Safety Factor for Thoma Stable Area Considering the Governor-Turbine-Penstock System

The surge tank plays a crucial role in moderating oscillations in hydropower stations, and its critical stable cross-sectional area (CSCA) is key to its stable operation. Normally, the Thoma stable area is widely used to calculate the CSCA, and a safety factor n(f) is multiplied for a safety margin. However, the safety factor n(f) is empirical and lacks theoretical basis. In this study, we present an analytical formula to calculate the safety factor n(f) considering the effect of the governor-turbine-penstock system (GTPS). Mathematical models of the surge tank-headrace tunnel system (SHTS) and GTPS are established, and amplitude-frequency characteristics are analyzed. The formula for n(f) is derived using the oscillation superposition method, and its accuracy is verified. Additionally, the effect of the governor on n(f) is investigated. The results indicate that the formula provides sufficient accuracy for the design of surge tanks. The effect of the governor can reduce the value of n(f) such that a sub-Thoma stable area can be used.(c) 2022 American Society of Civil Engineers.