During transients, hydroturbines may demonstrate some dynamic characteristics that differ from the corresponding static characteristics in steady operating conditions. To study the dynamic characteristics of a pump-turbine, we simulated the runaway transients in a model pumped-storage plant by coupling one-dimensional (1D) water conveyance system and three-dimensional (3D) pump-turbine. The results show that the runaway dynamic trajectories form loops in the S-shaped region in the unit discharge and unit torque charts of the pump-turbine, not following the corresponding static characteristics. Theoretical analysis and flow patterns comparisons illustrate that the looping trajectories are mainly caused by the successive features of transient flow patterns, namely, the transient flows in the pump-turbine are influenced by their previous status. These features induce different performances between similar dynamic operating points in different moving directions. Furthermore, through comparing the transient parameters calculated by the dynamic and static characteristics separately, we found that both methods are available to capture the unstable behaviors of the pump-turbine, but the dynamic method displays more accurate results when simulating the critical transient parameters. Therefore, in practical engineering applications, we suggest to use the static characteristics method for stability analysis while dynamic characteristics method for transient parameters, which is important for optimizing the layout of water conveyance systems.