A method is presented for the accurate simulation of the hydraulic and mechanical aspects of a hydroelectric power-generating system. The representation is suitable for incorporation into an overall power-system model. In the development of the detailed model, the hydraulic equations are solved by the method of characteristics, and the hydromachine is represented by its performance curves. Linear turbine transfer functions are subsequently derived from the detailed model using the method of fast Fourier transforms. Comparisons are made between the formulations, and these show that the range of applicability of the approximate linear models is limited. Representative results from two practical systems are collected together to illustrate the use of the models in power-system studies.