Amid profound transformations in the global energy landscape, the restructuring of electricity sectors has become a central element of national strategies to accelerate the growing integration of renewable energy sources (RES) into the power system. In parallel, the liberalization of the electricity industry in the 1990s has led to a significant transformation of this sector, rearranging the vertically integrated supply model into a market-regulated system. This has resulted in an increased need for flexible operation within power systems. Due to their high controllability, hydropower plants (HPPs) are expected to play a crucial role in providing flexible operation. However, this leads to off-design operations and frequent start and shutdown procedures, which are notoriously detrimental to the structural integrity of hydraulic machines due to the significant dynamic loads involved. Understanding the critical transient loading conditions remains challenging and the current literature falls short in providing methods to predict fatigue-induced damage for these machines. As a consequence, the available methods for improving operational sequences of ternary units are limited in securing flexible operations while preserving machines longevity. This Ph.D. thesis addresses the central research question: How can transient-induced structural damage in hydraulic machines be modeled through linear-elastic fracture mechanics methods and minimized through optimized start-up sequences? With focus on pumped-storage power plants (PSPPs) equipped with ternary units, this thesis introduces novel approaches for estimating the fatigue-induced damage of Pelton turbines and multistage centrifugal pumps, and proposes a comprehensive optimization framework designed to enhance operational strategies of ternary units during transient scenarios. The structural damage affecting Pelton turbines during transient operation is addressed in the first two chapters through a preliminary investigation based on an analytical model that predict the turbine's dynamic response and an experimental campaign on a reduced-scale model instrumented with strain gauges. The optimality of the sequences resulting from the optimization problem is validated experimentally, confirming the effectiveness of the quasi-steady-state approach for modeling transient crack propagation and highlighting the robustness of the proposed optimization framework. The impact of the validated optimal trajectories is experimentally assessed on the pumping side in the third chapter using a reduced-scale model of a multistage centrifugal pump. The key parameters influencing damage are identified, highlighting how both the acceleration strategy and the appearance of well-known hydrodynamic phenomena contribute to the structural degradation of the impeller during transient operation. In conclusion, this thesis introduces novel approaches for estimating the fatigue-induced damage in hydraulic machines in PSPPs and presents a comprehensive optimization framework designed to enhance operational strategies during transient scenarios. These strategies, experimentally validated on real-world case studies, demonstrate significant potential in monitoring and mitigating the propagation of pre-existing cracks in the machines during transient regimes, induced by years of operation. This Ph.D. thesis has been framed within the context of the HydroLEAP project, receiving support from the SFOE, grant agreement SI/502106-01.