clustering coefficients are used to compare the performance of our framework in modeling the power grids in Western USA and under ERCOT in Texas. The second problem discussed here involves a detailed study of malicious data attacks on state estimation in the power grid. Such data attacks pose a serious threat to efforts related to implementing distributed control for efficient operations in the grid. We develop a graph-theoretic framework to analyze the design of optimal data attacks and study cost-optimal techniques to build resilience against them. The study involves attacks by a practical adversary capable of modifying meter readings as well as of jamming the flow of information from meters to the grid controller. We prove that the design of optimal `hidden' and `detectable' attacks can be formulated as constrained graph-cut problems that depend on the relative costs of adversarial techniques, and present algorithms for attack construction. Further, we design a new `topology' attack regime where an adversary changes beaker statuses of grid lines to affect state estimation in systems where all meter measurements are encrypted and hence secure from manipulation. We discuss bounds on the security requirements imposed by the developed attack models and design algorithms for determining the optimal protection strategy. This helps present an accurate characterization of grid vulnerability to general data attacks and eavesdroppers and motivates efforts to expand the presence of new secure meters to foil cyber attacks in the grid.