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Development of Bayesian Component Failure Models in E1 HEMP Grid Analysis

Niladri Das, Ross Guttromson, Tommie A. Catanach

TL;DR

The study tackles the challenge of assessing E1 HEMP impacts on large power grids when deterministic analyses are computationally prohibitive and data are scarce. It develops a Bayesian hierarchical framework that fuses SME-derived priors with limited laboratory test data to produce CDF-based component failure models conditioned on HEMP-coupled voltage, enabling efficient grid-scale simulations. Key contributions include a prior construction via SME-informed distributions and Bayesian optimization, a SA-MCMC/NUTS-based posterior inference workflow, and a concrete application to breaker trip coils illustrating how new data can refine the failure model. The approach supports robust risk assessment for grid resilience under E1 HEMP events and provides a principled path to incorporate additional data and SME insights over time.

Abstract

Combined electric power system and High-Altitude Electromagnetic Pulse (HEMP) models are being developed to determine the effect of a HEMP on the US power grid. The work relies primarily on deterministic methods; however, it is computationally untenable to evaluate the E1 HEMP response of large numbers of grid components distributed across a large interconnection. Further, the deterministic assessment of these components' failures are largely unachievable. E1 HEMP laboratory testing of the components is accomplished, but is expensive, leaving few data points to construct failure models of grid components exposed to E1 HEMP. The use of Bayesian priors, developed using the subject matter expertise, combined with the minimal test data in a Bayesian inference process, provides the basis for the development of more robust and cost-effective statistical component failure models. These can be used with minimal computational burden in a simulation environment such as sampling of Cumulative Distribution Functions (CDFs).

Development of Bayesian Component Failure Models in E1 HEMP Grid Analysis

TL;DR

The study tackles the challenge of assessing E1 HEMP impacts on large power grids when deterministic analyses are computationally prohibitive and data are scarce. It develops a Bayesian hierarchical framework that fuses SME-derived priors with limited laboratory test data to produce CDF-based component failure models conditioned on HEMP-coupled voltage, enabling efficient grid-scale simulations. Key contributions include a prior construction via SME-informed distributions and Bayesian optimization, a SA-MCMC/NUTS-based posterior inference workflow, and a concrete application to breaker trip coils illustrating how new data can refine the failure model. The approach supports robust risk assessment for grid resilience under E1 HEMP events and provides a principled path to incorporate additional data and SME insights over time.

Abstract

Combined electric power system and High-Altitude Electromagnetic Pulse (HEMP) models are being developed to determine the effect of a HEMP on the US power grid. The work relies primarily on deterministic methods; however, it is computationally untenable to evaluate the E1 HEMP response of large numbers of grid components distributed across a large interconnection. Further, the deterministic assessment of these components' failures are largely unachievable. E1 HEMP laboratory testing of the components is accomplished, but is expensive, leaving few data points to construct failure models of grid components exposed to E1 HEMP. The use of Bayesian priors, developed using the subject matter expertise, combined with the minimal test data in a Bayesian inference process, provides the basis for the development of more robust and cost-effective statistical component failure models. These can be used with minimal computational burden in a simulation environment such as sampling of Cumulative Distribution Functions (CDFs).
Paper Structure (20 sections, 3 equations, 13 figures, 2 tables)

This paper contains 20 sections, 3 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. E1 EMP Component Testing
  3. Conducted and Radiated EMP Testing
  4. Test Methods
  5. Use and Interpretation of Statistical Component Failure Models in Grid Simulation
  6. Generating a non-Bayesian Statistical Failure Model
  7. Development of Bayesian Statistical Failure Model Using Limited Test Data
  8. Development of Prior$_{\boldsymbol{\lambda}}$ Distributions of Bayesian Hierarchical Model Parameters
  9. Bayesian Optimization
  10. Method of Bayesian Failure Model (CDF) Development
  11. Discussion on Statistical Failure Model Error
  12. Error Due to Bayesian Inferencing Computation
  13. Error Due to Bayesian Optimization Computation
  14. Finite Testing Error in Failure CDF
  15. Error due to SME Confidence Interval Estimates
  16. ...and 5 more sections

Figures (13)

  • Figure 1: High Altitude EMP Waveform 1
  • Figure 2: Process for Using Failure Model in Grid Simulations 7
  • Figure 3: Conducted pulse data for 12 breaker trip coils, testing insulation rupture b15. Green dots Indicate a passed test, while red dots indicate a failed test. The gray region is unknown. (Test data for devices 1, 10, and 12 are not available.)
  • Figure 4: Least Squares Gaussian Fit to Test Data (n=12) with 90 percent Confidence Intervals (CI). Red Dotted Lines Indicate LSE Gaussian Fit of CI with the Cumulative Test Data Having Values 0 and 1. Shape of CDF is Assumed to be Gaussian.
  • Figure 5: Bayesian Hierarchical Model Development using Limited Experimental Data. For the Hierarchy see fig. \ref{['fig:failurecdfexample']}. This process is repeated using a different sample from SME estimates, finding the mean and variance of the posterior$_{\boldsymbol{\lambda}}$, which is the statistical failure model.
  • ...and 8 more figures