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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 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.

We focus on large blackouts in electric distribution systems caused by extreme winds. Such events have a large cost and impact on customers. To quantify resilience to these events, we formulate large event risk and show how to calculate it from the historical outage data routinely collected by utilities' outage management systems. Risk is defined using an event cost exceedance curve. The tail of this curve and the large event risk is described by the probability of a large cost event and the slope magnitude of the tail on a log-log plot. 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 12% and 22% reduction in the probability of a large cost event due to 10% wind hardening and 10% faster restoration respectively. 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.

We quantify resilience with metrics extracted from the historical outage data that is routinely recorded by many distribution utilities. The outage data is coordinated with wind data to relate average outage rates in an area to wind speed measured at a nearby weather station. A past investment in wind hardening would have reduced the outage rates, and the effect of this on metrics can be calculated by sampling a reduced number of the historical outages and recomputing the metrics. This quantifies the impact that the hardening would have had on customers. This is a tangible way to relate an investment in wind resilience to the benefits it would have had on the lived experience of customers that could help make the case for the investment to the public and regulators. We also quantify the impact of earlier or faster restoration on customer metrics and compare this to the impact of investment in hardening. Overall this is a new and straightforward approach to quantify resilience and justify resilience investments to stakeholders that is directly driven by utility data. The approach driven by data avoids complicated models or modeling assumptions.

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 performance 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 derived 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 illustrated with a typical North American transmission event. Similarly nice formulas are obtained for the area metric for empirical power system data.

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.

We discuss ways to measure duration in a power transmission system resilience event by modeling outage and restore processes from utility data. We introduce novel Poisson process 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 metrics 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.

Resilience curves track the accumulation and restoration of outages during an event on an electric distribution grid. We show that a resilience curve generated from utility data can always be decomposed into an outage process and a restore process and that these processes generally overlap in time. We use many events in real utility data to characterize the statistics of these processes, and derive formulas based on these statistics for resilience metrics such as restore duration, customer hours not served, and outage and restore rates. The formulas express the mean value of these metrics as a function of the number of outages in the event. We also give a formula for the variability of restore duration, which allows us to predict a maximum restore duration with 95% confidence. Overall, we give a simple and general way to decompose resilience curves into outage and restore processes and then show how to use these processes to extract resilience metrics from standard distribution system data.

This paper develops a comprehensive framework of Area Angle Monitoring (AAM) to monitor the stress of bulk power transfer across an area of a power transmission system in real-time. Area angle is calculated from synchrophasor measurements to provide alert to system operators if the area angle exceeds pre-defined thresholds. This paper proposes general methods to identify these warning and emergency thresholds, and tests a mitigation strategy to relieve the area stress when the area angle exceeds the threshold. In order to handle the limited coverage of synchrophasor measurements, this paper proposes methods to estimate phase angles for boundary buses without synchrophasor measurements, which extends the application of AAM. AAM is verified for a power transmission area in the Western Electricity Coordinating Council system with both simulated data and synchrophasor measurements recorded from real events. A utility deployment to test the framework for monitoring area angle with live-stream and recorded synchrophasor data is described., Comment: 8 pages, 17 figures

Transmission line outage rates are fundamental to power system reliability analysis. Line outages are infrequent, occurring only about once a year, so outage data are limited. We propose a Bayesian hierarchical model that leverages line dependencies to better estimate outage rates of individual transmission lines from limited outage data. The Bayesian estimates have a lower standard deviation than estimating the outage rates simply by dividing the number of outages by the number of years of data, especially when the number of outages is small. The Bayesian model produces more accurate individual line outage rates, as well as estimates of the uncertainty of these rates. Better estimates of line outage rates can improve system risk assessment, outage prediction, and maintenance scheduling.

Given increasing risk from climate-induced natural hazards, there is growing interest in the development of methods that can quantitatively measure resilience in power systems. This work quantifies resilience in electric power transmission networks in a new and comprehensive way that can represent the multiple processes of resilience. A novel aspect of this approach is the use of empirical data to develop the probability distributions that drive the model. This paper demonstrates the approach by measuring the impact of one potential improvement to a power system. Specifically, we measure the impact of additional distributed generation on power system resilience.

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., Comment: to appear in IEEE Transactions on Power Systems

Observed transmission line outage data is grouped into successive generations of events. The empirical distribution of the number of generations in the cascades follows a Zipf distribution that implies the increasing propagation as cascades progress. The slope of the Zipf distribution gives a System Event Propagation Slope Index (SEPSI). This new metric quantifies the cascade propagation, varies as expected, and determines the probabilities of small, medium, and large cascades.

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.

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., Comment: Accepted for publication at the IEEE Transactions on Power Systems

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., Comment: Revised and expanded version with minor corrections and a new section illustrating use of data to validate a simulation. Will appear in IEEE Transactions on Power Systems

If an interarea oscillatory mode has insufficient damping, generator redispatch can be used to improve its damping. We explain and apply a new analytic formula for the modal sensitivity to rank the best pairs of generators to redispatch. The formula requires some dynamic power system data and we show how to obtain that data from synchrophasor measurements. The application of the formula to damp interarea modes is explained and illustrated with interarea modes of the New England 10-machine power system., Comment: To appear in IEEE Transactions on Power Systems, accepted September 2015

We use synchrophasor measurements of the complex voltage and current at both ends of multiple transmission lines that connect areas of a power system to monitor the online voltage collapse margin. A new reduction is used to reduce the multiple transmission lines to a single line equivalent and determine how to combine the synchrophasor measurements. Generator reactive power limits can be accommodated. The results show that this methodology can capture the effect of multiple contingencies inside the transmission corridors, giving awareness to the operators about the severity of contingencies with respect to voltage stability.

When power grids are heavily stressed with a bulk power transfer, it is useful to have a fast indication of the increased stress when multiple line outages occur. Reducing the bulk power transfer when the outages are severe could forestall further cascading of the outages. We show that synchrophasor measurements of voltage angles at all the area tie lines can be used to indicate the severity of multiple outages. These synchrophasor measurements are readily combined into an "area angle" that can quickly track the severity of multiple outages after they occur. We present a procedure to define thresholds for the area angle that relate to the maximum power that can be transferred through the area until a line limit is reached. Then in real time we would monitor the area angle and compare it to the thresholds when line outages occur to determine the urgency (or not) of actions to reduce the bulk transfer of power through the area. The procedure also identifies exceptional cases in which separate actions to resolve local power distribution problems are needed. We illustrate the thresholds and monitoring with the area angle across several states of Northwestern USA.

The area angle is a scalar measure of power system area stress that responds to line outages within the area and is a combination of synchrophasor measurements of voltage angles around the border of the area. Both idealized and practical examples are given to show that the variation of the area angle for single line outages can be approximately related to changes in the overall susceptance of the area and the line outage severity., Comment: adjusted version accepted at North American Power Symposium (NAPS), Pullman WA USA, September 2014

We consider the fast monitoring of voltage collapse margin using synchrophasor measurements at both ends of transmission lines that transfer power from two generators to two loads. This shows a way to extend the monitoring of a radial transmission line to multiple transmission lines. The synchrophasor voltages are combined into a single complex voltage difference across an area containing the transmission lines that can be monitored in the same way as a single transmission line. We identify ideal conditions under which this reduction to the single line case perfectly preserves the margin to voltage collapse, and give an example that shows that the error under practical non-ideal conditions is reasonably small., Comment: IEEE Power and Energy Society General Meeting, July 2014

The 20th-century engineering feat that most improved the quality of human life, the electric power system, now faces discipline-spanning challenges that threaten that distinction. So multilayered and complex that they resemble ecosystems, power grids face risks from their interdependent cyber, physical, social and economic layers. Only with a holistic understanding of the dynamics of electricity infrastructure and human operators, automatic controls, electricity markets, weather, climate and policy can we fortify worldwide access to electricity., Comment: Pages 1--2 are the opinion article published in PNAS 110 (30) 12159 (2013). Pages 4--10 are supplementary material, with more explanation of the main components and feedbacks in electric power systems, as well as a list of useful sources of data on power grids

We derive a new formula for the sensitivity of electromechanical oscillation damping with respect to generator redispatch. The formula could lead to some combination of observations, computations and heuristics to more effectively damp interarea oscillations., Comment: to appear at 2013 IREP Symposium-Bulk Power System Dynamics and Control-IX (IREP), August 25-30, 2013, Rethymon, Greece. This revision includes a needed generic assumption and corrects explanation of overdetermined coordinates

Universities are required by legislation to provide annual staff unit record files to the Department of Education, Science and Training (DEST). Most universities seem to undertake this task with appropriate diligence. This paper examines the latest staff aggregated data set released by DEST (2005 data), in order to compare average salaries paid by universities to general ("non-academic") staff, and to identify the top salaries paid. (Contains 4 tables and 2 figures.)

The recent Government inquiry into student income support noted that there was "conclusive evidence that the income support system is in a serious state of disrepair and that nothing short of a major policy review and overhaul of the system is required". The report of the inquiry produced 15 common sense recommendations, but Government senators registered their dissent to eight of them. The main scheme is called "Youth Allowance", and the majority of recipients are university students aged up to 24 years. There are two basic problems with Youth Allowance. First, the strict regime of means testing rules out most students (including students of very limited financial means). Most students are assessed for eligibility on their family's income and assets. If combined parental annual income exceeds a modest $28,500, the student's benefits are reduced by $1 for every $4 earned above that limit. To be assessed on one's own means, a student must be declared as "independent". It is all but impossible to be declared "independent" for at least 18 months after finishing secondary school. Second, the base amount paid to recipients is too low. Students eligible for the maximum payment face a poverty gap of over $100 per week. Many eligible students receive considerably less than the maximum. The Government refuses to release figures on the proportion of university students receiving less than the full amount. What is worse is that students are permitted to earn only $118 per week in addition to Youth Allowance before being penalized. This one aspect of Youth Allowance is not indexed against inflation, and in 2005 the additional earnings limit remained at the level it was in 1993. With indexation, the permitted additional earnings limit would have been $160 per week. As a consequence, many students work for cash payments in the black economy (predominantly in the hospitality industry). By earning more than the permitted maximum in the cashier of student income support (the first for 16 years) was funded privately, because the Government refused to it. That survey showed that many more full-time students are now in paid employment during semester, and that they work many hours more (on average) that had been the case in the mid 1980s. [This report is from the Educational Policy Institute.]