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Correction published on 22 June 2016, see Energies 2016, 9(6), 477.

Open AccessArticle
Energies 2015, 8(9), 10260-10275; doi:10.3390/en80910260

A Mathematical Model and Its Application for Hydro Power Units under Different Operating Conditions

1
The State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2
Department of Engineering Sciences, Uppsala University, Uppsala SE-751 21, Sweden
3
Vattenfall Research and Development, Älvkarleby SE-814 26, Sweden
*
Author to whom correspondence should be addressed.
Academic Editor: Ånund Killingtveit
Received: 9 June 2015 / Revised: 1 September 2015 / Accepted: 10 September 2015 / Published: 17 September 2015
(This article belongs to the Special Issue Hydropower)

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 hydro power units; governor system; Francis turbine; mathematical model; transient process; control mode; simulation; on-site measurement; frequency; active power
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. (CC BY 4.0).

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MDPI and ACS Style

Yang, W.; Yang, J.; Guo, W.; Zeng, W.; Wang, C.; Saarinen, L.; Norrlund, P. A Mathematical Model and Its Application for Hydro Power Units under Different Operating Conditions. Energies 2015, 8, 10260-10275.

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