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1. Models, Metrics, and Their Formulas for Typical Electric Power System Resilience Events

   https://doi.org/10.1109/TPWRS.2023.3300125  

   Dobson, Ian (November 2023, IEEE Transactions on Power Systems)

   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. 

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2. Assessing Transmission Resilience during Extreme Weather with Outage and Restore Processes

   https://doi.org/10.1109/PMAPS53380.2022.9810645  

   Ekisheva, Svetlana; Dobson, Ian; Rieder, Rachel; Norris, Jack (June 2022, Probability Methods Applied to Power Systems)

   We automatically extract resilience events and novel outage and restore processes from standard transmission utility detailed outage data. This new processing is applied to the outage data collected in NERC’s Transmission Availability Data System to introduce and analyze statistics that quantify resilience of the transmission system against extreme weather events. These metrics (such as outage rate and duration, number of elements outaged, rated capacity outaged, restore duration, maximum simultaneous outages, and element-days lost) are calculated for all large weather-related events on the North American transmission system from 2015 to 2020 and then by extreme weather type that caused them such as hurricanes, tornadoes, and winter storms. Finally, we study how performance of the system changed with respect to the resilience metrics by season and year. 

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3. Extracting Resilience Statistics from Utility Data in Distribution Grids

   https://doi.org/10.1109/PESGM41954.2020.9281596  

   Carrington, Nichelle'Le K.; Ma, Shanshan; Dobson, Ian; Wang, Zhaoyu (August 2020, IEEE Power and Energy Society General Meeting)

   It is useful to quantify electrical distribution system resilience based on historical performance. This paper systematically extracts resilience curves from historical utility outage data, extracts resilience metrics such as duration, average recovery rates, and maximum number of simultaneously outaged components, and examines the statistics of these resilience metrics for small, medium, and large events. The resilience metrics and their typical variabilities are expected to be helpful in predicting and bounding the likely outcomes of future resilience events. For example, we can calculate the restoration time that will be achieved with 95% confidence. 

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4. Optimal Decomposition of Utility Outage Sequence for Cascading Failure Interaction Estimation

   https://doi.org/10.1109/PMAPS53380.2022.9810630  

   Wang, Lei; Qi, Junjian (June 2022, 2022 17th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS))

   Estimated component failure interactions from utility outage data can capture the general failure propagation patterns and help identify key components of a power system. Conventionally, utility outages are grouped into cascades and generations according to inter-outage time based on arbitrarily chosen thresholds. In this paper, we propose an optimal decomposition approach for utility outage data. By approximating the temporal pattern of the outage sequence by a Poisson process, an adaptive generation duration threshold is calculated to group the generations for each cascade. Compared to the conventional method, the proposed method can reveal more failure interactions and mitigate heterogeneity. The results based on real utility outage data demonstrate the effectiveness of the proposed optimal decomposition approach. 

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5. The improvement in transmission resilience metrics from reduced outages or faster restoration can be calculated by rerunning historical outage data

   https://doi.org/10.1109/PESGM52009.2025.11225704  

   Ahmad, Arslan; Dobson, Ian; Ekisheva, Svetlana; Claypool, Christopher; Lauby, Mark (July 2025, IEEE)

   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. 

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