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As inverter-based generation becomes more common in distribution networks, it is important to create models for use in optimization-based problems that accurately represent their non-linear behavior when saturated. This work presents models for grid-following and grid-forming inverters, and demonstrates their use in optimization-based fault studies. The developed models are shown to provide results in line with experimental tests from literature; however, grid-forming inverter models fail to provide feasible solutions for certain fault types even when currents, voltages, and powers from the models seem reasonable. This work lays down the foundation for the development of relaxed models for both grid-following and grid-forming inverter models for use in optimization problems., Comment: 6 pages. 13 figures

A Cascadia Subduction Zone (CSZ) earthquake will cause widespread damage to numerous lifelines and infrastructure along the northern US west coast. The goal of the presented research is to provide a bottom up estimate of the impact on and subsequent recovery of a Cascadia Subduction Zone earthquake on the US western grid to supplement and enhance the expert opinion estimates provided to date. The scope is limited to consideration of shaking damage to utility substation equipment components of a power system model. The analysis utilizes probabilistic models of damage and recovery for substation power system assets, along with graph techniques for modeling connectivity, and Monte Carlo quasi steady state power flow solutions. The results show that a conservative estimate of the initial damage and loss of load is approximately 4,000 MW, with a recovery estimate of 230 days.

A major risk of geomagnetic disturbances (GMDs) is cascading failure of electrical grids. The modeling of GMD events and cascading outages in power systems is difficult, both independently and jointly, because of the many different mechanisms and physics involved. This paper introduces a relaxation based modeling of GMD-induced cascading failures:~the dc approximation-based DCSIMSEP solver was adapted to simulate cascading as a result of GMDs, the full set of ac power flow equations were relaxed to guarantee optimality, and the reactive power losses were modeled while keeping the problem convex. The developed algorithm was implemented in PowerModelsGMD.jl - an open-source software specifically designed to model and analyze geomagnetic hazards - and demonstrated to work on the RTS-GMLC-GIC-EAST synthetic test network., Comment: 7 pages. 5 figures. 3 tables

We investigate the vulnerability of a power transmission grid to load oscillation attacks. We demonstrate that an adversary with a relatively small amount of resources can launch a successful load oscillation attack to destabilize the grid. The adversary is assumed to be able to compromise smart meters at a subset of load buses and control their switches. In the studied attack scenarios the adversary estimates the line flow sensitivity factors (LFSFs) associated with the monitored tie lines by perturbing a small amount of load at compromised buses and observing the monitored lines flow changes. The learned LFSF values are used for selecting a target line and optimizing the oscillation attack to cause the target line to trip while minimizing the magnitude of load oscillation. We evaluated the attack impact using the COSMIC time-domain simulator with two test cases, the IEEE RTS 96 and Polish 2383-Bus Systems. The proposed attack strategy succeeded in causing 33% of load to be shed while oscillating only 7% of load in the IEEE RTS 96 test system, and full blackout after oscillating only 3% of the load in the Polish test system, which is much smaller than oscillation magnitudes used by other benchmarks., Comment: 10 pages, 10 figures

One of the most complex and devastating disaster scenarios that the U.S.~Pacific Northwest region and the state of Oregon faces is a large magnitude Cascadia Subduction Zone earthquake event. The region's electrical grid lacks in resilience against the destruction of a megathrust earthquake, a powerful tsunami, hundreds of aftershocks and increased volcanic activity, all of which are highly probable components of this hazard. This research seeks to catalyze further understanding and improvement of resilience. By systematizing power system related experiences of historical earthquakes, and collecting practical and innovative ideas from other regions on how to enhance network design, construction, and operation, important steps are being taken toward a more resilient, earthquake-resistant grid. This paper presents relevant findings in an effort to be an overview and a useful guideline for those who are also working towards greater electrical grid resilience., Comment: 5 pages. 1 figure. 1 table

Quick and reliable power system restoration is critically important after natural disasters or other sudden threats, such as cyber-attacks. Leveraging renewable resources in system restoration shortens recovery times, resulting in prevented life-loss and avoided economic-loss, and improves the resilience of the entire grid. However, it is not a common practice today; the inherent variability of these resources represents a challenge for a streamlined restoration process. This paper presents a prioritized method - starting with renewable generator units then lowering priority to conventional units - to plan the operational schedule of a power system during the restoration process. The goal is to achieve a well balanced system in the presence of significant renewable penetration. Validation and benchmarking experiments were performed on a customized version of the RTS-GMLC test system using six months out of year-long data, tested through hourly simulations. After evaluating the performance and computational costs, this method proved faster than common approaches: a MILP Unit Commitment algorithm, widely used today, and an "enable-and-try" algorithm. In summary, herein a more convenient method is provided to be utilized during time-sensitive restoration, as an online operation-planning aid., Comment: 8 pages. 5 figures

Geomagnetic disturbances and E3 high-altitude electromagnetic pulse events pose a substantial threat to the electrical grid by adversely impacting and damaging high-voltage transmission networks and equipment. To evaluate the risks and mitigate the potential effects of these hazards, this work proposes PowerModelsGMD.jl (abbr. PMsGMD). PMsGMD is an open-source Julia package that solves for quasi-dc line flow and ac power flow problems in a system subjected to geomagnetically induced currents. Unlike commercially available software solutions, it is extensible and applicable to a variety of problems. The flexibility of this framework is demonstrated by applying it to the problem of identifying mitigation strategies via line switching for a time-extended transformer heating problem. An overview of PMsGMD is presented in this paper: introduction to its design, validation of its implementation, demonstration of its performance and effectiveness, and a description of how it may be applied to aid system-operation decisions., Comment: Technical Report

Consider the problem of mitigating the impact on data integrity of phasor measurement units (PMUs) given a GPS spoofing attack. We present a sparse error correction framework to treat PMU measurements that are potentially corrupted due to a GPS spoofing attack. We exploit the sparse nature of a GPS spoofing attack, which is that only a small fraction of PMUs are affected by the attack. We first present attack identifiability conditions (in terms of network topology, PMU locations, and the number of spoofed PMUs) under which data manipulation by the spoofing attack is identifiable. The identifiability conditions have important implications on how the locations of PMUs affect their resilience to GPS spoofing attacks. To effectively correct spoofed PMU data, we present a sparse error correction approach wherein computation tasks are decomposed into smaller zones to ensure scalability. We present experimental results obtained from numerical simulations with the IEEE RTS-96 and IEEE 300 test networks to demonstrate the effectiveness of the proposed approach., Comment: 15 pages, 4 figures

Phasor measurement units (PMUs) provide high-fidelity data that improve situation awareness of electric power grid operations. PMU datastreams inform wide-area state estimation, monitor area control error, and facilitate event detection in real time. As PMU data become more available and increasingly reliable, these devices are found in new roles within control systems, such as remedial action schemes and early warning detection systems. As with other cyber physical systems, maintaining data integrity and security pose a significant challenge for power system operators. In this paper, we present a comprehensive analysis of multiple machine learning techniques to detect malicious data injection within PMU data streams. The two datasets used in this study come from two PMU networks: an inter-university, research-grade distribution network spanning three institutions in the U.S. Pacific Northwest, and a utility transmission network from the Bonneville Power Administration. We implement the detection algorithms with TensorFlow, an open-source software library for machine learning, and the results demonstrate potential for distributing the training workload and achieving higher performance, while maintaining effectiveness in the detection of spoofed data., Comment: 9 pages, 2 figures

In the traditional load flow analysis, a key assumption is that the input variables, i.e., generator output and customer demand, are fixed in time and the associated response has no variability. This assumption, however, is no longer valid as the adoption of renewable energy resources add more variability and uncertainty to the modern electrical system. Addressing these concerns is the definition of the Probabilistic Load Flow (PLF) problem. The challenge of the PLF problem lies in handling high-dimensional input uncertainties and the non-linearity of the load flow equations. The most straightforward way to address these problems, but at the cost of computational time, is to perform a Monte Carlo method. This work, however, solves these problems -- accuracy, high-dimensionality, and computational time -- with a coupled Karhunen-Lo\`eve (KL) expansion and Anisotropic Sparse Grid algorithm. The proposed method is implemented and tested on the IEEE 118-bus test system and a modernized version of the IEEE Reliability Test System - 1996, the Reliability Test System - Grid Modernization Lab Consortium (RTS-GMLC). Results for the 194-dimensional case show a decrease in computational time when compared to the 10,000 sample Monte Carlo method given a bound on mean and standard deviation error., Comment: 24 pages, 5 figures

Wide-area data and algorithms in large power systems are creating new opportunities for implementation of measurement-based dynamic load modeling techniques. These techniques improve the accuracy of dynamic load models, which are an integral part of transient stability analysis. Measurement-based load modeling techniques commonly assume response error is correlated to system or model accuracy. Response error is the difference between simulation output and phasor measurement units (PMUs) samples. This paper investigates similarity measures, output types, simulation time spans, and disturbance types used to generate response error and the correlation of the response error to system accuracy. This paper aims to address two hypotheses: 1) can response error determine the total system accuracy? and 2) can response error indicate if a dynamic load model being used at a bus is sufficiently accurate? The results of the study show only specific combinations of metrics yield statistically significant correlations, and there is a lack of pattern of combinations of metrics that deliver significant correlations. Less than 20% of all simulated tests in this study resulted in statistically significant correlations. These outcomes highlight concerns with common measurement-based load modeling techniques, raising awareness to the importance of careful selection and validation of similarity measures and response output metrics. Naive or untested selection of metrics can deliver inaccurate and misleading results., Comment: IEEE Transactions on Power Systems, in press, 2019

We propose a generative graph model for electrical infrastructure networks that accounts for heterogeneity in both node and edge type. To inform the model design, we analyze the properties of power grid graphs derived from the U.S. Eastern Interconnection, Texas Interconnection, and Poland transmission system power grids. Across these datasets, we find subgraphs induced by nodes of the same voltage level exhibit shared structural properties atypical to small-world networks, including low local clustering, large diameter, and large average distance. On the other hand, we find subgraphs induced by transformer edges linking nodes of different voltage types contain a more limited structure, consisting mainly of small, disjoint star graphs. The goal of our proposed model is to match both these inter and intra-network properties by proceeding in two phases: the first phase adapts the Chung-Lu random graph model, taking desired vertex degrees and desired diameter as inputs, while the second phase of the model is based on a simpler random star graph generation process. We test the model's performance by comparing its output across many runs to the aforementioned real data. In nearly all categories tested, we find our model is more accurate in reproducing the unusual mixture of properties apparent in the data than the Chung-Lu model. We also include graph visualization comparisons, a brief analysis of edge-deletion resiliency, and guidelines for artificially generating the model inputs in the absence of real data.

This paper introduces a potential learning scheme that can dynamically predict the stability of the reconnection of sub-networks to a main grid. As the future electrical power systems tend towards smarter and greener technology, the deployment of self sufficient networks, or microgrids, becomes more likely. Microgrids may operate on their own or synchronized with the main grid, thus control methods need to take into account islanding and reconnecting of said networks. The ability to optimally and safely reconnect a portion of the grid is not well understood and, as of now, limited to raw synchronization between interconnection points. A support vector machine (SVM) leveraging real-time data from phasor measurement units (PMUs) is proposed to predict in real time whether the reconnection of a sub-network to the main grid would lead to stability or instability. A dynamics simulator fed with pre-acquired system parameters is used to create training data for the SVM in various operating states. The classifier was tested on a variety of cases and operating points to ensure diversity. Accuracies of approximately 85% were observed throughout most conditions when making dynamic predictions of a given network., Comment: 10 pages, 5 figures

Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to solve these problems, but are subject to several limitations. One of the limitations is the ability to model a heterogeneous system in a consistent manner using the standard graph-theoretic formulation. In this paper, we propose a {\em network-of-networks} approach for modeling power transmission networks in order to explicitly incorporate heterogeneity in the model. This model distinguishes between different components of the network that operate at different voltage ratings, and also captures the intra and inter-network connectivity patterns. By building the graph in this fashion we present a novel, and fundamentally different, perspective of power transmission networks. Consequently, this novel approach will have a significant impact on the graph-theoretic modeling of power grids that we believe will lead to a better understanding of transmission networks.

Modern power systems have begun integrating synchrophasor technologies into part of daily operations. Given the amount of solutions offered and the maturity rate of application development it is not a matter of "if" but a matter of "when" in regards to these technologies becoming ubiquitous in control centers around the world. While the benefits are numerous, the functionality of operator-level applications can easily be nullified by injection of deceptive data signals disguised as genuine measurements. Such deceptive action is a common precursor to nefarious, often malicious activity. A correlation coefficient characterization and machine learning methodology are proposed to detect and identify injection of spoofed data signals. The proposed method utilizes statistical relationships intrinsic to power system parameters, which are quantified and presented. Several spoofing schemes have been developed to qualitatively and quantitatively demonstrate detection capabilities., Comment: 8 pages, 4 figures, submitted to IEEE Transactions

Dynamic model reduction in power systems is necessary for improving computational efficiency. Traditional model reduction using linearized models or online analysis is not adequate to capture dynamic behaviors of the power system, especially with the new mix of intermittent generation and intelligent consumption making the power system more dynamic and non-linear. Real-time dynamic model reduction has emerged to fill this important need. This paper explores using clustering techniques to analyze real-time phasor measurements to identify groups of generators with similar behavior, as well as a representative generator from each group for dynamic model reduction. Two clustering techniques -- graph clustering and k-means -- are considered. These techniques are compared with a previously developed dynamic model reduction approach using Singular Value Decomposition. Two sample power grid data sets are used to test these different model reduction techniques. Based on the algorithms' relative performance, recommendations are provided for practical use., Comment: Statistical Analysis and Data Mining, in press, 2017

Increased adoption and deployment of phasor measurement units (PMU) has provided valuable fine-grained data over the grid. Analysis over these data can provide insight into the health of the grid, thereby improving control over operations. Realizing this data-driven control, however, requires validating, processing and storing massive amounts of PMU data. This paper describes a PMU data management system that supports input from multiple PMU data streams, features an event-detection algorithm, and provides an efficient method for retrieving archival data. The event-detection algorithm rapidly correlates multiple PMU data streams, providing details on events occurring within the power system. The event-detection algorithm feeds into a visualization component, allowing operators to recognize events as they occur. The indexing and data retrieval mechanism facilitates fast access to archived PMU data. Using this method, we achieved over 30x speedup for queries with high selectivity. With the development of these two components, we have developed a system that allows efficient analysis of multiple time-aligned PMU data streams., Comment: Published in Electric Power Systems Research (2016), not available yet

The modeling of cascading failure in power systems is difficult because of the many different mechanisms involved; no single model captures all of these mechanisms. Understanding the relative importance of these different mechanisms is an important step in choosing which mechanisms need to be modeled for particular types of cascading failure analysis. This work presents a dynamic simulation model of both power networks and protection systems, which can simulate a wider variety of cascading outage mechanisms, relative to existing quasi-steady state (QSS) models. The model allows one to test the impact of different load models and protections on cascading outage sizes. This paper describes each module of the developed dynamic model and demonstrates how different mechanisms interact. In order to test the model we simulated a batch of randomly selected $N-2$ contingencies for several different static load configurations, and found that the distribution of blackout sizes and event lengths from the proposed dynamic simulator correlates well with historical trends. The results also show that load models have significant impacts on the cascading risks. This dynamic model was also compared against a QSS model based on the dc power flow approximations; we find that the two models largely agree, but produce substantially different results for later stages of cascading., Comment: 8 pages, 9 figures, 5 tables, submitted to IEEE transactions

In recent years there have been many improvements in the reliability of critical infrastructure systems. Despite these improvements, the power systems industry has seen relatively small advances in this regard. For instance, power quality deficiencies, a high number of localized contingencies, and large cascading outages are still too widespread. Though progress has been made in improving generation, transmission, and distribution infrastructure, remedial action schemes (RAS) remain non-standardized and are often not uniformly implemented across different utilities, ISOs, and RTOs. Traditionally, load shedding and islanding have been successful protection measures in restraining propagation of contingencies and large cascading outages. This paper proposes a novel, algorithmic approach to selecting RAS policies to optimize the operation of the power network during and after a contingency. Specifically, we use policy-switching to consolidate traditional load shedding and islanding schemes. In order to model and simulate the functionality of the proposed power systems protection algorithm, we conduct Monte-Carlo, time-domain simulations using Siemens PSS/E. The algorithm is tested via experiments on the IEEE-39 topology to demonstrate that the proposed approach achieves optimal power system performance during emergency situations, given a specific set of RAS policies., Comment: Full Paper Accepted to PSCC 2014 - IEEE Co-Sponsored Conference. 7 Pages, 2 Figures, 2 Tables

Many dynamical systems, including power systems, recover from perturbations more slowly as they approach critical transitions---a phenomenon known as critical slowing down. If the system is stochastically forced, autocorrelation and variance in time-series data from the system often increase before the transition, potentially providing an early warning of coming danger. In some cases, these statistical patterns are sufficiently strong, and occur sufficiently far from the transition, that they can be used to predict the distance between the current operating state and the critical point. In other cases CSD comes too late to be a good indicator. In order to better understand the extent to which CSD can be used as an indicator of proximity to bifurcation in power systems, this paper derives autocorrelation functions for three small power system models, using the stochastic differential algebraic equations (SDAE) associated with each. The analytical results, along with numerical results from a larger system, show that, although CSD does occur in power systems, its signs sometimes appear only when the system is very close to transition. On the other hand, the variance in voltage magnitudes consistently shows up as a good early warning of voltage collapse. Finally, analytical results illustrate the importance of nonlinearity to the occurrence of CSD., Comment: 14 Pages, 22 figures

Critical slowing down (CSD) is the phenomenon in which a system recovers more slowly from small perturbations. CSD, as evidenced by increasing signal variance and autocorrelation, has been observed in many dynamical systems approaching a critical transition, and thus can be a useful signal of proximity to transition. In this paper, we derive autocorrelation functions for the state variables of a stochastic single machine infinite bus system (SMIB). The results show that both autocorrelation and variance increase as this system approaches a saddle-node bifurcation. The autocorrelation functions help to explain why CSD can be used as an indicator of proximity to criticality in power systems revealing, for example, how nonlinearity in the SMIB system causes these signs to appear., Comment: Accepted for publication/presentation in Proc. North American Power Symposium, 2013

The topological (graph) structure of complex networks often provides valuable information about the performance and vulnerability of the network. However, there are multiple ways to represent a given network as a graph. Electric power transmission and distribution networks have a topological structure that is straightforward to represent and analyze as a graph. However, simple graph models neglect the comprehensive connections between components that result from Ohm's and Kirchhoff's laws. This paper describes the structure of the three North American electric power interconnections, from the perspective of both topological and electrical connectivity. We compare the simple topology of these networks with that of random (Erdos and Renyi, 1959), preferential-attachment (Barabasi and Albert, 1999) and small-world (Watts and Strogatz, 1998) networks of equivalent sizes and find that power grids differ substantially from these abstract models in degree distribution, clustering, diameter and assortativity, and thus conclude that these topological forms may be misleading as models of power systems. To study the electrical connectivity of power systems, we propose a new method for representing electrical structure using electrical distances rather than geographic connections. Comparisons of these two representations of the North American power networks reveal notable differences between the electrical and topological structure of electric power networks.

In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks using three measures of vulnerability: characteristic path lengths, connectivity loss and blackout sizes. The first two are purely topological metrics. The blackout size calculation results from a model of cascading failure in power networks. Testing the response of 40 areas within the Eastern US power grid and a standard IEEE test case to a variety of attack/failure vectors indicates that directed attacks result in larger failures using all three vulnerability measures, but the attack vectors that appear to cause the most damage depend on the measure chosen. While our topological and power grid model results show some trends that are similar, there is only a mild correlation between the vulnerability measures for individual simulations. We conclude that evaluating vulnerability in power networks using purely topological metrics can be misleading.