Abstract
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 nf is multiplied for a safety margin. However, the safety factor nf is empirical and lacks theoretical basis. In this study, we present an analytical formula to calculate the safety factor nf 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 nf is derived using the oscillation superposition method, and its accuracy is verified. Additionally, the effect of the governor on nf 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 nf such that a sub-Thoma stable area can be used.
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