To address grid variability caused by renewable energy integration and to maintain grid reliability and resilience, hydropower must quickly adjust its power generation over short time periods. This changing energy generation landscape requires advance technology integration and adaptive parameter optimization for hydropower systems via digital twin effort. However, this is difficult owing to the lack of characterization and modeling for the nonlinear nature of hydroturbines. To solve this issue, this paper first formulates a six-coefficient Kaplan hydroturbine model and then proposes a parametric optimization tuning framework based on the Nelder–Mead algorithm for adaptive dynamic learning of the six-coefficients so as to build models that describe the turbine. To assess the performance of the proposed optimal parametric tuning technique, operational data from a real-world Kaplan hydroturbine unit are collected and used to model the relationship between the gate opening and the generated power production. The findings show that the proposed technique can effectively and adaptively learn the unknown dynamics of the Kaplan hydroturbine while optimally tune the unknown coefficients to match the generated power output from the real hydroturbine unit with an inaccuracy of less than 5%. The method can be used to provides optimal tuning of parameters critical for controller design, operational optimization and daily maintenance for hydroturbines in general.

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.

Variable renewable generation is increasing the need for hydropower plants to provide fast and flexible grid support, which places new demands on plant-level dynamic models used for monitoring, control, and operational decision-making. This need is especially important for hydroelectric systems, where turbine and generator dynamics are strongly coupled, nonlinear, and time-varying, making accurate real-time representation difficult. To address this problem, this paper develops a digital twin (DT) framework for a synchronous generator–Kaplan turbine system using an explicit separation of slow turbine dynamics and fast generator dynamics. The turbine subsystem is represented by a six-coefficient model, whose parameters are identified offline using particle swarm optimization, while the generator subsystem is updated online through an extended Kalman filter for real-time state and parameter estimation. These models are integrated within a closed-loop simulation that includes a proportional–integral–derivative–double-derivative governor and excitation system, allowing the DT to track plant behavior under realistic operating conditions. Unlike prior studies that treat turbine and generator modeling separately or rely mainly on simulated inputs, the proposed framework is validated using real operational data from a hydropower plant. Results show that the DT reproduces terminal voltage, active power, and reactive power with a normalized root mean square error of approximately 5%. This hybrid offline–online formulation constitutes the main contribution of the work, providing an adaptive and practically deployable DT for hydropower systems with direct relevance to control improvement, performance monitoring, and grid-support applications under high renewable penetration.