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This work is a survey of current trends in applications of PMUs. PMUs have the potential to solve major problems in the areas of power system estimation, protection, and stability. A variety of methods are being used for these purposes, including statistical techniques, mathematical transformations, probability, and AI. The results produced by the techniques reviewed in this work are promising, but there is work to be performed in the context of implementation and standardization. As the smart grid initiative continues to advance, the number of intelligent devices monitoring the power grid continues to increase. PMUs are at the center of this initiative, and as a result, each year more PMUs are deployed across the grid. Since their introduction, myriad solutions based on PMU-technology have been suggested. The high sampling rates and synchronized measurements provided by PMUs are expected to drive significant advancements across multiple fields, such as the protection, estimation, and control of the power grid. This work offers a review of contemporary research trends and applications of PMU technology. Most solutions presented in this work were published in the last five years, and techniques showing potential for significant impact are highlighted in greater detail. Being a relatively new technology, there are several issues that must be addressed before PMU-based solutions can be successfully implemented. This survey found that key areas where improvements are needed include the establishment of PMU-observability, data processing algorithms, the handling of heterogeneous sampling rates, and the minimization of the investment in infrastructure for PMU communication. Solutions based on Bayesian estimation, as well as those having a distributed architectures, show great promise. The material presented in this document is tailored to both new researchers entering this field and experienced researchers wishing to become acquainted with emerging trends. 

High impedance faults present unique challenges for power system protection engineers. The first challenge is the detection of the fault, given the low current magnitudes. The second challenge is to locate the fault to allow corrective measures to be taken. Corrective actions are essential as they mitigate safety hazards and equipment damage. The problem of high impedance fault detection and location is not a new one, and despite the safety and reliability implications, relatively few efforts have been made to find a general solution. This work presents a hybrid data driven and analytical-based model for high impedance fault detection in distribution systems. The first step is to estimate a state space model of the power line being monitored. From the state space model, eigenvalues are calculated, and their dynamic behavior is used to develop zones of protection. These zones of protection are generated analytically using machine learning tools. High impedance faults are detected as they drive the eigenvalues outside of their zones. A metric called eigenvalue drift coefficient was formulated in this work to facilitate the generalization of this solution. The performance of this technique is evaluated through case studies based on the IEEE 5-Bus system modeled in Matlab. Test results are encouraging indicating potential for real-life applications.