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Efficient Probabilistic Assessment of Power System Resilience Using the Polynomial Chaos Expansion Method with Enhanced Stability

Aidan Gerkis, Xiaozhe Wang

TL;DR

This work addresses probabilistic resilience assessment of power systems under extreme weather by combining an extended AC-CFM cascading-failure model with an enhanced polynomial chaos expansion (PCE) framework. It introduces a novel Maximin-LHS design to stabilize the PCE moment estimates and reduce required samples, enabling efficient quantification of the resilience metric $\Phi_{LS}$ via the PCE representation $\hat{\Phi}_{LS} = \sum_{i=1}^{N_c} c_i\,\boldsymbol{\Psi}_i(\boldsymbol{\tau})$. The method is demonstrated on the IEEE 39-bus system under a windstorm, showing improved stability and faster convergence for the mean and variance estimates, and providing actionable resilience insights such as a robust backup-generation strategy derived from a $3\sigma$ bound. Overall, the approach enables global probabilistic resilience assessment with scalable computation, supporting more robust planning and adaptation for power systems facing extreme weather.

Abstract

Increasing frequency and intensity of extreme weather events motivates the assessment of power system resilience. The random nature of power system failures during these events mandates probabilistic resilience assessment, but state-of-the-art methods are computationally inefficient. In this paper, an enhanced PCE method to quantify power system resilience based on the extended AC Cascading Failure Model (AC-CFM) model is proposed. To address repeatability issues arising from PCE computation with different sample sets, we propose a novel experiment design method. Numerical studies on the IEEE 39-bus system illustrate the improved repeatability and convergence of the method. The enhanced PCE method is then used to efficiently assess the system's resilience and propose adaptation measures.

Efficient Probabilistic Assessment of Power System Resilience Using the Polynomial Chaos Expansion Method with Enhanced Stability

TL;DR

This work addresses probabilistic resilience assessment of power systems under extreme weather by combining an extended AC-CFM cascading-failure model with an enhanced polynomial chaos expansion (PCE) framework. It introduces a novel Maximin-LHS design to stabilize the PCE moment estimates and reduce required samples, enabling efficient quantification of the resilience metric via the PCE representation . The method is demonstrated on the IEEE 39-bus system under a windstorm, showing improved stability and faster convergence for the mean and variance estimates, and providing actionable resilience insights such as a robust backup-generation strategy derived from a bound. Overall, the approach enables global probabilistic resilience assessment with scalable computation, supporting more robust planning and adaptation for power systems facing extreme weather.

Abstract

Increasing frequency and intensity of extreme weather events motivates the assessment of power system resilience. The random nature of power system failures during these events mandates probabilistic resilience assessment, but state-of-the-art methods are computationally inefficient. In this paper, an enhanced PCE method to quantify power system resilience based on the extended AC Cascading Failure Model (AC-CFM) model is proposed. To address repeatability issues arising from PCE computation with different sample sets, we propose a novel experiment design method. Numerical studies on the IEEE 39-bus system illustrate the improved repeatability and convergence of the method. The enhanced PCE method is then used to efficiently assess the system's resilience and propose adaptation measures.
Paper Structure (13 sections, 9 equations, 6 figures, 2 tables)

This paper contains 13 sections, 9 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Resilience Event Modeling
  3. Polynomial Chaos Expansions
  4. Polynomial Chaos Expansion Theory & Computation
  5. Post-Processing of the PCE
  6. The Challenges in Experiment Design and Estimation Consistency
  7. A Novel Experiment Design Method
  8. Case Study
  9. Simulation Setup
  10. Variance Calculation
  11. Stability Enhancement by the MmLHS Method
  12. Insights from the Resilience Assessment Results
  13. Conclusion

Figures (6)

  • Figure 1: The AC-CFM model proposed by Noebels et al. Noebels-ACCFM.
  • Figure 2: The resilience model represented in \ref{['eq:fls-gen']}.
  • Figure 3: Sampling of a 2-D random vector with both components uniformly distributed in $[0, 1]$ using different methods.
  • Figure 4: The PCE uncertainty quantification method utilizing MmLHS experiment designs.
  • Figure 5: The mean of the moment approximations vs. $N_S$. The true moments are plotted in black.
  • ...and 1 more figures