Layer-Aware Physics-Informed Neural Networks with Condition Embedding for Electro-Thermal Coupled Temperature-Field Modeling of XLPE HVDC Cables

The conductor temperature of cross-linked polyethylene (XLPE) high-voltage direct-current (HVDC) cables governs ampacity assessment and insulation life management, yet it cannot be measured in service, and finite-element simulation is too expensive for real-time use. This paper presents a physics-informed neural network (PINN) that embeds the transient heat-conduction equation, a temperature-dependent Joule source, and the boundary and initial conditions into the training loss of a neural surrogate. Three ingredients adapt the framework to power cables: a layer-aware material mapping over the eight heterogeneous cable layers; an electro-thermal coupling through the temperature dependence of the conductor conductivity, handled during training by a convergent Picard-type evaluation of the Joule source; and a condition-embedding input treating the load current and ambient temperature as continuous parameters so that a single network covers the admissible current–ambient envelope of the studied cable configuration. Validated against finite-element references under fifteen operating conditions, the model attains a root-mean-square error of 0.0024 K (mean over five training seeds) on a held-out condition relative to a finite-element reference whose mesh-discretization error a refinement study bounds at about 0.04 K while reducing the governing-equation residual by approximately 28-fold relative to an identically sized data-driven network at statistically indistinguishable pointwise accuracy. The physics prior also renders degradation under training-data reduction more graceful and improves extrapolation to unseen ambient temperatures, whereas current extrapolation remains the most challenging transfer. The differentiable surrogate identifies the load current and the unmeasurable conductor hotspot from ten surface sensors within seconds, at below 9 ms per 105 queries. A loss-weight sensitivity study and a three-dimensional cable-end-effect case on a second material configuration are also reported. All reference data are numerical; experimental cable-loop validation remains for future work.