A Markovian influence graph formed from utility line outage data to mitigate cascading

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.

[1]  Daniel Kirschen,et al.  Survey of tools for risk assessment of cascading outages , 2011, 2011 IEEE Power and Energy Society General Meeting.

[2]  Janusz Bialek,et al.  Benchmarking and Validation of Cascading Failure Analysis Tools , 2016, IEEE Transactions on Power Systems.

[3]  P. Hines,et al.  Large blackouts in North America: Historical trends and policy implications , 2009 .

[4]  Zhaoyu Wang,et al.  Can an influence graph driven by outage data determine transmission line upgrades that mitigate cascading blackouts? , 2018, 2018 IEEE International Conference on Probabilistic Methods Applied to Power Systems (PMAPS).

[5]  I. Dobson,et al.  North American Blackout Time Series Statistics and Implications for Blackout Risk , 2016, IEEE Transactions on Power Systems.

[6]  Debashis Kushary,et al.  Bootstrap Methods and Their Application , 2000, Technometrics.

[7]  Ian Dobson,et al.  "Dual Graph" and "Random Chemistry" Methods for Cascading Failure Analysis , 2013, 2013 46th Hawaii International Conference on System Sciences.

[8]  Paul D. H. Hines,et al.  Cascading Power Outages Propagate Locally in an Influence Graph That is Not the Actual Grid Topology , 2015, IEEE Transactions on Power Systems.

[9]  I. Dobson,et al.  Estimating the Propagation and Extent of Cascading Line Outages From Utility Data With a Branching Process , 2012, IEEE Transactions on Power Systems.

[10]  Ian Dobson,et al.  Comparing a transmission planning study of cascading with historical line outage data , 2016, 2016 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS).

[11]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[12]  Pierre Henneaux,et al.  Benchmarking Quasi-Steady State Cascading Outage Analysis Methodologies , 2018, 2018 IEEE International Conference on Probabilistic Methods Applied to Power Systems (PMAPS).

[13]  E. Seneta,et al.  On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains , 1965, Journal of Applied Probability.

[14]  I. Dobson,et al.  Initial review of methods for cascading failure analysis in electric power transmission systems IEEE PES CAMS task force on understanding, prediction, mitigation and restoration of cascading failures , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[15]  Kai Sun,et al.  An Interaction Model for Simulation and Mitigation of Cascading Failures , 2014, IEEE Transactions on Power Systems.

[16]  Ian Dobson,et al.  Obtaining Statistics of Cascading Line Outages Spreading in an Electric Transmission Network From Standard Utility Data , 2015, IEEE Transactions on Power Systems.

[17]  Christin Wirth,et al.  Entropy Optimization And Mathematical Programming , 2016 .

[18]  Erik A. van Doorn,et al.  Quasi-stationary distributions for discrete-state models , 2013, Eur. J. Oper. Res..

[19]  Kai Sun,et al.  Efficient Estimation of Component Interactions for Cascading Failure Analysis by EM Algorithm , 2018, IEEE Transactions on Power Systems.

[20]  Robert E Weiss,et al.  Bayesian methods for data analysis. , 2010, American journal of ophthalmology.

[21]  Seth D. Guikema,et al.  Formulating informative, data-based priors for failure probability estimation in reliability analysis , 2007, Reliab. Eng. Syst. Saf..