Experimental investigation on characteristics of pressure fluctuation and vibration under hump instability of a pump-turbine

For pump-turbines, the hump region in a head curve under the pump mode is an extremely unstable zone that severely restricts the stable operating range. This study proposes a fractal theory-based framework that integrates quadratic mode decomposition for non-intrusive early warning and mechanistic analysis of hump instability in pump-turbines. A warning coefficient Wh = 2, derived from relative variations in the multifractal intensity of vibration, serves as a robust threshold for identifying critical rotating stall. Systematic investigations reveal that pressure fluctuation dominates vibration excitation during stability degradation. Under relatively stable conditions, strong linear coherence between pressure fluctuation and vibration is concentrated at rotor–stator interaction frequencies. However, as hump instability develops, the interaction shifts from a linear correlation dominance to nonlinear-dominant mode—linear coherence decreases, while nonlinear energy transfer efficiency increases, as evidenced by a more than 25% rise in transfer entropy. Moreover, hump instability induces divergent variation trends between long-range cross correlation and coupling intensity. During the transition from the critical stall to the hump region, a long-range cross correlation decreases, whereas multifractal cross correlation intensity increases by over 40%, indicating intensified multiscale interactions driven by flow destabilization. These findings provide theoretical foundations for instability mitigation and operational optimization in pumped-storage hydropower systems.