Ian Dobson

Paul D. H. Hines, Ian Dobson, Pooya Rezaei

In a cascading power transmission outage, component outages propagate non-locally, after one component outages, the next failure may be very distant, both topologically and geographically. As a result, simple models of topological contagion do not accurately represent the propagation of cascades in power systems. However, cascading power outages do follow patterns, some of which are useful in understanding and reducing blackout risk. This paper describes a method by which the data from many cascading failure simulations can be transformed into a graph-based model of influences that provides actionable information about the many ways that cascades propagate in a particular system. The resulting "influence graph" model is Markovian, in that component outage probabilities depend only on the outages that occurred in the prior generation. To validate the model we compare the distribution of cascade sizes resulting from $n-2$ contingencies in a $2896$ branch test case to cascade sizes in the influence graph. The two distributions are remarkably similar. In addition, we derive an equation with which one can quickly identify modifications to the proposed system that will substantially reduce cascade propagation. With this equation one can quickly identify critical components that can be improved to substantially reduce the risk of large cascading blackouts.

Kai Zhou, Ian Dobson, Zhaoyu Wang et al.

We use observed transmission line outage data to make a Markov influence graph that describes the probabilities of transitions between generations of cascading line outages, where each generation of a cascade consists of a single line outage or multiple line outages. The new influence graph defines a Markov chain and generalizes previous influence graphs by including multiple line outages as Markov chain states. The generalized influence graph can reproduce the distribution of cascade size in the utility data. In particular, it can estimate the probabilities of small, medium and large cascades. The influence graph has the key advantage of allowing the effect of mitigations to be analyzed and readily tested, which is not available from the observed data. We exploit the asymptotic properties of the Markov chain to find the lines most involved in large cascades and show how upgrades to these critical lines can reduce the probability of large cascades.

Ian Dobson, Benjamin A. Carreras, David E. Newman et al.

We show how to use standard transmission line outage historical data to obtain the network topology in such a way that cascades of line outages can be easily located on the network. Then we obtain statistics quantifying how cascading outages typically spread on the network. Processing real outage data is fundamental for understanding cascading and for evaluating the validity of the many different models and simulations that have been proposed for cascading in power networks.

Ian Dobson, NichelleLe K. Carrington, Kai Zhou et al.

We describe some bulk statistics of historical initial line outages and the implications for forming contingency lists and understanding which initial outages are likely to lead to further cascading. We use historical outage data to estimate the effect of weather on cascading via cause codes and via NOAA storm data. Bad weather significantly increases outage rates and interacts with cascading effects, and should be accounted for in cascading models and simulations. We suggest how weather effects can be incorporated into the OPA cascading simulation and validated. There are very good prospects for improving data processing and models for the bulk statistics of historical outage data so that cascading can be better understood and quantified.

Arslan Ahmad, Ian Dobson

The impact of routine smaller outages on distribution system customers in terms of customer minutes interrupted can be tracked using conventional reliability indices. However, the customer minutes interrupted in large blackout events are extremely variable, and this makes it difficult to quantify the customer impact of these extreme events with resilience metrics. We solve this problem with the System Average Large Event Duration Index SALEDI that logarithmically transforms the customer minutes interrupted. We explain how this new resilience metric works, compare it with alternatives, quantify its statistical accuracy, and illustrate its practical use with standard outage data from five utilities.

Arslan Ahmad, Ian Dobson, Anne Kimber

We leverage historical outage data to quantify the resilience benefits of undergrounding a circuit. The historical performance of the overhead circuit is compared to the performance if the circuit had been undergrounded in the past. The number of outages, customers affected, outage duration, and customer hours lost are used as metrics to quantify the benefits of undergrounding. Results show 75% and 78% reductions in customer hours lost per year for two selected circuits, as well as a significant reduction in the average number of outages and customers affected per year, highlighting the advantages of undergrounding. The benefits of investments that result in 10% faster outage restoration are also calculated by rerunning history with the faster restoration included.

Arslan Ahmad, Ian Dobson

We develop LENORI, a Large Event Number of Outages Resilience Index measuring distribution system resilience with the number of forced line outages observed in large extreme events. LENORI is calculated from standard utility outage data. The statistical accuracy of LENORI is ensured by taking the logarithm of the outage data. A related Average Large Event Number of Outages metric ALENO is also developed, and both metrics are applied to a distribution system to quantify the power grid strength relative to the extreme events stressing the grid. The metrics can be used to track resilience and quantify the contributions of various types of hazards to the overall resilience.

Arslan Ahmad, Ian Dobson

Accurate probabilistic modeling of the power system restoration process is essential for resilience planning, operational decision-making, and realistic simulation of resilience events. In this work, we develop data-driven probabilistic models of the restoration process using outage data from four distribution utilities. We decompose restoration into three components: normalized restore time progression, total restoration duration, and the time to first restore. The Beta distribution provides the best-pooled fit for restore time progression, and the Uniform distribution is a defensible, parsimonious approximation for many events. Total duration is modeled as a heteroskedastic Lognormal process that scales superlinearly with event size. The time to first restore is well described by a Gamma model for moderate and large events. Together, these models provide an end-to-end stochastic model for Monte Carlo simulation, probabilistic duration forecasting, and resilience planning that moves beyond summary statistics, enabling uncertainty-aware decision support grounded in utility data.