A Thermo-Electro-Mechanical Model for Long-Term Reliability of Aging Transmission Lines

TL;DR

This paper targets long-term reliability of aging transmission lines by coupling a thermo-electro-mechanical phase-field damage model with steady-state heat and electrical conduction to capture thermal runaway via aging. It employs non-intrusive Probabilistic Collocation Methods (PCM) for efficient uncertainty quantification, global sensitivity analysis, and computation of time-dependent failure probabilities, using a quasi-static FEM solver as a black box. Key contributions include a physics-based limit-state framework tied to maximum conductor temperature, a hierarchical multi-physics model linking damage, fatigue, heat, and resistivity, and demonstration that PCM can identify influential parameters (notably base current and temperature-rate) and produce probabilistic failure curves under four representative scenarios. The results provide actionable insights for risk assessment and planning in power grids, offering a path to incorporate regional data and extend to transient analyses and more complex conductor geometries. Overall, the framework advances long-term reliability prediction by fusing detailed material aging with probabilistic risk assessment grounded in first-principles physics.

Abstract

Integrity and reliability of a national power grid system are essential to society's development and security. Among the power grid components, transmission lines are critical due to exposure and vulnerability to severe external conditions, including high winds, ice, and extreme temperatures. The combined effects of external agents with high electrical load and presence of damage precursors greatly affects the conducting material's properties due to a thermal runaway cycle that accelerates the aging process. In this paper, we develop a thermo-electro-mechanical model for long-term failure analysis of overhead transmission lines. A phase-field model of damage and fatigue, coupled with electrical and thermal modules, provides a detailed description of the conductor's temperature evolution. We define a limit state function based on maximum operating temperature to avoid excessive overheating and sagging. We study four representative scenarios deterministically, and propose the Probabilistic Collocation Method (PCM) as a tool to understand the stochastic behavior of the system. We use PCM in forward parametric uncertainty quantification, global sensitivity analysis, and computation of failure probability curves in a straightforward and computationally efficient fashion, and we quantify the most influential parameters that affect the failure predictability from a physics-based perspective.

Figures (23)

• Figure 1: Effect of Ambient Temperature, Windspeed, and Current on Conductor Temperature.
• Figure 2: Schematic representation of the thermo-electro-mechanical framework for transmission line failure. A one-dimensional representation of an initially damaged conductor cable is subject to mechanical tension, heat exchange with the environment, and an electric current, which combined lead to thermal failure from overheating. The deterministic solution of the physical system through Finite-Element Method enters the PCM stochastic solver as a black-box, which generates physics-based predictions of probability of failure.
• Figure 3: Schematic diagram of the relationship between the thermal, electrical, and mechanical models based on their governing equations, in addition to an abstract, scenario-dependent environmental module that provides initial conditions and input parameters.
• Figure 4: Variable cross-section area as a function of parameter $A_\sigma$.
• Figure 5: Evolution of field variables over time at an interval of 5 years.

Theorems & Definitions (1)

• Remark 1