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  1. 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. 
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  3. State-of-the art physics-model based dynamic state estimation generally relies on the assumption that the system’s transition matrix is always correct, the one that relates the states in two different time instants, which might not hold always on real-life applications. Further, while making such assumptions, state-of-the-art dynamic state estimation models become unable to discriminate among different types of anomalies, as measurement gross errors and sudden load changes, and thus automatically leads the state estimator framework to inaccuracy. Towards the solution of this important challenge, in this work, a hybrid adaptive dynamic state estimator framework is presented. Based on the Kalman Filter formulation, measurement innovation analytical-based tests are presented and integrated into the state estimator framework. Gross measurement errors and sudden load changes are automatically detected, identified, and corrected, providing continuous updating of the state estimator. Towards such, the asymmetry index applied to the measurement innovation is introduced, as an anomaly discrimination method, which assesses the physics-model-based dynamic state estimation process in different piece-wise stationary levels. Comparative tests with the state-of-the-art are presented, considering the IEEE 14, IEEE 30, and IEEE 118 test systems. Easy-to-implement-model, without hard-to-design parameters, build-on the classical Kalman Filter solution, highlights potential aspects towards real-life applications. 
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    In the modern power system networks, grid observability has greatly increased due to the deployment of various metering technologies. Such technologies enhanced the real-time monitoring of the grid. The collection of observations are processed by the state estimator in which many applications have relied on. Traditionally, state estimation on power grids has been done considering a centralized architecture. With grid deregulation, and awareness of information privacy and security, much attention has been given to multi-area state estimation. Considering such, state-of-the-art solutions consider a weighted norm of residual measurement model, which might hinder masked gross errors contained in the null-space of the Jacobian matrix. Towards the solution of this, a distributed innovation-based model is presented. Measurement innovation is used towards error composition. The measurement error is an independent random variable, where the residual is not. Thus, the masked component is recovered through measurement innovation. Model solution is obtained through an Alternating Direction Method of Multipliers (ADMM), which requires minimal information communication. The presented framework is validated using the IEEE 14 and IEEE 118 bus systems. Easy-to-implement model, build-on the classical weighted norm of the residual solution, and without hard-to-design parameters highlight potential aspects towards real-life implementation. 
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    The high penetration of renewable sources of energy in electrical power systems implies an increase in the uncertainty variables of the economic dispatch (ED). Uncertainty costs are a metric to quantify the variability introduced from renewable energy generation, that is to say: wind energy generation (WEG), run-of-the-river hydro generators (RHG), and solar photovoltaic generation (PVG). On other side, there are associated uncertainties to the charge/uncharge of plug-in electric vehicles (PEV). Thus, in this paper, the uncertainty cost functions (UCF) and their marginal expressions as a way of modeling and assessment of stochasticity in power systems with high penetration of smart grids elements is presented. In this work, a mathematical analysis is presented using the first and second derivatives of the UCF, where the marginal uncertainty cost functions (MUCF) and the UCF’s minimums for PVG, WEG, PEV, and RHG are derived. Further, a model validation is presented, considering comparative test results from the state of the art of the UCF minimum, developed in a previous study, to the minimum reached with the presented (MUCF) solution. 
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    Contingency Constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch after the contingency occurs, the CCOPF is studied with a preventive perspective, whereas when the contingency occurs and the power dispatch needs to change to operate the system between limits in the post-contingency state, the problem is studied with a corrective perspective. As current power system software tools mainly focus on the traditional OPF problem, having the means to solve CCOPF will benefit power systems planning and operation. This paper presents a Quadratically Constrained Quadratic Programming (QCQP) formulation built within the matpower environment as a solution strategy to the preventive CCOPF. Moreover, an extended OPF model that forces the network to meet all constraints under contingency is proposed as a strategy to find the power dispatch solution for the corrective CCOPF. Validation is made on the IEEE 14-bus test system including photovoltaic generation in one simulation case. It was found that in the QCQP formulation, the power dispatch calculated barely differs in both pre- and post-contingency scenarios while in the OPF extended power network, node voltage values in both pre- and post-contingency scenarios are equal in spite of having different power dispatch for each scenario. This suggests that both the QCQP and the extended OPF formulations proposed, could be implemented in power system software tools in order to solve CCOPF problems from a preventive or corrective perspective. 
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