A Spatiotemporal Transformer–ConvLSTM Surrogate with Condition Embedding for Dynamic Three-Dimensional Temperature Field Prediction of XLPE HVDC Cables

The conductor temperature of a high-voltage direct-current (HVDC) cable limits its current-carrying capacity and governs the aging of the cross-linked polyethylene (XLPE) insulation. Transient finite-element (FE) simulation provides the full temperature field but is too expensive for online rating and digital-twin applications. This paper presents an autoregressive deep-learning surrogate for the three-dimensional cable temperature field. Exploiting axisymmetry, the network predicts the next field on a two-dimensional radial–axial grid from the previous H frames and the operating condition, and the three-dimensional field is reconstructed by revolution. ConvLSTM layers capture spatiotemporal correlations, a temporal Transformer fuses the history states, and a continuous condition embedding lets one model cover the operating space. A scaled residual-increment formulation and a rollout curriculum stabilize the 600 min closed-loop prediction. On a COMSOL dataset of 49 operating conditions (ambient temperature −20 to 40∘C, load current 0 to 1200 A), the surrogate achieves RMSEs of 0.28, 0.27, and 0.49∘C for training, interpolation, and extrapolation conditions, the latter being held-out corner combinations within the sweep ranges. It reduces the wall-clock time from about 110 s per FE simulation to 1.5 s per case (73× speed-up; 139× batched) and achieves lower mean RMSE than three baseline models.