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Water 2018, 10(2), 205; https://doi.org/10.3390/w10020205

# Prediction Method for the Complete Characteristic Curves of a Francis Pump-Turbine

1,2
,
2,* , 3
and
1
State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China
2
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
3
Technology Center of State Grid Xinyuan Company Limited, Beijing 100161, China
*
Author to whom correspondence should be addressed.
Received: 27 November 2017 / Revised: 10 February 2018 / Accepted: 11 February 2018 / Published: 14 February 2018

# Abstract

Complete characteristic curves of a pump-turbine are essential for simulating the hydraulic transients and designing pumped storage power plants but are often unavailable in the preliminary design stage. To solve this issue, a prediction method for the complete characteristics of a Francis pump-turbine was proposed. First, based on Euler equations and the velocity triangles at the runners, a mathematical model describing the complete characteristics of a Francis pump-turbine was derived. According to multiple sets of measured complete characteristic curves, explicit expressions for the characteristic parameters of characteristic operating point sets (COPs), as functions of a specific speed and guide vane opening, were then developed to determine the undetermined coefficients in the mathematical model. Ultimately, by combining the mathematical model with the regression analysis of COPs, the complete characteristic curves for an arbitrary specific speed were predicted. Moreover, a case study shows that the predicted characteristic curves are in good agreement with the measured data. The results obtained by 1D numerical simulation of the hydraulic transient process using the predicted characteristics deviate little from the measured characteristics. This method is effective and sufficient for a priori simulations before obtaining the measured characteristics and provides important support for the preliminary design of pumped storage power plants. View Full-Text
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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).

MDPI and ACS Style

Huang, W.; Yang, K.; Guo, X.; Ma, J.; Wang, J.; Li, J. Prediction Method for the Complete Characteristic Curves of a Francis Pump-Turbine. Water 2018, 10, 205.

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