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Sensitivity and stability analysis of a Kaplan turbine system considering synergistic regulation

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Abstract

Kaplan turbines, also known as movable propeller turbines, are attractive for power generation from water currents. They are controlled by guide vanes and runner blades, whose synergistic relationship plays an essential role in maintaining the stable operation of Kaplan turbine systems during transient process. Here we introduce a novel nonlinear dynamic model of a Kaplan turbine system with synergistic regulation by coupling the turbine, generator and governor. Sensitivity and stability analysis of the Kaplan turbine system are carried out based on EFAST method and stability theory. Effects of synergistic regulation on transient characteristic and stability of the Kaplan turbine system are investigated during transient process. Dynamics characteristic and stability region of the Kaplan turbine system suggest that transient performance improvement can be obtained by adjusting the synergistic relationship between the guide vanes and turning angle.

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Abbreviations

\(m_{t}\) :

Turbine torque (p.u.)

\(q\) :

Flow (p.u.)

\(h\) :

Water head (p.u.)

\(n\) :

Rotating speed (p.u.)

\(y\) :

Guide vane opening (p.u.)

\(z\) :

Runner blade turning angle (p.u.)

\(\alpha\) :

Hydraulic friction parameter (p.u.)

\(T_{w}\) :

Inertia time constant (s)

\(e_{x} ,e_{h} ,e_{y} ,e_{z}\) :

Partial derivatives of the turbine torque with respect to rotating speed, water head, guide vane opening and runner blade turning angle (p.u.)

\(e_{qx}\), \(e_{qh}\), \(e_{qy}\), \(e_{qz}\) :

Partial derivatives of the flow with respect to rotating speed, water head, guide vane opening and runner blade turning angle (p.u.)

\(P_{m}\) :

Mechanical input power (p.u.)

\(\delta\) :

Generator power-angle (p.u.)

\(w\) :

Rotor angle velocity (p.u.)

\(P_{e}\) :

Generator electromagnetic power (p.u.)

\(D\) :

Generator damping factor (p.u.)

\(K_{k}\) :

Synergistic regulation parameter (p.u.)

\(K_{p}\) :

Proportional adjustment parameter (p.u.)

\(K_{i}\) :

Integral adjustment parameter (s−1)

\(K_{d}\) :

Differential adjustment parameter (s)

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant number 51579208).

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Authors and Affiliations

  1. State Key Laboratory of Eco-Hydraulic in Northwest Arid Region, Xi’an University of Technology, Xi’an, 710048, Shaanxi, People’s Republic of China

    Peng Wei & Shouyi Li

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  1. Peng Wei
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Correspondence to Peng Wei.

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Wei, P., Li, S. Sensitivity and stability analysis of a Kaplan turbine system considering synergistic regulation. Nonlinear Dyn 103, 383–397 (2021). https://doi.org/10.1007/s11071-020-06134-z

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  • DOI: https://doi.org/10.1007/s11071-020-06134-z

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