Safety Factor for Thoma Stable Area Considering the Governor-Turbine-Penstock System
Publication: Journal of Hydraulic Engineering
Volume 149, Issue 3
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 is multiplied for a safety margin. However, the safety factor is empirical and lacks theoretical basis. In this study, we present an analytical formula to calculate the safety factor 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 is derived using the oscillation superposition method, and its accuracy is verified. Additionally, the effect of the governor on 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 such that a sub-Thoma stable area can be used.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by National Natural Science Foundation of China (Grant Nos. 51879087, 51839008, and 52179062).
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Published In
Journal of Hydraulic Engineering
Volume 149 • Issue 3 • March 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 8, 2022
Accepted: Nov 9, 2022
Published online: Dec 27, 2022
Published in print: Mar 1, 2023
Discussion open until: May 27, 2023
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