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A branching process approximation to cascading load-dependent system failure

I. Dobson, B.A. Carreras, D.E. Newman
2004 37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the  
We study a probabilistic model of loading dependent cascading failure by approximating the propagation of failures as a Poisson branching process.  ...  Networked infrastructures operated under highly loaded conditions are vulnerable to catastrophic cascading failures.  ...  Implications for risk of load-dependent cascading failure The following sections show how a model of loading dependent cascading failure can be approximated as a branching process.  ... 
doi:10.1109/hicss.2004.1265185 dblp:conf/hicss/DobsonCN04 fatcat:5ros26iz6reinglkzivtkasa24

Where is the edge for cascading failure?: challenges and opportunities for quantifying blackout risk

Ian Dobson
2007 IEEE Power Engineering Society General Meeting  
This critical loading could serve as a reference point for determining the "edge" for cascading failure risk.  ...  High-level probabilistic models of cascading failure and power system simulations suggest that there is a critical loading at which expected blackout size sharply increases and there is a power law in  ...  In a parameter range of the most interest, the CASCADE model is well approximated by a branching process [20] , so we proceed to explain the branching process in more detail.  ... 
doi:10.1109/pes.2007.385773 fatcat:3qp5ul3j6vgx3k7hy5qadvbhby

Approximating a Loading-Dependent Cascading Failure Model With a Branching Process

Janghoon Kim, Ian Dobson
2010 IEEE Transactions on Reliability  
For suitable parameters, the distributions of the total number of failures from the branching process and CASCADE models are close enough to make the branching process a useful approximation.  ...  In one model called CASCADE, failing components successively load the unfailed components, whereas the other model is based on a Galton-Watson branching process.  ...  ACKNOWLEDGMENTS This paper is an account of work sponsored in part by the Power Systems Engineering Research Center (PSERC).  ... 
doi:10.1109/tr.2010.2055928 fatcat:kwddzmni4rb2xhsloczmtfxsj4


Ian Dobson, Benjamin A. Carreras, Vickie E. Lynch, Bertrand Nkei, David E. Newman
2005 Probability in the engineering and informational sciences (Print)  
We compare and test statistical estimates of failure propagation in data from versions of a probabilistic model of loading-dependent cascading failure and a power systems blackout model of cascading transmission  ...  Approximations to the probabilistic model describe the forms of probability distributions of cascade sizes.  ...  CASCADE MODEL AND BRANCHING PROCESS PARAMETERS This section summarizes the CASCADE model of probabilistic load-dependent cascading failure and its branching process approximation [13] , [16] , [15  ... 
doi:10.1017/s026996480505031x fatcat:bl3bodnmjjapvbwmzlf3lbzqju

Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization

Ian Dobson, Benjamin A. Carreras, Vickie E. Lynch, David E. Newman
2007 Chaos  
Approximating cascading failure as a branching process suggests ways to compute and monitor criticality by quantifying how much failures propagate.  ...  Power system overall load relative to operating limits is a key factor affecting the risk of cascading failure.  ...  The approximation of CASCADE as a branching process allows the criterion to be expressed in terms of system loading.  ... 
doi:10.1063/1.2737822 pmid:17614690 fatcat:2dpyhomxh5gfxabotoikaq65yu

Stochastic load-redistribution model for cascading failure propagation

Jörg Lehmann, Jakob Bernasconi
2010 Physical Review E  
A new class of probabilistic models for cascading failure propagation in interconnected systems is proposed.  ...  Specifically, it is assumed that the load increments after a failure are proportional to the failed load and that the load redistribution among the remaining elements is stochastic.  ...  Their increased load, however, will eventually lead to a higher breakdown probability than predicted by the branching-process approximation, where this effect is neglected.  ... 
doi:10.1103/physreve.81.031129 pmid:20365719 fatcat:jhmxfl4vnnflpnv4rhjyqhbthu

Towards quantifying cascading blackout risk

Ian Dobson, Kevin R. Wierzbicki, Janghoon Kim, Hui Ren
2007 2007 iREP Symposium - Bulk Power System Dynamics and Control - VII. Revitalizing Operational Reliability  
We describe this complicated cascade using a bulk probabilistic model in which the initial failures propagate randomly according to a branching process.  ...  Blackouts become widespread by initial failures propagating in a diverse and intricate cascade of rare events.  ...  Acknowledgements We gratefully acknowledge that this paper is an account of work sponsored in part by the Power Systems Engineering Research Center (PSERC) and support in part from NSF grants ECCS-0606003  ... 
doi:10.1109/irep.2007.4410554 fatcat:zua4zjx3l5bozo772mqbjvwhmm

Estimating Propagation and Distribution of Load Shed in Simulations of Cascading Blackouts

Janghoon Kim, K. R. Wierzbicki, I. Dobson, R. C. Hardiman
2012 IEEE Systems Journal  
The average propagation of the simulated load shed data is estimated and then the initial load shed is propagated with two different branching process models of cascading failure to estimate the probability  ...  The first model discretizes the load shed and then applies a Galton-Watson branching process. The second model is a continuous state branching process.  ...  Branching processes have long been used in a variety of applications to model cascading processes [11] , [12] , but their application to the risk of cascading failure is recent [13] , [14] .  ... 
doi:10.1109/jsyst.2012.2192061 fatcat:icked3n2hvfu5gtpi6kdpc2ucq

An Estimator of Propagation of Cascading Failure

I. Dobson, K.R. Wierzbicki, B.A. Carreras, V.E. Lynch, D.E. Newman
2006 Proceedings of the 39th Annual Hawaii International Conference on System Sciences (HICSS'06)  
The estimator is derived from a simple and high-level branching process model of cascading failure.  ...  The estimator is tested on a saturating branching process model of cascading failure and on failure data generated by the OPA simulation of cascading blackouts.  ...  The most immediate motivation is that this branching process approximates a loading dependent model of cascading failure [17] and captures some, but not all, qualitative features of cascading failure  ... 
doi:10.1109/hicss.2006.54 dblp:conf/hicss/DobsonWCLN06 fatcat:x4r2zlwbtffgdgti73egyz65jy

Criticality in a cascading failure blackout model

Dusko P. Nedic, Ian Dobson, Daniel S. Kirschen, Benjamin A. Carreras, Vickie E. Lynch
2006 International Journal of Electrical Power & Energy Systems  
Table 1: Approximate power law exponents at criticality for several cascading failure models.  ...  We verify and examine criticality in a 1000 bus network with an AC blackout model that represents many of the interactions that occur in cascading failure.  ...  Branching process models that approximate CASCADE show similar results [7] . For single-type branching processes it is known analytically that the exponent of the power law region is -1.5.  ... 
doi:10.1016/j.ijepes.2006.03.006 fatcat:55lldniohrhcrhe6fyuolo6oh4

Testing Branching Process Estimators of Cascading Failure with Data from a Simulation of Transmission Line Outages

Ian Dobson, Janghoon Kim, Kevin R. Wierzbicki
2010 Risk Analysis  
We use a Galton-Watson branching process model of cascading failure and the standard Harris estimator of the mean propagation modified to work when the process saturates at a maximum number of components  ...  Index Terms-blackout risk, branching process, cascading failure, electric power transmission system, infrastructure  ...  APPENDIX: BIAS AND VARIANCE OF λ s We continue to assume that the branching process has Poisson initial failures with mean θ and a Poisson offspring distribution with mean λ.  ... 
doi:10.1111/j.1539-6924.2010.01369.x pmid:20199655 fatcat:7ryzl7gzfrfjrajjbs6gpk2ite

Cascading Failure Analysis With DC Power Flow Model and Transient Stability Analysis

Jun Yan, Yufei Tang, Haibo He, Yan Sun
2015 IEEE Transactions on Power Systems  
However, due to the complex nature of the power system and cascading failures, the underlying assumptions in DC power flow-based cascading failure simulators (CFS) may fail to hold during the development  ...  The DC power flow-based model has been a popular model to study the cascading failure problem due to its efficiency, simplicity and scalability in simulations of such failures.  ...  of using different power system models to approximate system behavior in cascading failures.  ... 
doi:10.1109/tpwrs.2014.2322082 fatcat:ovmk6sfcl5c77osqcopizhumxm

Cyber Physical Power System (CPPS): A review on measures and optimization methods of system resilience

Gongyu Wu, Zhaojun S. Li
2021 Frontiers of Engineering Management  
AbstractThe Cyber-Physical Power System (CPPS) is one of the most critical infrastructure systems in a country because a stable and secure power supply is a key foundation for national and social development  ...  The recent advances in modeling methods for cascading failures within the CPPS, which is the theoretical foundation for the resilience assessment and optimization research of CPPSs, are also presented.  ...  Zhou et al. (2020) considered the impact of system dependencies inside systems on cascading failures and built a cascading failure model with dependence clusters of nodes.  ... 
doi:10.1007/s42524-021-0163-3 fatcat:4dmf6nk7zvfenkj7p7qzqlsyn4

A Robust Optimization Approach for Terminating the Cascading Failure of Power Systems [article]

Chao Zhai
2019 arXiv   pre-print
Moreover, a robust optimization formulation is proposed to deal with the cascading blackouts by shedding load optimally for multiple cascading failure paths with relatively high probabilities.  ...  By incorporating uncertainties and stochastic factors of the cascades, a Markov chain model is developed in this paper to predict the cascading failure paths of power systems.  ...  The probability of branch outage due to hidden failure is dependent on the location of outage branches.  ... 
arXiv:1907.13452v2 fatcat:zuot7zpearckpdrismvmi4q6ie

Risk Assessment of Power System Considering Frequency Dynamics and Cascading Process

Chao Luo, Jun Yang, Yuanzhang Sun
2018 Energies  
Therefore, this paper proposes a novel frequency simulation model considering the influence of cascading failure to reveal the security level of power systems comprehensively.  ...  This is not enough, especially when the modern power system suffers the increasing threat of cascading failures.  ...  The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.  ... 
doi:10.3390/en11020422 fatcat:ssgdyo3nxza3dm5x3jgdb6f5oy
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