Global hydropower growth continues to accelerate with 25% of total capacity installed in just the last 10 years. This accelerating expansion and the important storage facility hydropower means it is increasingly important to understand the reasons for operational failures. This is a challenge because the major reason for failures involves the complex interaction of hydraulic, mechanical and electric subsystems. Historically, reliability modelling has been split in two directions, focusing on different sub-systems, and has not yet been unified. Here these approaches are unified with a novel expression of unbalanced forces. This model with operational data are validated and the important modes of oscillation in the shaft are identified. Finally, the mechanism of the first-order oscillation mode exciting a second-order mode is presented. This integrated and accurate mathematical model is a major advance in the diagnosis and prediction of failures in hydropower operation.