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Reconstruction of the complete characteristics of the hydro turbine based on inner energy loss

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Abstract

The power output characteristics of the hydro turbine is one of the core contents for transient calculation of the hydro turbine generating sets. In particular, the hydro turbine operates far beyond the given parameters region during the load rejection transient. As such, obtaining the complete characteristics of the hydro turbine becomes one of the key issues in calculating the transient process. In this study, methods for calculating the energy losses are proposed by analyzing the general characteristics of the inner energy losses within the hydro turbine. Characteristic parameters in the hydro turbine power model are calculated from the synthetical characteristics of the model hydro turbine. The transient power model of the hydro turbine has been established and applied to calculate and reconstruct the complete characteristics of the hydro turbine. Furthermore, the relationship curve between the mechanical friction loss power and the rotation speed under different head can be established by combing the runaway curve with the proposed turbine power model. This relationship is applied to construct the complete characteristics of the mechanical friction loss. Combining the proposed two complete characteristics, the power model of the hydro turbine is suitable for simulation with a wide range of fluctuations as well as the load rejection transient. Details of the computational procedures are presented and demonstrated using a case study.

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Abbreviations

D :

Equivalent damping coefficient of the generator

\(D_{1}\) :

Diameter of turbine runner in (m)

f(.):

Stands for function

F(.):

Stands for function

\(\varDelta F\) :

Correct function

\(f_{\mathrm{p}}\) :

Coefficient of the loss in the penstock

\(h_{\mathrm{q}}\) :

Transient head increment in relative value

\(h_{\Delta }\) :

Head convert coefficient

\(H_{0}\) :

Static head of the hydro turbine in (m)

\(H_{\mathrm{max}}\) :

Maximum head in (m)

\(H_{\mathrm{min}}\) :

Minimum head in (m)

\(H_{\mathrm{r}}\) :

Rated head in (m)

\(H_{\mathrm{t}}\) :

Turbine head in (m)

\(k_{\mathrm{h}}\) :

Coefficient of the flow channel loss

\(k_{\mathrm{v}}\) :

Coefficient of the volume loss

n :

Rotation speed of units in (rpm)

\(n_{\mathrm{r}}\).:

Rated rotation speed of unit in (rpm)

\(n_{1}^{\prime }\) :

Unit speed in (rpm)

\(p_{\mathrm{d}}\) :

Resistance power in relative value

\(P_{\mathrm{t}}\) :

Turbine power output in (KW)

\(p_{\mathrm{w}}\) :

Water flow power in relative value

\(p_{\mathrm{g}}\) :

Power of the generator in relative value

\(P_{\mathrm{d}}\) :

Resistance power in (KW)

Q :

Turbine flow discharge in (\(\hbox {m}^{3}/\hbox {s}\))

\(Q_{1}\) :

Turbine flow discharge in (\(\hbox {m}^{3}/\hbox {s}\))

\(Q_{2}\) :

Turbine flow discharge in (\(\hbox {m}^{3}/\hbox {s}\))

\(Q_{\mathrm{nl}}\) :

No-load flow in (\(\hbox {m}^{3}/\hbox {s}\))

\(Q_{\mathrm{r}}\) :

Rated flow in (\(\hbox {m}^{3}/\hbox {s}\))

\(Q_{\mathrm{z}}\) :

Flow rate at the peak efficiency point (\(\hbox {m}^{3}/\hbox {s}\))

\(Q_{p}\) :

Flow rate at the runaway operation

\(Q_{1}^{\prime }\) :

Unit flow in (\(\hbox {m}^{3}/\hbox {s}\))

\(Q_{\mathrm{zH}}\) :

Flow at the maximum efficiency point

\(\Delta Q\) :

Increment of turbine flow discharge in (\(\hbox {m}^{3}/\hbox {s}\))

\(\gamma \) :

Density of water in (\(\hbox {KN}/\hbox {m}^{3}\))

\(\Delta P_{\mathrm{h}}\) :

Turbine loss power in flow channel in (KW)

\(\Delta P_{\mathrm{i}}\) :

Impact loss power in (KW)

\(\Delta P_{\mathrm{m}}\) :

Mechanical friction loss power in (KW)

\(\Delta P_{\gamma }\) :

Volume loss power in (KW)

\(\delta P_{\mathrm{v}}\) :

Increment of volume loss power in (KW)

\(\delta P_{\mathrm{h}}\) :

Increment of turbine loss power in the flow channel in (KW)

\(\delta P_{\mathrm{i}}\) :

Increment of impact loss power in (KW)

\(T_{j}\) :

Inertia time constant in (s)

\(\omega \) :

Angular speed of the unit in relative value

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Acknowledgments

The research reported here is financially supported by the National Natural Science Foundation of China under Grant No. 51579124, 51469011,51279071. The constructive and insightful comments and suggestions made by three anonymous Reviewers have significantly improved the quality of the final manuscript.

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Authors and Affiliations

  1. College of Electric Power Engineering, Kunming University of Science and Technology, Kunming, 650500, China

    Jing Qian

  2. Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming, 650093, China

    Yun Zeng

  3. School of Engineering, University of Bradford, BD7 1DP, Bradford, UK

    Yakun Guo

  4. Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming, 650500, China

    Lixiang Zhang

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  1. Jing Qian
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  2. Yun Zeng
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Correspondence to Yun Zeng.

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Qian, J., Zeng, Y., Guo, Y. et al. Reconstruction of the complete characteristics of the hydro turbine based on inner energy loss. Nonlinear Dyn 86, 963–974 (2016). https://doi.org/10.1007/s11071-016-2937-4

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  • DOI: https://doi.org/10.1007/s11071-016-2937-4

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