Critical stable sectional area of downstream surge tank of hydropower plant with sloping ceiling tailrace tunnel

Abstract This paper investigates the critical stable sectional area (CSSA) of downstream surge tank (DST) of hydropower plant with sloping ceiling tailrace tunnel (SCTT). Firstly, two types of nonlinear mathematical model of hydropower plant with SCTT during transient process are established. Then, the criterion of operation stability of hydropower plant is obtained based on nonlinear stability theory. Formulae for CSSAs of DST under two types of mathematical model are derived. Finally, the similarities, differences, and relationships of different CSSAs are clarified. The effect mechanisms of the assumption of steady power output of hydro‐turbine and the SCTT on CSSA of DST are revealed. The recommended use conditions of different CSSAs are explained. The results indicate that, under the assumption of steady power output of hydro‐turbine, the formula for CSSA of DST of hydropower plant with SCTT is analytical and has a simple expression. Under the complete model, the formula for CSSA of DST of hydropower plant with SCTT is not analytical and has a complicated expression. The former formula is suggested to be given the priority of use because of good precision and concise expression. SCTT can improve the stability of hydropower plant and decrease the CSSA of DST