Fast extremum values calculation of electro‑thermal fields for ±800 kV valve‑side resin-impregnated paper bushing under multiple factors

Valve-side resin-impregnated paper (RIP) bushings are key insulation components of HVDC converter transformers. Combined AC–DC voltage, high current, and varying thermal boundaries produce non-uniform electro-thermal fields, potentially causing local overheating and electric-field concentration. A three-dimensional electro-thermal finite-element model was developed for a full-scale ±800 kV valve-side RIP bushing and its temperature-field calculation was validated through temperature-rise tests, yielding an MAE of 2.301 °C and an RMSE of 2.467 °C. Single- and multi-factor effects of load rate, ambient air temperature, and transformer oil temperature were investigated. The factors create different temperature and conductivity gradients, producing non-equivalent electric-field responses and non-monotonic variations with thermal boundaries. Temperature-dependent field distortion is dominated by DC redistribution, and electric-field concentration does not necessarily coincide with the thermal hot spot. Contribution analysis assigns 46.10%, 41.57%, and 5.94% of hot-spot-temperature variation to load rate, oil temperature, and air temperature, respectively, while load rate accounts for 88.76% of electric-field-extremum variation, showing joint load–oil control of the thermal response but predominant load control of electrical stress. An interpretable fast-prediction model combining a sparse high-order response surface with Kriging residual correction was developed. For 25 independent numerical test conditions, its MAE/RMSE values were 1.437/1.743 °C for hot-spot temperature and 0.060/0.076 kV/mm for electric-field extremum. Compared with conventional Kriging, BP, and LSTM, the proposed model achieved the lowest five-fold validation and independent-test RMSE values for electric-field-extremum calculation while retaining an explicit mathematical form. The model provides a rapid quantitative approach for condition evaluation and identification of potentially unfavorable RIP-bushing operating conditions.