Reconstructing transient states in hydropower plants during small-disturbance events using physics-informed neural networks

Reconstructing transient states in complex hydropower generating systems (HGSs), particularly under small-disturbance conditions, remains challenging due to strong multi-physics coupling, inevitable model simplifications, and limited measurement data. This study applies a physics-informed neural network (PINN) to reconstruct unmeasured hydraulic states of HGSs during small-disturbance transient events from limited hydro-unit observations. The PINN incorporates simplified physical representations, including an elastic water-column model and a linear turbine model, and integrates the large-scale coupled algebraic–differential equations of the HGS into the learning process. Its effectiveness is evaluated through numerical simulations and laboratory experiments, including three intentional data–model mismatches to examine its performance when the physical model used in the learning process does not perfectly represent the real-world system dynamics. Numerical results demonstrate accurate reconstruction of key hydraulic state variations during primary frequency regulation, with average L 2 errors of only 1.07 × 10 -2 and 1.70 × 10 -3 in two representative cases. Despite the simplified governing equations, incorporating high-fidelity observations enables the PINN to reduce the maximum L2 error by up to 9.43 × 10 -1 compared with the standalone simplified model. Laboratory experiments further verify the effectiveness of the reconstruction approach, with the PINN achieving lower L 2 errors for most hydraulic states and more accurate transient characteristics than the conventional physical models under the investigated conditions.