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Thermo-Electro-Mechanical Modeling of Power Transmission Line Failures across Four US States

Prakash KC, Maryam Naghibolhosseini, Mohsen Zayernouri

TL;DR

This work tackles the reliability of overhead transmission lines under wind, ambient temperature, and current demands by developing a thermo‑electro‑mechanical model that links mechanical fatigue via a phase‑field damage framework to thermal and electrical fields. It first solves the coupled system deterministically with finite elements, then extends to uncertainty quantification and reliability analysis using the Probabilistic Collocation Method (PCM). Applied to four US states (Texas, California, Michigan, Florida) with historical wind/temperature data, the study shows that pre‑existing damage strongly reduces structural life, while current load and fracture energy govern long‑term temperature evolution and damage. PCM enables efficient global sensitivity analysis and time‑dependent probability of failure estimates, offering practical insight for resilience planning and risk‑informed grid operations.

Abstract

The failure of overhead transmission lines in the United States can lead to significant economic losses and widespread blackouts, affecting the lives of millions. This study focuses on the reliability of transmission lines, specifically examining the effects of wind, ambient temperature, and current demands on lines, incorporating minimal and significant pre-existing damage. We develop a Thermo-Electro-Mechanical Model to analyze the transmission line failures across sensitive and affected states of the United States, integrating historical data on wind and ambient temperature. By combining numerical simulation with historical data analysis, our research assesses the impact of varying environmental conditions on the reliability of transmission lines. Our methodology begins with a deterministic approach to model temperature and damage evolution, using phase-field modeling for fatigue and damage, coupled with electrical and thermal models. Later, we adopt the Probability Collocation Method to investigate the stochastic behavior of the system, enhancing our understanding of uncertainties in model parameters, conducting sensitivity analysis, and estimating the probability of failures over time. This approach allows for a comprehensive analysis of factors affecting transmission line reliability, contributing valuable insights into improving power line's resilience against environmental conditions.

Thermo-Electro-Mechanical Modeling of Power Transmission Line Failures across Four US States

TL;DR

This work tackles the reliability of overhead transmission lines under wind, ambient temperature, and current demands by developing a thermo‑electro‑mechanical model that links mechanical fatigue via a phase‑field damage framework to thermal and electrical fields. It first solves the coupled system deterministically with finite elements, then extends to uncertainty quantification and reliability analysis using the Probabilistic Collocation Method (PCM). Applied to four US states (Texas, California, Michigan, Florida) with historical wind/temperature data, the study shows that pre‑existing damage strongly reduces structural life, while current load and fracture energy govern long‑term temperature evolution and damage. PCM enables efficient global sensitivity analysis and time‑dependent probability of failure estimates, offering practical insight for resilience planning and risk‑informed grid operations.

Abstract

The failure of overhead transmission lines in the United States can lead to significant economic losses and widespread blackouts, affecting the lives of millions. This study focuses on the reliability of transmission lines, specifically examining the effects of wind, ambient temperature, and current demands on lines, incorporating minimal and significant pre-existing damage. We develop a Thermo-Electro-Mechanical Model to analyze the transmission line failures across sensitive and affected states of the United States, integrating historical data on wind and ambient temperature. By combining numerical simulation with historical data analysis, our research assesses the impact of varying environmental conditions on the reliability of transmission lines. Our methodology begins with a deterministic approach to model temperature and damage evolution, using phase-field modeling for fatigue and damage, coupled with electrical and thermal models. Later, we adopt the Probability Collocation Method to investigate the stochastic behavior of the system, enhancing our understanding of uncertainties in model parameters, conducting sensitivity analysis, and estimating the probability of failures over time. This approach allows for a comprehensive analysis of factors affecting transmission line reliability, contributing valuable insights into improving power line's resilience against environmental conditions.
Paper Structure (24 sections, 64 equations, 23 figures, 3 tables, 1 algorithm)

This paper contains 24 sections, 64 equations, 23 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Representative Scenarios
  4. Discrete Fourier Transform
  5. Reliability of Transmission Lines
  6. Methodology
  7. Mechanical Model
  8. Thermal Model
  9. Electrical Model
  10. Sag Consideration
  11. Multi-Physics Framework
  12. Deterministic Solution
  13. Finite-Element Discretization
  14. Numerical Results
  15. Stochastic Solution
  16. ...and 9 more sections

Figures (23)

  • Figure 1: Discrete and continuous variation of wind and temperature data of Texas
  • Figure 2: Discrete and continuous variation of wind and temperature data of California
  • Figure 3: Discrete and continuous variation of wind and temperature data of Michigan
  • Figure 4: Discrete and continuous variation of wind and temperature data of Florida
  • Figure 5: Schematic representation of Transmission lines.
  • ...and 18 more figures