Stability and parameter sensitivity analysis of hydropower units under full operating conditions based on Pelton turbine refined models

This paper investigates the full-condition stability and parameter sensitivity of a Pelton turbine regulation system (PTRS) under high-head hydropower operation. A differentiable, data-driven turbine model based on neural networks is developed to ensure smooth transfer-coefficient extraction across all combinations of head and needle opening. Using Hopf bifurcation analysis, we map the stability domains under multiple operating conditions. Results show that, at a fixed head, the stability-domain area at 25% needle opening is nearly three times that at 65% opening, revealing a significant stability reduction from low to medium openings, with a mild recovery near the rated opening. A system-wide trajectory sensitivity framework is then established to rank the influence of parameters on speed and discharge states. Turbine parameters e_y and e_qy are identified as dominant, followed by the controller integral gain K_i, whereas surge-tank and pipeline parameters have smaller contributions. The sensitivity of the system to the parameters under different operating conditions shows a certain regularity along with the change of the needle opening and the head. This work provides valuable insights into the stability and parameter sensitivity analysis of the PTRS, which can help promote system identification, stability analysis, and optimal control of hydropower plants.