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Type: Journal article
Title: A mathematical model and its application for hydro power units under different operating conditions
Author: Yang, W.
Yang, J.
Guo, W.
Zeng, W.
Wang, C.
Saarinen, L.
Norrlund, P.
Citation: Energies, 2015; 8(9):10260-10275
Publisher: MDPI AG
Issue Date: 2015
ISSN: 1996-1073
Statement of
Weijia Yang, Jiandong Yang, Wencheng Guo, Wei Zeng, Chao Wang, Linn Saarinen and Per Norrlund
Abstract: This paper presents a mathematical model of hydro power units, especially the governor system model for different operating conditions, based on the basic version of the software TOPSYS. The mathematical model consists of eight turbine equations, one generator equation, and one governor equation, which are solved for ten unknown variables. The generator and governor equations, which are different under various operating conditions, are presented and discussed in detail. All the essential non-linear factors in the governor system (dead-zone, saturation, rate limiting, and backlash) are also considered. Case studies are conducted based on one Swedish hydro power plant (HPP) and three Chinese plants. The simulation and on-site measurements are compared for start-up, no-load operation, normal operation, and load rejection in different control modes (frequency, opening, and power feedback). The main error in each simulation is also discussed in detail. As a result, the model application is proved trustworthy for simulating different physical quantities of the unit (e.g., guide vane opening, active power, rotation speed, and pressures at volute and draft tube). The model has already been applied effectively in consultant analyses and scientific studies.
Keywords: Hydro power units; governor system; Francis turbine; mathematical model; transient process; control mode; simulation; on-site measurement; frequency; active power
Rights: © 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (
RMID: 0030064903
DOI: 10.3390/en80910260
Appears in Collections:Mathematical Sciences publications

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