Optimization of Pelton turbines start-up considering fatigue damage via a fracture mechanics model

The contribution of hydropower plants to power system flexibility is acknowledged to introduce structural loads that affect hydraulic machines, leading to a reduced expected lifetime due to fatigue. This paper proposes a methodology to quantify the fatigue-induced impact on the structure of Pelton turbines during operation by modeling the progressive growth of fractures due to cyclic stress loading. The fracture mechanics framework is developed based on stress measurements obtained from the steady-state operation of a Pelton turbine reduced-scale model, instrumented with on-board strain gauges and tested on a dedicated test-rig. Furthermore, by integrating the crack propagation model as a function of the turbine operating condition in a nonlinear constrained optimization problem, optimal start-up trajectories minimizing the propagation of cracks are computed by solving the problem with a gradient descent method. These trajectories are governed by the runner rotational speed and the injector opening. The optimality of the solutions provided by the algorithm is experimentally validated on the test-rig, highlighting the importance of optimal start-up procedures depending on the current state of the turbine service life. • Stress measurements of reduced scale Pelton turbine in operation. • Fracture mechanics method to compute crack propagation and related damage. • Constrained optimization problem to minimize damage in Pelton turbines during start-up. • Optimal start-up experimentally shows up to 15 % reduction in the crack growth.