The S-shaped characteristics of a pump turbine make its rotational speed unstable when it starts up under no-load conditions with low head, affecting its ability to connect to the grid. Although advanced strategies for controlling the speed governor can alleviate this problem, they cannot fundamentally resolve the internal mechanisms that cause difficulties with a grid connection. Therefore, this study set out to theoretically explore the root cause of the instability and the dominant factors influencing it. A correlation fitting process was used to simplify the transcendental function for the pipe flow in elastic mode into a high-precision and low-order linear equation. Next, a detailed study of the two key factors affecting system stability (pump turbine S-shaped characteristics and water elasticity) was carried out based on the system model, and a comprehensive parameter that reflects the no-load characteristics was extracted. Furthermore, the Laplace transform and inverse transform decomposition were used to obtain a mathematical expression for the no-load oscillation in order to analyze the oscillation characteristics. Finally, simulations of no-load oscillations under various heads were performed to further validate the accuracy of the extracted comprehensive parameter for the no-load stability. (C) 2016 Elsevier Ltd. All rights reserved.