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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 1504659, 13 pages
Research Article

Transient Simulations in Hydropower Stations Based on a Novel Turbine Boundary

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China

Received 11 March 2016; Accepted 31 May 2016

Academic Editor: Jian Guo Zhou

Copyright © 2016 Yanna Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Most accidents in hydropower stations happened during transient processes; thus, simulation of these processes is important for station design and safety operation. This study establishes a mathematical model of the transient process in hydropower stations and presents a new method to calculate the hydraulic turbine boundary based on an error function of the rotational speed. The mathematical derivation shows that the error function along the equal-opening characteristic curve is monotonic and has opposite signs at the two sides, which means that a unique solution exists to make the error function null. Thus, iteration of the transient simulation is unique and monotonous, which avoids iterative convergence or false solution and improves the solution efficiency compared with traditional methods. Simulation of an engineering case illustrates that the results obtained by the error function are reasonable. Then, the accuracy and feasibility of the mathematical model using the proposed solution are verified by comparison with model and field tests.