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Energy Systems and Infrastructure Analysis

Accurate and Tractable Cascade Failure Models for Resilience-Based Decisions in the Power Grid

(Start: May 1, 2020)

Project Background:

Power grid blackouts are primarily caused by cascading failures: these are sequences of dependent outages of individual system components (e.g., transmission lines, transformers, generators etc.) that despite being initiated by unpredictable events, remain sustained due to predictable yet random fluctuations in electric load. Moreover, the individual outages of a cascade are causally linked via well-known laws of power flow physics and the automatic control actions of protection relays. For example, the outage of a single component can lead to redistribution of power flows in the remainder of the network in a way that can cause large overcurrents on some transmission lines. This, in turn, may trigger protection relays to disconnect these lines automatically if the current flow exceeds some threshold rating, or it may lead to eventual thermal failure if the overcurrents remain sustained for a long time.

Scientific Opportunities:

Existing operational and planning decisions are unfortunately made by ignoring their underlying cascade potential. Instead, they rely on compute-intensive and non-interpretable surrogates, such as the de facto N-k security criterion. There is an urgent need for a predictive cascading failure methodology that is not only statistically rigorous and accurate, but also computationally tractable to be used for resilience planning and control purposes.

Statistical approaches based on large deviation theory are ideally suited for this purpose. On the one hand, they seek to provide closed-form expressions for the limiting probability of the occurrence of a random event in a stochastic dynamical system, such as a transmission line failure in a power network. On the other hand, they have never been explored for the cascading failure analysis of power systems. Moreover, it is unclear how one can systematically apply this theory towards building a practical tool that can not only accurately predict cascading failures via simulations but also tractably prevent them for planning and control purposes.

Research Goals:

The primary goal of this project is to develop computational tools that can:

  1. Quantify the probability of cascading failures for a given network operating state, and
  2. Control the probability of cascading failures by finding the optimal network operating state

These have remained open challenges for several years because of several complicating factors, including nonlinear power flow physics, lack of sufficient real-world data (indeed, blackouts are extremely rare events), and the fact that component outages don’t always propagate locally over the power network.

To that end, we propose to develop novel statistical approaches, inspired from large deviation theory and chemical thermodynamics, for representing system switching and cascading failure, as well as efficiently computing with them. Our goal is to demonstrate their utility in a resilience context. In particular, successful completion of the project shall provide tools to allow important decisions, such as planning or operations, to be efficiently and accurately constrained about a prescribed blackout probability level.

Deliverables and Impacts:

Thus far, we have developed the first-ever physics-based predictive model of cascades that explicitly controls endogenous drivers of blackout risk.

Some of our major applied mathematical and computational developments include:

  • Large deviation theory-based probability model and analytical formulae for individual component failure.
  • Kinetic Monte Carlo simulation model for simulating cascades at the scale of real networks.
  • Optimization tool to control cascading failure probability during power generation dispatch.

These developments have been enabled by the use and advancement of several tools including large deviation theory, Monte Carlo sampling, numerical linear algebra, and bilevel optimization.

The methodological developments have important practical implications as well:

More broadly, our approach has the potential to fundamentally impact more general complex system failures across science and engineering domains, beyond just power systems.

Publications:

[1] Roth, Jacob, David A. Barajas-Solano, Panos Stinis, Jonathan Weare, and Mihai Anitescu. A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line Failure.” Multiscale Modeling & Simulation 19, no. 1 (2021): 208—241.

[2] Subramanyam, Anirudh, Jacob Roth, Albert Lam, and Mihai Anitescu. Failure Probability Constrained AC Optimal Power Flow.” arXiv preprint arXiv:2011.02453 (2020).

[3] Zhou, Kai, Ian Dobson, Zhaoyu Wang, Alexander Roitershtein, and Arka P. Ghosh. A Markovian influence graph formed from utility line outage data to mitigate large cascades.” IEEE Transactions on Power Systems 35, no. 4 (2020): 3224—3235.

Team and contact:

Argonne National Laboratory (lead)
Iowa State University

Team Members:
Mihai Anitescu (Principal Investigator, ANL)
Ian Dobson (Professor, ISU)
Albert Lam (Predoctoral Appointee, ANL)
Daniel Adrian Maldonado (Assistant Energy Systems Scientist)
Jacob Roth, (Student Appointee, ANL),
Anirudh Subramanyam (Postdoctoral Appointee, ANL)
Kai Zhou (Graduate student, ISU)