Frequency-Domain Stability Analysis for Hydropower Plants with Complex Tailrace Flow Using the Overall Transfer Matrix Model

Abstract

Frequency-domain modeling is one of the paramount mathematical techniques for the stability analysis of hydraulic systems. This paper proposes an overall transfer matrix-based frequency-domain model for a hydropower plant in which the tailrace system contains both pipe flow and open-channel flow and investigates the system operation stability with the proposed model. First, the mathematical expression of the field transfer matrix for open channels is deduced by taking the flow rate and the head as complex variables. Then, the overall transfer matrix (OTM) of the complicated tailrace system is established by combining the field transfer matrices of pressurized pipes and open channels and the point transfer matrices of different hydraulic boundaries. Field experiments are conducted in a hydropower plant located in southwestern China and are taken as case studies. Comparative analyses of the information extracted from the measured data and the numerical results show that the proposed OTM model can accurately judge the stability of the multi-machine tailrace system of the hydropower plant under different conditions.