Stability analysis of ultra-low frequency oscillations in the large hydropower plant based on frequency-domain equivalent circuit modeling

This study addresses the analyses of the ultra-low frequency oscillation of active power in hydroelectric plant caused by flow factors in the tailrace channel. We focus on mathematically describing the hydraulic dynamic characteristics of the pipe and channel mixed flows in the tailrace system. First, a discrete frequency-domain equivalent circuit model is proposed. Based on the circuit equivalence principle, this model derives the transfer matrix for a complex hydraulic system consisting of pressurized pipelines, open channels, and branch channel junctions. Based on the proposed model, a novel stability evaluation strategy for the complicated hydraulic system is developed. By judging the oscillation order and then identifying the corresponding dominant eigen mode, the critical stability boundary of the observed ultra-low-frequency oscillation can be accurately determined by tracking the exact oscillation mode, thus avoiding searching for all the eigenvalues of the system that correspond to all oscillation orders. This scheme compensates for the limitations of the existing continuous frequency-domain model in the stability analysis of specific natural frequency orders. By comparing the critical stability turning points of ultra-low frequency oscillation obtained from field measurement data with those from simulation analysis, the model’s capability to accurately evaluate the stability of multi-unit hydropower systems under various operating conditions is validated.