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When there is a fault, the protection system automatically removes one or more transmission lines on a fast time scale of less than one minute. The outaged lines form a pattern in the transmission network. We extract these patterns from utility outage data, determine some key statistics of these patterns, and then show how to generate new patterns consistent with these statistics. The generated patterns provide a new and easily feasible way to model the overall effect of the protection system at the scale of a large transmission system. This new data-driven generative modeling of protection is expected to contribute to simulations of disturbances in large grids so that they can better quantify the risk of blackouts. Analysis of the pattern sizes suggests an index that describes how much outages spread in the transmission network at the fast timescale. 

Resilience risk metrics must address the customer cost of the largest blackouts of greatest impact. However, there are huge variations in blackout cost in observed distribution utility data that make it impractical to properly estimate the mean large blackout cost and the corresponding risk. These problems are caused by the heavy tail observed in the distribution of customer costs. To solve these problems, we propose resilience metrics that describe large blackout risk using the mean of the logarithm of the cost of large-cost blackouts, the slope index of the heavy tail, and the frequency of large-cost blackouts. 

The electric distribution system is a cornerstone of modern life, playing a critical role in the daily activities and well-being of individuals. As the world transitions toward a decarbonized future, where even mobility relies on electricity, ensuring the resilience of the grid becomes paramount. This paper introduces novel resilience metrics designed to equip utilities and stakeholders with actionable tools to assess performance during storm events. The metrics focus on emergency storm response and the resources required to improve customer service. The practical calculation of the metrics from historical utility data is demonstrated for multiple storm events. Additionally, the metrics’ improvement with added crews is estimated by “rerunning history” with faster restoration. By applying this resilience framework, utilities can enhance their restoration strategies and unlock potential cost savings, benefiting both providers and customers in an era of heightened energy dependency. 

Transmission utilities routinely collect detailed outage data, including resilience events in which outages bunch due to weather. The resilience events and associated metrics can readily be extracted from this historical outage data. Improvements such as asset hardening or investments in restoration lead to reduced outages or faster restoration. In this paper, we show how to rerun the historical events including the effects of the reduced outages or faster restorations to measure the resulting improvement in resilience metrics, thus quantifying the benefits of these investments. This is demonstrated with case studies for specific events (a derecho and a hurricane), and all large events or large thunderstorms in the Midwest USA. Instead of predicting future extreme events with models, which is very challenging, rerunning historical events readily quantifies the benefits of resilience investments if these investments had been made in the past. Rerunning historical events is particularly vivid in making the case for resilience investments as it quantifies the benefits for events actually experienced, rather than for uncertain future events. 

We discuss ways to measure duration in a power transmission system resilience event by modeling outage and re- store processes from utility data. We introduce novel Poisson pro- cess models that describe how resilience events progress and verify that they are typical using extensive outage data collected across North America. Some usual duration metrics show impractically high statistical variability, and we recommend new duration met- rics that perform better. Moreover, the Poisson process models have parameters that can be estimated from observed network data under different weather conditions, and are promising new models of typical resilience events. 

Poisson process models are defined in terms of their rates for outage and restore processes in power system resilience events. These outage and restore processes easily yield the perfor- mance curves that track the evolution of resilience events, and the area, nadir, and duration of the performance curves are standard resilience metrics. This letter analyzes typical resilience events by analyzing the area, nadir, and duration of mean performance curves. Explicit and intuitive formulas for these metrics are de- rived in terms of the Poisson process model parameters, and these parameters can be estimated from utility data. This clarifies the calculation of metrics of typical resilience events, and shows what they depend on. The metric formulas are derived with lognormal, exponential, or constant rates of restoration. The method is illus- trated with a typical North American transmission event. Similarly nice formulas are obtained for the area metric for empirical power system data. 

We focus on blackouts in electric distribution systems that have a large cost to customers. To quantify resilience to these events, we show how to calculate risk metrics from the historical outage data routinely collected by utilities' outage management systems. Risk is defined using a customer cost exceedance curve. The exceedance curve has a heavy tail that implies large fluctuations in large blackout costs, and this makes estimating the mean large cost in the usual way impractical. To avoid this problem, we use new resilience metrics describing the large event risk; these metrics are the probability of a large cost event, the annual log cost resilience index, and the average of the logarithm of the cost of large‐cost events or the slope magnitude of the tail on a log–log exceedance curve. Resilience can be improved by planned investments to upgrade system components or speed up restoration. The benefits that these investments would have had if they had been made in the past can be quantified by “rerunning history” with the effects of the investment included, and then recalculating the large event risk to find the improvement in resilience. An example using utility data shows a 2% reduction in the probability of a large cost event due to 10% wind hardening and 6%–7% reduction due to 10% faster restoration in two different areas of a distribution utility. This new data‐driven approach to quantify resilience and resilience investments is realistic and much easier to apply than complicated approaches based on modeling all the phases of resilience. Moreover, an appeal to improvements to past lived experience may well be persuasive to customers and regulators in making the case for resilience investments. 

Multiple line outages that occur together show a variety of spatial patterns in the power transmission network. Some of these spatial patterns form network contingency motifs, which we define as the patterns of multiple outages that occur much more frequently than multiple outages chosen randomly from the network. We show that choosing N-k contingencies from these commonly occurring contingency motifs accounts for most of the probability of multiple initiating line outages. This result is demonstrated using historical outage data for two transmission systems. It enables N-k contingency lists that are much more efficient in accounting for the likely multiple initiating outages than exhaustive listing or random selection. The N-k contingency lists constructed from motifs can improve risk estimation in cascading outage simulations and help to confirm utility contingency selection. 

Security concerns have been raised about cascading failure risks in evolving power grids. This paper reveals, for the first time, that the risk of cascading failures can be increased at low network demand levels when considering security-constrained generation dispatch. This occurs because critical transmission cor- ridors become very highly loaded due to the presence of central- ized generation dispatch, e.g., large thermal plants far from de- mand centers. This increased cascading risk is revealed in this work by incorporating security-constrained generation dispatch into the risk assessment and mitigation of cascading failures. A se- curity-constrained AC optimal power flow, which considers eco- nomic functions and security constraints (e.g., network con- straints, 𝑵 − 𝟏 security, and generation margin), is used to pro- vide a representative day-ahead operational plan. Cascading fail- ures are simulated using two simulators, a quasi-steady state DC power flow model, and a dynamic model incorporating all fre- quency-related dynamics, to allow for result comparison and ver- ification. The risk assessment procedure is illustrated using syn- thetic networks of 200 and 2,000 buses. Further, a novel preventive mitigation measure is proposed to first identify critical lines, whose failures are likely to trigger cascading failures, and then to limit power flow through these critical lines during dispatch. Results show that shifting power equivalent to 1% of total demand from critical lines to other lines can reduce cascading risk by up to 80%.