A Unifying Framework for the Electrical Structure-Based Approach to PMU Placement in Electric Power Systems

The electrical structure of the power grid is utilized to address the phasor measurement unit (PMU) placement problem. First, we derive the connectivity matrix of the network using the resistance distance metric and employ it in the linear program formulation to obtain the optimal number of PMUs, for complete network observability without zero injection measurements. This approach was developed by the author in an earlier work, but the solution methodology to address the location problem did not fully utilize the electrical properties of the network, resulting in an ambiguity. In this paper, we settle this issue by exploiting the coupling structure of the grid derived using the singular value decomposition (SVD)-based analysis of the resistance distance matrix to solve the location problem. Our study, which is based on recent advances in complex networks that promote the electrical structure of the grid over its topological structure and the SVD analysis which throws light on the electrical coupling of the network, results in a unified framework for the electrical structure-based PMU placement. The proposed method is tested on IEEE bus systems, and the results uncover intriguing connections between the singular vectors and average resistance distance between buses in the network.Comment: Submitted to IEEE Transactions on Smart Grid. arXiv admin note: text overlap with arXiv:1309.130

Hidden Attacks on Power Grid: Optimal Attack Strategies and Mitigation

Real time operation of the power grid and synchronism of its different elements require accurate estimation of its state variables. Errors in state estimation will lead to sub-optimal Optimal Power Flow (OPF) solutions and subsequent increase in the price of electricity in the market or, potentially overload and create line outages. This paper studies hidden data attacks on power systems by an adversary trying to manipulate state estimators. The adversary gains control of a few meters, and is able to introduce spurious measurements in them. The paper presents a polynomial time algorithm using min-cut calculations to determine the minimum number of measurements an adversary needs to manipulate in order to perform a hidden attack. Greedy techniques are presented to aid the system operator in identifying critical measurements for protection to prevent such hidden data attacks. Secure PMU placement against data attacks is also discussed and an algorithm for placing PMUs for this purpose is developed. The performances of the proposed algorithms are shown through simulations on IEEE test cases

Real-time Faulted Line Localization and PMU Placement in Power Systems through Convolutional Neural Networks

Diverse fault types, fast re-closures, and complicated transient states after a fault event make real-time fault location in power grids challenging. Existing localization techniques in this area rely on simplistic assumptions, such as static loads, or require much higher sampling rates or total measurement availability. This paper proposes a faulted line localization method based on a Convolutional Neural Network (CNN) classifier using bus voltages. Unlike prior data-driven methods, the proposed classifier is based on features with physical interpretations that improve the robustness of the location performance. The accuracy of our CNN based localization tool is demonstrably superior to other machine learning classifiers in the literature. To further improve the location performance, a joint phasor measurement units (PMU) placement strategy is proposed and validated against other methods. A significant aspect of our methodology is that under very low observability (7% of buses), the algorithm is still able to localize the faulted line to a small neighborhood with high probability. The performance of our scheme is validated through simulations of faults of various types in the IEEE 39-bus and 68-bus power systems under varying uncertain conditions, system observability, and measurement quality.Comment: 11 pages, 8 figure

Physics-Informed Learning for High Impedance Faults Detection

High impedance faults (HIFs) in distribution grids may cause wildfires and threaten human lives. Conventional protection relays at substations fail to detect more than 10\% HIFs since over-currents are low and the signatures of HIFs are local. With more $\mu$PMU being installed in the distribution system, high-resolution $\mu$PMU datasets provide the opportunity of detecting HIFs from multiple points. Still, the main obstacle in applying the $\mu$PMU datasets is the lack of labels. To address this issue, we construct a physics-informed convolutional auto-encoder (PICAE) to detect HIFs without labeled HIFs for training. The significance of our PICAE is a physical regularization, derived from the elliptical trajectory of voltages-current characteristics, to distinguish HIFs from other abnormal events even in highly noisy situations. We formulate a system-wide detection framework that merges multiple nodes' local detection results to improve the detection accuracy and reliability. The proposed approaches are validated in the IEEE 34-node test feeder simulated through PSCAD/EMTDC. Our PICAE outperforms the existing works in various scenarios and is robust to different observability and noise.Comment: 7 pages, 6 figure