Multi-Stage Correction and Dynamic Validation of Hydraulic Turbine Torque Characteristic Surfaces Using Operational Data

Torque characteristic surfaces in nonlinear hydraulic turbine models are typically derived from model tests. However, model–prototype discrepancies can reduce the accuracy of dynamic simulations of hydropower units. To improve hydraulic turbine modeling accuracy, this study uses measured operational data to perform a multi-stage correction of the torque characteristic surface. The method calibrates the input–output mapping of the original surface through sequential parameter estimation, with parameters fixed after each stage. Polynomial, Gaussian kernel and Sigmoid functions are combined with six port sequences to construct 18 correction schemes, with the parameters at each stage optimized using particle swarm optimization. The results show that correction accuracy and the preferred sequence depend on the function form. For the studied unit, the Gaussian kernel with the “guide-vane opening–unit torque–unit speed” sequence yields the lowest weighted composite error, reducing it by 80.76% relative to the original model. The corrected data in the normal operating region are further used to construct the zero-opening and zero-unit-speed boundaries, which are combined with the runaway-speed boundary to reconstruct the full-operating-range torque characteristic surface using a backpropagation neural network (BPNN). The resulting NRMSE and NMaxAE are 0.54% and 1.58%, respectively. The corrected model is then embedded in the hydropower unit for multi-condition validation under primary frequency regulation. The mean RMSE and MAE of active power decrease by 45.10% and 50.46%, respectively, while the mean accuracy of the response regulation magnitude increases to 99.27%. The prediction error of guide-vane opening is also reduced. These results demonstrate that the proposed method effectively reduces model–prototype discrepancies and improves the accuracy of dynamic prediction under primary frequency regulation.