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A model establishment and numerical simulation of dynamic coupled hydraulic–mechanical–electric–structural system for hydropower station

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Abstract

A nonlinear dynamic coupled model for hydropower station system, which contains the model of water-carriage system, water turbine system, speed governor system, generator’s electromagnetic system, grid, shaft system of hydroelectric generating set, as well as the powerhouse, is established in this paper. Firstly, the simultaneous differential equations for coupled hydraulic–mechanical–electric transient process are set up based upon the theories of hydraulics, electrical machinery, etc., while the coupled structural models for shaft system of unit and powerhouse are built by means of finite element method. Secondly, a new method for investigating nonlinear dynamic properties of structures influenced by coupled hydraulic–mechanical–electric factors in different conditions is introduced with the help of user-programmable features from Ansys software. Finally, in order to verify the rationality, several numerical calculation methods are used to study the starting-up process of hydropower station. The results indicate that the model presented in this paper is adoptable for simulating specified condition and reflect the nonlinear dynamic characteristics of hydropower station comprehensively. In addition, the model can also be used to assess the operation safety and predict the structures reliability of hydropower station system, so as to provide some profitable reference for dynamic regulation during limited and transient conditions for hydropower station.

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Abbreviations

A :

Area of penstock

a :

Water hammer wave velocity

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

Permanent droop

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

Temporary droop

\(c_{\mathrm{b}}\) :

Clearance of bearing

\(c_{ij}\) :

Damping cofficients, \(i=x, y\); \(j=x, y\)

\(c_\mathrm{r}\) :

Air gap length of rotor

D :

The cross section diameter of penstock

\(D_{1}\) :

The diameter of water turbine

\(E^\prime \) :

Transient electromotive force (EMF)

\(e_{\mathrm{b}}\) :

Eccentricity of shaft axis

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

Eccentricity of rotor center

\(E_\mathrm{fd}\) :

Imaginary open-circuit EMF generated by field voltage

\(E_\mathrm{q}\) :

No-load terminal EMF

\({E_\mathrm{q}^{\prime }}\) :

Transient EMF of q-axis

\(f_\mathrm{e}, f_\mathrm{m}\) :

Electric and mechanical frequency

\(f_\mathrm{es}, f_\mathrm{ms}\) :

Electric and mechanical synchronous frequency

h :

Thickness of oil film

\(H_{i}\) :

Head in penstock at the node i

\(H_{n}\) :

Net water head of water turbine

\(I, I_\mathrm{d}, I_\mathrm{q}\) :

Stator current and corresponding d- and q-component

\(I_\mathrm{f}\) :

Excitation current

J :

Moment inertia of the hydroelectric generating set

\(k_{ij}\) :

Stiffness coefficients, \(i=x, y\); \(j=x, y\)

\(K_\mathrm{P}, K_\mathrm{I}, K_\mathrm{D}\) :

Proportional, integral and differential gain of governor

\(L_\mathrm{p}\) :

Height of pad

\(L_\mathrm{r}\) :

Length of rotor

\(M_\mathrm{e}\) :

Electric torque

\(M_\mathrm{t}\) :

Mechanical torque

n :

Mechanical speed of water turbine

\(n_\mathrm{s}\) :

Mechanical synchronous speed of water turbine

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

Unit mechanical speed of water turbine

p :

Oil pressure

\(P_\mathrm{e}\) :

Electric power (active output)

\(P_\mathrm{t}\) :

Power of water turbine

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

Unit power of water turbine

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

Unit discharge of water turbine

\(Q_{i}\) :

Discharge in penstock at the node i

\(R_\mathrm{a}\) :

Radius of shaft

\(R_\mathrm{b}\) :

Radius of journal

\(R_\mathrm{e}\) :

Resistance of transmission line

\(R_\mathrm{i}\) :

Inner radius of pad

\(R_\mathrm{L}\) :

Resistance of system load

\(R_\mathrm{o}\) :

Outer radius of pad

\(R_\mathrm{r}\) :

Radius of rotor

\(T_\mathrm{d}\) :

Reset time or dashpot constant

\(T_{d0}^\prime \) :

Open-circuit transient time constant of d-axis

\(T_\mathrm{e}\) :

Time constant of excitation

\(T_\mathrm{m}\) :

Water turbine inertia time constant

\(T_\mathrm{n}\) :

Accelerating time constant

\(T_\mathrm{w}\) :

Water inertia time constant

\(T_\mathrm{y}\) :

Servomotor response time constant

\(U_\mathrm{f}\) :

Excitation voltage

\(U_\mathrm{L}\) :

Load voltage of system

\(U_\mathrm{G}, U_\mathrm{Gd}, U_\mathrm{Gq}\) :

Stator terminal voltage and corresponding d- and q-component

\(X_\mathrm{e}\) :

Reactance of transmission line

\(X_\mathrm{L}\) :

Reactance of system load

\(X_\mathrm{d}, X_\mathrm{q}\) :

Synchronous reactance of d-and q-component

\(X^\prime _\mathrm{d}\) :

Transient reactance of d-component

y :

Servomotor stroke of governor

\(\alpha _\mathrm{p}\) :

Opening angle of pad

\(\beta \) :

Angle between a point of support for pad and y-axis

\(\Delta y\) :

Deviation value of water turbine servomotor stroke

\(\delta \) :

Power angle

\(\delta _\mathrm{p}\) :

Swing angle of pad

\(\eta \) :

Efficiency of water turbine

\(\eta _{l}\) :

Angle between the calculation location and y-axis

\(\theta _\mathrm{b}\) :

Deviation angle of bearing axis

\(\theta _\mathrm{e}, \theta _\mathrm{m}\) :

Electric and mechanical rotation angle

\(\lambda \) :

Dimensionless coordinate of pad along the shaft

\(\tau \) :

Guide vane opening

\(\varphi \) :

Power factor

\(\psi \) :

Inner power factor

\(\omega _\mathrm{e}, \omega _\mathrm{m}\) :

Electric and mechanical speed

\(\omega _\mathrm{es}, \omega _\mathrm{ms}\) :

Electric and mechanical synchronous speed

References

  1. Chaudry, M.H.: Applied Hydraulic Transients. Springer, New York (2014)

    Book  Google Scholar 

  2. Collatz, L.: The Numerical Treatment of Differential Equations. Springer, Berlin (1960)

    Book  MATH  Google Scholar 

  3. Wylie, E.B., Streeter, V.L.: Fluid Transient in Systems. Prentice-Hall, Englewood Cliffs (1993)

    MATH  Google Scholar 

  4. Parmakian, J.: Water-Hammer Analysis. Prentice-Hall, Englewood Cliffs (1955)

    Google Scholar 

  5. Lighthill, J.: Waves in Fluids. Cambridge University Press, Oxford (1978)

    MATH  Google Scholar 

  6. Ghidaoui, M.S., Mansour, S.: Efficient treatment of the Vardy-Brown unsteady shear in pipe transients. J. Hydraul. Eng. ASCE 128(1), 102–112 (2002)

    Article  Google Scholar 

  7. Silva-Araya, W.F., Chaudhry, M.H.: Unsteady friction in rough pipes. J. Hydraul. Eng. ASCE 127(7), 607–618 (2001)

    Article  Google Scholar 

  8. Shuy, E.B.: Wall shear stress in accelerating and decelerating turbulent pipe flows. J. Hydraul. Res. 34(2), 173–183 (1996)

    Article  Google Scholar 

  9. Yang, J.C., Hsu, E.L.: On the use of the reach-back characteristics method of calculation of dispersion. Int. J. Numer. Methods Fluids 12(3), 225–235 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ruprecht, A., Helmrich, T.: Simulation of the water hammer in a hydro power plant caused by draft tube surge. In: 4th ASME/JSME Joint Fluids Engineering Conference. Honolulu (2003)

  11. Panov, L.V., Chirkov, D.V., Cherny, S.G., et al.: Numerical simulation of pulsation processes in hydraulic turbine based on 3D model of cavitating flow. Thermophys. Aeromech. 21(1), 31–43 (2014)

    Article  Google Scholar 

  12. Zhang, X.X., Cheng, Y.G.: Simulation of hydraulic transients in hydropower systems using the 1-D-3-D coupling approach. J. Hydrodyn. Ser. B. 24(4), 595–604 (2012)

    Article  MathSciNet  Google Scholar 

  13. Zhang, X.X., Cheng, Y.G., Yang, J.D., et al.: Simulation of the load rejection transient process of a Francis turbine by using a 1-D-3-D coupling approach. J. Hydrodyn. Ser. B. 26(5), 715–724 (2014)

    Article  Google Scholar 

  14. IEEE Committee, : Dynamic models for steam and hydro turbines in power system studies. IEEE Trans. Power Appar. Syst. PAS-92(6), 1904–1915 (1973)

  15. Oldenburge, R., Donelson, J.: Dynamic response of a hydroelectric plant. Trans. Am. Inst. Electr. Eng. Part 3 81(3), 403–418 (1962)

    Google Scholar 

  16. Hovey, L.M.: Optimum adjustment of hydro governors on Manitoba hydro system. Trans. Am. Inst. Electr. Eng. Part 3 81(3), 581–586 (1962)

    Google Scholar 

  17. Sanathanan, C.K.: Accurate low order model for hydraulic turbine-penstock. IEEE Trans. Energy Convers. EC–2(2), 196–200 (1987)

    Article  Google Scholar 

  18. Vournas, C.D.: Second order hydraulic turbine models for multimachine stability studies. IEEE Trans. Energy Convers. 5(2), 239–244 (1990)

    Article  Google Scholar 

  19. Paynter, H.M.: A Palimpsest on the Electronic Analog Art. A. Philbrick Researches Inc., Boston (1955)

    Google Scholar 

  20. Leum, M.: The development and field experience of a transistor electric governor for hydro turbines. IEEE Trans. Power Appar. Syst. PAS–85(4), 393–402 (1966)

    Article  Google Scholar 

  21. Phi, D.T., Bourque, E.J., Thorne, D.H., et al.: Analysis and application of the stability limits of a hydro-generating unit. IEEE Trans. Power Appar. Syst. PAS–100(7), 3203–3212 (1981)

    Article  Google Scholar 

  22. Hagihara, S., Yokota, H., Goda, K., et al.: Stability of a hydraulic turbine-generating unit controlled by PID governor. IEEE Trans. Power Appar. Syst. PAS–98(6), 2294–2298 (1979)

    Article  Google Scholar 

  23. Murphy, L.D., Wozniak, L., Whittemore, T.A.: A digital governor for hydro generators. IEEE Trans. Energy Convers. 3(4), 780–784 (1989)

    Article  Google Scholar 

  24. Anwar, M.N., Pan, S.: A new PID load frequency controller design method in frequency domain through direct synthesis approach. Int. J. Electr. Power Energy Syst. 67, 560–569 (2015)

    Article  Google Scholar 

  25. Kamwa, I., Lefebvre, D., Loud, L.: Small Signal Analysis of Hydro-Turbine Governors in Large Interconnected Power Plants. IEEE Power Engineering Society Winter Meeting, New York (2002)

    Book  Google Scholar 

  26. Wozniak, L., Filbert, T.L.: Speed loop cancellation governor for hydrogenerators—part I: development. IEEE Trans. Energy Convers. 3(1), 85–90 (1988)

    Article  Google Scholar 

  27. Li, H., Chen, D., Zhang, H., et al.: Nonlinear modeling and dynamic analysis of a hydro-turbine governing system in the process of sudden load increase transient. Mech. Syst. Signal Process. 80, 414–428 (2016)

    Article  Google Scholar 

  28. Zhang, H., Chen, D., Xu, B., et al.: Nonlinear modeling and dynamic analysis of hydro-turbine governing system in the process of load rejection transient. Energy Convers. Manag. 90, 128–137 (2015)

    Article  Google Scholar 

  29. Xu, B., Wang, F., Chen, D., et al.: Hamiltonian modeling of multi-hydro-turbine governing systems with sharing common penstock and dynamic analyses under shock load. Energy Convers. Manag. 108, 478–487 (2016)

    Article  Google Scholar 

  30. Kilgore, L.A.: Calculation of synchronous machine constants-reactances and time constants affecting transient characteristics. Trans. Am. Inst. Electr. Eng. 50(4), 1201–1213 (1931)

    Article  Google Scholar 

  31. Wright, S.H.: Determination of synchronous machine constants by test reactances, resistances and time constants. Trans. Am. Inst. Electr. Eng. 50(4), 1331–1350 (1931)

    Article  Google Scholar 

  32. Heffron, W.G., Phillips, R.A.: Effect of a modern amplidyne voltage regulator on underexcited operation of large turbine generators. IEEE Trans. Power Appar. Syst. 71(1), 692–697 (1952)

    Google Scholar 

  33. Sayidi, A.M., Nekoui, M.A., Boghrabidi, N.S.: Adaptive optimal control for a one-machine infinite-bus power system. In: International Conference on Computational Intelligence for Modeling Control and Automation, Vienna (2008)

  34. Demello, F.P., Laskowski, T.F.: Concepts of power system dynamic stability. IEEE Trans. Power Appar. Syst. PAS–94(3), 827–833 (1975)

    Article  Google Scholar 

  35. Demello, F.P., Concordia, C.: Concepts of synchronous machine stability as affected by excitation control. IEEE Trans. Power Appar. Syst. PAS–88(4), 316–329 (1969)

    Article  Google Scholar 

  36. Zhong, Y.E., He, Y.Z., Wang, Z., et al.: Rotor Dynamics. Tsinghua University Press, Beijing (1987)

    Google Scholar 

  37. Wen, B.C., Gu, J.L., Xia, S.B., et al.: Senior Rotor Dynamics. China Machine Press, Beijing (2000)

    Google Scholar 

  38. Earles, L.L., Palazzolo, A.B., Armentrout, R.W.: A finite element approach to pad flexibility effects in tilt pad journal bearings: part 1—single pad analysis. J. Tribol. 112(2), 178–182 (1990)

    Article  Google Scholar 

  39. Ma, Z.Y., Dong, Y.X.: Dynamic coefficients of tilting pad guide bearings of hydraulic turbine set. Power Eng. 10(6), 6–11 (1990)

    Google Scholar 

  40. Adiletta, G., Guido, A.R., Rossi, C.: Nonlinear dynamics of a rigid unbalanced rotor in journal bearings. Part I: theoretical analysis. Nonlinear Dyn. 14(1), 57–87 (1997)

    Article  MATH  Google Scholar 

  41. Adiletta, G., Guido, A.R., Rossi, C.: Nonlinear dynamics of a rigid unbalanced rotor in journal bearings. Part II: Experimental analysis. Nonlinear Dyn. 14(2), 157–189 (1997)

    Article  MATH  Google Scholar 

  42. Rho, B.H., Kim, K.W.: A study of the dynamic characteristics of synchronously controlled hydrodynamic journal bearings. Tribol. Int. 35(5), 339–345 (2002)

    Article  Google Scholar 

  43. Tiwari, R., Lees, A.W., Friswell, M.I.: Identification of speed-dependent bearing parameters. J. Sound Vib. 254(5), 967–986 (2002)

    Article  Google Scholar 

  44. Xu, Y., Li, Z.H., Lai, X.D.: Dynamic model for hydro-turbine generator units based on a database method for guide bearings. Shock Vib. 20(3), 411–421 (2013)

    Article  Google Scholar 

  45. Zhang, L.K., Ma, Z.Y., Song, B.W.: Dynamic characteristics of a rub-impact rotor-bearing system for hydraulic generating set under unbalanced magnetic pull. Arch. Appl. Mech. 83(6), 817–830 (2013)

    Article  MATH  Google Scholar 

  46. Zeng, Y., Zhang, L.X., Guo, Y.K., et al.: The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets. Nonlinear Dyn. 76(4), 1921–1933 (2014)

    Article  MATH  Google Scholar 

  47. Xu, B.B., Chen, D.Y., Zhang, H., et al.: Dynamic analysis and modeling of a novel fractional-order hydro-turbine-generator unit. Nonlinear Dyn. 81(3), 1263–1274 (2015)

    Article  Google Scholar 

  48. Gustavsson, R.K., Aidanpää, J.O.: Evaluation of impact dynamics and contact forces in a hydropower rotor due to variations in damping and lateral fluid forces. Int. J. Mech. Sci. 51(9–10), 653–661 (2009)

    Article  Google Scholar 

  49. Zhang, L.K., Ma, Z.Y., Wu, Q.Q., et al.: Vibration analysis of coupled bending-torsional rotor-bearing system for hydraulic generating set with rub-impact under electromagnetic excitation. Arch. Appl. Mech. (2016). doi:10.1007/s00419-016-1142-8

    Google Scholar 

  50. Xu, W., Ma, Z.Y., Zhi, B.P.: Analysis on power flow transmission of pressure fluctuation along the walls of hydropower house. J. Hydroelectr. Eng. 32(2), 233–239 (2013)

    Google Scholar 

  51. Zhang, Y.L., Ma, Z.Y., Chen, G.R., et al.: Strength and stiffness analysis of spiral casing with different embedded manners. J. Hydraul. Eng. 37(10), 1206–1211 (2006)

    Google Scholar 

  52. Zhang, C.H., Ma, Z.Y., Zhou, S.D., et al.: Analysis of fluid–solid interaction vibration characteristics of large-scale hydropower house. J. Hydroelectr. Eng. 31(6), 192–197 (2012)

    MathSciNet  Google Scholar 

  53. Sun, W.Q., Huang, X.H.: Identification of vibration transfer path for the coupled system of water turbine generator set and power house. J. Vib. Shock. 33(6), 23–28 (2014)

    Google Scholar 

  54. Song, Z.Q.: Research on Coupling Vibration Characteristics of Generator Set and Hydropower House. Dalian University of Technology, Dalian (2009)

    Google Scholar 

  55. Yang, X.M.: Research on Generating Set Vibration and Coupled that and Hydropower House Vibration in Hydropower Station. Dalian University of Technology, Dalian (2006)

    Google Scholar 

  56. Chen, Z., Chen, S.S., Zhang, Z.H., et al.: Effect of hydraulic system models on power system transient stability analysis. J. Tsinghua Univ. Sci. Technol. 36(7), 13–18 (1996)

    Google Scholar 

  57. Chen, Z., Diao, Q.H., Chen, S.S., et al.: Study on the effect of hydraulic system models on power system dynamic stability analysis. J. Tsinghua Univ. Sci. Technol. 36(7), 69–74 (1996)

    Google Scholar 

  58. Zhao, G.L.: Study on the United Transient Process for Hydraulic Mechanical and Power System. Wuhan University, Wuhan (2004)

    Google Scholar 

  59. Guo, W.C., Yang, J.D., Yang, W.J., et al.: Regulation quality for frequency response of turbine regulating system of isolated hydroelectric power plant with surge tank. Int. J. Electr. Power Energy Syst. 73, 528–538 (2015)

    Article  Google Scholar 

  60. Fang, H.Q., Chen, L., Dlakavu, N., et al.: Basic modeling and simulation tool for analysis of hydraulic transients in hydroelectric power plants. IEEE Trans. Energy Convers. 23(3), 834–841 (2008)

    Article  Google Scholar 

  61. Committee, I.E.E.E.: Hydraulic-turbine and turbine control-models for system dynamic studies. IEEE Trans. Power Syst. 7(1), 167–179 (1992)

  62. Bao, H.Y., Yang, J.D., Fu, L.: Study on nonlinear dynamical model and control strategy of transient process in hydropower station with Francis turbine. In: Asia-Pacific Power and Energy Engineering Conference, Wuhan (2009)

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Acknowledgments

This research is supported by the National Natural Science Foundation of China (No.51379030) and Youth Foundation of Taiyuan University of Technology (No. 2015QN029).

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Authors and Affiliations

  1. School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, 116024, Liaoning Province, China

    Qianqian Wu & Zhenyue Ma

  2. College of Water Resources Science and Engineering, Taiyuan University of Technology, Taiyuan, 030024, Shanxi Province, China

    Leike Zhang

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Correspondence to Leike Zhang.

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Wu, Q., Zhang, L. & Ma, Z. A model establishment and numerical simulation of dynamic coupled hydraulic–mechanical–electric–structural system for hydropower station. Nonlinear Dyn 87, 459–474 (2017). https://doi.org/10.1007/s11071-016-3053-1

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