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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

Transient Simulations in Hydropower Stations Based on a Novel Turbine Boundary