  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.
