Physics-Based Dynamic Modeling of Hydro Generator Cooling System Using Plant Data, Empirical Heat Transfer Correlations and Reduced Parameter Estimation

Hydro-generator cooling arrays are sparsely instrumented, limiting estimation of heat-exchanger (HX) parameters from plant data for thermal modeling. This study develops and validates a 48-state quasi-linear parameter-varying (qLPV) gray-box model for twelve fin-and-tube air-to-water HXs in a hydro generator cooling system. Four equivalent three-HX groups use four serial cells each, and manufacturer-specified geometry and empirical correlations provide operating-dependent conductance values rather than fitted parameters. Of 19 coefficients, eleven are fixed, and eight effective group coefficients are estimated. Rated predictions reproduce manufacturer outlet temperatures within 0.6 °C, providing catalog-consistency verification. Coefficient calibration uses a 4.03 h window from a 48,241-sample (13.4 h) plant record. With the estimated coefficients frozen, combined filtered root-mean-square error (RMSE) values on the full record are 0.183 and 0.179 °C on the north and south sides of the cooler array. Multistart Nelder–Mead and direct four-dimensional simplicial homology global optimization (SHGO) yield numerically equivalent coefficient estimates. The resulting model is computationally economical and provides a physics-based plant-specific baseline for record replay, recalibration and prospective monitoring.