The limited wave propagation speed in water permits the propagation of pressure surges in hydraulic transients to be tracked in the time series. This occurs by tracking the primary (F) and the reflected (f) waves. The wave tracking method has been demonstrated to be applicable to highly complex hydraulic systems. The wave propagation induced by passing through a T-junction in the flow complies with the wave conservation laws which concern both the wave reflection and the transmission. It has been shown that all computations can be simply implemented in a computation tool like MS Excel. This considerably ensures both the accuracy and the reliability of computations. At a hydraulic system of Felton turbines, excellent computational results have been achieved. The application to a highly complex hydraulic system with pump shut-off and the simultaneous closing of a spherical valve also showed excellent results, when compared with the field measurements. The key point in the presented computations is to unify the characteristics of the pump and the spherical valve. The entire computation covers the flow rate in the system, the reverse flow through the pump, the pressure response, the deceleration of the rotational speed and the system oscillations. (C) 2018 Elsevier Ltd. All rights reserved.